Crashworthy Design and Analysis of Aircraft Structures...Crashworthy Design and Analysis of Aircraft...

Crashworthy Design and Analysis of Aircraft Structures

A Thesis

Submitted to the Faculty

of

Drexel University

by

Deepak Siromani

in partial fulfillment of the

requirements for the degree

of

Doctor of Philosophy

December 2013

ii

© Copyright 2013

Deepak Siromani. All Rights Reserved

iii

DEDICATIONS

To my parents, Sumi and Anton, and to my sister, Shalini,

for their endless love and support

iv

ACKNOWLEDGEMENTS

As expected, the accomplishment of a Ph.D. Dissertation requires the advice,

help, and support of many. First and foremost, I would like to express my sincere

gratitude to my two advisors, Professors Jonathan Awerbuch and Tein-Min Tan of the

Department of Mechanical Engineering and Mechanics. This dissertation would not have

been possible without their guidance, their constant support, and their encouragement

throughout my studies at Drexel.

The members of my thesis committee are Professors Caglan Kumbur, Leslie

Lamberson, Matthew McCarthy, and Frank Moon. I appreciate their willingness to serve

in that capacity and review my work.

I am deeply grateful to Dr. Alan Byar of The Boeing Co., Seattle, Washington,

who developed the original Boeing 737 model which was the basis for my extended

modeling of aircraft crashworthiness, and for offering valuable advice on important

computational matters throughout the course of this study.

For the experimental work on the composite stanchions, credit is due to the

several undergraduate senior students who were instrumental in the process of fabricating

the specimens and performing the experiments, as part of their senior design projects.

They are: Gary Henderson, Doug Mikita, Kevin Mirarchi, Ryan Park, John Smolko,

Benjamin Cheng, Michael DeLuca, Daniel Donegan, Patrick Giberson and Christopher

Mucerino. I also wish to acknowledge the help of Mr. Douglas Ludin of The Boeing Co.,

Ridley Park, Pennsylvania, for providing the test materials and facilitating the fabrication

of the composite specimens.

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This research was supported in part by the FAA-Drexel Fellowship program, by

providing travel funds to various conferences, and the National Science Foundation

through XSEDE resources provided by Pittsburgh Supercomputing Center. The support

provided by the College of Engineering through the Freshman Engineering Design

Fellowship, where I served as a teaching fellow throughout my years in graduate school,

is deeply appreciated. Specifically, I am very grateful to Dr. Eli Fromm for giving me the

opportunity to take a leadership role in this course sequence which undoubtedly enhanced

my communication and teaching skills.

I am thankful to the MEM Department and Drexel University for providing an

excellent undergraduate and graduate education. The partial support provided by the

MEM Department, through its teaching assistantship program, was also highly valuable. I

am grateful for my colleagues and friends in the MEM department and in our research

group, especially Chris Swin, Reewanshu Chadha and Andrew Bergan, for their help

with numerous issues, for the thoughtful discussions and suggestions along the way and

their committed friendship that developed throughout these years.

Most importantly of all, I would like to thank my family for always supporting

me, encouraging me, and believing in me through all the major decisions I have had to

make so far. Without them, I would not be the person I am today. Last, but not the least, I

would like to thank all my friends for their help and support over the years, that has

undoubtedly helped me complete this dissertation.

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TABLE OF CONTENTS

List of Tables .................................................................................................................... xii

List of Figures .................................................................................................................. xiv

Abstract .......................................................................................................................... xxvi

Chapter 1: Introduction ........................................................................................................1

1.1. Aircraft Crashworthiness ...................................................................................1

1.2. Energy Absorbing Structures .............................................................................4

1.3. Summary of Research Program .........................................................................9

1.4. Dissertation Format ..........................................................................................11

Chapter 2: Crashworthiness Analysis of a Boeing 737 Fuselage Section: A Parametric

Study on the Effects of Friction and Angle of Impact .......................................................13

2.1. Abstract ............................................................................................................13

2.2. Introduction ......................................................................................................13

2.3. Drop Test of a B737 Fuselage Section ............................................................17

2.4. Finite Element Models of the B737 Fuselage Section .....................................20

2.5. Parametric Study ..............................................................................................24

2.5.1. Effect of Coefficient of Friction .............................................................25

2.5.2. Effect of Under Floor Luggage ...............................................................31

2.5.3. Effect of Angle of Impact .......................................................................32

2.6. Concluding Remarks ........................................................................................38

Chapter 3: Multi-terrain Crashworthiness Simulations of the Fuselage of a Narrow-body

Transport Aircraft ..............................................................................................................41

3.1. Abstract ............................................................................................................41

3.2. Introduction ......................................................................................................41

vii

3.3. Development of the Full-Length Fuselage Model ...........................................44

3.3.1. Development of the Modified Section Model ........................................46

3.3.2. Validation of the Modified Section Model .............................................47

3.3.3. Expansion of the Modified Section Model to a Full-length Fuselage

Model .................................................................................................................54

3.4. Full-length Model Simulations ........................................................................56

3.4.1. Crash Landing Simulation Results .........................................................58

3.4.2. Vertical Impact Simulation Results ........................................................68

3.4.3. Effect of Luggage on Fuselage Deformation, Energy Dissipation, and

Acceleration-Time Histories ..................................................................................73


Chapter 4: Application of an Energy Absorbing Device to the Boeing 737 Fuselage

Section ..............................................................................................................................79

4.1. Introduction ......................................................................................................79

4.2. Model Setup .....................................................................................................80

4.3. Simulation Results ...........................................................................................82


Chapter 5: An Experimental Study on the Effect of Failure Trigger Mechanisms on the

Energy Absorption Capability of CFRP Tubes under Axial Compression .......................87

5.1. Abstract ............................................................................................................87

5.2. Introduction ......................................................................................................88

5.3. Experimental Setup ..........................................................................................92

5.3.1. Specimen Fabrication..............................................................................92

5.3.2. Failure Trigger Mechanisms ...................................................................92

5.3.3. Test Setup and Testing Procedure...........................................................93

5.3.4. Specific Energy Absorption ....................................................................95

5.4. Experimental Results .......................................................................................96

viii

5.4.1. Load-Displacement Behavior of Group A Specimens............................96

5.4.2. Load-Displacement Behavior of Group B Specimens ..........................102

5.4.3. Failure Process ......................................................................................105

5.4.4. Strain Fields ..........................................................................................111

5.5. Conclusions ....................................................................................................114

Chapter 6: Experimental Investigation on the Energy Absorption Capacity During

Crushing of Axially Loaded Thin-Walled Gr/Ep Members ............................................116

6.1. Abstract ..........................................................................................................116

6.2. Introduction ....................................................................................................116

6.3. Experimental Procedure .................................................................................120

6.3.1. Specimen Fabrication............................................................................120

6.3.2. Failure Triggering Mechanisms ............................................................120

6.3.3. Test Setup and Testing Procedure.........................................................121

6.3.4. Specific Energy Absorption ..................................................................122

6.4. Experimental Results .....................................................................................123

6.4.1. Load-Crosshead Displacement .............................................................123

6.4.2. The Failure Process ...............................................................................125

6.5. Effect of Cross-Sectional Geometry on SEA.................................................138

6.6. Conclusion .....................................................................................................141

Chapter 7: Modeling Methodologies for Simulating the Axial Crushing Behavior of

CFRP Members ................................................................................................................143

7.1. Abstract ..........................................................................................................143

7.2. Introduction ....................................................................................................143

7.3. Specimen Configuration and Test Procedure ................................................147

7.4. Single-layer modeling approach ....................................................................149

7.4.1. Laminate Representation and Element Selection .................................149

ix

7.4.2. Material Model......................................................................................150

7.4.3. Boundary Conditions and Contact Definitions .....................................151

7.4.4. Simulation Results ................................................................................153

7.5. Multi-Layer Modeling Approach ...................................................................159

7.5.1. Laminate Representation ......................................................................159

7.5.2. Element Size and Formulation ..............................................................160


7.5.4. Time Step ..............................................................................................162

7.5.5. Delamination Interface..........................................................................164

7.5.6. Material Model......................................................................................169

7.5.7. Discussion of Results ............................................................................172

7.6. Concluding Remarks ......................................................................................177

Chapter 8: Finite Element Modeling of the Crushing Behavior of Thin-Walled CFRP

Tubes under Axial Compression ......................................................................................180

8.1. Abstract ..........................................................................................................180

8.2. Introduction ....................................................................................................180

8.3. Summary of Experimental Work ...................................................................184

8.3.1. Test Setup and Procedure ......................................................................184

8.3.2. Experimental Results ............................................................................184

8.4. Numerical Simulations...................................................................................186

8.4.1. Model Setup ..........................................................................................186



8.4.4. Material Model......................................................................................191

8.5. Simulation Results .........................................................................................192

8.5.1. Deformation ..........................................................................................192

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8.5.2. Load-Crosshead Displacement Behavior ..............................................195

8.5.3. Strain Fields ..........................................................................................198


Chapter 9: Finite Element Modeling of the Crushing Behavior of Thin-Walled Open

Cross-Section CFRP Members under Axial Compression ..............................................201

9.1. Abstract ..........................................................................................................201

9.2. Introduction ....................................................................................................201

9.3. Summary of Experimental Work ...................................................................205

9.3.1. Test Setup and Procedure ......................................................................205

9.3.2. Experimental Results ............................................................................207

9.4. Numerical Simulations...................................................................................208

9.4.1. Model Setup ..........................................................................................209



9.4.4. Material Model......................................................................................214

9.5. Simulation Results .........................................................................................215

9.5.1. Deformation ..........................................................................................215

9.5.2. Load-Crosshead Displacement Behavior ..............................................220

9.5.3. Strain Fields ..........................................................................................225


Chapter 10: Summary, Conclusions and Recommendations ...........................................229

10.1. Crashworthiness Study...................................................................................229

10.1.1. Key Conclusions ...................................................................................230

10.1.2. Scientific Contributions ........................................................................232

10.2. Energy Absorbing Structures: Experimental Study .......................................232

10.2.1. Key Conclusions ...................................................................................233

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10.3. Energy Absorbing Structures: Computational Study .....................................235

10.3.1. Key Conclusions ...................................................................................236


10.4. Future Work Recommendations ....................................................................238

10.4.1. Full-Length Aircraft Fuselage Model ...................................................238

10.4.2. Multi-layer Modelling Methodology ....................................................239

10.4.3. Stanchion Model Integration.................................................................240

10.4.4. Dynamic Effects....................................................................................240

List of References ............................................................................................................246

Vita ............................................................................................................................255

xii

LIST OF TABLES

Table 3-1: A comparison of the finite element modeling details between the original

and modified section models ...................................................................... 47

Table 5-1: Group A specimens, supplied by The Boeing Co. ..................................... 94

Table 5-2: Group B specimens, manufactured at Drexel ............................................. 95

Table 6-1: Specimen Configuration ........................................................................... 121

Table 7-1: Specimen configuration ............................................................................ 148

Table 7-2: Material properties for IM7/8552 [83,84] ................................................ 151

Table 7-3: Results of the parametric study showing the effect of DFAILC in MAT54

on the peak load, crush and SEA of the circular tube. ............................. 154

Table 7-4: Results of the parametric study showing the effect of SOFT in MAT54 on

the peak load, crush and SEA of the circular tube. .................................. 154


on the peak load, crush and SEA of the C-channel with a chamfer. ........ 157


the peak load, crush and SEA of the C-channel with a chamfer. ............. 157


on the peak load, crush and SEA of the C-channel with a steeple. .......... 158


the peak load, crush and SEA of the C-channel with a steeple. ............... 158

Table 7-9: Correlation between the experimental and simulation results for each cross-

section with (a) a chamfer trigger, and (b) a steeple trigger..................... 158

Table 7-10: Hourglass control options investigated for under-integrated elements .... 161

Table 7-11: Tiebreak input parameters for Option 8 and 11 ....................................... 169

Table 8-1: Material properties for IM7/8552 ............................................................. 190


Table 9-1: Specimen Configuration. .......................................................................... 206

xiii

Table 9-2: Tiebreak input parameters ........................................................................ 213


xiv

LIST OF FIGURES

Figure 1-1: An example of representative load-crosshead displacement curves for a

unmodified composite member compared to one optimized for energy

absorption. .................................................................................................... 6

Figure 2-1: Vertical drop test of a Boeing 737 fuselage section, conducted at the FAA

WJH Technical Center [13,20] ................................................................... 18

Figure 2-2: Boeing 737 fuselage section (a) before lifting the test article to conduct the

drop test, and (b) after impact [13,20] ........................................................ 19

Figure 2-3: Finite element model of the 10-ft long Boeing 737 fuselage section

[13,20,21] ................................................................................................... 20

Figure 2-4: Detailed finite element model of the frame and cargo door of the Boeing

737 fuselage section [13,20,21] .................................................................. 21

Figure 2-5: Heath-Tecna bin in test article (left) and its finite element model (right)

[13,20] ........................................................................................................ 22

Figure 2-6: Hitco bin in test article (left) and its finite element model (right) [13,20] . 22

Figure 2-7: MAT82 material model used for the aluminum alloys [21] ...................... 23

Figure 2-8: Deformation of frames, as viewed from top front side of the model, for four

different coefficients of friction (t = 200ms) .............................................. 25

Figure 2-9: Detailed comparison of deformation on the lower LHS of the frame (t =

200ms) ........................................................................................................ 26

Figure 2-10: Comparison of acceleration-time histories at the four FS 452 Seat Track

locations for different coefficients of friction ............................................ 28

Figure 2-11: Dissipation of kinetic energy by the entire fuselage, the frames, and the

luggage during the impact duration for a friction coefficient of 0.3 between

the fuselage and impact surface.................................................................. 30

Figure 2-12: Comparison of energy dissipated by (a) frames; and (b) luggage, for four

different coefficients of friction ................................................................. 30

Figure 2-13: Comparison of baseline deformation with and without luggage (coefficient

of friction = 1.0) ......................................................................................... 32

xv

Figure 2-14: Effect of luggage on the acceleration-time histories at two FS 452 seat

track locations............................................................................................. 32

Figure 2-15: Side views of the deformed fuselage section for six different angles of

impact at 200ms.......................................................................................... 33

Figure 2-16: Deformation of frames for six angles of impact as viewed from top front

side of the model at 200 ms ........................................................................ 34

Figure 2-17: Comparison of acceleration-time histories at four FS 452 Seat Track

locations for different angles of impact ...................................................... 35

Figure 2-18: Dissipation of kinetic energy by the entire fuselage, the frames, and the

luggage during the impact duration for impact angles of 15° and 90° ....... 36

Figure 2-19: Comparison of energy dissipated by (a) frames; and (b) luggage for six

different angles of impact ........................................................................... 37

Figure 2-20: Effect of angle of impact on luggage deformation/crushing ..................... 38

Figure 3-1: Stress-strain data for MAT82 ..................................................................... 45

Figure 3-2: The original and modified B737 section models. The masses of the

subcomponents that were excluded from the original model were assigned

to the nodes to which the subcomponents are connected. .......................... 47

Figure 3-3: A comparison of the deformation of the original and modified section

models at selected stages of a rigid-surface impact ................................... 48

Figure 3-4: A comparison of seat track acceleration-time histories at FS 418 for rigid

surface impact............................................................................................. 49

Figure 3-5: Setup of the original section model for water impact, including a layer of

air on top of the water surface .................................................................... 50

Figure 3-6: A comparison of the deformed fuselage at 200ms of the original and

modified section models under water impact conditions. .......................... 52

Figure 3-7: A comparison of damage progressions in the fine meshed model and the

coarse meshed model. Failures in coarse meshed model occurred more

abruptly, causing sudden transmission of load to surrounding elements ... 52

Figure 3-8: A comparison of seat track acceleration-time histories at FS 418 for water

impact ......................................................................................................... 53

Figure 3-9: The 30-m long full-length model with a cargo door, under-floor luggage,

and simple nose and tail cones. FWD (FS 300), MID (FS 480), and AFT

(FS 700) indicate the locations of accelerometer elements. ....................... 56

xvi

Figure 3-10: Crash landing scenario used in this study: The fuselage has a 110 knots

approach speed, a 9.27° approach angle, and a 3° pitch angle. .................. 57

Figure 3-11: Deformation of the full-length fuselage model crash landing onto a rigid

surface. ....................................................................................................... 59

Figure 3-12: Deformation of the full-length fuselage model crash landing onto soil. .... 59

Figure 3-13: Deformation of the full-length fuselage model crash landing onto water. . 60

Figure 3-14: The overall deformation and contours of effective plastic strain of the

frames at selected time steps resulted from crash landings on three types of

terrains. ....................................................................................................... 62

Figure 3-15: Example of (a) the formation of plastic hinges at t = 52 ms at FS 800, near

the aft section, (b) frames impacting the passenger floor at t = 152 ms., and

(c) the occurrence of local frame buckling at 200ms, FS 200. ................... 63

Figure 3-16: Seat tracks acceleration-time histories resulting from a crash landing of a

full-length fuselage on a rigid surface. The magnitude of the peak

acceleration pulses progressively increased from the AFT to FWD

locations...................................................................................................... 64

Figure 3-17: Seat track acceleration-time histories comparison at aft and forward

locations resulting from a crash landing of a full-length fuselage on rigid,

soil and water terrains................................................................................. 65

Figure 3-18: Energy dissipation for a crash landing of a full-length fuselage on a rigid

surface. Frames and skins dissipated most of the energy. .......................... 66

Figure 3-19: Energy dissipations for crash landing on soil and water surfaces. Frames

and skin dissipated most of the energy. ...................................................... 67

Figure 3-20: Energy dissipation by (a) frames, and (b) skin for crash landing on rigid,

soil and water surfaces. .............................................................................. 68

Figure 3-21: The overall deformation and contours of effective plastic strain of the

frames at t = 152 ms resulted vertical impact on three types of terrains .... 69

Figure 3-22: Seat tracks acceleration-time histories for full-length fuselage vertical

impact on a rigid surface. ........................................................................... 70

Figure 3-23: Seat track acceleration-time history comparison at aft and forward locations

resulting from vertical impact of a full-length fuselage on rigid, soil, and

water terrains. ............................................................................................. 71

Figure 3-24: Energy dissipation for vertical impact on rigid surface. Frames and skin

dissipated most of the energies. .................................................................. 72

xvii

Figure 3-25: Energy dissipation for vertical impact on soil and water. For both cases the

frames and skin dissipated most of the energies. ....................................... 72

Figure 3-26: Energy dissipation by (a) frames, and (b) skin for vertical impact on rigid,

soil and water surfaces. .............................................................................. 73

Figure 3-27: A comparison of the deformed fuselage with luggage at 200ms under rigid

and water impact conditions. ...................................................................... 74

Figure 3-28: Energy dissipation for rigid and water impact conditions, showing

significant energy absorbed by the luggage. .............................................. 75

Figure 3-29: Seat track acceleration-time histories showing the effect of luggage for the

case of vertical rigid surface impact. .......................................................... 76

Figure 3-30: Seat track acceleration-time histories for effect of luggage in the case of

vertical water surface impact. ..................................................................... 76

Figure 4-1: Load-displacement curve used in MAT S08 .............................................. 81

Figure 4-2: (a) B737 fuselage section showing spring elements as energy absorbers,

and (b) a close-up view of a spring element showing the rigid connectors 81

Figure 4-3: Comparison of the deformation of the B737 fuselage section models with

luggage, without luggage, and with spring elements as energy absorbers at

three time intervals. .................................................................................... 83

Figure 4-4: Comparison of the acceleration-time histories at two FS 452 seat track

locations: (a) LHS outer seat track, and (b) RHS outer seat track. ............ 84

Figure 4-5: Comparison of the energy dissipated by the luggage and the spring

elements ...................................................................................................... 84

Figure 5-1: Failure trigger mechanisms: (a) chamfered-end; (b) Inward-splaying crush-

cap; and (c) Outward-splaying crush-cap. .................................................. 93

Figure 5-2: A comparison of load-crosshead displacement curves of a flat-end

specimen and three chamfered specimens from Group A. ......................... 98

Figure 5-3: A comparison of initial peak loads and sustained crush loads for Group A

specimens tested in Phase I and II. ............................................................. 98

Figure 5-4: A comparison of SEA for Group A specimens tested in Phase I and II..... 99

Figure 5-5: A comparison of averaged load-crosshead displacement curves for flat-

ended specimens from Group A attached to (a) three inward-folding crush-

caps, and (b) three outward-splaying crush-caps with different corner radii.

.................................................................................................................... 99

xviii

Figure 5-6: A comparison of averaged load-displacement data of Group A specimens

with a combined, chamfered-end and inward-folding crush-cap, trigger

mechanism. ............................................................................................... 101

Figure 5-7: A comparison of (a) initial peak loads and sustained crush loads, and (b)

SEA of Group A specimens with a combined, chamfered-end and inward-

folding crush-cap, trigger mechanism. ..................................................... 102

Figure 5-8: A comparison of averaged load-crosshead displacement curves of Group A

and Group B specimens with chamfered-ends and combined trigger

mechanisms. ............................................................................................. 104

Figure 5-9: A comparison of (a) initial peak loads and sustained crush loads, and (b)

SEA of Group A and Group B specimens with chamfered-ends and

combined trigger mechanisms. ................................................................. 104

Figure 5-10: Progressive failure of a Group A flat-ended specimen at different stages of

crosshead displacements: a) Pre-test; b) 1 mm - Catastrophic failure due to

local tube wall and plies buckling and crushing; c) 10 mm - progressive

crush failure; d) 40 mm - Outward-splaying and inward-folding (not

visible)of plies, laminar bending, excessive matrix splitting and fiber

fracture; and e) Post-test view of crushed end of the specimen, showing two

outward-splaying plies and seven inward-folding plies. .......................... 106

Figure 5-11: Progressive failure of a Group A chamfered specimen at different stages of

crosshead displacements: a) Pre-test; b) 1.5 mm - Completion of chamfer

crushing; c) 10 mm - progressive crush failure; d) 40 mm - Outward and

inward-folding (not visible) of plies, laminar bending, excessive matrix

splitting and fiber fracture; and e) Post-test view of crushed end of the

specimen, showing two outward-splaying plies and seven inward-folding

plies. ......................................................................................................... 108

Figure 5-12: Progressive failure of a Group B chamfered specimen at different stages of

crosshead displacements: a) Pre-test; b) 1.5 mm - Completion of chamfer

crushing; c) 10 mm - progressive crush failure; d) 40 mm - Outward-

splaying and inward-folding (not visible) of plies, laminar bending,

excessive matrix splitting and fiber fracture; and e) Post-test view of

crushed end of the specimen, showing two outward-splaying plies and

seven inward-folding plies. ...................................................................... 108

Figure 5-13: Progressive failure of a Group A flat-ended specimen attached to an

inward- folding crush-cap with a 3.96 mm corner radius at different stages

of crosshead displacements : a) Pre-test; b) 5 mm - Initiation of matrix

splits and delamination along outer two plies; c) 15 mm - Delamination and

buckling of the two outer plies and inward-folding (not visible) of the

remaining seven plies; d) 40 mm – Further buckling and fracture of

xix

buckled strips; and e) Post-test view of the crushed end of the specimen,

showing the separation of the fiber strips from the tightly packed core. . 109

Figure 5-14: Progressive failure of a Group A flat-ended specimen attached to an

outward-splaying crush-cap with a 3.96 mm corner radius at different

stages of crosshead displacements: a) Pre-test; b) 5 mm – Initiation of

matrix splitting; c) 15 mm – Forced outward-splaying, laminar bending,

excessive matrix splitting and fibers fracture; d) 40mm – Progressive

crushing showing all plies splaying outwards; and e) Post-test view of the

crushed cap end of the specimen, showing the outward-splaying of all plies

induced by the crush-cap. ......................................................................... 110

Figure 5-15: Progressive failure of a Group A chamfered specimen attached to a inward-

folding crush-cap with a 1.58mm corner radius at different stages of

crosshead displacements: a) Pre-test; b) 5 mm; c) 15 mm; d) 40 mm – All

plies folded inward with no matrix splitting or delamination; e) Post-test

view of top of the specimen, showing the center “core” formed by the

inward-folding of the plies from the bottom progressing toward the top end

of the specimen; and e) Post-test view of the crushed end of the specimen,

showing the inward-folding of all plies caused by the inward-folding crush-

cap. ........................................................................................................... 111

Figure 5-16: Global axial strain field of a chamfered specimen. The load increased

gradually, reaching the peak level (23.8 kN) when the entire chamfer

crushed completely, followed by an abrupt load drop, from the peak level

to 17.0 kN, Hot spots representing matrix splitting can be seen clearly to

initiate from the crushed region and propagate upwards at 17.0 kN load

level. ......................................................................................................... 113

Figure 5-17: Global hoop strain field of a chamfered specimen. The load increased

gradually, reaching the peak level (23.8 kN) when the entire chamfer

crushed completely, followed by an abrupt load drop, from the peak level

to 17.0 kN, Hot spots representing matrix splitting can be seen clearly to

initiate from the crushed region and propagate upwards at 17.0 kN load

level. ......................................................................................................... 113

Figure 5-18: Local hoop strain field of a chamfered specimen recorded using a high-

speed DIC system. Hot spots, representing matrix splitting, initiated at 15.9

kN and continued to grow as the load increased. ..................................... 114

Figure 6-1: Open-cross-sections with the two failure trigger mechanisms, all having the

same cross-sectional area and attached to a potted base to ensure stability.

.................................................................................................................. 121

Figure 6-2: A comparison of load-crosshead displacement curves for each cross-section

having a: (a) chamfer trigger, and (b) steeple trigger. Each curve represents

xx

the average of three tests (except for the angle-stiffener with a chamfer

trigger which represents the average of two tests). .................................. 124

Figure 6-3: A comparison of the (a) peak load and crush load, and (b) SEA for each

cross-section having a chamfer trigger and steeple failure triggers (numbers

indicate average of three specimens except for the angle stiffener with a

chamfer trigger which represents the average of two tests). .................... 125

Figure 6-4: Progressive failure of a C-channel specimen with a chamfer trigger at

different stages of crosshead displacements: a) Pre-test; b) 1.5 mm -

Completion of chamfer crushing; c) 10 mm - progressive crush failure; d)

40 mm - Outward and inward (not visible) splaying of plies, laminar

bending, excessive matrix splitting and fiber fracture; and e) Post-test

(after load removal) view of crushed end of the specimen, showing five

outward splaying plies and five inward splaying plies............................. 126

Figure 6-5: Axial strain field throughout the web of a chamfered C-channel specimen.

.................................................................................................................. 128

Figure 6-6: Lateral strain field of a chamfered C-channel specimen showing sites of

matrix split initiation. ............................................................................... 128

Figure 6-7: Progressive failure of a C-channel specimen with a steeple trigger at

different stages of crosshead displacements: a) Pre-test; b) 10 mm -






Figure 6-8: Axial strain field of a steeple C-channel specimen showing steeple

crushing. ................................................................................................... 130

Figure 6-9: Lateral strain field of a steeple C-channel specimen showing sites of

initiation of matrix splitting. ..................................................................... 130

Figure 6-10: Progressive failure of an angle-stiffener specimen with a chamfer trigger at





(after load removal) view of crushed end of the specimen, showing ten

outward splaying plies and ten inward splaying plies. ............................. 131

Figure 6-11: Axial strain field of a chamfered angle-stiffener specimen. .................... 132

Figure 6-12: Lateral strain field of a chamfered angle-stiffener specimen showing site of


xxi

Figure 6-13: Progressive failure of an angle-stiffener specimen with a steeple trigger at


Completion of steeple crushing; c) 15 mm - progressive crush failure; d) 40

mm - Outward and inward (not visible) splaying of plies, laminar bending,

excessive matrix splitting and fiber fracture; and e) Post-test view (after

load removal) of crushed end of the specimen, showing ten outward

splaying plies and ten inward splaying plies. ........................................... 133

Figure 6-14: Axial strain field of a steeple angle-stiffener specimen. ............................ 134

Figure 6-15: Lateral strain field of a steeple angle--stiffener showing site of initiation of

matrix splitting. ........................................................................................ 134

Figure 6-16: Progressive failure of a hat-stiffener specimen with a chamfer trigger at







Figure 6-17: Axial strain field of a chamfered hat-stiffener specimen. ........................ 136

Figure 6-18: Lateral strain field of a chamfered hat-stiffener specimen, showing sites of


Figure 6-19: Progressive failure of a hat-stiffener specimen with a steeple trigger at





view (after load removal) of crushed end of the specimen, showing five


Figure 6-20: Axial strain field of a hat-stiffener specimen with a steeple trigger. ....... 138

Figure 6-21: Lateral strain field of a hat-stiffener specimen with a steeple trigger. ..... 138

Figure 6-22: Effect of the ratio of curved surfaces to the total perimeter on the SEA of

specimens with various cross-sections ..................................................... 139

Figure 6-23: Final deformation (after load removal) of: a) C-channel, b) angle-stiffener,

c) hat-stiffener, and d) Circular tube (from [81, Chapter 5]). .................. 140

Figure 7-1: Test specimens cross-sectional dimension (all dimensions in mm). ........ 148

Figure 7-2: Test specimens ......................................................................................... 148

xxii

Figure 7-3: Representations of the trigger mechanism in the single-layer finite element

models of (a) circular tube with a chamfer, and (b) C-channel with a

steeple. ...................................................................................................... 150

Figure 7-4: Penetration of the platen by tube elements according to the load-penetration

curve in the contact definition. ................................................................. 152

Figure 7-5: Final load-penetration curve for the contact definition used in single-layer

model. ....................................................................................................... 152

Figure 7-6: Unfiltered vs. filtered load-displacement curves obtained from the single-

layer chamfered model. An SAE 1000 Hz filter was used to obtain the

filtered data. .............................................................................................. 153

Figure 7-7: Single-layer simulation vs. experimental load-crosshead displacement

curve for the circular tubes having a chamfer trigger. ............................. 155

Figure 7-8: Single-layer simulation vs. experimental load-crosshead displacement

curve for the C-channels having (a) a chamfer trigger, and (b) a steeple

trigger. ...................................................................................................... 158

Figure 7-9: Representations of: (a) circular tube with a chamfer and (b) C-channel with

a steeple failure trigger mechanisms in the finite element models. .......... 160

Figure 7-10: Time-scaling investigation showing: a) loading rates used, and b) the

resulting load-crosshead displacements. .................................................. 163

Figure 7-11: Mass-scaling investigation showing the resulting load-crosshead

displacements. .......................................................................................... 164

Figure 7-12: A comparison of: (a) the unfiltered and filtered load-crosshead displacement

curves from a multi-layer simulation for a tube with a chamfer failure

trigger, and (b) the filtered simulation results and the experimental load-

crosshead displacement comparison for a tube with a chamfer failure

trigger. ...................................................................................................... 173

Figure 7-13: A comparison of: (a) the unfiltered and filtered load-crosshead displacement

curves from a multi-layer simulation for a C-channel with a chamfer failure

trigger, and (b) the filtered simulation results and the experimental load-

crosshead displacement comparison for a C-channel with a chamfer failure

trigger. ...................................................................................................... 174

Figure 7-14: Tiebreak investigation showing the comparison between: (a) the load-

crosshead displacement curves for the chamfered tube, and b) the final

deformation of the tubes. .......................................................................... 175

xxiii

Figure 7-15: Tiebreak investigation showing the comparison between: (a) the load-

crosshead displacement curves for the chamfered tube, and b) the

deformation of the steeple C-channel at ~23 mm of crush. ..................... 175

Figure 7-16: Material model investigation showing the comparison between: (a) the load-

crosshead displacement curves for the chamfered tube, and b) the final

deformation of the tubes. .......................................................................... 177

Figure 8-1: Failure trigger mechanisms: (a) a chamfered end, (b) an inward-folding

crush cap, and (c) an outward-splaying crush cap.................................... 185

Figure 8-2: (a) Experimental load-crosshead displacement curves, and (b) SEA of tubes

having a chamfer and combined failure triggers. The combined failure

trigger yielded a higher peak load, sustained crush load and SEA. ......... 185

Figure 8-3: Representations of the failure trigger mechanisms in the finite element

models. The chamfered end of the tube was modeled by staggering

element layers while the crush cap was modeled using rigid shell elements.

.................................................................................................................. 187

Figure 8-4: Comparison of the experimental and simulated deformation of the tube

with a chamfered trigger mechanism at various loading stages. .............. 194

Figure 8-5: A comparison of the experimental and simulated deformation of a tube

with a combined chamfer and inward-folding crush cap trigger mechanism.

.................................................................................................................. 195

Figure 8-6: A comparison of the unfiltered and filtered load-crosshead displacement

curves from a multi-layer simulation for a tube with a chamfer failure

trigger. ...................................................................................................... 196

Figure 8-7: Load-crosshead displacement comparison between experiment and

simulation for specimens with a chamfer trigger mechanism. ................. 196


simulation for specimens with a combined chamfer and inward-folding

crush cap trigger mechanism. ................................................................... 197

Figure 8-9: Comparison of simulated and experimental (a) peak loads and sustained

crush loads, and (b) SEA for the tubes with a chamfer trigger mechanism

and a combined trigger mechanism. ......................................................... 197

Figure 8-10: Comparison of simulated and experimental (DIC) local hoop strain fields

on a tube with a chamfer trigger mechanism. .......................................... 199

Figure 9-1: Open-cross-sections with two failure trigger mechanisms (chamfers and

steeples), all having the same cross-sectional area and attached to a potted

base to ensure stability during the 50.8 mm crush displacement. ............ 206

xxiv

Figure 9-2: Test specimens cross-sectional dimension (all dimensions in mm) ......... 207

Figure 9-3: A comparison of load-crosshead displacement curves for each cross-section

having a: (a) chamfer trigger, and (b) steeple trigger. Each curve represents

the average of three tests (except for the angle-stiffener with a chamfer

trigger which represents the average of two tests). .................................. 208

Figure 9-4: A comparison of: (a) initial peak load and crush load; and (b) SEA, for

each cross-section having a chamfer and steeple failure triggers (numbers

indicate average of three specimens except for the angle stiffener with a

chamfer trigger which represents the average of two tests). .................... 208

Figure 9-5: Representations of the C-Channel cross-section having: (a) chamfer and (b)

steeple failure trigger mechanisms in the finite element models. ............ 210

Figure 9-6: Comparison of the experimental and simulated deformation of the C-

channel with a chamfered trigger mechanism at selected crosshead

displacement stages. ................................................................................. 217

Figure 9-7: Comparison of the experimental and simulated deformation of the angle-

stiffener with a chamfered trigger mechanism at selected loading stages.

.................................................................................................................. 217

Figure 9-8: Comparison of the experimental and simulated deformation of the hat-

stiffener with a chamfered trigger mechanism at selected loading stages.

.................................................................................................................. 218

Figure 9-9: Comparison of the experimental and simulated deformation of the C-

channel with a steeple trigger mechanism at selected loading stages. ..... 219

Figure 9-10: Comparison of the experimental and simulated deformation of the angle-

stiffener with a steeple trigger mechanism at selected loading stages. .... 219

Figure 9-11: Comparison of the experimental and simulated deformation of the hat-

stiffener with a steeple trigger mechanism at selected loading stages. .... 220

Figure 9-12: A comparison of unfiltered and filtered load-crosshead displacement curves

from a multi-layer simulation for a C-channel with a chamfer failure

trigger. ...................................................................................................... 221


simulation for C-channels with (a) a chamfer, and (b) a steeple trigger

mechanism. ............................................................................................... 222


simulation for angle-stiffeners with (a) a chamfer, and (b) a steeple trigger

mechanism. ............................................................................................... 223

xxv


simulation for hat-stiffeners with (a) a chamfer, and (b) a steeple trigger

mechanism. ............................................................................................... 223

Figure 9-16: Comparison of simulated and experimental peak loads and sustained crush

loads for the specimens with (a) a chamfer, and (b) a steeple failure trigger

mechanism. ............................................................................................... 224

Figure 9-17: Comparison of simulated and experimental SEA for the specimens with (a)

a chamfer, and (b) a steeple failure trigger mechanism. .......................... 224

Figure 9-18: Comparison of simulated and experimental (DIC) axial strain fields in a C-

channel with a chamfer failure trigger mechanism. ................................. 226

Figure 9-19: Comparison of simulated and experimental (DIC) lateral strain fields in a

C-channel with a chamfer failure trigger mechanism. ............................. 226

Figure 9-20: Comparison of simulated and experimental (DIC) of the axial strain fields

in a C-channel with a steeple trigger mechanism. .................................... 227

Figure 9-21: Comparison of simulated and experimental (DIC) of the lateral strain fields

in a C-channel with a steeple trigger mechanism. .................................... 227

xxvi

ABSTRACT

Crashworthy Design and Analysis of Aircraft Structures

Deepak Siromani

Advisors:

Prof. Jonathan Awerbuch and Prof. Tein-Min Tan

Crashworthiness of an aircraft fuselage and its structural components was

investigated experimentally and numerically in this study. A finite element model

developed previously for simulating the drop test of a 3m long Boeing 737 fuselage

section was used to evaluate the effect of the friction coefficient between the fuselage and

the ground, and of the aircraft’s angle of impact on the dynamic response of the structure.

The 3m section model was subsequently expanded to a full-length fuselage model

representing a narrow-body transport aircraft in order to simulate realistic crash-landing

scenarios on different terrains (i.e., rigid, soil, and water). The results from these studies

highlighted the importance of the subfloor structure and its components in the energy

absorption process during a crash landing, as well as the need for energy absorbing

devices, integrated with the subfloor structure, to mitigate the impact energy.

A comprehensive experimental study was performed to investigate the energy

absorbing capabilities of graphite/epoxy members that could serve as stanchions in the

subfloor structure of aircraft or rotorcraft. First, tubes of circular cross sections with

chamfered-ends, inward-folding and outward-splaying crush-caps, and combined

(chamfered-end and crush-cap) failure trigger mechanisms, were investigated. Next,

members with open cross-sections (C-channels, angle-stiffeners, and hat-stiffeners) with

chamfered-ends and steeple failure trigger mechanisms were investigated. The optimal

xxvii

configuration that resulted in the lowest initial peak load while providing the highest

possible specific energy absorption (SEA) was identified.

Finite element models were developed to simulate the crushing behavior of the

graphite/epoxy members observed experimentally using two different modeling

methodologies. First, an existing single-layer approach was utilized that required careful

calibration of key parameter values used in defining the contact/penetration behavior and

material failure. This approach predicted the initial failure peak load and the load-

crosshead displacement curve but provided no insight into the failure process. Next, a

multi-layer modeling methodology was developed by determining the most effective

laminate configuration, element size and formulation, contact definitions, time step

control, delamination interface, and material model. This approach captured the failure

process and predicted the sustained crush load quite accurately. Such modeling could

thus support the future design of aircraft stanchions.

1

CHAPTER 1: INTRODUCTION

1.1. AIRCRAFT CRASHWORTHINESS

A recent report to congress [1] on the survivability of rotorcraft stated that

between October 2001 and September 2009, the U.S. military lost 375 rotorcraft causing

496 fatalities. Only 19 percent of losses were due to combat hostile action whereas the

remaining 81 percent were due to mishaps. A high percent of these loses were deemed

survivable as most of the fatalities resulted from the crash. Rotorcraft crashworthiness,

which includes airframe crashworthiness and occupant protection, was identified as a key

area of focus to improve survivability in the event of a crash [1]. However,

crashworthiness is not only limited to rotorcraft or small aircraft as, over the past decade,

several aircraft crashes have occurred in which narrow and wide-body transport airplanes

were forced to perform emergency landings either during takeoff or landing. Some of

these involved the collapse of the landing gear, causing the aircraft fuselage to impact the

ground resulting in severe, but survivable damage [2-6]. In each of these examples, a

majority of the occupants survived the crash landings that caused severe damage to the

aircraft.

During a crash, the aircraft structure must be able to absorb the kinetic energy and

limit the forces and decelerations that are transmitted to the occupants, through the seat

and restraint system, to tolerable levels. The airframe must survive with minimal

collapse, to the extent that a livable volume is provided to the occupants through the

crash sequence. Crashworthiness studies aim at minimizing the likelihood of injuries or

fatalities and reduce the amount of structural damage to the airframe and payload in the

2

event of a severe, but survivable, crash [7]. The larger the energy absorbed by the

structure the lower the propensity of injuries or fatalities.

While the history of crashworthiness studies can be traced back to 1910 [7], the

first modern approach to defining crashworthiness requirements for rotorcraft and small

fixed-wing aircraft was undertaken by the U.S. Army in the 1960’s. Studies conducted as

part of this program determined that the vertical load transmitted to the occupant during a

crash was a key factor in causing injury to the lumbar spine [7]. Thus, the attenuation of

this load has long been recognized as a vital component of a crashworthy design.

To address this design issue, there is a need for experimental data on the impact

response of aircraft under survivable crash conditions. Over the past few decades, there

have been various research programs on aircraft crashworthiness conducted by the U.S.

Department of Defense [8,9], NASA [8] and the FAA [8,9] to determine the dynamic and

impact responses of aircraft structures and the survivability of the occupants under severe

but survivable crash conditions. A summary of the impact tests performed at NASA

Langley’s Impact Dynamics Research Facility (IDRF) from 1975 until 2003 is provided

in [8]. These tests ranged from a full-scale crash test of a CH-47 Chinook helicopter to an

external fuel qualification test of a UH-60 Black Hawk helicopter. The IDRF facility has

the ability to perform full-scale crash tests of light aircraft and rotorcraft for a wide range

of combined forward and vertical velocity conditions. For example, a crash test of a

Sikorsky prototype helicopter, with a forward velocity of 9.6 m/s and a vertical velocity

of 11.6 m/s, was performed [10]. The FAA has performed impact tests on some larger

aircraft structures, including full-scale drop tests of commuter-class aircraft (ATR42-300)

[12], a Lear Fan fuselage [11], and two Boeing 737 fuselage sections [13,14].

3

While considerable research has been performed on testing of an aircraft

impacting hard surfaces, no such studies have been reported on full transport aircraft

fuselages impacting other terrains, such as soil and water. Yet, there have been cases

where the aircraft have crash-landed onto such surfaces [4,5]. Additionally, it has been

reported that more than 80% of rotorcraft crashes occur on non-rigid terrains and that

helicopters designed for hard surface impact do not perform well when impacting onto

water and soft-soil [15]. The US Army Research Lab conducted a series of vertical drop

tests of composite helicopter fuselages on concrete [16], soft-soil [17], and water [18].

The dynamic response of each case was evaluated and compared with the other cases

[18]. Similarly, as a part of a European Union helicopter crashworthiness program, a drop

test of a metallic helicopter subfloor structure onto water was conducted and reported in

[19].

The prohibitively high cost of conducting such impact tests calls for the use of a

reliable computational model that could replicate as closely as possible the actual impact

conditions. Several of the test programs described previously have also included the

development of computational models to simulate the tests. The FAA’s several civil

aircraft research and certification programs used analytical methods at multiple levels,

from seat occupant models and simulations to support certification tests, to full-scale

impact tests of commuter-class aircraft, [9]. The level of computational analysis ranges

from the use of an early crash analysis program, KRASH, to simulate crash tests and

investigate airplane accidents, to the use of finite element programs such as MSC.Dytran

and LS-DYNA to simulate a drop test of an ATR42-300 and two drop tests of 3 m long

Boeing 737 fuselage sections, [14,20,21]. Further, for the drop tests conducted by the US

4

Army Research Lab and the European Union crashworthiness program discussed above,

non-linear finite element models were developed in LS-DYNA to simulate the drop tests,

[18]. These validated models can be used to study a variety of impact conditions and a

wide range of design alternatives, thus eliminating the need for repeated testing. Finite

element models have also been developed to analyze the deformation and energy

absorption processes of individual components and substructures, for which the

experimental options are very limited.

1.2. ENERGY ABSORBING STRUCTURES

One common result from the drop tests and analysis performed in the various

studies discussed above is that the subfloor structure is a critical component in absorbing

impact energy during a crash landing. Thus optimizing the energy absorption capability

of the subfloor structure and its components could aid in improving the overall

crashworthy response of the aircraft or rotorcraft.

The NASA Subsonic Rotary Wing Aeronautics Program recently demonstrated

the use of Deployable Energy Absorbers (DEAs) fitted on an MD-500 helicopter for a

full-scale crash test [22]. The DEAs consist of a composite honeycomb structure,

fabricated using fiber reinforced fabrics, which can be deployed externally to absorb

energy in the event of a crash. While test results showed that DEAs offer a high level of

energy absorption due to the large crushing zone available, their resulting parasitic

weight, however, has yet to be addressed.

An alternative approach is to modify existing subfloor structural members, such

as adding floor beams, stanchions and stiffeners, to enable increased energy absorption.

Such structural members should add minimal weight while being able to sustain regular

5

flight load conditions and maximizing energy absorption in the event of a crash. For

small aircraft and rotorcraft, this can prove challenging due to the space constraints in the

subfloor region [23].

Composite materials are now widely used in the aerospace industry and are

considered viable candidates for developing light weight energy absorbing devices due to

their high strength-to-weight ratio and their high specific energy absorption (SEA)

characteristics. When designing a structural member for energy absorbing purposes, it is

important that the initial peak load be kept low to minimize the G forces while the

sustained crush load is kept high as the damage progresses to maximize the energy

absorption. Two examples of the load-crosshead displacement behavior for composite

members are shown in Figure 1-1. An unmodified member would typically crush with a

high initial peak load, resulting in a catastrophic failure (e.g., local wall buckling),

followed by a low sustained crush load as the damage progresses. Since the SEA is

directly proportional to the area under the curve, such a member would yield a low SEA

as well. Thus, in order to prevent catastrophic failure at the beginning of the crushing

process, a failure trigger mechanism must be used. Several different failure trigger

mechanism options have been studied in order to determine the optimal design to

attenuate this initial peak load [23-32]. Failure trigger mechanisms can be classified as

internal failure triggers (e.g., chamfer, steeple, and ply drop-off) and external failure

triggers (e.g., crush-caps and plug initiators), which are added at one end of the

stanchion. These failure trigger mechanisms are capable of significantly reducing the

initial peak load, similar to the “energy absorbing member” curve in Figure 1-1.

6

Figure 1-1: An example of representative load-crosshead displacement curves for a unmodified composite

member compared to one optimized for energy absorption.

In order to maximize the SEA, the sustained crush load must be increased. This is

heavily dependent on the material system used. The most common composite materials

investigated for energy absorption purposes have been graphite/epoxy (Gr/Ep) [23-29,33-

42], glass/epoxy (Gl/Ep) [24,25,30-34,43-52] and Kevlar/epoxy (K/Ep) [24,25,33-38].

The laminate stacking sequence has also been shown to have a great influence on the

SEA and a limited number of studies have been performed to determine the optimal lay-

up for the laminates [25,28]. Various cross-sectional geometries have been investigated

to determine their effect on the energy absorbing capacity. These include tubes with

circular [23,25-27,33-35,45,48,52-54], square [42,47,52] and hexagonal [52] cross-

sections, hourglass [52] and cone [43,43,52,55] shaped tubes, angle-stiffeners [28,42], C-

channels [28,42], flat plates [28,37,38], sandwich panels [49-51], foam-filled blocks [56],

hat stiffeners [39], and sine-wave members [29,36]. Finally, the type of failure trigger

mechanism used can also have an effect on the SEA. A few studies have specifically

investigated the effect of external failure trigger mechanisms on the SEA of tubular

7

members [31,32]. Hence, an optimal combination of these factors can yield a higher

sustained crush load and SEA, similar to the “energy absorbing member” curve in Figure

1-1.

The high cost of conducting experimental studies, however, presents a need for

reliable computational models capable of predicting the crushing response of composite

members. Commercially available explicit finite element codes such as LS-DYNA,

ABAQUS and PAM-CRASH are typically used to simulate the behavior of a wide

variety of structures, including composite materials. Despite the minor differences in

these codes, they all contain similar libraries of material models, contact definitions and

other modeling options required to simulate the behavior of composite structures. Thus

the selection of a finite element code is merely a matter of preference, availability, or

prevalence in the industry of interest.

Due to their complex failure mechanisms, the energy absorption and crushing

process of composite materials are not easily predicted using numerical methods. There

have been several attempts to develop explicit finite element models, with varying

degrees of success, for circular tubes [57-60], square tubes [59-63], C-channels [61,62],

angle-stiffeners [61,62], and hat-stiffeners [67]. Several modeling approaches have been

utilized that can primarily be differentiated based on their techniques of representing the

laminate, the use of different types of material models, and their method for representing

delamination between the plies.

Composite structures can be modeled using either solid or shell elements; it has

been well-established that shell element models require less computation time and are

more widely used to model the axial crushing of composite members. The laminate can

8

be modeled using either a single layer or multiple layers of shell elements. In the ‘single-

layer’ model the laminate is modeled by using a single layer of shell elements, with each

ply being represented by an integration point in the thickness direction. In the ‘multi-

layer’ model, the laminate is modeled as multiple layers of shell elements, each layer may

represent either a single ply or a group of plies, and the layers are tied together using a

tiebreak contact definition or a cohesive zone model. The single-layer approach has the

advantage of requiring a short computation time, but is not capable of replicating the

deformation process observed during progressive crushing of composite members.

Furthermore, the accuracy of single-layer approach is heavily dependent on correctly

fitting input parameters to experimental results. The multi-layer approach is capable of

accurately representing progressive crushing, but requires significantly more computation

time and is sensitive to the selection of material models and delamination interface

definitions. The tiebreak contact definition and cohesive zone model allow for the

simulation of delamination between the shell element layers. However, no methodology

has been established to correctly account for the energy absorbed due to delamination

during the crushing process. Further, the selection of material models range from

simplistic progressive failure models to more complex continuum damage mechanics

models. These include material models integrated within commercially available FE

codes, as well as user-developed material models. The input parameters required to

define the different types of material models also vary significantly and typically involve

a number of parameters that need to be obtained by correlating the simulation results to

experimental data. While various material models have been used to simulate the

9

crushing of composite members, there is no definite consensus on the most appropriate

model that can be used for all cases.

1.3. SUMMARY OF RESEARCH PROGRAM

The goals of this dissertation are to:

(i) Develop a finite element model of a full-length representative narrow-

body transport aircraft to investigate the differences in impact response on

various terrains and quantify the effect of various structural components

on the energy absorption process;

(ii) Experimentally investigate the energy absorption characteristics of

graphite/epoxy members having different cross-sections with various

failure trigger mechanisms by monitoring the initiation and progression of

damage, and measuring the load-displacement behavior during the

crushing process1;

(iii) Develop computational models to predict the load-displacement behavior,

to quantify the energy absorption capacity, and to simulate the failure

characteristics and crushing process of such composite members.

The previously developed finite element model [20,21] of a 3 m long Boeing 737

fuselage section was used to investigate the effect of the coefficient of friction and the

angle of impact between the fuselage and the surface. The results from this study

prompted the development of a new model to simulate the impact of full-length,

1The experimental work was conducted by two senior design teams, as explain in the Acknowledgement

section of this Dissertation. The data reduction and analysis were conducted under my supervision. All ten

members of the Senior Design teams became co-authors in four of the conference proceedings

publications and presentations and in the two corresponding peer review publications.

10

representative, narrow-body transport aircraft fuselage onto rigid, soil and water terrains.

The dynamic response of the fuselage structure, including the deformation, acceleration-

time histories, and the energy absorption of various components for the B737 fuselage

section and the full-length fuselage model are analyzed and presented. Chapter 2

discusses the parametric studies on the impact event of the 3 m long fuselage section.

Chapter 3 presents the results of the impact event of the full-length fuselage at the three

different terrains under different impact scenarios.

The results from the crashworthiness simulations highlighted the importance of

improving the energy absorbing capabilities of the aircraft subfloor structure. To

investigate the viability of using energy absorbing stanchions to improve the

crashworthiness of the B737 fuselage, a simple example using spring elements to model

the stanchions in the subfloor structure of the B737 fuselage section is presented in

Chapter 4.

Subsequently, the energy absorption mechanisms of CFRP members with

different cross-sections and different failure trigger mechanisms were investigated for use

as energy absorbing devices in the subfloor structure. Pre-fabricated graphite/epoxy tubes

along with material to manufacture new specimens were provided by The Boeing Co.,

Ridley Park, PA. These specimens were used to investigate the various types of failure

trigger mechanisms (i.e. chamfered-ends, inward-folding and outward-splaying crush-

caps). The most effective option was determined by the lowest initial peak load and

highest SEA achieved. New cylindrical specimens were fabricated and were tested with

the previously determined optimal trigger mechanism. The experimental procedure and

results obtained are discussed in Chapter 5.

11

This study was extended to include three different cross-sectional geometries that

are more prevalent in the aerospace industry: C-channels, hat-stiffeners, and angle-

stiffeners. Two failure trigger mechanisms were investigated, chamfered-ends and steeple

triggers, and the most effective option was determined. The experimental procedures and

results are discussed in Chapter 6.

Finite element models were developed to simulate the experimental results: the

load-displacement data, SEA and failure process. Two different modeling approaches,

namely, a single-layer and a multi-layer approach were employed. The single-layer

approach utilized an existing methodology that required careful calibration of key

parameter values used in defining the contact/penetration behavior and material failure.

The multi-layer approach required the development of a new modeling methodology by

determining the most effective laminate configuration, element size and formulation,

contact definitions, time step control, delamination interface, and material model. The

two modeling methodologies are discussed in Chapter 7.

In Chapter 8 and 9, the multi-layer modeling methodology developed in Chapter 7

is used to simulate the crushing behavior of the specimens tested in Chapter 5 and 6,

respectively. Summary of the work performed in this dissertation are discussed in

Chapter 10, along with key conclusions, scientific contributions, and recommendation for

future work.

1.4. DISSERTATION FORMAT

This dissertation is presented in a “journal article style” format, where the main

chapters comprise of individual, self-contained, journal articles. Therefore, each chapter

includes its own abstract and introduction sections, and may reiterate some information

12

presented in other chapters. These chapters have been submitted for publication to

various journals, as indicated on the first page of each chapter.

13

CHAPTER 2: CRASHWORTHINESS ANALYSIS OF A BOEING 737

FUSELAGE SECTION: A PARAMETRIC STUDY ON THE EFFECTS OF

FRICTION AND ANGLE OF IMPACT

2

2.1. ABSTRACT

A finite element model developed previously for simulating the drop test of a 10

feet long Boeing 737 fuselage section was used in this study to evaluate the effect of the

friction coefficient between the fuselage and the ground and of the aircraft’s angle of

impact on the deformation characteristics and acceleration-time histories. These two

impact parameters represent different terrains (e.g., rigid, soil, grass, water surfaces) and

aircraft crash landing scenarios, respectively. The dynamic responses of the fuselage

structure under four coefficients of friction and six impact angles were simulated. The

overall deformation of the structure, the acceleration-time histories at selected locations

on the fuselage, and the energy dissipation of key structural components were studied.

Results indicate that both the friction between the fuselage and the impact platform and

the angle of impact markedly affect the deformation of the entire structure, the

acceleration- time histories, and the energy dissipation by the frame and under-floor

luggage. In all cases, the frames and the luggage absorbed most of the impact energy.

2.2. INTRODUCTION

Over the past decade, several aircraft crashes have occurred in which narrow and

wide-body airplanes were forced to perform emergency landings either during takeoff or

2 Siromani, D., Awerbuch, J. and Tan, T-M., “Crashworthiness Analysis of a Boeing 737 Fuselage Section:

A Parametric Study on the Effects of Angle of Impact and Friction”, Submitted to: International Journal

of Crashworthiness.

14

landing. Some of these involved the collapse of the landing gear, causing the aircraft

fuselage to impact the ground resulting in severe, but survivable damage [2-6]. In each of

these examples, most of the occupants survived the crash landings that caused severe

damage to the aircraft. These examples illustrate the importance of understanding the

dynamic response of an aircraft structure to various impact conditions and its capacity to

absorb impact energy to protect its occupants. The type of impact terrain and the angle of

impact play a significant role in the amount of damage sustained by the aircraft, and

consequently, the energy dissipated by the structure and the impact forces transmitted to

the passengers. These five incidents are prime examples of the importance of aviation

crashworthiness studies under low impact velocity conditions.

The subject of aviation crashworthiness deals with an aspect of survivability, as

opposed to aviation safety, which deals with accident prevention. During a crash, the

aircraft structure must be able to absorb the kinetic energy and limit the forces and

decelerations that are transmitted to the occupants, through the seat and restraint system,

to tolerable levels. The airframe must survive with minimal collapse, to the extent that a

livable volume is provided to the occupants through the crash sequence. Crashworthiness

studies aim at minimizing the likelihood of injuries or fatalities and reduce the amount of

structural damage to the airframe and payload in the event of a severe, but survivable,

crash [7]. The larger the energy absorbed by the structure the lower the propensity of

injuries or fatalities.

While full-scale crash tests of vehicles are routinely being conducted in the

automotive industry, crash tests of thoroughly instrumented aircrafts is prohibitively

expensive and extremely time consuming. Also, it is not feasible to perform repeated

15

tests to study various impact scenarios and design modifications. Further, while crash

tests provide voluminous and valuable data, it is not possible to study the effect and

contribution of individual components on the dynamic response of the entire aircraft

structure and/or measure experimentally the energy absorbed by each component

separately. The available procedures to quantify the energy dissipated by the structure

and its individual components are quite limited. Hence, the use of analytical methods,

coupled with crash tests, is necessary to address these issues. Experimental data are

essential to validate the simulation results and understand the strengths and limitations of

the model. A validated model can then be used to study a variety of impact conditions

and a wide range of design alternatives, thus eliminating the need for repeated testing.

In the latter half of the 20th century, there were various research programs in

aircraft crashworthiness conducted by the U.S. Department of Defense [8,9], NASA [8]

and the FAA [9]. A summary of the impact tests performed at NASA Langley’s Impact

Dynamics Research Facility (IDRF) from 1975 until 2003 is provided in [8]. These tests

ranged from a full-scale crash test of a CH-47 Chinook helicopter in 1975 to an external

fuel qualification test of a UH-60 Black Hawk helicopter in 1999. The IDRF facility had

the ability to perform full-scale crash tests of light aircraft and rotorcraft for a wide range

of combined forward and vertical velocity conditions. For example, a crash test was

performed of a Sikorsky prototype helicopter in 1999 with a forward velocity of 9.6 m/s

and a vertical velocity of 11.6 m/s [10].

A summary review of the FAA’s several civil aircraft research and certification

programs using analytical methods is provided in [9]. These research programs range

from seat occupant models and simulations to support certification tests, to full-scale

16

impact tests of commuter-class aircraft (ATR42-300) [12] and fuselage sections of

transport aircraft (Boeing 737) [13,14]. The review also describes the use of an early

crash analysis program, KRASH, to simulate crash tests and investigate airplane

accidents. The use of finite element programs such as MSC.Dytran and LS-DYNA to

simulate a drop test of an ATR42-300 and two drop tests of 3 m (10 ft) long Boeing 737

fuselage sections was also discussed in [9].

A vertical drop test of a B737 fuselage section was conducted in November 2000

at the FAA William J. Hughes Technical Center [13,20]. The 10ft long fuselage section

was outfitted with seats, mannequins, anthropomorphic test dummies, overhead stowage

bins and under-floor luggage. It was instrumented with strain gages, accelerometer, and

onboard cameras recording acceleration-time histories at locations on the floor (seat

tracks), frames, and overhead stowage bins, as well as the overall structural deformation.

The primary goal of this drop test was to characterize the dynamic response of the two

different overhead stowage bins. Simultaneously, a detailed finite-element model was

developed using LS-DYNA, based on hand measured dimensions of the actual test

article, to simulate the impact event and the consequent dynamic structural response of

the fuselage [20]. Results of the simulation compared very well with the experimental

measurements, in terms of the overall structural response and the acceleration-time

histories. Subsequently, the model was further refined, based on actual design dimensions

of the various structural components [21].

In this study, the refined model was used to perform a detailed parametric

analysis. The parameters studied are the friction coefficients between the fuselage and the

impact surface and the angle of impact. For each case, deformation characteristics of the

17

fuselage and its key components, the acceleration-time histories (at various locations in

the fuselage), and the energy dissipation of key structural components, were computed

and compared. The purpose of the friction parametric study was to investigate how the

fuselage will react to various impact terrains, which is necessary for further expanding

the model to more realistic impact conditions. The impact angle parametric study

provided an insight into the structural response of the aircraft to different emergency

landing and crash scenarios, such as those shown in [2-6].

2.3. DROP TEST OF A B737 FUSELAGE SECTION

As mentioned earlier, in November, 2000 a drop test of a 3 m (10 ft) long Boeing

737 fuselage section was conducted at the FAA William J. Hughes Technical Center

[13,20]. The section was dropped from a 4.3 m (14 ft) height (Figure 2-1), resulting in a

9.14 m/s (30 ft/s) initial impact velocity, which was chosen to represent a severe but

survivable impact.

The test article included seven frames that were spaced 0.5 m (20 in) apart. The

location of each frame on the actual fuselage is identified by a Fuselage Station (FS)

number, which is the distance, in inches, from a reference point located in the front of the

aircraft. The frames of the test article were located from FS 380 to FS 500. Note that the

left- and right-hand sides of the aircraft are with respect to the pilot, when looking at the

front of the fuselage section.

To minimize open-end effects and emulate a continuous fuselage, a second under-

floor beam was added at each end of the fuselage section at FS 380 and FS 500. The

added under-floor beam at FS 380 can be seen in Figure 2-2(a). The under-floor

compartment was filled with actual passenger luggage, Figure 2-2(a). The test article also

18

included a cargo door; the forward edge of the door was in line with FS 420, while the aft

edge of the frame ended between FS 460 and FS 480. The frames of the door were

reinforced with short beams, which were connected to the nearest forward and aft

fuselage frames. The fuselage frames, connecting to the upper edge of the doorframe,

were also reinforced.

Figure 2-1: Vertical drop test of a Boeing 737 fuselage section, conducted at the FAA WJH Technical

Center [13,20]

Three rows of triple-occupant seats were installed on each side of the fuselage

section. The seats were attached to four longitudinal seat tracks, two on each side, and

19

were occupied by twelve mannequins and six anthropomorphic test dummies (ATD’s),

Figure 2-2(a) [13,20].

Two different types of overhead stowage bin were installed on the fuselage

section, one on each side, Figure 2-2(a). The details of the bins and their connections to

the fuselage structure are described in the following section. These overhead stowage

bins were loaded with wooden blocks to simulate luggage. The fuselage, its structural

components, and the joints are described in detail in [13,20].

The fuselage and its components were instrumented with numerous strain gauges

and accelerometers mounted strategically at various locations of the fuselage and its

components, as described in detail in [13,20]. The recorded data were used to correlate

with the simulation results at corresponding locations. Figure 2-2(b) shows the front view

of the final deformed state of the fuselage section after the drop test. The entire impact

event lasted approximately 500 ms.

(a) (b)

Figure 2-2: Boeing 737 fuselage section (a) before lifting the test article to conduct the drop test, and (b)

after impact [13,20]

20

2.4. FINITE ELEMENT MODELS OF THE B737 FUSELAGE SECTION

The finite element model, developed in [20] to simulate the drop test of the 2000

drop test of the Boeing 737 fuselage section [13], was based on hand-measurements of

the test article. This model has since been updated with accurate geometry and material

properties [21]. The updated model was used in this study. Its key features are

summarized as follows:

The key components of the model include the fuselage skin, frames, floor, under-

floor beams, luggage, overhead stowage bins, camera mounts, and the cargo door. The

test dummies and mannequins were not modeled, but their masses were distributed on the

seat surfaces. The model of the test section is shown in Figure 2-3.

Figure 2-3: Finite element model of the 10-ft long Boeing 737 fuselage section [13,20,21]

As mentioned earlier, the test article included a cargo door; with reinforcements

to connect the doorframe to the surrounding fuselage frames, Figure 2-4. It will be shown

later that these reinforcements, which provided an added stiffness on the right-hand side

21

of the fuselage, had a major effect on the overall dynamic response of the entire structure.

The cargo door made the fuselage asymmetric, causing the fuselage to deform differently

on the left-hand side than on the right-hand side, and differently in the forward than in the

aft.

Figure 2-4: Detailed finite element model of the frame and cargo door of the Boeing 737 fuselage section

[13,20,21]

One of the primary goals of the drop test was to determine the responses of the

two different types of overhead stowage bin to severe but survivable impact conditions

[13,20]. The primary difference between the two stowage bins was in their support

systems. Figure 2-5 shows the Heath Tecna bin, installed on the right-hand side, and the

corresponding finite element model. It was connected to fuselage frames by L-shaped

22

brackets on the side and vertical struts attached to longitudinal channels on top. Figure

2-6 shows the Hitco bin, installed on the left-hand side, and the corresponding model. It

was connected to fuselage frames by vertical and horizontal links to the side and tie rods

at the top. Further details are provided in [13,20].

Figure 2-5: Heath-Tecna bin in test article (left) and its finite element model (right) [13,20]

Figure 2-6: Hitco bin in test article (left) and its finite element model (right) [13,20]

The fuselage section, which included the skin, frames, floor, floor beams, cargo

door, and camera mounts, was modeled using shell elements. The seat frames were

modeled with beam elements, and seat surfaces with shell elements. All supports for the

23

overhead stowage bins were modeled using beam elements, and the bins themselves were

modeled with shell elements.

The material properties used in the finite element model were based on standard

materials used in a Boeing 737 fuselage. The skin panels were assigned Aluminum 2024-

T3 properties and all other structural members were assigned Aluminum 7075-T6

properties. Material model MAT82 in LS-DYNA was used to represent each aluminum

alloy. This material model allows the element to fail in tension only. At the onset of

failure the properties are gradually softened at a preselected rate, gradually reducing the

stresses in the element. The element is deleted once the stresses reduce to zero. In

compression, the elements are allowed to continue to deform according the stress-strain

curve without being deleted, Figure 2-7.

Figure 2-7: MAT82 material model used for the aluminum alloys [21]

The role of the luggage stored in the under-floor compartment is highly

significant: it directly affects the extent of crushing during impact, the intensity of the

24

acceleration pulses transmitted to the test dummies, and the energy dissipated during the

impact event. The luggage was modeled using solid elements with properties of viscous

foam. A parametric study was conducted in [20] and results were compared to available

experimental data to determine the appropriate foam properties (nonlinear stiffness and

viscous damper, to represent the increasing stiffness during crushing and to simulate

energy dissipation) that yielded the most accurate crushing distance.

The final model consisted of 128,960 nodes, 107,212 shell elements, 13,824 solid

elements, and 3,953 beam elements (compared with 68,007 nodes, 53,407 shell elements,

13,824 solid elements, and 691 beam elements of the model developed in [2]). The total

weight of the model was 4,069 kg (8,970 lbs), as compared to the total weight of 4,023

kg (8,870 lbs) of the test article. This small difference in weight did not have any

significant effect on the simulation results [20].

2.5. PARAMETRIC STUDY

The model presented in [20] and modified in [21] was used to perform this

parametric study. The parameters of interest are the coefficient of friction between the

fuselage and surface, and the angle of impact. Four issues are discussed below for each

case: i) the dynamic structural response, ii) the acceleration time-histories at selected

locations, iii) the energy dissipation by key structural components; and iv) the effect of

the luggage on the structural deformation. The case of vertical drop with friction

coefficient of 1.0, investigated in [20], is referred herein as the ‘baseline’ case. All

simulations were performed up to 200 ms after impact, since it was determined that all

major deformations in the structure were completed at approximately 125 ms [20].

25

2.5.1. EFFECT OF COEFFICIENT OF FRICTION

i) Fuselage Deformation:

The simulations were performed under the vertical drop condition with friction

coefficient values between the fuselage and the impacted platform of 0.3, 0.5, 0.8, and

1.0 (baseline case). The deformed fuselage for the four cases, at the end of the simulation

(200 ms), is shown in Figure 2-8. On the cargo door side (right-hand side of the aircraft,

from pilot’s position) there is no noticeable sliding between the fuselage and the platform

in all four cases. This is due to the added stiffness provided by the cargo doorframe

reinforcements, limiting the frame deformation on the right-hand side, which is discussed

in detail in [20]. The left-hand side of the fuselage, however, shows a marked effect of

the friction coefficient. As expected, the most sliding occurs for the lowest friction

coefficient of 0.3, Figure 2-8a. The frames tend to slide and buckle toward the cargo

section of the fuselage. This effect is progressively diminished with increasing friction

coefficients of 0.5 and 0.8, Figure 2-8b and Figure 2-8c, respectively, with no sliding

occurring for the baseline simulation, Figure 2-8d.

Figure 2-8: Deformation of frames, as viewed from top front side of the model, for four different

coefficients of friction (t = 200ms)

26

A detailed view of the deformation that occurs on the left-hand side of the

fuselage is shown for each of the four cases in Figure 2-9. The figure highlights the

location and degree of frame plastic deformation and buckling. At the lowest friction

coefficient (of 0.3), the buckling of all seven frames occurs at the bottom of the fuselage,

along its left-hand side. This buckling is caused by the frames sliding laterally along the

bottom and toward the center of the fuselage, parallel to the impacted surface. For the

higher friction coefficients (of 0.5 and 0.8), the amount of siding is reduced resulting in

the frames buckling, along the left-hand side, further away from the center of the

fuselage. In all cases, the buckling is more severe in the aft section. This is a result of the

location of the stiffened cargo doorframe, located towards the front to the fuselage

section [20]. For the baseline case, where sliding is restricted, the buckling of the frames

occur primarily along the sidewalls, yielding fracture of all seven frames. In all cases, all

frames in contact with the surface are highly deformed. This plastic deformation extends

along the length of the frame, toward the fuselage floor.

Figure 2-9: Detailed comparison of deformation on the lower LHS of the frame (t = 200ms)

27

ii) Acceleration-time Histories:

Accelerometers were installed on the seat tracks and overhead storage bins of the

test article to record the acceleration-time histories [13,20]. Accelerometer elements were

included in the finite element model at the corresponding locations. Figure 2-10 shows

representative acceleration-time histories for the seat track accelerometers at FS 452. The

plots show the simulation results for each friction coefficient, plotted along with the

experimental results for comparison. The simulations results for all four cases, at each

location on the right-hand side of the fuselage, are very similar and agree very well with

the experimental data in terms of magnitude and timing of the acceleration pulses. This is

due to the negligible effect of varying the coefficient of friction on the right-hand side

(cargo door side) of the fuselage, as discussed in the previous section. The results on the

left-hand side show that the accelerations fluctuate more significantly for the lower

friction coefficients. Further, while the friction coefficient of 0.3 yields slightly higher

peak accelerations, no particular trend on the effect of friction is noticed. This is due to

the complex structure, which results in a multifaceted dynamic structural response and

failure process of the frames in that region, as described previously.

It should be noted that the outer seat tracks are located closer to the frames and

therefore more accurately represent the effect of the impact being transmitted from the

frames to the under-floor beams. The inner seat tracks, closer to the center, are more

influenced by oscillations of the floor beams. For this reason, the outer seat tracks are

subjected to higher accelerations compared with the inner seat tracks, and mainly on the

right-hand side, near the doorframes. The magnitudes of the right-hand side acceleration

pulses are typically higher by 7 g’s to 8 g’s than the acceleration pulses on left-hand side.

28

This is due to the fact that the right-hand side response is influenced by the higher

stiffness of the cargo doorframe reinforcements, as discussed above and in further detail

in [20]. Similar behavior and agreement were recorded at all other seat track locations

(not shown here), however, with different peak accelerations and their timing.

Figure 2-10: Comparison of acceleration-time histories at the four FS 452 Seat Track locations for different

coefficients of friction

iii) Energy Absorption:

The effect of the friction coefficients on the energy dissipation is shown in Figure

2-11. The figure shows the energy dissipated by the entire fuselage, the frames, and the

luggage, for a friction coefficient of 0.3. The results are normalized with respect to the

initial kinetic energy of the simulation, i.e., the energy before the fuselage section

impacts the ground, at 0 ms. In all four cases, the luggage and the frame accounted for

29

most of the energy dissipated, approximately two-thirds of the initial kinetic energy. The

remaining energy was dissipated by the many other structural components such as the

skin, floor, floor beams, overhead bins, and camera mounts, etc. A comparison of the

energy dissipated only by the frames and luggage, for all four friction coefficients is

shown in Figure 2-12. These values were normalized with respect to the final energy

dissipated by the respective components in the baseline case (friction coefficient of 1.0).

It can be seen that varying the friction coefficient affects the energy absorbed by the

frames only marginally, Figure 2-12a. At the lowest friction coefficient the energy

dissipated by the frames, primarily starting at 75ms after impact, is between 5-10% lower

compared with the baseline case. This is due to the fact that for the lower friction

coefficients the left-hand side frames initially slide under the fuselage instead of

plastically deforming. On the other hand, the luggage dissipates higher energy when the

friction coefficient is lower, by nearly 20% compared with the baseline case. This is due

the greater extent of luggage crushing with the lower friction coefficients as a result of

the frames sliding and buckling beneath the fuselage. Finally, the slight fluctuations seen

in Figure 2-11 and Figure 2-12 results from the sequential events occurring during the

impact and crush processes. These details could be analyzed via the simulation; however,

they are beyond the scope of this paper.

30

Figure 2-11: Dissipation of kinetic energy by the entire fuselage, the frames, and the luggage during the

impact duration for a friction coefficient of 0.3 between the fuselage and impact surface

Figure 2-12: Comparison of energy dissipated by (a) frames; and (b) luggage, for four different coefficients

of friction

31

2.5.2. EFFECT OF UNDER FLOOR LUGGAGE

To further investigate the effect of the under floor luggage on energy dissipation,

a simulation of the case with friction coefficient of 1.0 with luggage removed was

performed and results are compared with that of the baseline simulation (which included

the luggage). The structural deformation at three different time intervals,

Figure 2-13, indicates that as a result of removing the luggage the lower frames

on the left-hand side of the fuselage fracture and subsequently impact the under floor

beams (not visible due to the forward beam reinforcement placed beneath the forward

floor beam). The damping effect of the luggage affects also the upper section of the

fuselage including skin and frames. For example, at 200ms, the left-hand side frames

deform plastically, and even buckle, much more severely without the luggage. Further,

removing the luggage increases the effect of the stiffened cargo doorframe on the overall

asymmetric deformation of the entire fuselage. This sequence of events causes the seat

track on the left-hand side to experience a much higher g-load; approximately 9 g’s

higher than that of the baseline case in the left-hand side outer track seat, Figure 2-14.

The right-hand side, on the other hand, experiences approximately the same amount of g-

load as the baseline case, although the arrival time of the pulse is delayed by

approximately 100ms. Similar behavior was recorded at all other seat track locations,

however, with varying peak accelerations and timing.

32

Figure 2-13: Comparison of baseline deformation with and without luggage (coefficient of friction = 1.0)

Figure 2-14: Effect of luggage on the acceleration-time histories at two FS 452 seat track locations

2.5.3. EFFECT OF ANGLE OF IMPACT

Five different angles of impact were analyzed and compared with the vertical

impact simulation. The five angles studied were 15°, 30°, 45°, 60°, 75°, and 90° from the

horizontal. For all six cases, the vertical component of the velocity was the same as in the

vertical drop test (9.14 m/s (30 ft/s). Thus, the horizontal velocity components, added to

33

the model to simulate the different angles of impact, were 34.1 m/s, 15.8 m/s, 9.14 m/s,

5.3 m/s, and 2.4 m/s, respectively. A friction coefficient of 0.5 was used for all six

simulations. As in the previous study, these simulations were performed up to a

termination time of 200 ms.

i) Fuselage Deformation:

The post impact structural response of the frames was compared for all six angles

of impact. Particular attention was placed on the bottom section of the fuselage, where

contact occurs between the fuselage and platform. The deformed states at the end of the

simulations (200 ms) for the six angles of impact are shown in Figure 2-15. As expected,

for the smaller impact angles the forward section of the fuselage experiences the highest

deformation and most severe frame bucking, Figure 2-16. Also, for the smaller angles,

the deformation of the right-hand side of the frame is less prominent than that recorded

on the left-hand side, showing again the effect of the doorframe discussed earlier [13,20].

Figure 2-15: Side views of the deformed fuselage section for six different angles of impact at 200ms

34

Figure 2-16: Deformation of frames for six angles of impact as viewed from top front side of the model at

200 ms

ii) Acceleration-time Histories:

The acceleration-time histories for the seat track accelerometers at FS 452 were

compared with the test data. The locations of the accelerometer elements on the seat

tracks were shown previously in [13,20]. Acceleration-time histories for each impact

angle are shown in Figure 2-17 for the right- and left-hand sides’ inner and outer seat

tracks. The simulation results for the right-hand side seat tracks, with the stiff cargo

doorframe located underneath, are quite similar for all angles in terms of peak

acceleration and timing of the first peak acceleration. The timing of the subsequent peak

acceleration marginally depends upon the angle of impact. The results for the left-hand

side seat track, however, vary significantly for different angle of impact. The varying

horizontal velocity causes the frames on the left-hand side to crush to a different extent

35

for each angle, as they are now subjected to horizontal forces as well. These horizontal

forces are generated by the friction between the fuselage and the impact surface.

Figure 2-17: Comparison of acceleration-time histories at four FS 452 Seat Track locations for different

angles of impact

iii) Energy Absorption:

The energy dissipation by the entire fuselage, the frames, and the luggage during

the impact event is shown in Figure 2-18 for two representative angles of impact. Similar

results were obtained for all other angles of impact (not shown here). The kinetic energy

and the energy dissipated during the impact event shown the Figure 2-18 have been

normalized with respect to the respective initial kinetic energy. Due to the large different

horizontal velocity components, the amount of initial kinetic energy changes significantly

36

in each case, with 90° impact being the lowest and 15° impact angle the highest, as

expected. As before, the frames and luggage account for most of the energy dissipated for

all angles of impact. All six cases show the same trend in the amount of energy dissipated

by the frames and luggage. Compared to the significant increase in kinetic energy (due to

the large increase in the horizontal component of velocity to yield the desired angle of

impact), the total energy dissipated by the fuselage structure barely changes between the

six angles. The remaining kinetic energy is due to the horizontal velocity component that

is reduced (by 36% and 98% for the 15° and 75° cases, respectively) by the friction

between the fuselage section and the surface by the end of the simulation.

Figure 2-18: Dissipation of kinetic energy by the entire fuselage, the frames, and the luggage during the

impact duration for impact angles of 15° and 90°

A comparison of the energy dissipated by the frames and luggage for all six cases

is shown in Figure 2-19. These plots are normalized with respect to the final energy

dissipated by the respective structural components in the vertical (90°) impact case. The

37

results show that the lower the impact angle the larger the energy dissipated by the

frames and the under-floor luggage (by 24% and 50%, respectively), relative to the

vertical impact. As mentioned earlier, the frames on the left-hand side of the fuselage

tend to crush very differently for the different angles of impact. For lower impact angles,

the left-hand side frames – towards the front of the fuselage – were crushed to a much

greater extent than for the higher impact angles, Figures 18 and 19. This caused the

luggage in those areas to be crushed to a greater extent, thus, increasing the energy

dissipated. A comparison of the final deformation of the luggage for impact angles of 15°

and 90° is shown in Figure 2-20.

Figure 2-19: Comparison of energy dissipated by (a) frames; and (b) luggage for six different angles of

impact

38

Figure 2-20: Effect of angle of impact on luggage deformation/crushing

2.6. CONCLUDING REMARKS

The objective of this study was to use the validated Boeing 737 model, developed

earlier in [20] and updated in [21], to investigate the effects of two key impact

parameters, namely, the friction between the fuselage and the impacted surface and the

angle of impact, on the dynamic response of the fuselage section in terms of the structural

deformation and the acceleration-time histories at selected sites.

The results show that the coefficient of friction greatly affects the deformation of

the entire structure, primarily in term of the degree of lateral sliding between the bottom

of the fuselage and the impacted platform. As expected, the lower the friction coefficient

the higher the lateral sliding. Consequently, the lower friction yields higher plastic

deformation and more extensive buckling of the bottom frames.

The acceleration-time histories, particularly along the seat track (where

deceleration affects the occupants the most), are all quite similar and are marginally

affected by the degree of friction. Because of the significant effect of the reinforcement

of the cargo doorframe on the right-hand side of the fuselage, as discussed in detail in

[20], the lateral sliding occurs mostly on the left-hand side. The resulting acceleration-

39

time histories along the left-hand side seat tracks fluctuated more significantly for lower

coefficients of friction, but the peak accelerations varied by no more than 2g’s in all

cases. The peak accelerations on the right-hand side are much higher, particular along the

outer seat tracks (closer to the cargo door), by up to 7 g’s, as was the case in [20],

independent of the friction coefficient. While the friction coefficient of 0.3 yields slightly

higher peak accelerations, no particular trend on the effect of friction is noticed. The

friction coefficient affects the amount of energy dissipated by the luggage only when it is

low enough to enable significant lateral sliding that causes added cargo crushing. In each

case, the luggage and frame together account for most of the energy dissipated.

The angle of impact study ranged from a vertical drop (90°) to a 15° angle of

descent. As with the friction coefficient study, the effect of the cargo doorframe

reinforcements was evident as the seat track acceleration-time histories on the right-hand

side were minimally affected by the change in angle of impact. The higher angles of

impact reduce the peak accelerations by up to 7g’s, primarily along the outer right-hand

side seat tracks. The acceleration-time histories for the left-hand side fluctuated more

significantly due to the varying degree of deformation of the frames on that side caused

by different horizontal component of velocity in each case. The peak accelerations are

much higher on the right-hand side, particular along the outer seat tracks (closer to the

cargo door), by up to 7 g’s, as was the case in [20]. The luggage dissipates more energy

for the lower impact angles due to the greater extent of deformation of the bottom frames

and the subsequent crushing of the luggage. As in the friction study, the luggage and

frame together account for most of the energy dissipated for all impact angles. These

40

results serve as a precursor to study the impact of full-length fuselage at various terrains

of rigid, soil, and water surfaces [71, Chapter 3].

41

CHAPTER 3: MULTI-TERRAIN CRASHWORTHINESS SIMULATIONS OF

THE FUSELAGE OF A NARROW-BODY TRANSPORT AIRCRAFT

3

3.1. ABSTRACT

A full-length fuselage finite element model of a representative narrow-body

transport aircraft was developed to simulate crash-landing on different terrains (i.e., rigid,

soil, and water). To emphasize the effect of terrain on the dynamic structural

deformation, vertical impact of the full-length fuselage was also studied. The model was

constructed by expanding, to the full length, a previously developed 3-m long B737

section model that has been validated by experimental data from a drop test, excluding

the wings and replacing the structural details of the nose cone and tail section with a

simple shell model. Results include deformation patterns of the fuselage structure,

acceleration-time histories at selected locations on the fuselage, and the energy

dissipation of key structural components. The effect of under-floor luggage on the

dynamic responses of the fuselage was also investigated for the case of vertical impact.

The results quantified the effect of the different terrains on the structural deformation and

acceleration-time histories.

3.2. INTRODUCTION

Several aircraft crashes have occurred over the past decade in which narrow- and

wide-body airplanes were forced to perform emergency landings. Some of these incidents

involved the collapse of the landing gear, causing the aircraft fuselage to impact the

3Siromani, D., Awerbuch, J. and Tan, T-M., “Multi-terrain Crashworthiness Simulations of the Fuselage of

a Narrow-body Transport Aircraft”, Submitted to: International Journal of Crashworthiness.

42

ground, resulting in severe but survivable damage [3]. While considerable research has

been performed on testing and analysis of an aircraft impacting hard surfaces [8-

14,20,21], no such studies have been reported on full transport aircraft fuselages

impacting other terrains, such as soil and water. Yet, there have been cases where the

aircraft have crash-landed onto such surfaces [4,5]. Furthermore, it has been reported that

more than 80% of rotorcraft crashes occur on non-rigid terrains and that helicopters

designed for hard surface impact do not perform well when impacting onto water and

soft-soil [15].

The US Army Research Lab has conducted a series of vertical drop tests of

composite helicopter fuselage on concrete [16], soft-soil [17], and water [18]. The

dynamic response of each case was evaluated and compared [18]. For vertical impact

onto a concrete surface, the subfloor structure crushed and absorbed most of the kinetic

energy. For the soft-soil and water impacts tests, the deformation of the impacted media

dissipated a large part of the kinetic energy. The unsupported portion of the skin

underneath the subfloor structure was subjected to large in-plane membrane forces,

causing the skin to either fail in the case of water impact, or deform plastically in the case

of soft-soil impact. For all three cases, non-linear finite element models were developed

to simulate the drop tests. All three models reviewed in [18] compared well with the

experimental data.

As a part of a European Union helicopter crashworthiness program, a drop test of

a metallic helicopter subfloor structure onto water was conducted and reported in [19]. A

finite element model was also developed to simulate this drop test. The model proved

useful in analyzing the initial stages of impact, when most of the structural deformation

43

and energy absorption occurred. However, there was a poor correlation with experiments

at the final stages of impact. The authors concluded two primary areas for potential

improvement of the existing helicopter design: i) maximizing skin deflection prior to

failure is critical to load transmission to other energy absorbing components; and ii)

degrading joints’ stiffness will significantly improve the crashworthiness.

In an earlier study, a vertical drop test of a 3-meter long Boeing 737 fuselage

section was conducted at the FAA William J. Hughes Technical Center [13,20]. The test

article was outfitted with seats, mannequins, anthropomorphic test dummies, two

overhead stowage bins and under-floor luggage. The primary goal of this drop test was to

characterize the dynamic response of the two overhead stowage bins. The test section was

instrumented with strain gages and accelerometers to record the strain- and acceleration-

time histories at various locations on the floor (along seat tracks), frames, and overhead

stowage bins. High-speed cameras were used to capture the overall structural responses.

Simultaneously, a detailed finite-element model of the B737 fuselage section was

developed, using LS-DYNA, to simulate the drop test [20]. The model was constructed

based on the hand-measured dimensions of the actual test article. Simulation results, in

terms of the overall structural responses and the acceleration-time histories, were

compared with the experimental data, showing excellent agreement. Subsequently, the

model was further refined based on actual design dimensions of the various structural

components, including a more realistic connection of the overhead bins to the airframe,

etc. [21].

In a subsequent study, the refined model was used to perform a detailed

parametric study [72, Chapter 2] on the effects of the friction coefficients between the

44

impacting surfaces and of the impacting angle of obliquity. For each case, the

deformation of the fuselage, the acceleration-time histories at different locations on the

fuselage, and the energy dissipation of key structural components were analyzed.

The purpose of the friction parametric study was to investigate the effect of

various friction coefficients, which are associated with different terrains, on the structural

response of the aircraft. The study illustrated how the fuselage reacts to various impact

surfaces, which is necessary for further expanding the model to realistic impact

conditions.

The angle of impact parametric study provided an insight into the structural

response of the aircraft to different angles of impact, which better represents actual

aircraft crash landing scenarios. However, results of this study also revealed that the 3-m

long section could not realistically represent a full-length fuselage, because the former

tended to topple over when a horizontal velocity component is included.

This model was further expanded to study the impact response of a full-length

fuselage impacting three different terrains, namely: rigid surfaces, soil, and water, under

vertical and crash-landing impact conditions.

3.3. DEVELOPMENT OF THE FULL-LENGTH FUSELAGE MODEL

The objective of the current study was to develop a full-length (approximately 30

m long) fuselage finite element model of a representative narrow-body transport aircraft

and to use the model to study the effects of crash landing on different terrains (i.e., rigid

surface, soft soil, and water) on the deformation of the fuselage, acceleration-time

histories along the seat tracks, and energy dissipation of various subcomponents. The

full-length model was to be constructed by expanding the original 3-m long section

45

model (hereafter referred to as the ‘original’ section model) developed in [20]. However,

a preliminary vertical water impact simulation conducted using the 3-m long original

section model showed that it required approximately 25 hours of CPU time using 64

parallel processors. This indicates that a full-length fuselage, having the same level of

modeling details as the original section model, would not be a viable option

computationally. Therefore, a new computationally efficient section model, having fewer

structural details, was developed. The new model is henceforth referred to as the

‘modified’ section model. It is noted that both the original and modified section models

used type 16 fully integrated shell elements in LS-DYNA. For the material modeling, LS-

DYNA material type 82 (MAT 82) with a linear strain softening behavior after the failure

initiation was used to model aluminum alloys 2024-T3 and 7075-T6, which were used for

skin and other structural components, respectively, Figure 3-1. [13,20,21].

Figure 3-1: Stress-strain data for MAT82

46

3.3.1. DEVELOPMENT OF THE MODIFIED SECTION MODEL

The criterion used for building the modified section model was to reduce the

number of elements while keeping the deformation of the subfloor structure and the seat

track acceleration-time histories similar to those of the original section model. The

original section model consisted of approximately 126,000 elements, which included the

various subcomponents, such as two overhead stowage bins, passenger seats, stringer

clips, rivets, and camera mounts. Detailed modeling of these subcomponents was deemed

unnecessary because of their marginal effect on the dynamic response of the fuselage

structure and acceleration-time histories along the seat tracks. Yet, the masses of the

excluded subcomponents were assigned to the nodes to which they were attached. For the

remaining fuselage structure, a mesh sensitivity study was conducted with the aim of

keeping the overall impact response and the acceleration-time histories (at strategically

selected locations throughout the fuselage section) similar to those of the original model.

For example, the mesh for the upper frames and skin did not have to be as detailed since

those sections experienced mostly elastic deformation throughout the impact event and

had little bearing on the overall response of the structure [20]. On the other hand, the

lower frames and skin experienced significant plastic deformation and failures (i.e.,

buckling and crushing), thus required a relatively fine mesh to achieve the desired

accuracy. The resulting number of nodes, elements and total mass of the modified section

model is compared with the original section model in Table 3-1 (test article total mass

was 4,023 kg). Both the original and the modified section models are shown in Figure

3-2. It is noted that the simulations using the modified section model required

47

approximately one-fifth of the computation time needed for the original section model

(i.e., 20 min. vs. 100 min. on a 64 CPU cluster for rigid surface impact).

Table 3-1: A comparison of the finite element modeling details between the original and modified

section models

Nodes Shell Elements Solid Elements Beam Elements Total Mass

Modified Model 38,571 30,850 8,490 0 3,842 kg

Original Model 128,960 107,212 13,824 3,953 4,069 kg

(a) B737 Original Section Model

(b) B737 Modified Section Model

Figure 3-2: The original and modified B737 section models. The masses of the subcomponents that were

excluded from the original model were assigned to the nodes to which the subcomponents are

connected.

3.3.2. VALIDATION OF THE MODIFIED SECTION MODEL

Two vertical impact simulations were conducted to validate the reliability of the

modified section model: a) a rigid surface impact and b) a water impact. Simulation

results, in terms of deformation and acceleration-time histories, were compared with the

original section model, as follows:

48

i) Rigid Surface Impact

A comparison of the deformation of the original and modified section models at

selected stages of impact on a rigid surface is shown in Figure 3-3. It should be recalled

that the original section model has been validated against the actual drop test data in

terms of the structural deformation and the acceleration-time and force-time histories of

the fuselage structure and its individual components [20]. The comparison shown in

Figure 3-3 indicates that the modified section model was able to capture the key

structural deformation such as the tilting of the fuselage to the left, and the excessive

failure of the lower left-hand side frames. The particular deformation characteristics

resulted primarily from the presence of the stiff cargo doorframes on the right-hand side,

as discussed in detail in [20]. Note that the left- and right-hand sides of the aircraft are

with respect to the pilot’s position, when looking at the front of the fuselage section.

(a)

Ori

gin

al S

ecti

on

Mo

del

(b)

Mod

ifie

d S

ecti

on

Mo

del

t = 32 ms t = 64 ms t = 96 ms t = 128 ms

Figure 3-3: A comparison of the deformation of the original and modified section models at selected

stages of a rigid-surface impact

49

A comparison of the acceleration-time histories at four different locations on the

seat tracks at Frame Station 418 (FS 418, i.e., 418 inches from a reference point located

in the front of the aircraft is shown in Figure 3-4. A good agreement has been established

between the results from the two models, as well as with the experimental data reported

in [20,21]. The specific characteristics of these acceleration-time histories are discussed

in detail in [20,21]. It should be noted that in the drop test the accelerometers were

installed along the seat tracks and overhead storage bins of the test article to record the

acceleration-time histories [13]. In this study, accelerometer elements were placed only at

the corresponding seat track locations.

Figure 3-4: A comparison of seat track acceleration-time histories at FS 418 for rigid surface impact.

50

ii) Water Impact

The setup of the original section model for water impact simulations is shown in

Figure 3-5. A layer of air, situated on top of the water, was included so that the wave

propagation in the water during the impact event could be visualized. There are two

different methods that have been used in modeling water, namely, the Arbitrary

Lagrangian-Eulerian (ALE) method and the Smooth Particle Hydrodynamics (SPH)

method. Both methods have been shown to work well, but the SPH method is more

computationally intensive than the ALE method [15]. Hence, for this study, the ALE

method was selected to model the fluid-structure interaction.

Figure 3-5: Setup of the original section model for water impact, including a layer of air on top of the

water surface

LS-DYNA offers several different equations-of-state for modeling fluids, most of

which have a number of parameters that need to be determined experimentally. For this

study the Gruneisen equation-of-state was selected due to its successful use in similar

water impact studies [15]. The interaction between the fluid and the structure was

accomplished by using a penalty method. For the fluid-structure interaction to occur, the

51

Lagrangian mesh (for the fuselage structure) must spatially overlap with the Eulerian

mesh (for water and air). This spatial intersection is searched for continuously to

determine when the interaction between the water and structure will occur [73].

A comparison of structural deformation of the two section models at 200 ms after

initial impact is shown in Figure 3-6. In both cases, the lower frames deformed and

buckled into the luggage in the subfloor region of the fuselage section. However, the

location of the buckling was different in the two models. In the original section model the

buckling occurred toward the center of the fuselage, whereas in the modified model it

occurred towards the left-hand side.

As expected, the structural damage that occurred in the regions, modeled by the

finer mesh, tended to progress more gradually compared to the regions with modeled by a

coarser mesh; the latter tends to fail rapidly, causing abrupt transmission of the load to

the surrounding elements. Such a dynamic response is expected to lead to a more severe

failure. An example of the effect of mesh refinement is shown in Figure 3-7. The

modified section model, which had a coarser overall mesh compared to the original

model, was initially developed and validated with the original model for rigid surface

impact. The mesh in the modified section model was refined at selective regions to

achieve a better agreement with the deformation of the original section model,

particularly at the lower frames where deformation was most severe. When the same

modified section model was used for water impact, damage would initiate at regions in

the lower frames where a coarser mesh was used, resulting in deformation that was not at

the same location as in the original section model.

52

(a) Original Section Model

(b) Modified Section Model

Figure 3-6: A comparison of the deformed fuselage at 200ms of the original and modified section models

under water impact conditions.

Coarse mesh, t = 0ms

Fine mesh, t = 0ms

Coarse mesh, t = 200ms

Fine mesh, t = 200ms

Figure 3-7: A comparison of damage progressions in the fine meshed model and the coarse meshed

model. Failures in coarse meshed model occurred more abruptly, causing sudden transmission

of load to surrounding elements

Despite the above difference in deformation, the acceleration-time histories at the

selected locations along the seat track were very similar, Figure 3-8. The difference in

magnitude of the peak acceleration between the two models, other than that at the outer-

left location, was less than 2 g’s. The timing of the peak acceleration of the modified

section model was behind that of the original section model by approximately 10-20 ms

as the result of the delayed occurrence of buckling at the lower frames. It is noted that the

water impact simulations using the modified section model required approximately one-

53

tenth of the computation time needed for the original section model. (i.e., 2.5 hrs. vs. 25

hrs. on a 64 CPU cluster).

Figure 3-8: A comparison of seat track acceleration-time histories at FS 418 for water impact

The above comparisons indicate that the simulation of the modified section model

demonstrated a high level of agreement for the rigid surface impact (Figure 3-4) and an

acceptable level of agreement for the water impact (Figure 3-8). In other words, the

computationally efficient model produces similar results to the original section model;

54

accordingly, this modified section model was adopted to construct the full length fuselage

model.

3.3.3. EXPANSION OF THE MODIFIED SECTION MODEL TO A FULL-LENGTH

FUSELAGE MODEL

The fuselage length of Boeing 737 family ranges from approximately 28 m to 42

m [75]. To keep the full-length model computationally efficient, a fuselage of

approximately 30 m long (i.e., B737-200) was used for this study. The primary section of

the fuselage, excluding the nose cone and the tail cone, was approximately 16 m long.

This primary section was assumed to be of constant cross-section and of the same

structural details as the original section model, which was constructed by replicating the

modified 3 m long section model. The lengths of the nose and tail cones were assumed to

be approximately 5 m and 9 m, respectively. The actual geometry and structural details of

the nose cone, tail cone, and wings are unavailable in the open literature and considered

mostly as manufacturer propriety. Obviously, these three major components, and the

accompanying complex substructures, greatly affect the impact response of the full-

length fuselage. Once the details on the geometry, material, and weight of each

component are made available, the current model could integrate the complete aircraft

structure. However, since the purpose of this study is to evaluate the effect of different

terrains on the structural dynamic response (and the associated acceleration-time

histories) of an aircraft fuselage, the use of the simplified full-length model was deemed

appropriate. Since in this study only results from the primary fuselage section were of

interest, for simplicity, the nose cone and tail section are represented by two shell element

models, in the general shapes of the B737 (attached to both ends of the primary section),

55

containing no substructures or tail stabilizers, Figure 3-9. It is noted that the lack of

substructure support for the nose cone would cause it to undergo excessive deformation

in certain impact scenarios. The two ends of the primary fuselage section were designated

as FS 200 (200 inches from the nose) and FS 820, respectively. A cargo door, similar to

that in the 3 m long section model, was placed from FS 340 to FS 420 in the full-length

model. In addition, the landing gear was not included in the model either as the focus of

this study was to investigate the crashworthiness of the fuselage structure under

emergency landing conditions in which the landing gears could be out of order or have

collapsed [3]. As with the nose cone and tail section, the effect of the landing gear’s

substructure and weight was ignored.

It was noted in the previous study on the 3-m long B737 fuselage section [20,72,

Chapter 2] that the luggage played an important role in energy dissipation during the

impact event. In order to investigate the effect of under-floor luggage on the full-length

fuselage, the luggage model developed in the 3 m section model [20] was also replicated

to fill the full-length fuselage model from FS 200 to FS 820, excluding the nose and tail

cones, Figure 3-9. The total mass of the full-length fuselage model with the simplified

nose and tail cones, and without wings, landing gears and luggage, was 14,758 kg. With

the luggage included, the total mass of the full-length model was 22,733 kg. The mass of

the nose cone and tail section was 245 kg and 657 kg, respectively.

Accelerometer elements were placed along the inner and outer seat tracks on both

sides of the passenger floor at a number of fuselage stations throughout the entire

fuselage to record the dynamic responses during an impact event. For the purpose of this

paper, the focus is placed on those accelerometers located at FS 300, FS 480 and FS 700,

56

denoted by forward (FWD), middle (MID), and aft (AFT), respectively, Figure 3-9. Of

the four accelerometers at each fuselage station location, only the results from the one

that had the highest peak acceleration are presented and compared.

Figure 3-9: The 30-m long full-length model with a cargo door, under-floor luggage, and simple nose and

tail cones. FWD (FS 300), MID (FS 480), and AFT (FS 700) indicate the locations of

accelerometer elements.

3.4. FULL-LENGTH MODEL SIMULATIONS

Crash landings on three different types of terrains, namely, rigid surfaces (e.g., a

concrete runway), soil, and water, were simulated. For all simulations, a 110 knot (203.7

km/hr, or 56.6 m/s) approach speed was selected which is at the lower end of landing

speeds of typical transport aircraft. The same vertical component of velocity (9.14 m/s)

as the vertical drop test of the 3 m section was used [20]. This resulted in an initial

horizontal velocity component of 56 m/s and a 9.3° approach angle. It should be noted

that the 9.3° approach angle is much larger than the typical approach angle of 3° for a

normal landing [74]. In addition, the fuselage was given a 3° pitch angle, but with no yaw

or roll, to simulate realistic landing conditions [75], Figure 3-10.

Cargo Door

FS 200 FS 820 FWD

FS 300 MID

FS 480 AFT

FS 700

57

Since the landing gear was not included in the model, all landing scenarios

studied herein were belly landings or gear-up landings. Further, the luggage, which has

been shown to absorb a substantial amount of impact energy [20,72, Chapter 2], was not

included in the crash landing simulations. Therefore, the results presented herein

represent worst-case scenarios.

Figure 3-10: Crash landing scenario used in this study: The fuselage has a 110 knots approach speed, a

9.27° approach angle, and a 3° pitch angle.

The effect of the luggage stored in the under-floor luggage bay was excluded

from the crash landing simulation. To demonstrate the effect of the luggage, a separate

study was conducted on vertical impact simulations, with and without under-floor

luggage, onto a rigid surface and water. The effect of the luggage was quantified by

comparing the deformation of the frames, the acceleration-time histories along the seat

tracks, and the energy dissipation of the various subcomponents of the fuselage with and

without luggage.

For the rigid surface landing, a friction coefficient of 0.5 between the fuselage and

the rigid surface was used [68]. The detailed discussion on the effect of friction

coefficient between the impacting surfaces is given in [72, Chapter 2].

LS-DYNA offers a number of different material models for soil. The general

viscous foam material models, which allow the user the flexibility of using experimental

58

load-displacement curves, have been successfully used to model soil [17]. In addition,

there are numerous material models for specific ‘geomaterials’. One of the more common

models used to represent soil is *Mat_Soil_And_Foam, which was selected for this study.

As part of an effort to model Crew Exploration Vehicles subjected to soil impact [76],

NASA Langley Research Center (LaRC) required soil property inputs for their use of LS-

DYNA’s *Mat_Soil_And_Foam [77]. Applied Research Associates (ARA) gathered soil

samples from NASA LaRC and Kennedy Space Center and conducted a series of tests to

derive the required parameters that best represent the material and loading conditions for

different types of soil such as unwashed sand, low density dry sand, high density in-situ

moisture sand, and high density flooded sand [77]. For this study, the unwashed soil

properties were used for the material model since the other three types are typically only

found in coastal regions. The soil was modeled using solid elements with an eroding

contact definition between the fuselage and the soil. Any severely distorted elements

would be assumed to have failed and be removed from the simulation. A friction

coefficient of 0.3 between the fuselage and the soil was used. For the water landing

simulations, the ALE method described earlier was used to model the fuselage structure

and water interaction.

3.4.1. CRASH LANDING SIMULATION RESULTS

i) Deformation and Effective Plastic Strain

Figure 3-11 shows the deformation of the full-length fuselage model, at three

selected time steps, as a result of crash landing onto a rigid surface, i.e., (a) at t = 0 ms

when the aft end of the primary fuselage section contacted the ground, (b) at t = 80 ms

when the forward end of the primary fuselage section contacted the ground, and (c) at t =

59

200 ms when the simulation terminated. Due to the lack of substructure support, the

lower portion of the nose cone and tail section underwent excessive deformation

immediately after the forward section of the primary fuselage contacted the ground at t =

80 ms and eventually separated from the primary fuselage section, Figure 3-11(c).

Similar results for crash landings on soil and water are shown in Figure 3-12 and Figure

3-13, respectively. Unlike the case of rigid surface landing in which no deformation

occurred to the landing surface, both the soil and water underwent significant

deformation, dissipating appreciable amount of the kinetic energy, as will be discussed

below.

(a) t = 0 ms (b) t = 80 ms (c) t = 200 ms

Figure 3-11: Deformation of the full-length fuselage model crash landing onto a rigid surface.

(a) t = 0 ms (b) t = 80 ms (c) t = 200 ms

Figure 3-12: Deformation of the full-length fuselage model crash landing onto soil.

60

(a) t = 0 ms (b) t = 80 ms (c) t = 200 ms

Figure 3-13: Deformation of the full-length fuselage model crash landing onto water.

The overall deformation and contours of effective plastic strain of the frames, at

selected time steps, resulted from crash landings on three types of terrains are shown in

Figure 3-14 in a perspective view from the front of the fuselage. The occurrences of the

key events during the impact are as follows:

i) At 12 ms: Initial plastic deformation occurred at the lower frames of the aft

section, which came in contact with the terrains the earliest, due to the 3° pitch

angle.

ii) At 52 ms: Plastic deformation spreads forward as additional frames come in

contact with the terrains. Plastic hinges formed first in the aft sections followed by

frame buckling. An example of plastic hinge formation is shown in Figure

3-15(a). As seen in the Figure, the extent and magnitude of the plastic strain

varies form frame-to-frame, depending upon the time of impact. The overall

appearance of the effective plastic strain field is quite similar in all three terrains;

yet, the rigid surface impact yields the largest plastic strain and the water impact

the least.

iii) At 92 ms: Plastic deformation extended throughout the lower frames of the entire

fuselage length. The bottoms of the aft frames have flattened out and failure (i.e.,

61

element deletion) has occurred. Note the similarity in the deformation between all

three terrains at this stage.

iv) At 152 ms: The bottoms of all lower frames have flattened out and most frames -

from the mid to the aft of the fuselage - have come in contact with the passenger

floor. An example of frames impacting the passenger floor is shown in Figure

3-15(b). All frames in the aft section have undergone severe plastic deformation,

buckling, and fracture.

v) At 200 ms: All lower frames have been completely crushed and have come in

contact with the passenger floor. An example of frames buckling is shown in

Figure 3-15(c). Frame buckling occurs both in the middle and side of the fuselage.

The extent and location of the buckling depends, to a great extent, on the friction

coefficient between the contacting surfaces [72]. No elastic rebound is observed

at this stage at any of the three terrains in any of the frames throughout the

fuselage length. The fuselage continued to move forward at the termination of the

simulations.

It is noted that the overall deformation of the frames caused by crash landings on

all three types of terrains was very similar at the end of the simulations. This can be

attributed to the fact that during the crash landings the fuselage moves forward

continuously onto un-deformed terrain, thus resulting in similar deformation regardless of

the type of terrain the fuselage impacts.

62

Time Rigid Soil Water

a) 12ms

b) 52ms

c) 92ms

d) 152ms

e) 200ms

Figure 3-14: The overall deformation and contours of effective plastic strain of the frames at selected time

steps resulted from crash landings on three types of terrains.

63

(a) (b) (c)

Figure 3-15: Example of (a) the formation of plastic hinges at t = 52 ms at FS 800, near the aft section, (b)

frames impacting the passenger floor at t = 152 ms., and (c) the occurrence of local frame

buckling at 200ms, FS 200.

ii) Acceleration-Time Histories

The acceleration-time histories along the seat tracks on the passenger floor at

forward, middle and aft locations of the fuselage resulted from crash landings onto a rigid

surface are shown in Figure 3-16. The magnitudes of the peak acceleration pulses at the

three locations are significantly different due to the different times and velocity at which

the three sections of the fuselage impacted the surface. Due to the 3 pitch angle the aft

section impacted the surface first, resulting in an earlier peak pulse (at 125 ms), followed

by the middle (at 150 ms), and then in the forward regions (at 190 ms). Furthermore, the

3 pitch angle also resulted in the forward location being approximately 0.8 m higher

than the aft location at the time of initial impact, causing the forward section to accelerate

downwards and impact the surface at a velocity of which the vertical component was

20% higher than that when the aft section impacted the surface. Consequently, the

magnitudes of the acceleration pulses were progressively higher when proceeding from

aft to forward locations. The highest acceleration, of 40 g’s, occurred at the forward

location at approximately 190 ms after the initial impact. Beyond 200 ms, the vertical

velocity rapidly subsided, but the fuselage continues to move forward with a horizontal

64

velocity of 52.4 m/s, i.e., only 7.5% lower than the initial velocity. Thus, only

approximately 15% of the initial kinetic energy has dissipated as discussed in further

detail below.

Figure 3-16: Seat tracks acceleration-time histories resulting from a crash landing of a full-length fuselage

on a rigid surface. The magnitude of the peak acceleration pulses progressively increased

from the AFT to FWD locations.

The simulation yielded similar results for crash landing on soil and water terrains.

For comparison, the acceleration-time histories at aft and forward locations, for all three

terrains are shown in Figure 3-17. Results at the aft locations, Figure 3-17(a), show that

the magnitudes of the first peak accelerations and their arrival times varied slightly for

the three terrains: 9.5 g’s at 65 ms for rigid surface landing, 6 g’s at 53 ms for soil surface

landing, and 8 g’s at 60 ms for water surface landing,. The subsequent peak accelerations

and their arrival times varied further, with the maximum peak accelerations for all three

cases being approximately 20 g’s within the first 200 ms.

The acceleration-time histories at the forward location for all three terrains were

nearly identical, Figure 3-17(b), with initial peak accelerations of 10 g’s, 13 g’s, and 6

65

g’s, for the rigid, soil, and water terrains, respectively, all occurring nearly at the same

time (110 ms). The peak acceleration for all three terrains is approximately 40 g’s, all

occurring at approximately 190 ms after initial impact.

Figure 3-17: Seat track acceleration-time histories comparison at aft and forward locations resulting from a

crash landing of a full-length fuselage on rigid, soil and water terrains.

iii) Energy Dissipation

The normalized energy dissipated during the first 200 ms of the crash landing on a

rigid surface is shown in Figure 3-18. The kinetic energy was normalized with respect to

the initial kinetic energy (at 0 ms), and the energy dissipated was normalized with respect

to the total energy dissipated at 200 ms. Due to the large horizontal component of the

approach speed, only 15.4% of the initial kinetic energy was dissipated at 200 ms as the

fuselage was still moving forward at a relatively high speed. Approximately 19% of the

energy dissipated, or 2.9% of the initial kinetic energy, was absorbed by the fuselage

structure, with the frames and the skin absorbing approximately 11.5% and 7.5%,

respectively. The landing surface, being rigid, did not absorb any energy through

66

deformation; however, friction between the fuselage and the rigid surface accounted for

approximately 80% of the dissipate energy.

The energies dissipated during the first 200 ms of the crash landings on soil and

water are shown in Figure 3-19. Due to the lower friction, the initial kinetic energy

dissipated by the end of the simulation (200 ms) in each case was less than the rigid

surface case, with soil and water dissipating approximately 11% and 6% of the initial

kinetic energy, respectively. In the soil impact case, approximately 30% of the dissipated

energy, or 3.3% of the initial kinetic energy, was absorbed by the fuselage structure, as

compared to 70% and 4.2%, respectively, in the water impact case. It is noted that the soil

and water absorbed approximately 4.3% and 1.75%, respectively, of the dissipated

energy.

Figure 3-18: Energy dissipation for a crash landing of a full-length fuselage on a rigid surface. Frames and

skins dissipated most of the energy.

67

Figure 3-19: Energy dissipations for crash landing on soil and water surfaces. Frames and skin dissipated

most of the energy.

Figure 3-20 compares the energy dissipated by the frames and the skin for all

three terrains, normalized with respect to the energy dissipated in the rigid surface case at

200 ms. The rigid and soil terrains result in similar energy dissipation by the frames and

skin, with the soil being approximately 8% lower. In the water impact case, the energy

dissipated by the frames and skin was approximately 20% and 33% higher than the rigid

impact case, respectively. This indicates that the frame and skin in the water impact case

underwent higher plastic deformation than the rigid and soil cases. Apparently, the

continuous contact pressure applied by water over the entire subfloor structure (frames

and skin) has a greater effect on the overall deformation than the rigid and soil surfaces,

whose primary points of contact for load transfer are the frames.

68

Figure 3-20: Energy dissipation by (a) frames, and (b) skin for crash landing on rigid, soil and water

surfaces.

3.4.2. VERTICAL IMPACT SIMULATION RESULTS

It has been shown that only a small amount of the initial kinetic energy dissipates

in a crash landing event, as the fuselage continued moving forward with a relatively high

velocity. In order to gain a better understanding on how the energy dissipates by the

various subcomponents, simulations were conducted for the case of vertical impacts of

the full-length fuselage, on all three terrains. For all three simulations, the fuselage was

dropped onto the surfaces with no pitch angle and with the same initial vertical velocity

of 9.14 m/s as the crash landing simulations.

i) Deformation and Effective Plastic Strain

Figure 3-21 shows the effective plastic strain of the fuselage without luggage at

152 ms after the initial impact onto the three terrains. The plastic deformation in the

frames and the skin has been completed at this stage and the upper portion of the frames

69

began to reverberate elastically. The reverberation was not as noticeable in the soil and

water impact cases because these terrains deformed under the impact loading enabling the

fuselage to further sink into these two terrains. The asymmetrical deformation, caused by

the stiff cargo doorframe [20,72, Chapter 2], was most prominent in the water impact

case where the severe deformation and failure occurs along the more compliant lower

left-hand side frames. No specific conclusions could be drawn regarding the behavior of

the nose cone and the tails sections because of the lack of sufficient structural details.

Rigid Soil Water

Figure 3-21: The overall deformation and contours of effective plastic strain of the frames at t = 152 ms

resulted vertical impact on three types of terrains

ii) Acceleration-Time Histories

The acceleration-time histories at the forward, middle and aft locations on the

passenger floor resulted from vertical impact of the full-length fuselage, without luggage,

onto a rigid surface are shown in Figure 3-22. The magnitudes of the peak acceleration

pulses are quite similar at the forward and aft locations, with the maximum acceleration

being approximately 19 g’s, occurring at 190 ms at the aft location. Furthermore, the

peak acceleration at the aft location occurred approximately 40 ms later than that at the

forward location. It should be noted that the tail section, which is approximately 168%

heavier than the nose cone caused the aft frames to crush further, thus delaying the arrival

70

of the peak acceleration pulse. The addition of the nose and tail cones also resulted in

higher peak acceleration pulses at the forward and aft locations as compared with the

middle location.

Similar results were obtained for vertical impact on soil and water surfaces. For

soil impact, the peak acceleration at the aft section was approximately 22 g’s (at at 190

ms), whereas for water impact it was approximately 13 g’s (at 100 ms), Figure 3-23. As

expected, the acceleration pulses in water impact were mostly lower than in rigid and soil

impacts due to the large deformation of the water. The acceleration pulses in soil impact

were higher than in rigid and water impacts due to the different coefficient of friction

between the fuselage and the impact terrain used in this study (0.3 for soil and 0.5 for

rigid surface). A similar observation, on the effect of friction between the fuselage and

impact terrain, was made in a previous study [72, Chapter 2]. It should be noted that the

above discussion is merely to offer a preliminary glance on the significance of nose cone

tail section and on the overall impact response of the full-length fuselage. It should be

expected that the effect of the actual nose cone and tail section would be quite different.

Figure 3-22: Seat tracks acceleration-time histories for full-length fuselage vertical impact on a rigid

surface.

71

Figure 3-23: Seat track acceleration-time history comparison at aft and forward locations resulting from

vertical impact of a full-length fuselage on rigid, soil, and water terrains.

iii) Energy Dissipation

The energy dissipated during the first 200 ms of the vertical impact on a rigid

surface is shown in Figure 3-24. All energies are normalized with respect to the initial

kinetic energy (at 0 ms). More than 90% of the initial kinetic energy was dissipated

within the first 150 ms after initial impact. Of the total dissipated energy, more than 90%

was absorbed by the frames and skin to form plastic deformation. By 150 ms, all plastic

deformation was completed and the structure underwent an elastic reverberation for the

remainder of the simulation time.

The energy dissipation plots for soil and water impacts are shown in Figure 3-25.

The plastic deformation in the frames and the skin dissipate most of the energy. For the

water impact case, a negligible amount of energy was dissipated by the water, whereas

for the soil impact case the soil deformed and absorbed nearly 8% of the dissipated

energy.

72

Figure 3-24: Energy dissipation for vertical impact on rigid surface. Frames and skin dissipated most of the

energies.

Figure 3-25: Energy dissipation for vertical impact on soil and water. For both cases the frames and skin

dissipated most of the energies.

Figure 3-26 compares the energy dissipated by the frames and the skin for all

three terrains, normalized with respect to the final energy dissipated in the rigid surface

impact at 200 ms. The rigid and soil terrains resulted in similar energy dissipation by the

frames, with the soil being only 6% higher. In the water impact case, the energy

73

dissipated by the frames was 36% lower than the rigid impact case. The soil and water

terrains resulted in similar dissipation by the skin, which were approximately 20% and

26% lower than the rigid terrain, respectively. The rate of energy absorption by the skin

depends, as expected, on the dynamic response of the frames.

Figure 3-26: Energy dissipation by (a) frames, and (b) skin for vertical impact on rigid, soil and water

surfaces.

3.4.3. EFFECT OF LUGGAGE ON FUSELAGE DEFORMATION, ENERGY

DISSIPATION, AND ACCELERATION-TIME HISTORIES

It was noted in a previous study [20,72, Chapter 2] that the luggage played an

important role in energy dissipation during the impact event. In fact, for vertical impact

of the single-section fuselage, the luggage dissipates approximately one third of the total

initial kinetic energy. This issue was further investigated herein by conducting vertical

impact simulations of the full-length fuselage model on the rigid and water terrains with

luggage contained in the cargo bay. The luggage was modeled in the same way as that in

[20,72, Chapter 2]. For both simulations, the fuselage was dropped onto the surfaces with

74

no pitch angle and with the same initial vertical velocity of 9.14 m/s as the crash landing

simulations. Figure 3-27 shows a comparison of the deformed fuselage at 200 ms for

both, rigid and water, impact conditions. As expected, soil impact (not shown here)

should yield intermediate deformation behavior relative to these two extreme cases.

Clearly, the presence of luggage in the cargo bay prevented the lower frames from

deforming upwards and contacting the floor beams. In terms of energy dissipation, results

show that for both terrains the luggage dissipated approximately 45% of the total kinetic

energy, Figure 3-28

.

With Luggage Without Luggage

(a)

Rig

id i

mp

act

(b)

Wat

er i

mp

act

Figure 3-27: A comparison of the deformed fuselage with luggage at 200ms under rigid and water impact

conditions.

75

Figure 3-28: Energy dissipation for rigid and water impact conditions, showing significant energy absorbed

by the luggage.

The effect of the luggage on the acceleration-time histories at the forward and aft

locations of the fuselage is shown in Figure 3-29 for the case of rigid surface impact.

Results show that the presence of the luggage reduced the acceleration pulses by more

than 6 g’s at both the forward and aft locations.

76

Figure 3-29: Seat track acceleration-time histories showing the effect of luggage for the case of vertical

rigid surface impact.

For water impact, the luggage was not as effective in lowering the maximum peak

acceleration. For example, the presence of luggage increased the first peak acceleration at

the forward location from 8 g’s to 12 g’s, Figure 3-30. Overall, the luggage acted like a

damper - reducing the amplitude of subsequent oscillations, yielding nearly a single long

duration pulse.

Figure 3-30: Seat track acceleration-time histories for effect of luggage in the case of vertical water surface

impact.

77


A full-length fuselage model of a representative narrow-body transport aircraft,

excluding wings, and landing gears, was developed to simulate crash-landing on different

terrains, such as rigid surfaces, soils, and water. The full-length model consisted of a

primary fuselage section, a nose cone, and a tail cone, the latter two represented by

simple shell elements, excluding all structural subcomponents. A previously developed

3-m long B737 single-section model, which has been validated against drop test

experimental data, was first simplified to enable a computationally efficient model for the

full-scale fuselage impacting different terrains. A verification study, comprised of vertical

impact simulations on rigid and water surfaces was conducted to ensure that the

simplified section model was capable of replicating the deformed configuration and

acceleration-time histories similar to that of the original section model. The results

indicated that the computationally efficient modified model provided accurate

simulations, while requiring one-fifth of the computation time. The full-length fuselage

model was then constructed by expanding a simplified section model which was

employed to conduct a series of crash landing simulations on a rigid, soil, and water

terrains.

Simulation results showed that the peak accelerations for all three terrains were

very similar, with the highest peak acceleration being 40 g’s and occurring at the forward

section. The aft section typically showed lower peak acceleration pulses, arriving at

different times for each terrain. In all three cases the frames absorbed more energy than

the skin and, in the soil and water impact cases, the terrain also deformed, dissipating a

portion of the initial kinetic impact energy. The effect of luggage on the dynamic

78

response of the fuselage structure, impacting the three terrains, was also investigated by

conducting vertical impact simulations. The luggage played an important role as the

major energy absorber, as well as acting as a damping mechanism that rapidly diminished

the reverberation of the fuselage structure.

79

CHAPTER 4: APPLICATION OF AN ENERGY ABSORBING DEVICE TO THE

BOEING 737 FUSELAGE SECTION

4.1. INTRODUCTION

In Chapter 2, a previously developed finite element model of a 3m long Boeing

737 fuselage section was used to study the effect of friction and the angle of impact

between the fuselage section and a rigid surface. This model was extended in Chapter 3

to model a full-length narrow-body transport aircraft fuselage which was used to study

the dynamic response during impact at various terrains (rigid, soil and water). Both

studies highlighted several important differences between various crash landing

scenarios. One common result was the significant effect of the under-floor luggage on the

overall energy absorption process and, specifically, in reducing the forces (accelerations)

transmitted to the occupants. Hence, integrating energy absorbing mechanisms into the

existing subfloor structures could be a viable option to mitigate the impact energy. In this

chapter, a simple example on the effect of using energy absorbing structural members on

the Boeing 737 fuselage section is presented. The setup of the model is discussed first,

followed by a comparison of the results with that of the original B737 fuselage section

models with and without under-floor luggage. This brief and preliminary study serves as

a precursor to an extended study, described in Chapters 5 to 9, on the load-displacements,

peak loads, energy absorption capacity, and failure processes of various composite-made

stanchions.

80

4.2. MODEL SETUP

Complete modeling details of the B737 fuselage section model were described in

Chapter 2. For the present study, the luggage was removed from the subfloor region of

the model and replaced with energy absorbing stanchions. However, integrating realistic

models of stanchions into the subfloor structure of the B737 model requires additional

information, such as connections and joints to the surrounding frames, that is not readily

available. Therefore, the stanchions were modeled using spring elements. It should be

noted that using springs elements to represent the stanchions is a significant

simplification of the actual geometry, affecting the accuracy of the results. Hence, the

purpose of this study is merely conceptual: to test the concept of using stanchions to

decrease the decelerations on the occupant. Further, the results presented herein should be

viewed considering the following assumptions: i) the load will always be transmitted

axially, where no bending or twisting of the stanchions is permitted; ii) the sustained

crush load on the stanchion remains constant throughout the entire impact event; and iii)

the stanchions remain connected to the nodes, including during rebound of the fuselage.

In this study, discrete spring elements with an inelastic spring material model

(MAT S08) [73] were used to model the stanchions. MAT S08 material model requires a

user-defined load-displacement curve for both tension and compression. A typical load-

displacement curve during the crushing of a graphite/epoxy member, as shown in Figure

4-1, was used. Detailed discussions on the load-displacement curves of different

graphite/epoxy composite stanchions will be provided in Chapters 5 and 6.

A total of 14 spring elements were used in the 3 m long section model; two at

each frame, seven on the left- and seven on the right-hand sides, corresponding with their

81

location shown in Figure 2-4. The springs were connected between nodes located at the

top of the floor beams and the bottom of the lower frames, and were aligned vertically,

Figure 4-2(a). By connecting the spring elements directly to nodes in the beams and the

frames, the forces in the springs could be transmitted only through these nodes, yielding

artificially high stress concentrations in the connecting elements. To prevent unrealistic

distortion and severe failure of the elements surrounding these nodes, rigid elements were

used to distribute the load over a larger area, Figure 4-2(b).

Figure 4-1: Load-displacement curve used in MAT S08

Figure 4-2: (a) B737 fuselage section showing spring elements as energy absorbers, and (b) a close-up

view of a spring element showing the rigid connectors

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Load

(kN

)

Displacement (mm)

MAT S08 (Spring)

82

4.3. SIMULATION RESULTS

The simulation results of the B737 model with spring elements are compared with

that of the B737 models with and without luggage, shown in Chapter 2. The structural

deformation of the fuselage at three different time intervals shows that the spring

elements substantially reduced the deformation of the subfloor structure, as well as the

overall deformation of the frames, Figure 4-3. The passenger floor displaces vertically

down by approximately 300 mm in the spring model, compared to nearly 450 mm in the

model with luggage. That is, compared with the luggage, the spring elements provide a

stiffer crushing response. It is worth noting that a stanchion could provide only local-

support to the passenger floor, while the effect of the luggage is distributed nearly

uniformly across the entire floor.

Comparing the acceleration-time histories on the left-hand side of the fuselage,

Figure 4-4(a), shows that the spring model results in an acceleration peak that is

marginally lower than that of the model without luggage but higher than the model with

luggage. This is expected since the spring selected herein exhibited higher stiffness

compared to the luggage and were located in discrete points under the floor. On the right-

hand side, Figure 4-4(b), all three models result in very similar acceleration peaks. At

both the left- and right-had side locations, the spring model results in earliest arrival of

the acceleration peak. Similar to the case with luggage, the spring model typically results

in a single acceleration pulse with a longer duration, compared to the several short pulses

resulting from the impact with no luggage. Similar behavior, but with varying peak

accelerations and timing, was recorded at all other seat track locations (not shown here).

83

Figure 4-3: Comparison of the deformation of the B737 fuselage section models with luggage, without

luggage, and with spring elements as energy absorbers at three time intervals.

Figure 4-5 shows the comparison between the energy dissipated by the luggage

and the spring elements, normalized with respect to the total energy dissipated by the

luggage. It can be seen that the spring elements absorb approximately half the amount of

energy absorbed by the luggage. Further, the spring elements only absorb energy up to

approximately 75 ms after the initial impact, while the luggage continues to absorb

84

energy till the end of the simulation. This indicates that the spring elements stopped

crushing at around 75 ms. The energy absorption characteristics could be modified by

using the appropriate stanchion material, laminate configuration, and cross-sectional

geometry, as discussed in Chapters 5-9.

Figure 4-4: Comparison of the acceleration-time histories at two FS 452 seat track locations: (a) LHS

outer seat track, and (b) RHS outer seat track.

Figure 4-5: Comparison of the energy dissipated by the luggage and the spring elements

-15

-10

-5

0

5

10

15

20

25

0 50 100 150 200

Acc

eler

atio

n (

G's

)

Time (msec)

With Luggage

Without Luggage

With Spring Elements-15

-10

-5

0

5

10

15

20

25

0 50 100 150 200

Acc

eler

atio

n (

G's

)

Time (msec)

With LuggageWithout LuggageWith Spring Elements

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200

No

rmal

ized

En

ergy

Dis

sip

ated

Time (msec)

With Luggage

Spring Elements

(a)

(a)

(b)

(b)

85


This brief study demonstrated the feasibility of using energy absorbing members

(i.e. stanchions) to dissipate the impact energy during a crash event. The deformation

comparison shows that stanchions, modeled as spring elements, are able to prevent

excessive failure of the frames, similar to that recorded for the case without luggage.

However, the crushing response of the spring elements selected in this study is slightly

stiffer than that of the luggage. The energy dissipation comparison reveals that the spring

elements do not crush for the entire duration of the impact event, compared to the case

with the luggage, which crushes till the end of the simulation. This obviously affects the

amount of impact energy dissipated by the spring elements, which ultimately absorb

approximately 50% of the energy absorbed by the luggage. In terms of the acceleration-

time histories, the spring elements result in a lower acceleration peak than the case with

luggage on the left-hand side, and a comparable acceleration peak to the other two cases

on the right-hand side of the fuselage.

In addition to the assumptions discussed earlier regarding the use of spring

elements to model the energy absorbing members, there are other factors that could

significantly affect the results of the simulation. For example, the location of the springs

was arbitrarily assigned, based on the alignment of pre-existing nodes in the beams and

the frames. Relocating the springs, either outward or inward, could alter the dynamic

response of the structure. Further, the number of springs used needs to be taken into

consideration as well. In this study, two stanchions per frame were modeled; however,

increasing or decreasing the number of stanchions could significantly affect the results. It

should be noted that the luggage described in Chapters 2 and 3 was distributed nearly

86

uniformly under the floor. Finally, the stanchions were modeled using a representative

load-displacement curve of a graphite/epoxy member, whereas actual experimental data

could have a very different effect on the dynamic response of the fuselage structure.

Therefore, an investigation is warranted to evaluate the effect of the various parameters

on the crushing behavior of stanchions as well as a more accurate alternative to using

spring elements to represent the stanchions. These results are essentially the foundation

that motivated the further research into the energy absorption capabilities of

graphite/epoxy members, discussed in Chapters 5 and 6, as well as the development of

finite element models capable of simulating the crushing process of these members,

discussed in Chapters 7 to 9.

87

CHAPTER 5: AN EXPERIMENTAL STUDY ON THE EFFECT OF FAILURE

TRIGGER MECHANISMS ON THE ENERGY ABSORPTION CAPABILITY OF

CFRP TUBES UNDER AXIAL COMPRESSION

4

5.1. ABSTRACT

The energy absorption characteristics of graphite/epoxy tubes of circular cross

sections, subjected to quasi-static axial compression, were experimentally investigated.

Tubes with chamfered-ends, inward-folding or outward-splaying crush-caps, or combined

(chamfered-end and crush-cap) failure trigger mechanisms, were investigated to identify

the optimal configuration that would result in the lowest initial peak load while providing

the highest possible specific energy absorption (SEA). The chamfer failure trigger proved

to be the most effective at lowering the initial peak load while yielding a high SEA. The

inward-folding crush-caps were more effective than the outward-splaying crush-caps in

terms of decreasing the initial peak load and increasing the SEA. These results were

significantly affected by the corner radii of the crush-caps: the smaller the radius the

higher the initial peak load and the SEA. It was determined that combining a chamfered

tube with an inward-folding crush-cap yielded the lowest initial peak load and the highest

SEA.

4Siromani, D., Henderson, G., Mikita, D., Mirarchi, K., Park, R., Smolko, J., Awerbuch, J. and Tan, T.,

“An Experimental Study on the Effect of Failure Trigger Mechanisms on the Energy Absorption

Capability of CFRP Tubes under Axial Compression,” Submitted to: Composites Part A: Applied Science

and Manufacturing.

88

5.2. INTRODUCTION

Rotorcraft crashworthiness, which includes airframe crashworthiness and

occupant protection, has been identified as a key area of focus to improve survivability in

the event of a crash [1]. Studies have shown that the vertical load transmitted to the

occupants during a crash is a key factor in causing injury to the lumbar spine [78]. Thus,

the mitigation of this impact load has long been recognized as a vital consideration of a

crashworthy design. The design of energy absorbing structures, however, must be

accomplished with minimal parasitic weight.

The NASA Subsonic Rotary Wing Aeronautics Program recently demonstrated

the use of Deployable Energy Absorbers (DEAs) fitted on an MD-500 helicopter for a

full-scale crash test [22]. The DEAs consist of a composite honeycomb structure,

fabricated using fiber reinforced fabrics, which can be deployed externally to absorb

energy in the event of a crash. While test results showed that DEAs offer a high level of

energy absorption due to the large crushing zone available, the resulting parasitic weight,

however, has not been addressed.

An alternative approach is to modify existing subfloor structural members, such

as floor beams, stanchions and stiffeners, to provide for higher energy absorption. Such

members must sustain normal flight load conditions while reducing initial peak loads

upon impact and maximizing energy absorption during a crash. For small aircraft and

rotorcraft, this can prove challenging due to the space constraints in the subfloor

compartment [23].

Composite materials are considered as possible candidates for energy absorbing

structural components due to their high strength-to-weight ratio and their high specific

89

energy absorption (SEA) characteristics, particularly during crushing [53,54]. Several

research groups have investigated the energy absorbing characteristics of composite

materials for crashworthy applications in the aircraft and automotive industries. For

simplicity, cost effectiveness, and for the purpose of understanding the fundamental

crushing process of composite stanchions, most studies were conducted under quasi-static

axial compression loading conditions. The most common composite materials

investigated have been graphite/epoxy (Gr/Ep) [23-29,33-42], glass/epoxy (Gl/Ep)

[24,25,30-34,43-52] and Kevlar/epoxy (K/Ep) [24,25,33-38]. Results showed that in

similar laminate configurations Gr/Ep absorbed the highest energy while K/Ep absorbed

the least. However, all three material systems exhibited higher energy absorption

capabilities than conventional metallic structures, such as aluminum and steel [33,53].

Simply, the extensive damage that occurs during the crushing process of brittle

composites, due to the combination of multiple failure mechanisms, absorbs a much

higher energy than during the elastic/plastic deformation of metals. In most cases

(depending upon laminate configuration and fabrication processes) the more brittle the

material system the higher the energy absorbed under compression [35].

The effect of fiber orientation for all three material systems have been

investigated using [0/±θ]n laminates [25], showing that the highest energy absorption was

achieved using a [0/±15]n laminate. Similarly, it was shown that increasing the number

of 0° plies in [452/0n/452]s laminates increased the energy absorption of the specimens

[28].

Various cross-sectional geometries have been investigated to determine their

effect on the energy absorbing capacity. These include tubes with circular [23,25-27,33-

90

35,45,48,52-54], square [42,47,52] and hexagonal [52] cross-sections, hourglass [52] and

cone [43,43,52,55] shaped tubes, angle-stiffeners [28,42], C-channels [28,42], flat plates

[28,37,38], sandwich panels [49], foam-filled blocks [56], hat stiffeners [39], and sine-

wave members [29,36]. Tubular specimens have been used extensively due to their self-

supporting capability that does not require end fixtures. Open cross-section specimens, on

the other hand, need supporting devices to maintain stability during the crushing process,

e.g., [28,42], which add complexities to proper load introduction. Results have shown

that circular tubes can achieve SEA values well over 100 kJ/kg [23], which is much

higher than any other cross-sections investigated, e.g., [28,37-39,42]. However, when

integrated into a beam structure, designed for a rotorcraft subfloor, their energy

absorption capacity is significantly reduced [23]. Possible causes for this unexpected

result were being examined and were not discussed in detail by the authors in [23].

An important aspect to consider when designing a cylinder to absorb energy is its

diameter-to-thickness (D/t) ratio [25]. The results obtained with [±45°] graphite/epoxy

tubes indicate that a reduction in tube D/t ratio results in an increase in energy absorption.

For tubes with the same D/t ratio, the SEA decreases with increasing tube diameter.

It has been well established that introducing an effective failure initiation site,

which triggers progressive failure, is crucial for reducing the initial peak crush load and

maximizing energy absorption. Without an effective failure trigger mechanism,

composite tubes fail abruptly and catastrophically, with a high initial peak load followed

by a very low energy absorption capacity. Failure trigger mechanisms can be classified as

internal triggers (e.g., chamfer, steeple, and ply drop-off) and external triggers (e.g.,

crush-caps and plug initiators), which are added at one end of the stanchion.

91

Numerous studies have shown that chamfer failure triggers are very effective at

reducing the initial peak crush load while maintaining high sustained crush loads and

SEA [23-28]. The crush behaviors of thin-walled hollow square [42,52] and circular

tubes [52] with chamfer failure triggers have been compared against those with steeple

failure triggers. Results showed that the for square tubes steeple failure trigger was

significantly more effective than the chamfer failure trigger at maintaining a higher

sustained crush load, but the opposite was recorded for circular tubes. The effect of

external failure trigger mechanisms, using crush-caps, on the initial peak load and the

SEA of graphite/epoxy cylinders were studied in [31,32]. In [31] two different types of

crush-caps were studied, forcing fibers to splay outward and inward, respectively. Each

type of crush-cap was fabricated with two different corner radii (3 mm and 5 mm) used to

cause stress concentrations at the end of the tube. The results indicate that the inward-

folding crush-caps increased material interaction and provided higher SEA. Also, in both

cases, the crush-cap with the smaller corner radius provided a higher SEA. A “load-

control” attachment was developed in [32], similar to an outward-splaying crush-cap with

the addition of an outer-curvature constrainer designed to increase the SEA. The results

indicated that the smaller curvature radius of the load-control attachment yielded a higher

SEA.

The objective of this study is to perform a comprehensive investigation on the

crushing behavior of circular graphite/epoxy tubes using chamfered-ends, crush-caps, and

combined (chamfered-end and crush-cap) failure trigger mechanisms. The effect of the

corner radii of the crush-caps on peak load, SEA and crush behavior of the tubes is also

92

evaluated. Results of this experimental study have been used to validate the numerical

simulation of the crushing process developed in [79, Chapter 8].

5.3. EXPERIMENTAL SETUP

5.3.1. SPECIMEN FABRICATION

The specimens were fabricated using Hexcel IM7/8552 Graphite/Epoxy

unidirectional tape pre-preg with a 12 K tow and a 180° C curing resin (350° F), provided

by the Structures Technology group of The Boeing Company in Ridley Park,

Pennsylvania. All specimens were 101.6 mm (4.0 in) long with an inner diameter of 29.4

mm (1.16 in) and a wall thickness of 1.47 mm (0.058 in), resulting in a D/t ratio of 20.

Two different sets of tubular specimens were tested. The first set consisted of cylindrical

tubes donated by The Boeing Co. The lay-up consisted of nine plies of unidirectional

material oriented in 0° and ±15° directions. The exact lay-up remains company

proprietary. The second set was prepared in house with a lay-up of [+15/-15/+15/03/-

15/+15/-15]. This lay-up was selected based on the work reported in [25].

5.3.2. FAILURE TRIGGER MECHANISMS

The conventional approach to introduce a failure trigger mechanism is to chamfer

one end of the tubular specimen, Figure 5-1(a). Alternatively, failure could be triggered

by attaching a crush-cap at one end of the tube. In this study, two different types of crush-

caps were studied, each causing the crushed material to fold either inward (Figure 5-1(b))

or splay outward (Figure 5-1(c)). The effect of the corner radius of the crush-caps on the

peak load, SEA, and crush behavior was investigated. Based on these results, a combined

93

failure trigger, i.e., chamfered specimens with inward-folding crush-caps, were also

studied.

(a) (b) (c)

Figure 5-1: Failure trigger mechanisms: (a) chamfered-end; (b) Inward-splaying crush-cap; and (c)

Outward-splaying crush-cap.

5.3.3. TEST SETUP AND TESTING PROCEDURE

All tests were conducted under quasi-static axial compression conditions. The

tests were carried out on an Instron Testing Machine, Model 5800R. Loading was applied

under stroke control mode at a displacement rate of 0.127 mm/s (0.3 in/min). All

specimens were subjected to a maximum of 50.8 mm (2.0 in) crosshead displacement.

Utilizing a 101.6 mm (4.0 in) long specimen, the 50.8 mm (2 in) crushing length

provided sufficient crush data from which the amount of energy absorbed, and the

corresponding SEA, could be calculated.

A digital image correlation (DIC) system (an ARAMIS 4M system from GOM)

was used to capture the full deformation and strain fields during loading. The system is

based on two charged coupled device (CCD) cameras, having 4 megapixels resolution,

and is capable of measuring strains ranging from 0.01% to over 100%. Between 150 -

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220 images were taken during each test, at one- second intervals. High definition videos

were taken during all tests.

Test specimens were divided into two groups. Group A consists of 37 specimens

made from Boeing-supplied tubes, which were tested in three Phases: In Phase I the

effect of chamfer trigger mechanism was investigated by comparing the load-crosshead

displacement curves of chamfered specimens with that of a flat-end specimen. In Phase II

the effect of the two crush-cap failure trigger mechanisms (inward-folding and outward-

splaying), each having three different corner radii, on the crushing process was studied

using flat-end specimens. In Phase III, the effect of combining the chamfer with crush-

cap trigger was examined. Detailed test matrix is given in Table 5-1.

Table 5-1: Group A specimens, supplied by The Boeing Co.

Phase End condition Crush-Cap Corner Radius # of specimens

I Flat None N/A 1

Chamfer None N/A 3

II Flat

Inward-

Folding

2.38 mm (3/32 in) 3

3.96 mm (5/32 in) 3

5.55 mm (7/32 in) 3

Outward-

Splaying

2.38 mm (3/32 in) 3

3.96 mm (5/32 in) 3

5.55 mm (7/32 in) 3

III Chamfer Inward-

Folding

0.01 mm (1/256 in)* 3

0.79 mm (1/32 in) 3

1.58 mm (1/16 in) 3

2.38 mm (3/32 in) 3

3.17 mm (1/8 in) 3

* Estimated, by machining the sharpest possible corner radius.

95

Group B consists of six Drexel-manufactured specimens, which were tested in

two phases. In Phase I, baseline data were established by testing chamfered specimens. In

Phase II, the optimal failure trigger mechanism, based on the results of the Group A tests,

focusing on the effect of combining a chamfered specimen with an inward-folding crush-

cap, was investigated. Three specimens were tested for each failure trigger scenario and a

single flat-ended specimen was tested in Phase I of Group A. Detailed test matrix is given

in Table 5-2.

Table 5-2: Group B specimens, manufactured at Drexel

Phase End Condition Crush-Cap Corner Radius # of specimens

I Chamfer None N/A 3

II Chamfer Inward

Folding 1.58 mm (1/16 in) 3

5.3.4. SPECIFIC ENERGY ABSORPTION

The energy absorption capability of each failure trigger mechanism is quantified

by specific energy absorption (SEA), which is defined by:

∫ ( )

(1)

where δCR is the crushing length, δ is the crosshead displacement, (0 ≤ δ ≤ δCR ),

P(δ) is the corresponding load, and ρ and A are the mass density and cross-sectional area,

respectively. Accordingly, the SEA was obtained for each test by dividing the area of the

load-displacement curve by the total mass of the crushed section of the specimen.

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5.4. EXPERIMENTAL RESULTS

5.4.1. LOAD-DISPLACEMENT BEHAVIOR OF GROUP A SPECIMENS

Group A specimens were used to investigate the effectiveness of chamfered-end

and crush-cap failure trigger mechanisms, and the combination of the two mechanisms.

All specimens were made from The Boeing Co. supplied tubes.

i) Phase I: Chamfer Trigger Mechanism

A comparison of the load-crosshead displacement curve recorded for a flat-ended

specimen and three chamfered specimens are shown in Figure 5-2. Results of the three

chamfered specimens are highly reproducible, indicating a reliable centric load

introduction. Clearly, in the absence of a failure trigger mechanism, the crushing of the

flat-ended specimen initiated with a very high initial peak load (75 kN), followed by an

instant drop, by nearly 15 folds, in the load, yielding a low sustained crush load, Figure

5-3 and Figure 5-4. This crushing behavior resulted in a low SEA value. The results of

the chamfered specimens, on the other hand, show a much lower average initial peak load

(27 kN) and a slower and smaller load drop, yielding a slightly higher average sustained

crush load and a 16% higher SEA, Figure 5-3 and Figure 5-4.

ii) Phase II: Crush-Cap Trigger Mechanism

The deformation characteristics and failure process of the flat-ended and chamfer-

ended tubes (discussed below) show that during the crushing process the outer two plies

splayed outward and the inner seven plies folded inward and compacted into the hollow

tube. Clearly, the peak load, the sustain crush load, the corresponding SEA, and the crush

behavior could be greatly affected if all plies are forced to either fold inward or splay

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outward. Therefore, in the Phase II of this study, crush-caps were used as failure triggers

to initiate failure in flat-ended specimens. Two types of crush-caps were used, causing

either inward-folding or outward-splaying of the crushed cylinder wall. Each type of

crush-cap was manufactured with three different corner radii, Table 5-1. Three tests were

performed per crush-cap. Results indicate that the load-crosshead displacements curves

were highly reproducible. Thus, the average values from the three specimens for each

case are presented here.

Effect of Inward-Folding Crush-caps: Results of specimens attached to inward-

splaying crush-caps with three different corner radii, in terms of load-displacement

curves are shown in Figure 5-5. It can be seen that the inward-splaying crush-caps

reduced the peak loads significantly, to 52%, 27%, and 23% of that of the flat-end

specimen for corner radii of 2.4 mm, 4.0 mm, and 5.6 mm, respectively, Figure 5-3. The

crush-cap with the smallest corner radius (2.38 mm) also yielded much higher sustained

crush load (1.4 times) and SEA (1.4 times) than the flat-end specimen, Figure 5-4. The

crush-caps with the two larger corner radii (4.0 mm and 5.6 mm), on the other hand, did

not yield favorable results in terms of lowering the peak load and increasing the SEA as

compared to the flat-end specimen.

Effect of Outward-Splaying Crush-caps: Results of specimens attached to

outward-splaying crush-caps with three different corner radii are shown in Figure 5-5.

The outward-splaying crush-caps reduced the initial peak loads to 80%, 12%, and 13% of

that of the flat-end specimen for corner radii of 2.4 mm, 4.0 mm, and 5.6 mm,

respectively. However, none of these crush-caps were effective in increasing the

sustained crush load or SEA, Figure 5-3 and Figure 5-4. The crush-cap with the smallest

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corner radius (2.4 mm) yielded the highest sustained crush load and SEA. This corner

radius, however, yielded a sustain crush load and SEA approximately 53% of the flat-

ended specimen, Figure 5-3 and Figure 5-4.

Figure 5-2: A comparison of load-crosshead displacement curves of a flat-end specimen and three

chamfered specimens from Group A.

Figure 5-3: A comparison of initial peak loads and sustained crush loads for Group A specimens tested in

Phase I and II.

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Figure 5-4: A comparison of SEA for Group A specimens tested in Phase I and II.

Figure 5-5: A comparison of averaged load-crosshead displacement curves for flat-ended specimens from

Group A attached to (a) three inward-folding crush-caps, and (b) three outward-splaying

crush-caps with different corner radii.

Summary of Crush-cap Trigger Mechanisms: The results shown in Figure 5-3 and

Figure 5-4 indicate that the smallest corner radius (2.4 mm) yielded the highest sustained

crush loads and SEA in both types of crush-caps. The inward- folding crush-cap yielded

the highest SEA (120 kJ/kg) and sustained crush load (27 kN). It also resulted in a

relatively higher initial peak load (39 kN) as compared to that of chamfered specimen (19

kN), but was still 48% lower than that of the flat-end specimen (75 kN).

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Comparing the results discussed above with those reported in [31], shows a

similar trend where smaller radii crush-caps yield higher SEA for both types of crush-

caps. Further, both studies show that the inward-folding crush-caps yield higher SEA the

outward-splaying crush-caps.

iii) Phase III: Combined Trigger Mechanisms

Based on the results of Phase II study, it was established that the chamfered end

was most effective at reducing the initial peak load while the inward splaying crush-cap

having the smallest corner radius resulted in a higher sustained crush load and SEA. In

Phase III, a combined failure trigger mechanism consists of a chamfered-end and an

inward-splaying crush-cap was used to accomplish the aforementioned goals of reducing

the initial peak load and increasing the sustained crush load and SEA. The effect of the

corner radius of the crush-cap was further characterized, particularly at the smaller radius

range, using four additional radii along with the original smallest radius (2.4 mm), Table

5-1.

Figure 5-6 shows the results of the combined failure trigger mechanism with five

different inward-splaying crush-cap corner radii, in terms of the load-displacement curve.

Results indicate that the crush-cap corner radius affected the initial peak load

significantly. The larger the corner radius the lower the initial peak load. The initial peak

load reduced from 45 kN for the sharp corner (0.05mm) to 13 kN for the largest radius

(3.2 mm), Figure 5-7(a). The SEA initially increases with the corner radius to a

maximum of 157 kJ/kg for 1.6 mm corner radius before dropping to as low as 37 kJ/kg

for the largest radius (3.2 mm), Figure 5-7(b). The sustained crush load shows a similar

trend since it is directly proportional to the SEA, Figure 5-7(a). It should be noted that the

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maximum SEA occurs when the corner radius is similar to tube’s wall thickness (1.47

mm). This suggests that the tube wall thickness-to-the corner radius ratio is directly

related to the SEA resulting from the crushing process.

Comparing the results of the 2.4 mm corner radius crush-cap with corresponding

Phase II results, it can be seen that the chamfer helped to reduce the initial peak load from

39 kN to 23 kN, but was not effective in increasing the sustained crush load (17 kN vs. 27

kN) or SEA (78 kJ/kg vs. 120 kJ/kg). The smaller corner radius (1.6 mm) crush-cap, on

the other hand, yielded an SEA (157 kJ/kg) twice as high as that of the 2.4 mm corner

radius crush-cap, but also resulted in an initial peak load (37 kN) that was approximately

61% higher. These results guided the test program of Group B specimens, as discussed

below.

Figure 5-6: A comparison of averaged load-displacement data of Group A specimens with a combined,

chamfered-end and inward-folding crush-cap, trigger mechanism.

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Figure 5-7: A comparison of (a) initial peak loads and sustained crush loads, and (b) SEA of Group A

specimens with a combined, chamfered-end and inward-folding crush-cap, trigger

mechanism.

5.4.2. LOAD-DISPLACEMENT BEHAVIOR OF GROUP B SPECIMENS

Results of Group A specimens showed that the chamfer failure trigger is very

effective at reducing the initial peak load while maintaining a high sustained crush load

and SEA. The inward-folding crush-cap, with a small corner radius, was not as effective

as the chamfer failure trigger at reducing the initial peak load, but was quite effective at

maintaining a higher sustained crush load and SEA. A combination of the two failure

trigger mechanisms, a chamfered cylinder attached to a crush-cap with a corner radius of

1.6 mm, yielded a low initial peak load while maintaining a high sustained crush load and

SEA, proved to be the optimal combination for this particular set up. This optimal failure

trigger configuration was used to study the crush behavior of Group B specimens,

manufactured in-house at Drexel, for which the lay-up and material properties were

known. Two phases of study were conducted with Phase I for establishing baseline data

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using chamfered specimens and Phase II using chamfered specimens combined with the

inward-folding crush-cap.

i) Phase I: Chamfer Failure Trigger

Tests were conducted with three chamfered specimens to establish the baseline

data. Results are shown in Figure 5-8 and Figure 5-9, along with data from the Group A

chamfered specimens for comparison. It can be seen that Group B specimens have a

slightly lower average initial peak load than that of Group A specimens (24 kN vs. 27

kN) and yielded higher sustained crush load (28 kN vs. 22 kN) and SEA (126 kJ/kg vs.

101 kJ/kg). While the two specimen groups were of the same material, the slight changes

in laminate stacking sequence and curing processes yielded the above differences.

ii) Phase II: Combined Failure Trigger

In this phase three specimens with chamfered-ends attached to inward-splaying

crush-caps with a corner radius of 1.6 mm were tested. Results are shown in Figure 5-8

and Figure 5-9, together with data from the corresponding Group A (Phase III) test

results for comparison. The results show similar trend as in Phase I: lower initial peak

load (by 19%) and slightly higher SEA (by 7%) than the corresponding results obtained

with Group A specimens, attributed to the small differences in laminate stacking

sequence and fabrication process. Compared with the baseline data, obtained in Phase I

of Group B specimens, the combined failure trigger yielded a 25% higher initial peak

load (30 kN vs. 24 kN) and a 33% higher SEA (168 kJ/kg vs. 126 kJ/kg).

In summary, the optimal failure triggers mechanism with a combined chamfered

end and crush-cap (with a 1.6 mm corner radius) failure trigger was more effective in

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increasing the sustained crush load and SEA, with a moderate level of initial peak load. It

should be noted that the added parasitic weight of the crush-caps could be mitigated by

integrating the caps into the supporting structures.

Figure 5-8: A comparison of averaged load-crosshead displacement curves of Group A and Group B

specimens with chamfered-ends and combined trigger mechanisms.

Figure 5-9: A comparison of (a) initial peak loads and sustained crush loads, and (b) SEA of Group A and

Group B specimens with chamfered-ends and combined trigger mechanisms.

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5.4.3. FAILURE PROCESS

The entire testing process, including loading up to initial crushing of the

specimen, post-crushing loading, and unloading, for each specimen was recorded using a

high definition digital video camera. Photographs of the specimen were also taken before,

during, and after each test. The discussion below is divided according to the type of test

configuration performed, namely: i) flat-ended specimen; ii) chamfer-ended specimens;

iii) effect of inward-folding crush-caps; iv) effect of outward-splaying crush-caps; and v)

specimens with combined failure trigger.

i) Flat-Ended Specimen

The crush process of Group A flat-ended specimen, shown in Figure 5-10, shows

the deformation and crushing at three crosshead displacements of 1.0 mm (immediately

upon first collapse), 10 mm (during the crush process) and 40 mm (near the end of the

50.8 mm crosshead displacement). The crushing process began by a catastrophic fracture

manifested by an abrupt local wall and plies buckling and crushing at the lower end of the

specimen that was in contact with the lower support platen of the testing machine, Figure

5-10(b), which corresponds to the abrupt load drop seen in Figure 2. This sudden fracture

was accompanied with significant audible level noise and a large amount of Gr/Ep dust.

Thereafter, the specimen continued to crush progressively, Figure 5-10(c). Matrix

splitting was observed along the outer 0° plies and propagated along the length of the

specimen with increasing crosshead displacement, Figure 5-10(d). These matrix splits

were nearly evenly spaced along the circumference of the specimen, forming

approximately 40 narrow, 1.0-4.0 mm wide, Gr/Ep strips. Two of the nine outer plies

splayed outward, sliding along the lower rigid support platen of the testing machine as

106

the crosshead displacement continued to increase, Figure 5-10(d). Post-test examination

of the specimen revealed that approximately seven inner plies folded inward and

compacted into the inner tube, Figure 5-10(e).

(a)

(b)

(c)

(d)

(e)

Figure 5-10: Progressive failure of a Group A flat-ended specimen at different stages of crosshead

displacements: a) Pre-test; b) 1 mm - Catastrophic failure due to local tube wall and plies

buckling and crushing; c) 10 mm - progressive crush failure; d) 40 mm - Outward-splaying

and inward-folding (not visible)of plies, laminar bending, excessive matrix splitting and fiber

fracture; and e) Post-test view of crushed end of the specimen, showing two outward-splaying

plies and seven inward-folding plies.

ii) Chamfer-Ended Specimens

The failure of a typical Group A and Group B chamfered specimens is depicted in

the photographs in Figure 5-11 and Figure 5-12, respectively, showing the deformation

and crushing at three crosshead displacements of 1.5 mm (end of chamfer crushing), 10

mm (intermediate level of the crush process) and 40 mm (near the end of the 50.8 mm

crosshead displacement). Unlike the flat-ended specimen, the chamfered specimens

crushed gradually, with no apparent local wall and/or plies buckling. The matrix splits

appear nearly evenly spaced along the circumference, Figure 5-11(b). These matrix splits

initiated at the chamfered region and progressed, with increasing crosshead displacement,

along its length, Figure 5-11(c), forming narrow (approximately 1.0-4.0 mm wide)

graphite/epoxy strips that extended with increasing crosshead displacement, Figure

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5-11(d). Post-test examination of Group A specimens indicated that matrix splitting

occurred primarily along the outer two-three plies with six-seven inner plies folded

inwards and compacted inside the hollow tube, Figure 5-11(e).

The failure process of the Group B chamfered specimens, Figure 5-12, is nearly

identical. Comparing Figure 5-11 and Figure 5-12 at the same crosshead displacement

shows little difference in the failure process of the two groups of specimens, with matrix

splitting occurring immediately at the completion of the chamfer crushing. The matrix

splitting, however, progressed more rapidly in Group A, Figure 5-11(c) compared with

Group B, Figure 5-12(c). Significant matrix splitting occurred also with the Group B

specimens, yielding similar narrow laminate strips, Figure 5-12(d). The apparent twisted

lamina segments in Figure 5-12(d) and Figure 5-12(e) are due to matrix splitting along

the outer 15° plies. The difference in the post-failure appearance after load removal of the

two Groups, Figure 5-11(e) and Figure 5-12(e), is attributed to the difference in laminate

stacking sequence. Detailed examination of the post-test Group B specimens indicates the

outermost -15°/+15°/-15° ply group in the Group B specimens delaminated along the

inner neighboring 0° ply group. As a consequence, the ply group of the outer three plies

splayed outward, while the inner six plies (two ply groups) folded and compacted inward

into the inner space of the hollow tube, in a manner similar to Group A specimens.

108

(a)

(b)

(c)

(d)

(e)

Figure 5-11: Progressive failure of a Group A chamfered specimen at different stages of crosshead

displacements: a) Pre-test; b) 1.5 mm - Completion of chamfer crushing; c) 10 mm -

progressive crush failure; d) 40 mm - Outward and inward-folding (not visible) of plies,

laminar bending, excessive matrix splitting and fiber fracture; and e) Post-test view of crushed

end of the specimen, showing two outward-splaying plies and seven inward-folding plies.

(a)

(b)

(c)

(d)

(e)

Figure 5-12: Progressive failure of a Group B chamfered specimen at different stages of crosshead

displacements: a) Pre-test; b) 1.5 mm - Completion of chamfer crushing; c) 10 mm -

progressive crush failure; d) 40 mm - Outward-splaying and inward-folding (not visible) of

plies, laminar bending, excessive matrix splitting and fiber fracture; and e) Post-test view of

crushed end of the specimen, showing two outward-splaying plies and seven inward-folding

plies.

iii) Effect of Inward-Folding Crush-Caps

The deformation and failure of a typical Group A flat-ended specimen supported

by an inward-folding crush-cap at three selected crosshead displacement stages is shown

in Figure 5-13. Significant matrix splitting and delamination of the outer two plies

occurred immediately, Figure 5-13(b). Since the crush-cap prevented outward-splaying,

significant buckling of the thin Gr/Ep strips along the outer 0° ply, having a high

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slenderness ratio, occurred, Figure 5-13(c) and Figure 5-13(d). The buckled region

progressed from the bottom, along the specimen length, corresponding to the extension of

the matrix splitting which formed long and narrow (1.0-4.0 mm-wide) Gr/Ep strips. Upon

load removal the buckled strips separated and scattered away from the core cylinder,

clearly exposing the inward-folding and the compacted nature of the crushed material,

Figure 5-13(e).

(a)

(b)

(c)

(d)

(e)

Figure 5-13: Progressive failure of a Group A flat-ended specimen attached to an inward- folding crush-

cap with a 3.96 mm corner radius at different stages of crosshead displacements : a) Pre-test;

b) 5 mm - Initiation of matrix splits and delamination along outer two plies; c) 15 mm -

Delamination and buckling of the two outer plies and inward-folding (not visible) of the

remaining seven plies; d) 40 mm – Further buckling and fracture of buckled strips; and e)

Post-test view of the crushed end of the specimen, showing the separation of the fiber strips

from the tightly packed core.

Post-test examination of the crushed end of the Group A specimens showed that

the inward-folding crush-caps forced the inner plies to fold toward the center of the tube.

This resulted in a large amount of material interactions and a tightly packed core. As

loading continued, the Gr/Ep material was forced into the packed core of the specimen,

thus increasing the amount of energy absorption during loading.

110

iv) Effect of Outward-Splaying Crush-Caps

The failure process observed with Group A specimens having outward-splaying

crush-caps, is shown in Figure 5-14 at the same three crosshead displacements.

Significant matrix splitting and delamination of the all plies occurred, forming the typical

narrow (1.0-4.0mm wide) strips, Figure 5-14(b). As the crosshead displacement

increases, the plies are forced to splay outward, Figure 5-14(c) and Figure 5-14(d), which

prevented fibers packing at the core, thus reducing fiber interactions, Figure 5-14(e). This

resulted in a much lower SEA when compared to the specimens having inward-folding

crush-caps.

(a)

(b)

(c)

(d)

(e)

Figure 5-14: Progressive failure of a Group A flat-ended specimen attached to an outward-splaying crush-

cap with a 3.96 mm corner radius at different stages of crosshead displacements: a) Pre-test;

b) 5 mm – Initiation of matrix splitting; c) 15 mm – Forced outward-splaying, laminar

bending, excessive matrix splitting and fibers fracture; d) 40mm – Progressive crushing

showing all plies splaying outwards; and e) Post-test view of the crushed cap end of the

specimen, showing the outward-splaying of all plies induced by the crush-cap.

v) Specimens with Combined Failure Trigger

It was shown that the optimal energy absorption could be accomplished with a

combination of chamfered specimens having inward-folding crush-caps of a specified

corner radius, Figure 5-4. The typical failure process of the combined failure trigger

specimen is shown in Figure 5-15. The deformation and crushing observed are similar to

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that of the flat-end specimens with inward-folding crush-caps, Figure 5-13, where all

plies fold into and compact inside the hollow tube. However, the chamfered-end

specimen crushed gradually without buckling of the outer plies, as is the case with the

flat-ended specimens, Figure 5-13. Since the entire folding and crushing process occurs

in the interior, no visible damage on the outside could be seen.

.

(a) (b) (c) (d) (e) (f)

Figure 5-15: Progressive failure of a Group A chamfered specimen attached to a inward- folding crush-cap

with a 1.58mm corner radius at different stages of crosshead displacements: a) Pre-test; b) 5

mm; c) 15 mm; d) 40 mm – All plies folded inward with no matrix splitting or delamination;

e) Post-test view of top of the specimen, showing the center “core” formed by the inward-

folding of the plies from the bottom progressing toward the top end of the specimen; and e)

Post-test view of the crushed end of the specimen, showing the inward-folding of all plies

caused by the inward-folding crush-cap.

5.4.4. STRAIN FIELDS

The strain fields of six chamfered tubes were monitored via a Digital Image

Correlation (DIC) system. Three of the specimens were recorded using a low-speed DIC

system and three were recorded using a high-speed DIC system. In this section,

representative results from the lows speed and high speed DIC images are presented.

The global fringe patterns, showing the axial and hoop strain fields, respectively,

of a representative chamfered specimen at six representative load levels are shown in

Figure 5-16. The axial strain field indicates that failure occurs near or at the maximum

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load level of 23.8 kN, upon chamfer crushing, resulted in an abrupt load drop from 23.8

kN to 17.0 kN. At this stage, the entire crush region at the bottom of the specimen was

experiencing an axial strain of approximately 1%. Several ‘hot spots’ can be seen in the

crush region at 17.0 kN in both figures. These hot spots corresponded to initiation sites of

matrix splitting along the fibers, which was confirmed, at later stages of crosshead

displacements, via the recorded videos. These local failures occurred nearly

simultaneously with the load drop. Similar results were observed in all other chamfered

specimens.

Figure 5-18 shows the local strain fields, taken with a high-speed DIC system, at

eight different load stages (from 14.9 kN to 25.8 kN) in a 10 mm x 10 mm region in the

crush zone just above the chamfer region. The chamfered zone is the dark region beneath

the photogrammetry images in the figure. The first hot spots, representing matrix splits,

initiated just above the chamfer between 14.9 kN and 15.9 kN, well before they were

captured with the low speed DIC system, Figure 5-16. This indicates that these matrix

splits initiated before the chamfer was completely crushed, i.e., before the load drop

(Figure 5-2). With increasing crosshead displacement the extent and number of these

splits increases with spacing nearly identical to those observed in the post-test

examinations of the specimens, e.g. Figure 5-12, which ultimately generated the 1.0-4.0

mm wide Gr/Ep strips.

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Load [kN]: 2.1 8.9 16.6 22.9 23.8 17.0 Displacement [mm]: 0.1 0.5 0.9 1.1 1.3 2.1

Figure 5-16: Global axial strain field of a chamfered specimen. The load increased gradually, reaching the

peak level (23.8 kN) when the entire chamfer crushed completely, followed by an abrupt load

drop, from the peak level to 17.0 kN, Hot spots representing matrix splitting can be seen

clearly to initiate from the crushed region and propagate upwards at 17.0 kN load level.

Load [kN]: 2.1 8.9 16.6 22.9 23.8 17.0

Displacement [mm]: 0.1 0.5 0.9 1.1 1.3 2.1

Figure 5-17: Global hoop strain field of a chamfered specimen. The load increased gradually, reaching the

peak level (23.8 kN) when the entire chamfer crushed completely, followed by an abrupt load

drop, from the peak level to 17.0 kN, Hot spots representing matrix splitting can be seen

clearly to initiate from the crushed region and propagate upwards at 17.0 kN load level.

114

Load [kN]: 14.9 15.9 17.6 18.5

Displacement [mm]: 0.86 0.92 0.96 1.04

Load [kN]: 19.3 21.1 23.7 25.8 Displacement [mm]:1.07 1.15 1.32 1.45

Figure 5-18: Local hoop strain field of a chamfered specimen recorded using a high-speed DIC system.

Hot spots, representing matrix splitting, initiated at 15.9 kN and continued to grow as the load

increased.

5.5. CONCLUSIONS

Composite tubes, made of graphite/epoxy laminates, were crushed under axial

quasi-static compression. Tests were conducted with flat-ended, chamfer-ended, and with

inward-folding and outward-splaying crush-caps failure trigger mechanisms. The goal

was to determine the most effective approach to decrease the initial peak crush load while

increasing the sustained crush load and SEA. Two groups of specimens were tested, both

having similar lay-ups and manufacturing procedures: Group A specimens were provided

by The Boeing Co. and Group B specimens were fabricated in-house at Drexel.

It was determined that the chamfer failure trigger was most effective at reducing

the initial peak load while maintaining a high-sustained crush load and high specific

energy absorption (SEA). The inward-folding failure trigger approach was not as

effective at reducing the initial peak load, but was more effective than using a chamfer

for maintaining a high-sustained crush load and SEA. On the other hand, the outward-

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splaying crush-cap was ineffective at reducing the initial peak load or in maintaining a

high-sustained crush load and SEA. These key results highlight the importance of forcing

inward-folding deformation and the consequent material crushing. Further, the results

obtained with different corner crush-cap radii showed that the smaller radii provide better

results in terms of sustained crush loads and SEA.

Based on these results, a combined chamfered-end and inward-folding crush-cap

trigger mechanism was use to further study the effect of corner radius of the crush-caps.

Results showed that the crush-cap with a 1.6 mm (1/16 in) corner radius yielded a

moderate level of initial peak load and the highest sustained crush load and SEA (60%

lower and 82% higher, respectively, than that of a flat-end specimen without crush-caps).

These quantitative results depend on laminate configuration and tube geometry (length,

diameter, and wall thickness). Results obtained from this study have been used to

validate a finite element model for simulating the quasi-static crushing process of

composite tubes. Results of the simulation study are reported in [79, Chapter 8].

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CHAPTER 6: EXPERIMENTAL INVESTIGATION ON THE ENERGY

ABSORPTION CAPACITY DURING CRUSHING OF AXIALLY LOADED

THIN-WALLED GR/EP MEMBERS

5

6.1. ABSTRACT

An experimental study was performed to investigate the energy absorption

capacity and failure characteristics of open thin-walled graphite/epoxy members (C-

channels, right angle-stiffeners, and hat-stiffeners) under quasi-static axial compression.

The effect of two failure trigger mechanisms (chamfers and steeples) on initial peak

loads, crush loads, and failure progression and crushing was studied. Strain fields

(measured via digital image correlation system) captured the damage initiation and

progression throughout the crushing process. Results showed that the steeple trigger is

more effective at reducing the initial peak loads of the C-channel and hat-stiffeners, while

the chamfer trigger yields a lower initial peak load for the angle-stiffener. The angle- and

hat-stiffeners absorb similarly high specific energy absorption (SEA) while the C-

channels absorb the lowest.

6.2. INTRODUCTION

Rotorcraft crashworthiness has been identified as a key area of focus to improve

survivability in the event of a crash [1]. Several studies, investigating the dynamic

response of aircraft structures and the survivability of occupants, have shown that the

5Siromani, D., Cheng, B., DeLuca, M., Donegan, D., Giberson, P., Mucerino, C., Awerbuch, J. and Tan, T.,

“Experimental Investigation on the Energy Absorption Capacity During Crushing of Axially Loaded

Thin-Walled Gr/Ep Members,” Submitted to: Journal of Composite Materials.

117

subfloor structure is a critical component in absorbing impact energy [20,71,72, Chapters

2-4]. Hence, integrating energy absorbing structural members into the existing subfloor

structures could mitigate the impact energy.

Composite materials are considered as possible candidates for energy absorbing

structural components due to their high strength-to-weight ratio and their high specific

energy absorption (SEA) characteristics, particularly during crushing. Several research

groups have investigated the energy absorbing characteristics of composite materials for

crashworthy applications in the aircraft and automotive industries. For simplicity, cost

effectiveness, and for the purpose of understanding the fundamental crushing process of

composite stanchions, most studies were conducted under quasi-static axial compression

loading conditions. The most common composite materials investigated have been

graphite/epoxy (Gr/Ep) e.g., [23-29,33-42], glass/epoxy (Gl/Ep) e.g., [24,25,30-34,43-

52], and Kevlar/epoxy (K/Ep) e.g., [24,25,33-38], studying different thin-walled cross

sections such as circular tubes [23,25-27,33-35,45,48,52-54], square tubes [42,47,52],

hexagonal and hourglass tubes [52], cones [43,43,52,55], open cross sections [28, 39,42],

flat plates [28,37,38], and sandwiched panels [49-51]. Results showed that in similar

laminate configurations Gr/Ep absorbed the highest energy while K/Ep absorbed the

least. However, all three material systems exhibited higher energy absorption capabilities

than conventional metallic structures, such as aluminum and steel [33,53]. Simply, the

extensive damage that occurs during the crushing process of brittle composites, due to the

combination of multiple failure mechanisms, absorbs a much higher energy than during

the elastic/plastic deformation of metals. In most cases (depending upon laminate

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configuration and fabrication processes) the more brittle the material system the higher

the energy absorbed under compression [35].

The effect of fiber orientation for all three material systems have been

investigated using [0/±θ]n laminates [25], showing that the highest energy absorption was

achieved using a [0/±15]n laminate. Similarly, it was shown that increasing the number of

0° plies in [452/0n/452]s laminates increased the energy absorption of the members [28].

A prior study was conducted to investigate the energy absorption characteristics

of thin-walled graphite/epoxy circular tubes (IM7/8552) subjected to quasi-static axial

compression [81, Chapter 5]. Emphasis was placed on determining the optimal failure

trigger mechanisms, including chamfers, crush-caps (forcing inward folding and outward

splaying of the entire tube wall), and their combinations, to reduce the initial peak load

and increase SEA. It was determined that the chamfer trigger was most effective at

reducing the initial peak load. The inward-folding failure trigger approach was not as

effective at reducing the initial peak load, but was more effective than the chamfer failure

trigger at maintaining a high sustained crush load and high SEA. On the other hand, the

outward-splaying failure trigger was ineffective at reducing the peak crush load and in

maintaining a high sustained crush load and SEA. These key results highlighted the

importance of forcing inward-folding of the crushed material to provide added energy

absorption mechanism. Further, the results obtained with different crush cap radii showed

that the smaller radii provide higher sustained crush loads and SEA. Based on these

results, a series of tests was performed combining both failure trigger mechanisms; i.e.,

chamfered-end specimens integrated with an inward-folding crush-cap. In this series of

tests, five crush-caps with different corner radii were tested to determine the optimal

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configuration. Results showed that the combined failure trigger mechanism yielded a

relatively low initial peak load and the highest sustained crush load and SEA.

However, circular tubes are not typically used in the aerospace industry and

cannot easily be integrated into a rotorcraft subfloor structure [23]. A limited number of

studies have been performed on thin-walled members of other cross-sections, often used

in the aerospace industry, such as angle-stiffeners and C-channels e.g., [28,42], and hat-

stiffeners e.g., [39]. The effect of the radius of curvature of angle-stiffeners and C-

channels was studied in [42] for plain-weaved Gr/Ep, showing that the larger the ratio of

the corner radius to the perimeter of the specimen the higher the SEA. Results have

shown that these thin-walled cross-sections yielded SEA values between 30 and 85 kJ/kg

[28,39,42]. The available data, however, are not sufficient to rank the different cross-

sections in terms of initial peak loads, sustained crush load, and SEA.

Effective triggering of failure has been well established as a crucial design

component to reduce the initial peak load and maximize energy absorption. Failure

triggering could be classified as internal triggers (e.g., chamfer, steeple, and ply drop-off)

or external triggers (e.g., crush caps and plugs). Numerous studies have shown that

chamfer triggers are very effective at reducing the initial peak crush load while

maintaining sustained crush loads, e.g., [23-28]. The crushing behaviors of hollow square

[42,52] and circular tubes [52] with chamfer triggers have been compared against those

with steeple triggers. Results showed that the steeple trigger was significantly more

effective than the chamfer trigger at maintaining a higher sustained crush load for square

tubes but the opposite was recorded for circular tubes.

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The objective of this study is to experimentally investigate the failure process and

the energy absorbing characteristics of graphite/epoxy members of three thin-walled open

cross-sections having two failure triggering mechanisms. These results were used to

validate the simulations developed in [80, Chapter 9] on the load-displacement behavior

and failure process of such cross sections.

6.3. EXPERIMENTAL PROCEDURE

6.3.1. SPECIMEN FABRICATION

Three thin-walled open cross-sectional geometries were selected: C-channel,

angle-stiffener, and hat-shaped stiffener. The specimens were made of Hexcel IM7/8552

Graphite/Epoxy unidirectional tape pre-preg with a 12 K tow and a 180° C curing resin

(350° F),, provided by the Structures Technology group of The Boeing Company at

Ridley Park, Pennsylvania. Lay-up and dimensions are listed in Table 6-1. To ensure

stability during compressive loading, the specimens were supported by a 25.4 mm (1.0

in.) thick potted base, Figure 6-1. The cross-sectional areas were the same for all cross-

sections. As a result, the wall thickness of the angle-stiffener was twice the thickness (and

number of plies) of the other two cross-sections, Table 6-2.

6.3.2. FAILURE TRIGGERING MECHANISMS

Two failure trigger mechanisms were studied: a chamfer trigger and a steeple

trigger. Figure 6-1 shows the three cross-sections with a 45° chamfer and a 15° steeple

ends on the top of each specimen

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Table 6-1: Specimen Configuration

Cross

Section Geometry Lay-up

Cross-sectional

area

mm2 (in

2)

Length

mm (in)

Wall

thickness mm

(in)

1 Angle-Stiffener [02/+45/-45/02/-

45/+45/02]s 180 (0.28)

101.6

(4) 3.04 (0.12)

2 C-channel [02/+45/-45/02/-

45/+45/02] 180 (0.28)

101.6

(4) 1.52 (0.06)

3 Hat-Stiffener [02/+45/-45/02/-

45/+45/02] 180 (0.28)

101.6

(4) 1.52 (0.06)

Figure 6-1: Open-cross-sections with the two failure trigger mechanisms, all having the same cross-

sectional area and attached to a potted base to ensure stability.

6.3.3. TEST SETUP AND TESTING PROCEDURE

All tests were conducted under quasi-static axial compression conditions. The

tests were carried out on an Instron Testing Machine, Model 5800R. Loading was applied

under stroke control mode at a displacement rate of 3.81 mm/min (0.15 in/min). All

specimens were subjected to a maximum of 50.8 mm (2.0 in) displacement. Utilizing a

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101.6 mm (4.0 in) long specimen, the 50.8 mm (2.0 in) stroke provided sufficient crush

data from which the amount of energy absorbed could be calculated and compare with

the simulation results [80, Chapter 9]. Three specimens were tested for each cross

section and each failure trigger, for a total of 18 specimens Table 6-1.

A digital image correlation (DIC) system (an ARAMIS 4M system from GOM)

was used to capture the full deformation and strain fields during loading. The system is

based on two charged coupled device (CCD) cameras, having 5 megapixels resolution,

and is capable of measuring strains ranging from 0.01% to over 100%. Between 150 -

220 images were taken during each test, at one- second intervals.

6.3.4. SPECIFIC ENERGY ABSORPTION

The energy absorption of capability of each triggering mechanism is quantified by

specific energy absorption (SEA), which is defined by:

∫ ( )

(1)

where δCR is the crushing length, 0 ≤ δ ≤ δCR is the crosshead displacement, P(δ)

is the corresponding load, and ρ and A are the mass density and cross-sectional area,

respectively. Accordingly, the SEA was obtained for each test by simply calculating the

area of the load-displacement curve.

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6.4. EXPERIMENTAL RESULTS

6.4.1. LOAD-CROSSHEAD DISPLACEMENT

The average load-crosshead displacement curves of three chamfered specimens

for each cross-section are shown in Figure 6-2(a). All three cross-sections reach similar

initial peak loads, of approximately 32 kN, at which point the chamfer has fully crushed,

followed by a sudden load drop, reaching the lower sustained crush load for the

remainder of the crush displacement. The C-channel experienced the largest load drop

caused by the partial flange buckling and crack formation along the two corners.

The angle- and hat-stiffeners experienced load drops less severe than exhibited by

the C-channel. Also in these two cases the load drop is attributed to partial wall buckling

and crack formation along the cross-sections’ corners.

The average load-displacement curves of the three steeple specimens for each

cross-section are shown in Figure 6-2(b). Unlike the sudden load drop exhibited by the

chamfered specimens, here the load gradually increases to its highest value. This load

increase corresponds to the gradual crushing of the steeple and the simultaneous increase

in the contact area with the compression platen of the testing machine. In all three cases,

the highest load occurs when the compression platen comes in full contact with the entire

cross-sectional area. The crosshead displacement at the highest load, Figure 6-2(b), is a

direct result of the height of the steeple: 10 mm for the C- channels, 6 mm for the angle-

stiffeners, and 12 mm for the hat-stiffeners. The subsequent load drop is relatively small

with the sustained load staying relatively constant for the C-channels and angle-stiffeners,

but gradually decreasing (marginally) in the hat-stiffener case for the remainder of the

50.8 mm crush displacement. The peak load for C-channel is the lowest among the three

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cross-sections, and it occurs later into the crushing process (at approximately 10 mm of

the crosshead displacement) when the crosshead comes into contact with the two flanges

of the C-channel. The angle-stiffener exhibited the highest peak load of the three cross-

sections, which also occurred earlier into the crushing process. The lower subsequent

sustained crush load is due to significant crack propagation at the specimens’ corners.

The hat-stiffener exhibited an initial peak load which is 20% lower than the angle-

stiffeners’, exhibiting a marginal load drop and very similar sustained load.

Figure 6-2: A comparison of load-crosshead displacement curves for each cross-section having a: (a)

chamfer trigger, and (b) steeple trigger. Each curve represents the average of three tests

(except for the angle-stiffener with a chamfer trigger which represents the average of two

tests).

Figure 6-3(a) shows the comparison between the initial peak load and sustained

crush load for all three cross-sections with both trigger mechanisms. For the C-channels

and the hat-stiffeners, the steeple trigger is more effective at reducing the initial peak load

by 36% and 12%, respectively. However, for the angle-stiffener, the steeple trigger

resulted in an initial peak load that is 19% higher than the chamfer failure trigger. For all

three cross-sections, the steeple failure trigger resulted in sustained crush loads that were

between 10% and 20% higher than the chamfer failure trigger. This, in turn, yielded SEA

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values for the steeple specimens that were 5%, 21%, and 4% higher than the C-channel,

angle-stiffener, and hat-stiffener with chamfer failure triggers, respectively, Figure

6-3(b). For both trigger mechanisms, the angle- and hat-stiffeners yielded similarly high

SEAs, which were higher than the C-channels’ SEA.

Figure 6-3: A comparison of the (a) peak load and crush load, and (b) SEA for each cross-section having

a chamfer trigger and steeple failure triggers (numbers indicate average of three specimens

except for the angle stiffener with a chamfer trigger which represents the average of two

tests).

6.4.2. THE FAILURE PROCESS

The failure process (recorded via the video cameras) and the axial and lateral

strain fields (recorded via the DIC) are discussed below for the three cross-sections and

the two failure triggers.

i) C-Channel

Chamfer End: The failure process at four selected crosshead displacements of a

typical chamfered C-channel is shown in Figure 6-4. The chamfered specimen began to

crush gradually with partial inward buckling of the flanges and outward buckling of the

web towards the mid-length of the specimen, Figure 6-4(b). After the chamfer was

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completely crushed, several matrix splits appeared at the corners of the specimen that

relieved the outward buckling of the web and caused it to bend and splay outwards,

Figure 6-4(c). The matrix splits, which initiated at the corners, progressed along the

length of the specimen with many more matrix splits occurring along the flanges with

increasing displacement, Figure 6-4(d). The extension of the matrix splits reduced the

buckling, increasing the bending and the outward and inward ply splaying. As expected,

initial failure at some random site (post-chamfer crushing) causes an asymmetric crush

process. The web tends to bend and splay outwards further on the left side than on the

right side of the specimen, Figure 6-4(b) to Figure 6-4(d). The outer plies of the web

stayed relatively intact throughout the crushing process but experienced excessive

bending. Detailed examination of the post-test specimens indicated that approximately

half of the plies in the web and flanges splayed inwards while the remaining plies splayed

outwards, Figure 6-4(e).

(a) (b) (c) (d) (e)

Figure 6-4: Progressive failure of a C-channel specimen with a chamfer trigger at different stages of

crosshead displacements: a) Pre-test; b) 1.5 mm - Completion of chamfer crushing; c) 10 mm

- progressive crush failure; d) 40 mm - Outward and inward (not visible) splaying of plies,

laminar bending, excessive matrix splitting and fiber fracture; and e) Post-test (after load

removal) view of crushed end of the specimen, showing five outward splaying plies and five

inward splaying plies.

The axial and lateral strain fields for the chamfered C-channel are shown in

Figure 6-5 and Figure 6-6, respectively, at four representative load levels. Note that the

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DIC images shown in the figure are shortly after the completion of chamfer crushing,

thus the crosshead displacement at this stage is less than 2.5 mm, Figure 6-2(a). The

compressive axial strain concentration occurs first at the web/flange corners, as is evident

by the hot-spots located at the top left and top right hand sides of the C-channel, Figure

6-5. Beyond the peak load, the compressive axial strain increases throughout the web as a

result of the chamfer crushing, followed by extensive crushing, bending, and partial

buckling at the top of the flange. The non-uniform strain field in the specimen is a result

of the asymmetric deformation of the specimen.

The DIC images indicate high tensile lateral strains throughout the web, increasing up to

the peak load (35 kN), Figure 6-6. This is due to the outward buckling that occurs at the

center of the web. Initially, small lateral tensile strains are observed in the flange/web

corners. After the chamfer is completely crushed, and the load drops (e.g., to 25.8 kN),

high lateral tensile strains occurred along the web/flange corners, causing the matrix

splits. At the same time, the high lateral strains in the web are completely reduced due to

the matrix splits at the corners, relieving the outward buckling in the web. The initiation

of these matrix splits is clearly manifested by the hot-spots seen along these corners,

extending throughout the length of the specimen with further crosshead displacement.

These matrix splits extend along the entire specimen, enabling further bending and

buckling of the web and flanges, yielding significant reduction of the lateral strain at the

center of the web. Thereafter, the lateral strain field is affected by the bending and

outward splaying of the web, as evident in the photographs of Figure 6-4. The non-

uniform lateral strain field is a result of the asymmetric deformation of the specimen and

the effect of the formation of matrix splits, which relieved some of lateral strain. Viewing

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the sequence of the many strain contour recorded (not shown here) provides a vivid

picture of the strain distribution during the initial crush process.

Load [kN]: 33.3 34.0 31.8 25.8 % Peak Load: 95.1 97.1 90.9 73.7 Displacement [mm]: 2.0 2.2 2.4 2.5

Figure 6-5: Axial strain field throughout the web of a chamfered C-channel specimen.

Load [kN]: 22.1 29.9 35.0 25.8 % Peak Load: 63.1 85.4 100 73.7 Displacement [mm]: 1.4 1.7 2.3 2.5

Figure 6-6: Lateral strain field of a chamfered C-channel specimen showing sites of matrix split initiation.

Steeple End: The steeple specimen began to crush gradually with matrix splits

appearing along the top surface of the flanges and the web with increasing crosshead

displacement, Figure 6-7(b). Unlike the chamfered specimen, however, no buckling of

the flanges was observed and only minor outward buckling of the web occurred, which

was relieved almost immediately upon the steeple crushing. After the steeple was fully

crushed, the specimen continues to crush progressively (Figure 6-7(c)) with the

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remainder of the crushing process being very similar to the chamfered specimen. The

only noticeable difference was the larger number of matrix splits that were observed in

the web of the steeple specimen, Figure 6-7(b), Figure 6-7(c) and Figure 6-7(d).

(a) (b) (c) (d) (e)

Figure 6-7: Progressive failure of a C-channel specimen with a steeple trigger at different stages of

crosshead displacements: a) Pre-test; b) 10 mm - Completion of chamfer crushing; c) 15 mm





Figure 6-8 and Figure 6-9 show the axial and lateral strain fields for the steeple C-

channel, respectively; up to shortly before the completion of the steeple crushing, thus the

crosshead displacement at this stage is less than 7.5 mm, Figure 6-2(b). As discussed

earlier, Figure 6-7, steeple crushing begins immediately upon load application, e.g., at 2.4

kN, resulting in the high compressive axial strain at the tip of the steeple, Figure 6-8.

With further steeple crushing, the high axial compressive strain propagates towards the

remainder of the steeple. The lateral tensile strain begins to form at both the tip of the

steeple and in the web of the specimen. Some outward buckling was observed in the web,

which resulted in the formation of moderate lateral strains in this region. As the steeple

continues to crush, high lateral strains occurred at the top of the specimen, while the

lateral tensile strain in the web reduces due the decrease in buckling of the web.

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Load (kN): 2.4 4.9 6.0 6.6 % Peak Load: 9.0 18.4 22.6 24.8 Displacement [mm]: 0.5 1.2 2.0 3.3

Figure 6-8: Axial strain field of a steeple C-channel specimen showing steeple crushing.


Figure 6-9: Lateral strain field of a steeple C-channel specimen showing sites of initiation of matrix

splitting.

ii) Angle-Stiffener

Chamfer End: The failure process of a typical chamfered angle-stiffener specimen

is shown in Figure 6-10 at four selected stages of crosshead displacement. Similar to the

C-channel, the chamfered angle-stiffener specimen crushed gradually accompanied with

matrix splits, appearing along the corner along with partial inward buckling of the legs,

Figure 6-10(b). After the chamfer was completely crushed, large cracks appeared along

the corner of the specimen that progressed with increasing load, Figure 6-10(c) and

Figure 6-10(d). As with the C-channel, the legs initially buckled, however, with the

occurrence of matrix splitting (first in the corner and later across the legs) the

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deformation of the legs was predominantly in bending, as expected. Again, the

asymmetric failure process is manifested by the left leg buckling significantly more than

the right leg, Figure 6-10(b) and Figure 6-10(c). Examination of the post-test specimens

revealed that approximately half the plies splayed inwards while the remainder splayed

outwards, Figure 6-10(e).

(a) (b) (c) (d) (e)

Figure 6-10: Progressive failure of an angle-stiffener specimen with a chamfer trigger at different stages of




removal) view of crushed end of the specimen, showing ten outward splaying plies and ten


The axial and lateral strain fields for the chamfered angle-stiffener are shown in

Figure 6-11 and Figure 6-12 respectively, at five selected load levels, up to

approximately 3.0 mm crosshead displacement, Figure 6-2(a). As the specimen is being

crushed, compressive axial strain develops throughout both legs caused by inward

buckling. As the load is increased to 32.3 kN, the left leg developed higher compressive

axial strain due to excessive buckling, Figure 6-11, as discussed earlier. Once the chamfer

is fully crushed and the peak load is reached, the high strain transferred to the top of the

specimen and initiated the progressive crushing of the two legs, as manifested by the

photographs in Figure 6-10.

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Load (kN): 26.9 31.5 32.3 33.7 21.4 % Peak Load: 79.8 93.5 95.8 100 63.5 Displacement [mm]: 1.3 2.2 2.3 2.4 3.0

Figure 6-11: Axial strain field of a chamfered angle-stiffener specimen.

The lateral strain fields in Figure 6-12 shows high tensile strains at the top corner,

initiating matrix splits at that location. Higher strains are observed on the left leg due to

the excessive buckling on that side, as discussed earlier. As the crushing progresses, these

cracks extend along the corner, reducing the tensile strain in the legs as the load reached

the peak load value of 33.7 kN. The somewhat non-uniform lateral strain field seen at the

top of the specimen is due to the asymmetric deformation of the specimen and the effect

of the formation of matrix splits which relieved some of the lateral strain.

Load (kN): 27.1 28.5 30.5 33.1 33.7 % Peak Load: 80.4 84.6 90.5 98.2 100 Displacement [mm]: 1.4 2.0 2.1 2.3 2.4

Figure 6-12: Lateral strain field of a chamfered angle-stiffener specimen showing site of initiation of

matrix splitting.

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Steeple End: In the case of the steeple angle-stiffener, since the steeple is located

at the corner of the specimen, the matrix splits appear at the corner immediately upon

loading, Figure 6-13(a) and Figure 6-13(b). With the completion of steeple crushing, the

remaining crushing process becomes very similar to that of the chamfered angle-stiffener

specimen, Figure 6-13(c) to Figure 6-13(e). The only noticeable difference is the greater

extent of damage that occurred at the corner of the steeple specimen, Figure 6-13(e),

which is caused by the early damage initiation that occurs immediately upon loading.

Consequently, little if any buckling of the leg occurs: the primary deformation is leg

bending, i.e., outward splaying of the plies.

(a) (b) (c) (d) (e)

Figure 6-13: Progressive failure of an angle-stiffener specimen with a steeple trigger at different stages of

crosshead displacements: a) Pre-test; b) 6 mm - Completion of steeple crushing; c) 15 mm -

progressive crush failure; d) 40 mm - Outward and inward (not visible) splaying of plies,

laminar bending, excessive matrix splitting and fiber fracture; and e) Post-test view (after

load removal) of crushed end of the specimen, showing ten outward splaying plies and ten


Figure 6-14 and Figure 6-15 show the axial and lateral strain fields, respectively,

for steeple angle-stiffeners at very low crosshead displacements of less than 2.5 mm.

Similar to the C-channel specimen, it can be seen that at a very low load of 0.37 kN, high

compressive strain developed at the tip of the steeple, Figure 6-14. As the displacement

increases, the high strain propagates towards the intact regions of the steeple. Similar

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behavior was observed for the lateral tensile strains at the top of the steeple in Figure

6-15. As the steeple crushed further, lateral strains increased moderately along the entire

length of the corner, spreading out into the legs. This indicated the start of the legs

bending and splaying outwards. Both figures show relatively uniform strain fields.

Load (kN): 0.37 4.1 6.7 8.8 12.8 % Peak Load: 0.96 9.1 17.4 22.9 33.3 Displacement [mm]: 0.04 0.4 0.6 0.7 1.1

Figure 6-14: Axial strain field of a steeple angle-stiffener specimen.

Load (kN): 5.7 8.4 10.7 14.5 19.5 % Peak Load: 14.8 21.9 27.9 37.8 50.8 Displacement [mm]: 0.5 0.6 0.8 1.5 2.5

Figure 6-15: Lateral strain field of a steeple angle--stiffener showing site of initiation of matrix splitting.

iii) Hat-Stiffener

Chamfer End: The failure process of a typical chamfered hat-stiffener, at four

selected stages of crosshead displacements, is shown in Figure 6-16. Matrix splits

appeared along the corners of the chamfer with partial buckling of the flanges as it started

135

to crush gradually, Figure 6-16(a). After the chamfer was completely crushed, large

cracks developed along the outer plies of the entire specimen, which progressed along

their length with increasing crosshead displacement, Figure 6-16(c) and Figure 6-16(d).

The massive accumulation of matrix splits limited the degree of buckling, causing

primarily bending and outward and inward splaying of the plies. Post-test examination of

the specimens (after load removal) revealed that approximately half the plies splayed

inwards while the remaining plies splayed outwards, Figure 6-16(e).

(a) (b) (c) (d) (e)

Figure 6-16: Progressive failure of a hat-stiffener specimen with a chamfer trigger at different stages of






The axial and lateral strain fields for the chamfered hat-stiffener are shown in

Figure 6-17 and Figure 6-18 respectively, at four selected load levels, up to

approximately 3.0 mm crosshead displacement, well beyond the peak load, Figure 6-2(a).

As the specimen is crushed, axial strain developed along the right side of the web, and

built up along the right side of the specimen after the peak load of 32.5 kN was reached,

Figure 6-17. This was followed by extensive crushing and bending at the top of the

specimen.

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Load (kN): 28.9 32.5 26.5 22.1 % Peak Load: 88.9 100 81.5 68 Displacement [mm]: 1.5 2.1 2.5 3.0

Figure 6-17: Axial strain field of a chamfered hat-stiffener specimen.

The lateral strain developed on the left and middle faces and spread to the right

face when the peak load was reached, Figure 6-18. After the chamfer is completely

crushed and the peak load was reached, high tensile strains developed along the corners

causing the formation and progression of axial cracks. These matrix splits extend along

the entire specimen, enabling further bending and splaying of the web and flanges.

Load (kN): 20.4 27.2 32.5 24.0 % Peak Load: 62.8 83.7 100 73.8 Displacement [mm]: 1.2 1.4 2.1 2.7

Figure 6-18: Lateral strain field of a chamfered hat-stiffener specimen, showing sites of initiation of matrix

splitting.

Steeple End: Similar to the previous two cases, the steeple specimen began to

crush gradually with matrix splits occurring throughout the entire top surface in contact

with the compression platen, Figure 6-19(a) and Figure 6-19(b). Unlike the chamfered

137

specimen, no buckling of the flanges was observed. After the steeple was fully crushed,

the specimen continued to crush progressively with the remainder of the crushing process

being very similar to the chamfered specimen, Figure 6-19(c) to Figure 6-19(e).

(a) (b) (c) (d) (e)

Figure 6-19: Progressive failure of a hat-stiffener specimen with a steeple trigger at different stages of

crosshead displacements: a) Pre-test; b) 12 mm - Completion of chamfer crushing; c) 20 mm


laminar bending, excessive matrix splitting and fiber fracture; and e) Post-test view (after

load removal) of crushed end of the specimen, showing five outward splaying plies and five


Figure 6-20 and Figure 6-21 show the axial and lateral strain fields, respectively,

for the steeple hat-stiffener, at four selected load levels, up to approximately 2.2 mm

crosshead displacement, well below the peak load, Figure 6-2(b). As expected,

subsequent to steeple crushing high axial strain developed at the top of the middle web,

beginning at the two corners, Figure 6-20. At the same time moderate axial strains build

up in the web indicating the beginning of outward bending of the middle web. As the

steeple crushes, very high axial strains were observed at the top of the web, with the

strains in the web continuing to increase as well.

The lateral tensile strains develop at the top corners of the web before progressing

to the center of the web, Figure 6-21. As the load increases, the strains in the web

increased and started to move towards the steeple. As the steeple is crushed further, high

strains are visible at the top of the web only. This indicates minor outward buckling at the

138

middle of the web which resulted in outward bending and splaying once the steeple was

completely crushed.


Figure 6-20: Axial strain field of a hat-stiffener specimen with a steeple trigger.


Figure 6-21: Lateral strain field of a hat-stiffener specimen with a steeple trigger.

6.5. EFFECT OF CROSS-SECTIONAL GEOMETRY ON SEA

A study performed in [42] examined the effect of cross-sectional geometry on

SEA using small and large thin-walled angle-stiffeners and C-channels, and hollow

square tubes, all fabricated with T700/2510 plane weave carbon fiber/epoxy prepreg

having a lay-up of [0/90]4S. The authors attempted to identify the influence of the curved

corners by varying the ratio of the curved surfaces to the total perimeter of the specimens.

This ratio, , can be calculated using the following equation,

139

(1)

where r is the radius of the corner, n is the fraction of a circle representing the

corners, and P is the total length of the cross-section perimeter. The data recorded in this

study are plotted together with the data reported in [42] in Figure 6-22. The results show

that both sets of data abide by the same linear relations proposed in [42], suggesting that

the more curved a specimen is the larger its energy absorbing capacity.

The C-channel with the lowest yields the lowest SEA, while the hat-stiffener

with the highest yields the highest SEA. Further, a previous study performed in [81,

Chapter 5] showed that circular tubes, fabricated from the same material but with a

different lay-up, can absorb significantly higher energy (approximately 126 kJ/kg). The

tube data ( =100%), fall on the same line on Figure 6-22 (not shown here for clarity).

Hence, this further confirms that the SEA is greatly dependent on the cross-sectional

geometry and is directly related to the shape of the cross section.

Figure 6-22: Effect of the ratio of curved surfaces to the total perimeter on the SEA of specimens with

various cross-sections

140

To further investigate this trend in SEA, the final deformation of the C-channel,

angle-stiffener, hat-stiffener, and circular tube (from [81, Chapter 5]), after load removal,

are compared in Figure 6-23, in increasing order of SEA from (a) to (d). The C-channel,

Figure 6-23(a), has the least amount of damage to the inward-splaying plies as compared

to the other cross-sections. The inner plies of the flanges are severely damage, however,

the web stayed relatively intact with a few major matrix splits. On the other hand, the

angle- and hat-stiffeners show a much greater amount of damage and interaction between

the inward-splaying plies, Figure 6-23(b) and Figure 6-23(c), respectively. The circular

tube shows that most of the material (7 of 9 plies) is severely damaged and has been

compacted into the center of the tube, Figure 6-23(d). Hence, increasing interaction

amongst material that is crushed and forcing it towards the inside of the cross-sections

greatly increases the SEA of the specimen. Cross-sections that contained a longer

‘curved’ segments (i.e. have a larger ) promote the desired material interaction and

displacement towards the inner sides of the curved sections, thus increasing the overall

energy absorbed.

(a) (b) (c) (d)

Figure 6-23: Final deformation (after load removal) of: a) C-channel, b) angle-stiffener, c) hat-stiffener,

and d) Circular tube (from [81, Chapter 5]).

141

6.6. CONCLUSION

Thin-walled composite members, with three different cross-sections (C-channels,

angle-stiffeners and hat-stiffeners) and two types of failure trigger mechanisms (chamfer

and steeple) were investigated to determine which approach is best in terms of decreasing

the initial peak load while increasing the sustained crush load and SEA. The results show

that the angle- and hat-stiffeners were the most effective at absorbing energy, having very

similar SEA values. The C-channel, on the other hand, has a much lower SEA value. The

steeple failure trigger was able to provide a lower initial peak load than the chamfer

failure trigger for the C-channel and hat-stiffener. For angle-stiffeners, both failure

trigger mechanisms resulted in similar initial peak loads.

The analysis of the failure processes and DIC strain fields highlighted several

important differences between the three cross-sections and the two failure trigger

mechanisms. During chamfer crushing, significant buckling occurs in the web and

flanges of the C-channel, and in the legs of the angle-stiffener. The hat-stiffener exhibited

some minor buckling in the flanges. Upon complete crushing of the chamfer, failure

would typically initiate at the corners of the cross section, in the form of matrix splits and

axial cracks due to the high local lateral strains. The cracks continue to grow in the

corners, along the length of the specimen, resulting in bending and splaying of the plies

in both, the inward and outward, directions. With the steeple specimens, failure that

initiates at the tip of the steeple causes the bending and splaying of the plies in both,

inward and outward, directions. The C-channel and hat-stiffeners exhibit some minor

web and flange buckling during the crushing process, however, no buckling occurs in the

angle-stiffener. Further, investigating the effect of cross-sections on the SEA, following

142

the work done in [42], showed that the cross-sections that had a larger ratio of curved

sections resulted in a higher SEA due to the greater extent of damage and interaction

amongst the inward-splaying plies. Additional studies are warranted to determine the

effect of constituents, laminate configuration (where the optimal orientation of the off

axis plies depends on cross section size and geometry), wall thickness, and cross-

sectional area on the crush behavior.

143

CHAPTER 7: MODELING METHODOLOGIES FOR SIMULATING THE

AXIAL CRUSHING BEHAVIOR OF CFRP MEMBERS

6

7.1. ABSTRACT

Finite element models were developed to simulate the crushing behavior of

graphite/epoxy members with different cross-sections and failure trigger mechanisms.

Two different modeling approaches, namely, a single-layer approach and a multi-layer

approach, were employed and results were compared with experiments. By carefully

calibrating the values of certain parameters used in defining the contact/penetration

behavior and material model response, the single-layer approach is capable of predicting

the initial failure peak load and the load-crosshead displacement curve, but provided no

insight into the failure process. For the multi-layer approach, a comprehensive

investigation was performed to determine the most effective and accurate method to

model the crushing behavior of the composite members. This included determining the

most efficient way of modeling the laminate and its interfaces, and the most effective

element size and formulation, contact definitions, time-step control, and material model.

The multi-layer approach captured the failure process and predicted the sustained crush

load and compared very well with the experimental results.

7.2. INTRODUCTION

Composite materials are considered as feasible candidates for constructing energy

absorbing devices that can be integrated into the subfloor structure of rotorcraft to

6 Siromani, D., Awerbuch, J. and Tan, T-M., “Modeling Methodologies for Simulating the Axial Crushing

Behavior of CFRP Members,” Submitted to: Finite Elements in Analysis and Design.

144

increase its energy absorption capability and improve the crashworthiness of the structure

[23]. The high specific energy absorption (SEA) of composites is a result of the

combination of failure mechanisms under compressive loading, including fiber fracture,

matrix splitting, fiber-matrix debonding, and delamination, e.g. [24-28]. As part of this

study, a two-part experimental study was conducted to investigate the energy absorption

characteristics of graphite/epoxy members (IM7/8552) subjected to quasi-static axial

compression. The first part of the study focused on the crushing behavior of circular

tubes. Emphasis was placed on determining the optimal failure trigger mechanisms,

including chamfered-ends, two types of crush-caps (forcing inward folding and outward

splaying, respectively, of the material), and their combinations, to reduce the initial peak

load and to increase SEA [81, Chapter 5]. The second part of the study focused on

investigating the crush behavior of structural members having open cross-sections that

are more prevalent in the aerospace industry, including C-channels, angle-stiffeners, and

hat-stiffeners, with two different failure trigger mechanisms, namely, chamfered-ends and

steeple failure triggers [82, Chapter 6].

Due to the high cost of conducting experimental studies, there is a need for

developing reliable computational models capable of predicting the crushing response of

composite members. Such models could serve as design tools to optimize the energy

absorption capacity of composite members when subjected to crush loading. There have

been several attempts to develop explicit finite element models, with varying degrees of

success, for circular tubes [57-60], hollow square tubes [59-63], C-channels [61,62],

angle-stiffeners [61,62], and hat-stiffeners [67]. Composite structures can be modeled

using either solid or shell elements. Using shell element models requires less computation

145

time and they are more widely used to model the axial crushing of composite members.

The laminate can be modeled using either a single layer or multiple layers of shell

elements. In the ‘single-layer’ model the laminate is modeled by using a single layer of

shell elements, with each ply being represented by an integration point in the thickness

direction. In the ‘multi-layer’ model, the laminate is modeled using multiple layers of

shell elements, each layer may include either a single ply, or a group of plies, and the

layers are tied together using a tiebreak contact definition. Grouping plies together can

decrease the computation time required to run the simulation.

The single-layer modeling approach has been used in a number of recent studies

to simulate the crushing behavior of various composite members. For example, in

studying the crushing of thin-walled square tubes [58], it was shown that the single-layer

approach was capable of accurately capturing the local wall buckling and unstable

collapse. However, the approach could not depict the progressive failure process. By

carefully adjusting the values of key material and numerical parameters in the material

model (e.g., the failure strain parameters in MAT 54) and the contact characteristic

between the end of the test specimen and the loading fixture, the single-layer model was

able to yield good correlation with experimental load-displacement curves for the cross-

sections studied in [61,62]. However, the single-layer representation cannot depict the

progressive failure process and crush behavior.

The multi-layer modeling approach, on the other hand, is capable of

approximately capturing the progressive failure process for tubes undergoing progressive

crushing e.g., [57-60]. However, this approach has not always yielded good correlation

with the experimental load-displacement curves. The crush behavior of a graphite/epoxy

146

hollow tube was simulated in [57] using LS-DYNA with MAT 54 material model. A

good agreement with the experimental load-displacement was achieved, but the

simulation showed significant local buckling of the tube, rather than the brittle failure

observed experimentally. A simulation of progressive crushing of a thin-walled square

carbon fiber reinforced plastic (CFRP) tube was performed in [58]. The multi-layer finite

element model was able to accurately predict the peak load, but the overall SEA was

underestimated by 33%. The difference in SEA was attributed to the model’s inability to

reproduce the formation of debris wedged between the fronds of the tube’s wall due to

excessive element deletion. In [59,60], the simulations of the crushing behavior of hollow

glass-polyester circular and square tubes were performed using the multi-layer approach;

results did not agree well with the experimental load-displacement curves, deformation,

and failure behavior due to the model’s inability to reproduce the axial matrix cracks

observed experimentally. To overcome the modeling deficiency, pre-defined seams along

the element edges in the axial direction of the tubes were introduced to simulate the

propagation of axial cracks, which yielded a better agreement. A continuum damage

mechanics model (CODAM) was used in studying the behavior of braided composite

tubes [64], with multiple layers of shell elements and a tiebreak contact definition to

capture delamination. A “debris wedge” model formed between the delaminated surfaces

of neighboring plies during the crushing process was incorporated to improve the

accuracy of the simulation. While this approach can induce ply splaying in the

experimentally observed direction, it may not be applicable to more general cases

involving multiple failure processes. Further, it was noted in [66] that some of the

material parameters in the CODAM model require extensive characterization processes,

147

which are not readily available. As a result, these parameters have to be obtained by

correlating the simulation with experiments. A simulation of the crushing of a plain

woven carbon fiber epoxy prepreg made hat-stiffener was performed using multi-layer

approach in [67]. It was shown that increasing Mode I and Mode II energy release rates

for the cohesive interface yielded better correlation with experimental results than those

obtained by using the experimentally obtained energy release rates.

The primary focus of this paper is on the finite element modeling and simulations

performed to capture the crushing behavior of circular tubes and open cross-section

members. Two different modeling approaches using LS-DYNA were employed, namely,

the single-layer approach and the multi-layer approach. For each approach, the setup of

the model is discussed in detail followed by examples of the results obtained from the

simulations and comparison with experiments in terms of load-displacement behavior,

SEA, and crush behavior. Details of the experimental results have been reported in [81,

Chapter 5] and [82, Chapter 6] and their comparison with multi-layer models results have

been reported in [79, Chapter 8] and [80, Chapter 9], respectively. This paper provides

specific details on the development of the modeling methodology employed.

7.3. SPECIMEN CONFIGURATION AND TEST PROCEDURE

The test specimens were fabricated using Hexcel IM7/8552 Graphite/Epoxy pre-

preg. All specimens were 101.6 mm long and the open cross-section specimens were

fabricated with the same cross-sectional area. Lay-up sequences and specimen

dimensions are listed in Table 7-1 and shown in Figure 7-1. The circular tubes were self-

supported while the open cross-section specimens were supported by a 25.4 mm thick

potted base, Figure 7-2, to ensure stability. All specimens included a failure trigger

148

mechanism to initiate progressive failure during the crushing process. The circular tubes

were tested with chamfers and crush-caps [81, Chapter 5], while the open cross-sections

were tested with chamfer and steeple ends [82, Chapter 6].

Figure 7-1: Test specimens cross-sectional dimension (all dimensions in mm).

Table 7-1: Specimen configuration

Geometry Lay-up Length (mm)

Cross-

sectional area

(mm2)

Wall

thickness

(mm)

Failure

trigger

mechanism

Circular Tube [-15/+15/03/-15/+15/02] 101.6 142 1.37 Chamfer/

Crush-cap

C-channel [02/+45/-45/02/-45/+45/02] 101.6 180 1.52 Chamfer/

Steeple

Hat Stiffener [02/+45/-45/02/-45/+45/02] 101.6 180 1.52 Chamfer/

Steeple

Angle

Stiffener [02/+45/-45/02/+45/-45/02]S 101.6 180

3.04

Chamfer/

Steeple

Figure 7-2: Test specimens

All tests were carried out under quasi-static axial compression at a crosshead

displacement rate of 7.6 mm/min and were terminated at a maximum displacement of

149

50.8 mm, which provided sufficient crush data to calculate the SEA. The full-field

deformation and strain fields on the surfaces of selected specimens were also recorded

using Digital Image Correlation (DIC). The experimental results for the circular tubes are

described in [81, Chapter 5] and the open cross-sections in [82, Chapter 6].

7.4. SINGLE-LAYER MODELING APPROACH

7.4.1. LAMINATE REPRESENTATION AND ELEMENT SELECTION

The single-layer modeling approach used in [61,62] was adopted for this study. A

single layer of shell elements was used to represent the laminate. Individual plies were

modeled using through-the-thickness integration points, with one integration point per

ply in the thickness direction. Each integration point was assigned a ply thickness and an

orientation corresponding to the stacking sequence listed in Table 7-1. The 45° chamfer

was approximated by reducing the number of plies in the first row of elements to three

plies, Figure 7-3, with the height of the first row being the same as that of the chamfer.

The steeple trigger was modeled by making two 15° cuts to the top of the model, Figure

7-3, to realistically represent the test specimen. All specimens were modeled using

rectangular elements of size 1.27 x 1.27 mm, resulting in approximately 6,400 elements

for the chamfered tube model, 5,500 and 4,800 elements for the chamfered and steeple C-

channel, respectively, and a similar number of elements for the other two open cross-

sections.

For the single-layer models, the four-node Belytschko-Tsa shell element (type 2

in LS-DYNA [73]) with single integration point and hourglass control (type 1, hourglass

coefficient = 0.1) to suppress zero energy modes was used. This is a computationally

150

efficient element formation that yields accurate results as long as no zero energy

deformation modes occur.

Figure 7-3: Representations of the trigger mechanism in the single-layer finite element models of (a)

circular tube with a chamfer, and (b) C-channel with a steeple.

7.4.2. MATERIAL MODEL

Material model 54 (MAT54) in LS-DYNA was used to simulate the crushing

behavior of the specimens. MAT54 is a progressive failure model that uses the Chang-

Chang failure criterion to determine failure of each ply (associated with an integration

point) [73]. This model allows the user to create a local material coordinate system to

specify the orientation of each ply. There are 21 parameters in MAT54 that need to be

specified; 15 of which are physical parameters and six are numerical parameters [73]. Of

the 15 physical parameters, 10 parameters are material constants the values of which

were obtained from [83] and [84], as shown in Table 7-2.

151

Table 7-2: Material properties for IM7/8552 [83,84]

E1 E2 G12/13 G23 ν12

171.42 GPa 9.08 GPa 5.29 GPa 3.92 GPa 0.32

XT XC YT YC SL

2326.2 MPa 1200.1 MPa 62.3 MPa 199.8 MPa 92.3 MPa

The remaining five physical parameters are the tensile and compressive failure

strains (element deletion strains) in the fiber direction (DFAILT and DFAILC), the matrix

and shear failure strains (DFAILM and DFAILS), and the effective failure strain (EFS).

The six numerical parameters can be adjusted to yield desired material behavior. Based

on an extensive parametric study, it was concluded that of these six parameters, the crash-

front element softening parameter (SOFT) is of key importance to this study. This

parameter reduces the strength of elements surrounding a damaged or deleted element.

Details are discussed in the next section, along with the results.

7.4.3. BOUNDARY CONDITIONS AND CONTACT DEFINITIONS

A fixed boundary condition was assigned to the nodes along the flat end of all

finite element models. For single-layer models, only one contact definition between the

loading platen and the chamfer/steeple end of the specimen is needed. The contact

definition used to model this interaction was contact rigid nodes to rigid body, following

the approach outlined in [61,62]. The advantage of using this contact definition is that it

distributes the contact force over multiple rows of elements, thus preventing the load

from dropping to zero after the deletion of each row of elements. This is accomplished by

allowing the nodes of the tube to penetrate into the platen by a specified distance, Figure

152

7-4. As the nodes penetrate, they are resisted by the forces calculated based on a user

specified load-penetration curve.

Figure 7-4: Penetration of the platen by tube elements according to the load-penetration curve in the

contact definition (Figure 7-5).

The initial load-penetration curve used in this contact definition was estimated

from the compressive failure load and cross-sectional area of the element. It was

subsequently fine-tuned to ensure that at least two rows of elements penetrated the platen

prior to any element deletion. Figure 7-5 shows the selected load-penetration curve used.

Figure 7-5: Final load-penetration curve for the contact definition used in single-layer model.

0

1

2

3

4

0 1 2 3 4

Co

nta

ct L

oad

(kN

)

Penetration (mm)

Platen

Penetration

Tube with chamfer

153

The modified load-penetration curve prevented a sudden drop of the load to zero,

but still resulted in a very noisy load-displacement behavior that resembled a saw-tooth

pattern, Figure 7-6. Various filtering schemes were investigated and it was determined

that the SAE 1000 Hz filter resulted in a reasonable load-displacement curve, Figure 7-6.

Figure 7-6: Unfiltered vs. filtered load-displacement curves obtained from the single-layer chamfered

circular tube model. The SAE 1000 Hz filter was used to obtain the filtered data.

7.4.4. SIMULATION RESULTS

i) Circular Tubes

As mentioned in the previous section, there are five physical parameters (failure

strains) and six numerical parameters in MAT54 whose values need to be determined

numerically. A comprehensive parametric study was performed to investigate the effect

of these parameters on the simulated load-displacement behavior. It was determined that

the physical parameter DFAILC (fiber compression failure strain) had the greatest effect

on the value of initial peak load while the numerical parameter SOFT (crash-front

element softening parameter) had the greatest effect on the value of sustained crush load,

which determined the value of SEA. By adjusting these two parameters it is possible to

obtain simulation results that agree with experiment. Table 7-3 and Table 7-4 show the

0

20

40

60

80

100

120

0 10 20 30

Load

(kN

)

Crosshead Displacement (mm)

UnfilteredFiltered (SAE 1000Hz)

154

effect of varying these two parameters on the initial peak load, sustained crush load and

SEA. Parameters DFAILT, DFAILM and DFAILS were found to have a marginal effect

on the results and were kept constant at arbitrarily selected values of 0.02, 0.02 and 0.03,

respectively. It was found that simulations with DFAILC = -0.0075 and SOFT = 0.22

yielded the load-crosshead displacement behavior for chamfered tubes that matched very

well with experimental data, as shown in Figure 7-7. The SEA obtained from the

simulation (129 kJ/kg) also compared well with the experimental SEA (127 kJ/kg).

Table 7-3: Results of the parametric study showing the effect of DFAILC in MAT54 on the peak load,

crush and SEA of the circular tube.

DFAILC Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

-0.0100 158.7% 162.5% 161.3%

-0.0050 61.4% 83.1% 83.9%

-0.0060 83.2% 83.1% 83.9%

-0.0075 103.3% 83.1% 83.9%

-0.0080 105.1% 83.1% 83.9%

Table 7-4: Results of the parametric study showing the effect of SOFT in MAT54 on the peak load, crush

and SEA of the circular tube.

SOFT Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

0.22 103.3% 104.7% 101.5%

0.25 103.3% 118.2% 120.1%

0.28 103.3% 131.2% 132.5%

0.30 103.3% 158.5% 160.3%

The single-layer approach seemingly yielded excellent agreement with

experimental results in terms of load-crosshead displacement curve and SEA. However it

should be emphasized that such agreement could be established based on empirically

fitting the MAT 54 parameters to the experimental data. Further, it could not replicate

the deformation and failure processes of the composite structure, such as matrix splitting,

155

delamination, outward-splaying, inward-folding and crushing of material, etc. Further,

this approach could not be used to simulate the crushing behavior of tubes having crush-

cap failure trigger mechanism becuase the contact definition could not capture the effect

of crush-caps.

Figure 7-7: Single-layer simulation vs. experimental load-crosshead displacement curve for the circular

tubes having a chamfer trigger.

ii) Open Cross-Sections

An attempt was made to determine whether a common set of values of the 11

MAT 54 parameters could be used to simulate the crushing behavior of the three open

cross-sections and two failure trigger mechanisms. A comprehensive parametric study

was conducted to determine the required parameters for the C-channel specimen. Similar

to the case of the circular tubes, it was found that DFAILC and SOFT were the only two

parameters that have noticeable effects on the crushing behavior. By adjusting the values

of the DFAILC and SOFT parameters it was possible to obtain simulation results that

correlated well with the experimental data for the C-channel with a chamfer trigger,

Figure 7-8(a). Parameters DFAILT, DFAILM and DFAILS were kept constant at values of

0.02, 0.013 and 0.03, respectively. Table 7-5 and Table 7-6 show the effect of varying

0

10

20

30

40

50

0 10 20 30 40 50

Load

(kN

)


ExperimentSimulation

156

these two parameters on the initial peak load, sustained crush load and SEA. The optimal

values obtained for DFAILC and SOFT were -0.008 and 0.10, respectively.

In [61,62] it was found that the by applying the same DFAIL parameters to all

cross-sectional geometries and by varying SOFT, good correlation between the simulated

and experimental load-displacement curves was obtained. Further, a linear relationship

between the SEA and SOFT was observed, which could be related to the shape of the

cross-section [61,62]. A similar approach was used in this study: the DFAIL parameters

determined from the C-Channel parametric study were applied to the angle and hat

stiffener models. The SOFT parameter was then varied to match the sustained crush load

and SEA in the simulations to the experimental results. Good correlation was obtained

with the crush load and SEA, however, the initial peak loads were not predicted

accurately, Table 7-9. This indicated that the DFAILC parameter needed to be modified

for each cross-section as well.

The reason for the differing results obtained in this study as compared to those

reported in [61,62] is a direct consequence of the contact definition used in the single-

layer approach. As explained earlier, the load applied to the nodes is directly proportional

to their penetration distance into the loading platen. Therefore, for cross-sections with the

same area, as was the case for this study, the load applied by the contact definition will

always be the same, regardless of the shape of the cross-section. In other words, a

different set of SOFT and DFAILC values are needed for different cross-sectional

geometries in order to accurately predict the peak load, sustained crush load, and SEA.

157


crush and SEA of the C-channel with a chamfer.

DFAILC Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

-0.013 73.1% 158.5% 145.6%

-0.002 77.7% 174.4% 160.9%

-0.004 90.1% 197.5% 182.5%

-0.006 96.2% 208.6% 192.7%

-0.008 102.3% 212.8% 197.0%

Table 7-6: Results of the parametric study showing the effect of SOFT in MAT54 on the peak load,

crush and SEA of the C-channel with a chamfer.

SOFT Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

0.05 104.5% 50.6% 54.2%

0.10 105.1% 108.7% 106.1%

0.15 103.1% 158.5% 149.4%

0.20 100.8% 194.2% 180.5%

A similar parametric study was performed for the C-channel having a steeple

trigger, Table 7-7 and Table 7-8. For this case, it was not possible to establish a similar

level of correlation as with the chamfered specimens. The reason is that the steeple lacks

the weakened first row of elements (present in the chamfered case) to take advantage of

the SOFT parameter. Figure 7-8(b) shows a comparison of the simulation and

experimental load-displacement curves. This model was very sensitive to minor changes

to the DFAILC and SOFT parameters, often resulting in unstable collapse. When the C-

channel stiffener parameters were applied to the hat and angle stiffener models, poor

correlation was obtained, Table 7-9. Hence, similar to the chamfered case, al cross-

sections would require a separate set of parameters in order to obtain accurate and stable

results.

158


crush and SEA of the C-channel with a steeple.

DFAILC Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

-0.013 89.7% 104.8% 104.2%

-0.005 71.3% 83.0% 81.8%

-0.010 81.6% 100.0% 99.4%

-0.015 91.5% 106.6% 106.0%

-0.020 94.9% 111.5% 110.8%

Table 7-8: Results of the parametric study showing the effect of SOFT in MAT54 on the peak load, crush

and SEA of the C-channel with a steeple.

SOFT Peak Load

(Num/Exp %)

Crush Load

(Num/Exp %)

SEA

(Num/Exp %)

0.05 18.7% 16.9% 17.4%

0.10 42.4% 45.4% 45.2%

0.15 56.7Z% 63.9% 63.2%

0.20 65.6% 75.6% 74.6%

(a)

(b)

Figure 7-8: Single-layer simulation vs. experimental load-crosshead displacement curve for the C-

channels having (a) a chamfer trigger, and (b) a steeple trigger.

Table 7-9: Correlation between the experimental and simulation results for each cross-section with (a) a

chamfer trigger, and (b) a steeple trigger.

(a) (b)

Specimen

Peak

Load

[Error %]

Crush

Load

[Error %]

SEA

[Error %]

C-Channel 3.9% 6.4% 7.2%

Angle

Stiffener 20.1% 5.1% 5.4%

Hat Stiffener 20.5% 3.1% 1.4%

Specimen

Peak

Load

[Error %]

Crush

Load

[Error %]

SEA

[Error %]

C-Channel 21.9% 17.8% 0.4%

Angle

Stiffener 66.7% 58.1% 64.0%

Hat Stiffener 30.3% 24.6% 33.3%

0

10

20

30

40

0 10 20 30

Load

(kN

)



0

10

20

30

40

0 10 20 30

Load

(kN

)



159

7.5. MULTI-LAYER MODELING APPROACH

7.5.1. LAMINATE REPRESENTATION

In the multi-layer approach the laminate was divided into multiple layers of shell

elements, each layer may contain multiple plies to improve computational efficiency, and

layers were tied together using a tiebreak contact definition. All layers contain an equal

number of plies to maintain equal spacing between the individual layers. The circular

tubes consisted of a nine-ply [+15/-15/+15/03/-15/+15/-15] laminate and were modeled

by three layers of shell elements, with the inner [+15/-15/+15] plies, the middle [03]

plies, and the outer [-15/+15/-15] plies represented by the inner, middle, and outer layers,

respectively. The open cross-sections consisted of ten plies ([02/+45/-45/02/-45/+45/02])

and were modeled by five layers of shell elements, with each layer representing two plies

(i.e., layer 1: [02], layer 2: [+45/-45], layer 3: [02], layer 4: [-45/+45], and layer 5: [02]).

It is noted that angle stiffeners are twice as thick as the other open cross-sections (to

maintain the same cross-sectional area in all three open cross-sections) and were modeled

by 10 layers of shell elements.

Each ply was represented by a single integration point through the thickness of

the shell element layer. The 45° chamfer was modeled by staggering the length of each

shell layer such that the inner layer’s first row of elements represented the start of the

chamfer, and the outer layer represented the end of the chamfer, Figure 7-9(a). The

steeple trigger was modeled by making two 15° cuts to the one end of the model, Figure

7-9(b).

160

(a)

(b)

Figure 7-9: Representations of: (a) circular tube with a chamfer and (b) C-channel with a steeple failure

trigger mechanisms in the finite element models.

7.5.2. ELEMENT SIZE AND FORMULATION

A mesh density study performed on the circular tube concluded that a maximum

element size of 0.635 x 0.635 mm was required in order to accurately simulate the

initiation and progress of damage. The same element size was used for the curved

surfaces in all cross-sections (i.e., tubes and corners of open cross-section models). For

the flat sections (i.e., web and flanges) in the models, it was determined that an element

size of 1.27 x 1.27 mm was sufficient. This resulted in the tube model having

approximately 77,000 elements and the open cross-section models having approximately

55,000 elements. It should be noted that for the steeple specimens the auto-meshing

process resulted in an asymmetric mesh, which may have affected the crushing process.

To improve computational efficiency the Belytschko-Tsay shell element with

single-integration point (type 2 in LS-DYNA, [73]) was chosen to model the specimens.

Various hourglass control options, with both viscous and stiffness formulations, Table

7-10, were investigated to suppress zero energy deformation modes that accompany the

one-point quadrature. However, none of these options were capable of preventing

hourglass deformation modes. Therefore, either the mesh would need to be refined to

further investigate the use of this element formulation, or the fully-integrated elements

161

would need to be used. Since both options would results in a significant increase in

computation time, to ensure accurate results, fully-integrated elements (type 16, [73])

were used for all simulations.

Table 7-10: Hourglass control options investigated for under-integrated elements

Type Formulation Coefficient

1 Standard - viscous 0.1

2 Flanagan-Belytschko - viscous 0.1

4 Flanagan-Belytschko - stiffness 0.05

4 Flanagan-Belytschko - stiffness 0.1


All boundary conditions used were accurate representations of the experimental

setup. The circular tubes did not require any boundary conditions as they were placed

standing upright between the loading platen and the base of the testing machine, with

corresponding contact definitions. The open cross-sections required the nodes along the

flat end of the models to be fixed in all degrees of freedom to simulate the potted base

used for support.

The loading platen of the testing machine was modeled as a rigid surface and the

interaction between the loading platen and the specimens was modeled using a surface to

surface contact definition (contact automatic surface to surface). The contact between the

base and the circular tube was defined using a “rigid wall” contact definition

(rigidwall_planar), which does not allow node penetration. For the simulation of the

chamfered tube with a crush cap, the crush cap was assumed to be rigid and was defined

using the same surface-to-surface contact definition as the platen-tube contact. To prevent

self-penetration of any of the shell layers, a single surface contact definition (contact

162

automatic single surface) was added to all layers. A friction coefficient of 0.3 was used

between the specimens and the Instron loading platen and base.

7.5.4. TIME STEP

In the experimental tests, a quasi-static loading rate of 7.6 mm/min (

) was used for all specimens. However, in the simulation, this low loading rate

would result in a prohibitively long computation time due to the small time-step required

by explicit time integration codes. There are two methods to address this issue, namely,

time-scaling method and mass-scaling method [85,89]. Both methods were evaluated in

this study to improve the computational efficiency of the simulations.

i) Time-scaling

In the time-scaling method the load is applied at a much higher rate, thus reducing

the total simulation time. However, in a quasi-static simulation, it is important that the

load is applied in a manner that would yield a minimal inertial effect on the results, i.e.,

the ratio of the kinetic energy to the internal energy must be reasonably small [57,85].

Four different loading rate functions were investigated, Figure 7-10(a). These include 1)

a sinusoidal loading rate function to slowly ramp up the loading rate from 0 m/s to 2.5

m/s [85], 2) a constant loading rate of 0.65 m/s [57], 3) a step function, from a 0.65 m/s

rate for the first 0.01 seconds to a 2.5 m/s rate thereafter [67], and 4) a step function, from

a 1.3 m/s rate for the first 0.02 seconds to a 2.5 m/s thereafter [67]. For all cases the ratios

of the kinetic energy to the internal energy were less than 10% upon initial contact and

less than 5% throughout the remainder of the crushing process, thus indicating that the

inertial effects are minimal. Comparing the load-displacement curves among the four

163

loading functions show that the results were not sensitive to the first three loading rate

functions, Figure 7-10(b). The fourth function, however, appears to have a more

noticeable effect on the load-displacement curve. Hence, the third function (step function

increasing the loading rate from 0.65 m/s to 2.5 m/s) was selected as it yielded the least

computation time of the first three cases.

(a)

(b)

Figure 7-10: Time-scaling investigation showing: a) loading rates used, and b) the resulting load-crosshead

displacements.

ii) Mass-scaling

The mass-scaling method effectively increases the simulation time-step by adding

a non-physical mass to selective elements in the structure. There are two options

available in LS-DYNA for mass-scaling [85]: 1) a user-specified scaling factor to scale

up the masses of the selective parts; and 2) automatic mass-scaling with a user specified

minimum time-step. Both options were investigated in this study. For the first option a

scaling factor of 100 was used (for comparison, the mass was scaled by a factor of 1000

0

0.5

1

1.5

2

2.5

3

0 0.01 0.02

Load

ing

Rat

e (m

/s)

Time (sec)

Sinusoidal (0 m/s to 2.5 m/s)Constant (0.65 m/s)Step (0.65 m/s to 2.5 m/s)Step (1.3 m/s to 2.5 m/s)

0

5

10

15

20

25

30

35

40

0 5 10

Load

(kN

)


164

in [57,58]), and for the second option the minimum time-step was set to 4x10-8 sec,

which was more than double the average time-step through the crushing process of the

un-scaled simulation. Figure 7-11 shows the load-crosshead displacement curves of the

two mass-scaled simulations compared to the un-scaled simulation. Results of the first

option (with a scaling factor of 100) is seen to be significantly different from the un-

scaled simulation, indicating a substantial effect of the added nonphysical mass. Results

of the second option are very similar to that with no mass-scaling and the time-step was

affected only after 3 mm of crushing, yielding a slightly lower crush load from that point

forward. While both options resulted in shorter computation times (10x and 2x faster than

the un-scaled simulation), the adverse effect of the added mass could not be ignored.

Therefore, mass-scaling was not used in any of the simulations in this study.

Figure 7-11: Mass-scaling investigation showing the resulting load-crosshead displacements.

7.5.5. DELAMINATION INTERFACE

The tiebreak contact definition implemented in LS-DYNA allows for the

simulation of delamination at the interface between adjacent shell element layers. Two

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8 9 10

Load

(kN

)


No Mass ScalingMass x100Automatic Mass Scaling (dt = 4e-8 sec)

165

tiebreak formulations were investigated for the purpose of this study; namely, tiebreaks

with a bilinear traction-separation law and a tiebreak implementation of the cohesive

zone formulation [86] (option 8 and 11 in LS-DYNA, respectively [73]). The former,

which requires interlaminar normal and shear strengths and a critical distance to interface

failure as input parameters, has been used to model delamination in crush simulations

e.g., [63,64]. However, the optimal selection of the critical failure distance parameter has

not been thoroughly studied in open literature. The latter, the formulation of which is

similar to that of cohesive zone elements, requires the standard input parameters, such as

interlaminar normal and shear strengths, fracture toughness under pure Mode I and Mode

II loading, interfacial stiffness for normal and shear modes, and a parameter for the

power-law or the Benzeggagh-Kenane law (B-K law) that describes crack propagation

[73]. This formulation has been used to model delamination in ballistic impact [86], but

not for crush simulations. A description of the model setup using each formulation is as

follows:

i) Option 8

In this tiebreak formulation, damage initiates when the stresses on the interface

satisfy the following failure criterion [73]:

(| |

)

(| |

)

(1)

in which and are the normal and shear stresses acting at the interface, and

NFLS and SFLS are the normal and shear strengths of the tie, respectively. Once the

damage has initiated, the two surfaces begin to separate and the interfacial stresses are

then scaled down as a linear function of the separation distance. The critical distance,

166

denoted by CCRIT, at which failure occurs (i.e., deletion of tiebreak and advancing of

delamination) is given by [73]:

(2)

where:

√ ( ) | |

(3)

and is the energy released due to the failure of the tiebreak interface. A

sensitivity study was conducted, to determine the relative effect(s) of Mode I and Mode II

on the tiebreak failure process, using the circular tubes. It was determined that for

simulating the crushing of composite tubes, Mode II fracture is the dominant mode of

failure during the tie-break failure process. Thus, to simplify the simulations, a pure

Mode II delamination was assumed. Consequently, and were used,

and the critical distance to failure is now given by:

(4)

where is the Mode II critical energy release rate, the value of which

was obtained from [87] for IM7/8552, as shown in Table 7-11. Any lower values

will cause the ties to break prematurely, yielding a high rate of delamination progression.

It is noted that the simulation of progressive delamination is mesh size dependent

and typically requires a very fine mesh. To improve the computational efficiency, the

methodologies discussed in [88] were adopted. The proposed solution involves lowering

the interlaminar strengths whilst keeping the fracture toughness constant in order to adapt

167

the length of the cohesive zone for a given mesh size. While this approach is intended to

be used with cohesive zone models, it can also be applied to the tiebreak formulation

used here since the tiebreaks follow a traction-separation law similar to that used in

cohesive zone formulations. The required interfacial strength can be calculated from

[88]:

√

(5)

where is the transverse modulus for orthotropic materials, is the fracture

energy release rate, is the desired number of elements in the cohesive zone, and is

the mesh size in the direction of the delamination progression. The minimum number of

elements required for the cohesive zone has not been well established. Various studies

have used anywhere from two elements to 10 elements [88]. Although no cohesive

elements are required for the tiebreak formulation applied herein, the same concept used

for cohesive elements has been applied to the tiebreaks. A separate sensitivity study

conducted here concluded that five elements were sufficient to simulate the propagation

of delamination. Hence, with , Equation (5) was used to solve for the new NFLS

and SFLS values. The new SFLS was substituted into equation (4) to calculate the

CCRIT value.

Since the laminate of the open cross-sections was modeled as five and ten layers

of shell elements with each layer representing two plies, the tiebreak contact was defined

only between these shell layers, rather than between individual plies. However, in reality,

delamination could occur along any, if not all, ply interfaces during specimen crushing,

as was observed experimentally [81,82, Chapters 5 and 6]. In order to account for the

168

energy dissipated by these additional for delamination interfaces, CCRIT was scaled by

the ratio of the number of ply interfaces to the number of tiebreak interfaces ,

defined as:

(6)

That is, it was assumed (based on the experimental observations discussed in

[81,82, Chapters 5 and 6]) that delamination occurred among all plies. The values used

and calculated in Equations (4), (5) and (6) are listed in Table 7-11. It should be noted

that was calculated using the smaller element size (0.635 mm) for the circular

tube and the larger element size (1.27 mm) for the open cross-section specimens

(including the corners).

ii) Option 11

For this tiebreak formulation the critical failure distance, CCRIT, is not required

because the energy release rates, and , are directly input into the simulation.

However, these energy release rates still need to be scaled by the same ratio that CCRIT

was scaled by, Equation 6, in order to account for the delamination occurring at the

interfaces that are not accounted for in this model. Also, the new values calculated for

NFLS and SFLS using Equation 5 were required to address mesh size dependency

discussed earlier. Further, this formulation requires tiebreak interfacial stiffness, , for

normal and shear modes, which can be calculated from [88] as:

(7)

169

where, is a parameter much larger than 1, assumed to be equal to 50 in [88], and

is the thickness of the adjacent sub-laminate, in this case, the shell element layer (i.e.,

the thickness of three plies for the circular tube and two plies for the open cross-sections).

The resulting interfacial stiffness for each cross-section is listed in Table 7-11. Further,

simple DCB simulations were performed with this tiebreak formulation and it was found

that the simulations were very sensitive to the contact viscous damping coefficient and

the part stiffness damping coefficient [73,89]. A stable solution was achieved by using a

viscous damping coefficient of 1.0 and a part stiffness damping coefficient of 0.02. A

comparison of the results obtained from the two tiebreak formulations is discussed after

the description of the material model selection in the next section.

Table 7-11: Tiebreak input parameters for Option 8 and 11

[GPa]

[kJ/m2]

[kJ/m2]

[mm]

[MPa]

[MPa]

[mm]

[mm]

[N/mm3]

Circular

Tube 9.08 0.2 1.33 5 0.635 22.5 57.3 0.046 0.185 1.2 x 106

C-channel/

Hat-

stiffener

9.08 0.2 1.33 5 1.27 15.9 40.5 0.065 0.148 1.8 x 106

Angle-

stiffener 9.08 0.2 1.33 5 1.27 15.9 40.5 0.065 0.139 1.8 x 106


In the multi-layer modeling approach, two material models, MAT54 and MAT58,

were investigated to simulate the crushing behavior of the specimens. MAT 54 is a

progressive failure model that uses the Chang-Chang failure criterion to determine the

failure of each ply (associated with an integration point) [73]. This material model has

been studied extensively to model the crushing process of brittle composites e.g., [57,58].

MAT58 is a Continuum Damage Mechanics (CDM) model based on the Matzenmiller-

170

Lubliner-Taylor (MLT) damage model and the Hashin failure criteria [73]. This model

allows for stiffness degradation based on the accumulation of damage such as micro-

cracks and cavities. MAT58 has been studied extensively to model the crushing process

of braided composites [66]. The material properties used to define both materials models

are listed in Table 7-2. A description of the model setup using each material model is as

follows:

i) MAT54

As discussed in the single-layer modeling setup, MAT54 has several parameters

that need to be determined parametrically, most importantly the tensile and compressive

failure strains in the fiber direction, the matrix and shear failure strains, and the effective

failure strain. A parametric study was conducted to determine the optimal values of the

unknown parameters for the multi-layer modeling approach. It was found that the only

MAT54 parameter that needed to be adjusted was DFAILM, which is the failure strain in

the matrix direction [73]. Adjusting the value of DFAILM enabled matrix splitting to

occur, as observed in the experiments [81,82, Chapters 5 and 6]. DFAILM values ranging

from 5% to 30% were analyzed and it was determined that, for the chamfered tube, a

value of 10% strain yielded the most accurate representation of the crushing process. This

DFAILM value was used for the elements in the corner regions of the open cross-section

specimens as well since they had the same element size as that of the circular tube model.

To determine the optimal DFAILM value for the flat surface regions where elements are

twice the size of the corner elements, a separate parametric study was conducted. It was

found that a DFAILM value of 5% strain would provide the most accurate representation

of the crushing process.

171

ii) MAT58

The MAT58 material model uses the maximum effective strain criterion to

determine failure. An integration point (or ply) fails and ceases to carry any load if the

effective strain computed at that point reaches the maximum effective strain, defined by

the input parameter ERODS. All plies in an element must fail before the element is

deleted. A parametric study was performed to determine an ERODS values using the

chamfered tube having three layers of shell elements. It was found that, even with

ERODS values as high as 50% strain, the high compressive axial and hoop strains in the

elements representing the tube chamfer typically caused premature element deletion,

resulting in a catastrophic failure in the chamfer. Ultimately, it was determined that the

ERODS values for the inner two shell layers needed to be set to a much higher value (i.e.,

100%) to prevent catastrophic failure of the chamfer. The ERODS value for the outer

shell layer was set to 25% in order to enable matrix splitting to occur.

Further, MAT58 allows the user to specify a stress limit factor, SLIMXX, which

scales down the stress in any direction that has reached its respective strength, thus

achieving an elastoplastic like behavior in the damaged elements. A SLIMXX value of 1.0

gives an elastic-perfectly plastic like behavior until the failure strain (ERODS) is reached,

which is recommended for compression and shear [73]. In tension, a smaller SLIMXX

value is recommended and a value of 0.2 was selected for this study. Finally, MAT58

also allows the user to specify the strain at the strength for each direction. In this study,

this strain in each direction was calculated by dividing the strength by the elastic

modulus, effectively assuming a linearly elastic behavior before the strength was reached.

172

7.5.7. DISCUSSION OF RESULTS

In developing this methodology, chamfered circular tubes were used to

investigate the various modeling options and parameters discussed in the previous

section. In some cases, the options/parameters in question were evaluated using the C-

channel with a steeple failure trigger in order to determine their effect on a different

cross-section and failure trigger mechanism. The final modeling methodology was then

applied to all other cross-sections and trigger mechanisms.

The results obtained from the two tiebreak options and the two material models,

in terms of the load-crosshead displacement curves and deformation, are discussed in

detail. It is noted that the simulation results typically were very noisy and filtering

processes needed to be applied in order to properly interpret these results. A discussion

on the filtering of the load-crosshead displacement curves is presented first.

i) Filtering

The load-crosshead displacement curve of the chamfered tube shows three load

spikes, regardless of the tiebreak or material model used, occurring within the first 2 mm

of the crosshead displacement, Figure 7-12(a). These three load spikes correspond to the

crushing of the three shell element layers in the chamfered region. With the current three-

layer model, the curve could be smoothed using various data filtering schemes. Clearly,

the ‘smoothness’ of the curve depends on the degree of data filtering, noting that

excessive filtering will reduce the utility of the results. A range of filter frequencies

raging from SAE 180 Hz to SAE 1,000 Hz were studied and results indicated that SAE

300 Hz filter provided the best continuous initial load-displacement behavior that also

compared well with the experimental data, Figure 7-10(b). Similarly, the unfiltered

173

simulation results from the C-channel chamfer, show five load spikes, correspond to the

crushing of the five shell element layers in the chamfered region, Figure 7-13(a). It was

found that in this particular case an SAE 600 Hz filter provided the most accurate results,

Figure 7-13(b). It is noted that by modeling each individual ply as a separate shell

element layer, (hence with a much higher computational cost), the number of load spikes

would increase to nine (or ten for the C-channel) and the magnitude of each spike would

reduce significantly, rendering a much smoother load-displacement curve.

For the C-channel with a steeple failure trigger the load-crosshead displacement

curves did not require any filtering as the steeple geometry could be modeled accurately

without any approximation.

(a)

(b)

Figure 7-12: A comparison of: (a) the unfiltered and filtered load-crosshead displacement curves from a

multi-layer simulation for a tube with a chamfer failure trigger, and (b) the filtered simulation

results and the experimental load-crosshead displacement comparison for a tube with a

chamfer failure trigger.

0

10

20

30

40

50

0 5 10 15 20

Load

(kN

)


Simulation unfilteredSimulation filtered (SAE 300Hz)

0

10

20

30

40

50

0 5 10 15 20 25

Load

(kN

)


Chamfer tube test 1Chamfer tube test 2Chamfer tube test 3Simulation filtered (SAE 300Hz)

174

(a)

(b)

Figure 7-13: A comparison of: (a) the unfiltered and filtered load-crosshead displacement curves from a

multi-layer simulation for a C-channel with a chamfer failure trigger, and (b) the filtered

simulation results and the experimental load-crosshead displacement comparison for a C-

channel with a chamfer failure trigger.

ii) Tiebreak Formulations

A comparison the load-crosshead displacement curves obtained from the

chamfered tube for each tiebreak formulation show very similar results in terms of the

initial peak load and sustained crush load, Figure 7-14(a). This indicated that either

option was capable of simulating delamination in the models and the computational cost

was the same for both options. Further, comparing the final deformation of the tubes with

the test specimen also showed that both options give similar results in terms of the extent

of damage and direction of material splaying, Figure 7-14(b).

The tiebreak options were further investigated in the simulations of the crushing

of the C-channel with a steeple trigger. In this case, the initial peak load was very similar

for both options, but the sustained crush load predicted by option 11 was approximately

30% of that predicted by option 8, Figure 7-15(a). Comparing the deformation of the

simulation results with the experiments (at ~25 mm of crush) showed that option 11

caused more buckling in the web than option 8, yielding a lower sustained crush load,

0

10

20

30

40

50

0 5 10 15 20 25

Load

(kN

)



0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


C Chamfer Test 1C Chamfer Test 2C Chamfer Test 3Simulation (Filtered - SAE 600Hz)

175

Figure 7-15(b). Based on these results, further investigation of option 11 is warranted at

the coupon level, i.e. correlating the simulation with experimental DCB and MMB tests.

Experiment

Option 8

Option 11

(a) (b)

Figure 7-14: Tiebreak investigation showing the comparison between: (a) the load-crosshead displacement

curves for the chamfered tube, and b) the final deformation of the tubes.

Experiment

Option 8

Option 11

(a) (b)

Figure 7-15: Tiebreak investigation showing the comparison between: (a) the load-crosshead displacement

curves for the steeple C-channel, and b) the deformation of the steeple C-channel at ~23 mm

of crush.

0

10

20

30

40

50

0 2 4 6 8 10 12

Load

(kN

)

Displacement (mm)

Option 8Option 11Experiment (Avg)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25

Load

(kN

)


Option 8Option 11

176

As noted earlier, option 11 was very sensitive to various damping coefficients and

it is not possible to parametrically analyze their effect at the structural level. This must be

performed at the coupon level which is beyond the scope of this study. Therefore,

tiebreak option 8 was selected for the remainder of this study as it yielded the most

accurate results.

iii) Material Models

A comparison the load-crosshead displacement curves obtained from the crushing

simulations of the chamfered tube using material models MAT54 and MAT58,

respectively, are shown in Figure 7-16(a). While the initial peaks loads predicted by both

models are almost identical and very similar to the experimental peak load, the sustained

crush load predicted by MAT58 model is approximately 35% less than that predicted by

MAT54 model. Comparing the deformation shows that both models correctly predict the

direction of splaying of each layer. However, more element deletions in the outer layer

were predicted by the MAT58 model as compared to the MAT54 model. In the inner two

layers, barely any element deletion was visible in the MAT58 model due to ERODS

being set to 100%. Hence, despite using a much higher failure strain for the inward-

folding plies, MAT58 model was not capable of simulating the accurate sustained crush

load. This could be due to the effective failure strain calculation that takes into account

all strain components. In the MAT54 model, elements were only allowed to fail in the

matrix direction, similar to what was observed in the experiments. Hence, a possible

improvement to the MAT58 model could be an option of allowing the user to specify a

separate failure strain in each direction. For the purpose of this study, the MAT54 model

was used for all simulations.

177

Experiment

MAT54

MAT58

(a) (b)

Figure 7-16: Material model investigation showing the comparison between: (a) the load-crosshead

displacement curves for the chamfered tube, and b) the final deformation of the tubes.


In this study, finite element models were developed using LS-DYNA to simulate

the crushing behavior of composite stanchions. Two approaches were employed to model

the crushing process, namely, a single-layer approach and a multi-layer approach. The

single-layer approach was able to accurately replicate the load-crosshead displacement

curve of the circular tube and the C-channel with a chamfer trigger. This approach

involved performing an extensive parametric study to obtain the values of certain

parameters required by material model 54 (MAT54) to correctly fit the simulation results

to the experimental load-crosshead displacement data. It was determined that two

parameters, DFAILC and SOFT, play a key role in predicting the initial peak load and

sustained crush load, respectively. An attempt was made to find a common set of

parameters that could be used across the different cross-sections. Results indicated,

0

10

20

30

40

50

0 5 10 15 20

Load

(kN

)

Displacement (mm)

MAT54MAT58Experiment (Avg)

178

however, that each cross-section requires a separate DFAILC and SOFT definition. This

method proved to be even less successful when applied to specimens with a steeple

trigger mechanism due to the lack of the chamfer row of elements to effectively use the

SOFT parameters. Not only the simulations of steeple specimens were mostly unstable

numerically, but also it was not possible to find a common set of parameters to use

between the different cross-sections.

For the multi-layer approach, a comprehensive investigation was performed to

determine the most accurate method to model the crushing behavior of the composite

members. This included determining the most efficient way of modeling the laminate and

its interfaces, and the most effective element size and formulation, contact definitions,

time-step control, and material model. It was determined, in order to maintain consistent

spacing between each layer, the laminate needed to be divided into an equal number of

plies per shell element layer. Fully-integrated, four-node elements were used to generate

the mesh, with a finer mesh required for curved surfaces (circular tube and corners of

open cross-sections) that the flat surfaces (web and flanges of open cross-sections). The

quasi-static experimental loading rate was modeled using a two-step function to ramp us

the loading rate while minimizing the dynamic effects. In order to simulate delamination,

two tiebreak options were investigated and it was determined that option 8 (a simple

bilinear traction-separation law) was capable of accurately simulating delamination using

an energy based approach. Finally, two material models were investigated (MAT54 and

MAT58) and it was determined that MAT54 provided the best results in terms of the

load-crosshead displacement and deformation. However, a parametric study needed to be

performed in order to obtain the values of the unknown parameters. It was determined

179

that DFAILM was the only parameter that needed to be adjusted in order to obtain good

correlation with the experimental results. A parametric study was performed to determine

an optimal set of input parameters for the circular tube and the C-channel. These

parameters were then used across the remaining case studies [79,80, Chapters 8 and 9].

Overall, the results obtained were highly satisfactory with the approach being able to

accurately replicate the crushing process observed in the experiments. In most cases, the

load-crosshead displacement curve and SEA was well predicted.

180

CHAPTER 8: FINITE ELEMENT MODELING OF THE CRUSHING

BEHAVIOR OF THIN-WALLED CFRP TUBES UNDER AXIAL

COMPRESSION

7

8.1. ABSTRACT

Finite element models were developed using LS-DYNA to simulate the crushing

processes of graphite/epoxy laminated circular tubes having either a chamfered end or a

chamfered end with a crush cap failure trigger mechanisms. Laminated tubes were

modeled by using multiple layers of shell elements with tiebreak contact definitions

between layers. Each layer contained multiple plies. Delamination was simulated by

failure of the tiebreaks, which was determined using an energy-based approach. Material

model 54 (MAT54) in LS-DYNA was used to define the material ply properties. Results

were compared with experiments in terms of the load-displacement curve, specific energy

absorption (SEA), failure process, and surface strain distribution. The multi-layer

approach was capable of accurately predicting the sustained crush load, SEA, damage

initiation, and provided a good depiction of the failure process.

8.2. INTRODUCTION

Crashworthiness of aircraft and rotorcraft has been identified as a key area of

focus to improve occupant survivability in the event of a crash [1]. The subfloor structure

is a critical component in protecting the occupants against sudden deceleration by

dissipating energy during the impact event. Several studies have been performed over the

7 Siromani, D., Awerbuch, J. and Tan, T., “Finite Element Modeling of the Crushing Behavior of Thin-

Walled CFRP Tubes under Axial Compression,” Submitted to: Composites Part B: Engineering.

181

past three decades to investigate the dynamic response of aircraft structures and the

survivability of occupants subjected to severe but survivable impact conditions. Results

of these studies showed the need for energy absorbing devices, integrated with the

subfloor structure, to mitigate the impact energy. Composite materials are considered as

possible candidates for such integrated energy absorbing devices due to their high

strength-to-weight ratio and their high specific energy absorption (SEA) capacity, e.g.

[24-28], resulting from their particular failure characteristics during the crushing process.

The maximum crush load and SEA depend greatly on the selected cross-sections, wall

thickness-to-diameter ratio, constituents, laminate configuration, end constraints, and the

failure trigger mechanisms employed.


characteristics of carbon fiber-reinforced polymer (CFRP) composite tubes subjected to

axial compressive (crush) loads [81, Chapter 5]. Tubes of circular cross sections with

three types of failure triggering mechanisms, (i.e., a chamfered end, a flat end attached to

a crush cap, or a combined chamfered end and crush cap) to initiate progressive failure,

were investigated to identify the optimal configuration that would result in the lowest

initial peak load while providing the highest possible SEA. It was shown in [81, Chapter

5] that a combined chamfered end with an inward-folding crush cap yielded the highest

SEA with a moderate initial peak load.

Due to the high cost of conducting experimental studies, there is a need for

reliable computational models capable of predicting the crushing response of composite

members. There have been several attempts to develop explicit finite element models,

with varying degrees of success, for circular tubes [57-60], square tubes [59-63], C-

182

channels [61,62], angle-stiffeners [61,62], and hat-stiffeners [67]. The composite

structures can be modeled using either solid or shell elements. In general, shell element

models require less computation time and are more widely used to model the axial

crushing of composite members. The laminate can be modeled using either a single layer

or multiple layers of shell elements. In the ‘single-layer’ model the laminate is modeled

by using a single layer of shell elements, with each ply being represented by an

integration point in the thickness direction, as was done for C-channels, angle-stiffeners,

and hollow square tubes in [61,62]. In the ‘multi-layer’ model, the laminate is modeled

by using multiple layers of shell elements, each layer may represent either a single ply or

a group of plies, and the layers are ‘tied’ together using a tiebreak contact definition.

The single-layer modeling approach has been used in a number of recent studies,

to simulate the crushing behavior of various composite members. For example, in the

case of thin-walled square tubes, this approach was capable of accurately capturing the

local wall buckling and unstable collapse; however, it could not depict the progressive

failure process [58]. By carefully adjusting the values of key material and numerical

parameters in the material model (e.g., eleven parameters in MAT 54), and the contact

definition between the end of the test specimen and the loading fixture, the single-layer

model was able to yield good correlation with experimental load-displacement curves for

the cross-sections studied in [61,62]. However, the single-layer representation is not

appropriate for describing the failure and crush behavior. The utility of the single-layer

model is further discussed in [90,Chapter 7].

The multi-layer modeling approach, on the other hand, can better capture the

failure process for tubes undergoing progressive crushing e.g., [57-60]. However, this

183

approach has not always yielded good correlation with the experimental load-

displacement curves. The crush behavior of a hollow tube was simulated in [57] using

LS-DYNA with MAT 54. The simulation results agreed quite well with the experimental

load-displacement curves, but showed significant local buckling of the tube, instead of

brittle failure that was observed in the experiments. A simulation of progressive crushing

of a thin-walled square CFRP tube was performed in [58]. The finite element model was

able to accurately predict the peak load, but the overall SEA was underestimated by 33%.

In the experiment debris wedged between the fronds of the tube’s wall contributed to

energy absorption while in simulations, instead of forming debris, the crushed elements

were deleted and did not contribute to energy absorption. In [59,60] the simulations of the

crushing behavior of hollow circular and square tubes were conducted and compared with

experimental observations. It was shown that the model was not able to reproduce the

axial matrix splits observed experimentally. As a result, the simulation did not agree well

with the experimental load-displacement curves, deformation, and failure behavior. To

overcome the modeling deficiency, pre-defined seams were introduced along the element

edges in the axial direction of the tubes to simulate the propagation of axial cracks, which

yielded better agreement.

The primary focus of this study is to use the multi-layer modelling methodology

developed in [90, Chapter 7] to simulate the crushing behavior of CFRP circular tubes

having two different failure trigger mechanism. The experimental work, reported in [81,

Chapter 5], is briefly summarized first, followed by a description of the finite element

models and the results of the numerical simulations.

184

8.3. SUMMARY OF EXPERIMENTAL WORK

8.3.1. TEST SETUP AND PROCEDURE

Circular tube specimens, made of Hexcel IM7/8552, were tested in [81, Chapter

5] to investigate the effectiveness of various failure triggering mechanisms, including

chamfered ends (Figure 5-1a), inward-folding crush caps (Figure 5-1b), outward splaying

crush caps (Figure 5-1c), and a combined chamfered end and inward-folding crash cap,

on increasing the SEA and reducing the initial peak crush load. The effect of corner

radius of the crush cap on the peak load and SEA was further investigated to determine

the optimal crush cap configuration. The experimental results obtained with a [+15/-

15/+15/03/-15/+15/-15] laminate, are used in this numerical study. The specimens were

101.6 mm long with an outer diameter of 32.3 mm and wall thickness of 1.47 mm. Two

failure triggering mechanisms have been modeled: i) a 45° chamfered end tube, Figure

5-1a; and ii) a chamfered end tube with an attached inward-folding crush cap having a

1.58 mm corner radius, Figure 5-1b [81, Chapter 5]. The latter was found to yield the

best results among all cases studied in [81, Chapter 5].



50.8 mm, which provided sufficient crush data to calculate the SEA. The full-field

deformation and strain on the surfaces of selected specimens were also recorded using a

Digital Image Correlation (DIC) system.

8.3.2. EXPERIMENTAL RESULTS

Test results showed that the chamfer was very effective at reducing the initial

peak load; while the inward-folding crush-cap was most effective at increasing the

185

sustained crush load and SEA. Further, combining an edge chamfered tube with an

inward-folding crush-cap (‘combined’ failure trigger) yielded the highest SEA with a low

initial crush load. Figure 8-2 shows the average load-crosshead displacement curves and

SEA of tubes with the chamfered end and the combined failure trigger mechanisms.

Additional results and discussion are provided in [81, Chapter 5].

(a) (b) (c)

Figure 8-1: Failure trigger mechanisms: (a) a chamfered end, (b) an inward-folding crush cap, and (c) an

outward-splaying crush cap.

(a) (b)

Figure 8-2: (a) Experimental load-crosshead displacement curves, and (b) SEA of tubes having a chamfer

and combined failure triggers. The combined failure trigger yielded a higher peak load,

sustained crush load and SEA.

0

10

20

30

40

50

0 10 20 30 40 50

Load

(kN

)


Chamfer-endCombined

0

50

100

150

SEA

SEA

(kJ

/kg)

Chamfer-endCombined

186

8.4. NUMERICAL SIMULATIONS

LS-DYNA finite element code was used in this study. Four-node, fully integrated,

shell elements (Type 16) were used to model the tubes. A multi-layer approach,

developed in [90, Chapter 7], was used to model the specimens and MAT54 material

model was used to simulate the crushing behavior of composite tubes under axial

compressive load.

8.4.1. MODEL SETUP

In the multi-layer approach the laminate is divided into multiple layers of shell

elements, each layer consists of either a single ply or multiple plies, and layers are tied

together using a tiebreak contact definition. To improve the computational efficiency, the

laminate ([+15/-15/+15/03/-15/+15/-15]) was modeled as three layers of shell elements,

with the inner [+15/-15/+15] plies, the middle [03] plies, and the outer [-15/+15/-15] plies

represented by the inner, middle, and outer layers, respectively. The diameters of the

mid-planes of the inner, middle, and outer layers were 29.8 mm, 30.8 mm and 31.8 mm,

respectively. Each layer of elements was assigned three through-thickness integration

points corresponding to the three plies represented by that layer. An element size of 0.635

x 0.635 mm was used, resulting in the model having approximately 77,000 elements. The

resulting computation time for these models was approximately 30 hours on a cluster

with 24 cores.

The chamfer was modeled by staggering the length of each shell layer such that

the inner layer’s first row of elements represented the start of the chamfer, and the outer

layer’s first row of elements represented its end, Figure 8-3(a). The steel crush caps were

187

modeled using rigid shell elements, Figure 8-3(b). The inner corner radius of the crush

cap was 1.58 mm.

Figure 8-3: Representations of the failure trigger mechanisms in the finite element models. The

chamfered end of the tube was modeled by staggering element layers while the crush cap was

modeled using rigid shell elements.


The shell element layers were tied to each other using a tiebreak contact definition

(contact one way surface to surface tiebreak) with option 8 in LS-DYNA [73]. This

tiebreak formulation allowed for simulating delamination at the interface between shell

element layers. Damage initiates when the stresses on the interface satisfy the failure

criterion [73]:

(| |

)

(| |

)

(1)

in which and are the normal and shear stresses acting on the interface, and






(2)

188

where:

√ ( ) | | (3)

and is the energy released due to the failure of the interface. A sensitivity

study was conducted and it was determined that for simulating the crushing of composite

tubes, Mode II fracture was the dominant mode of failure during the tie-break failure

process. Thus, to simplify the simulations, a pure Mode II delamination was assumed.

Consequently, and , and the critical distance for failure is given by:

(4)


was obtained from [87] for IM7/8552, as shown in Table 8-1. A further investigation

showed that any lower values will cause the ties to break prematurely, yielding high

rate of delamination progression.



methodologies discussed in [88] were adopted. While these methodologies were intended

for use with cohesive zone models, they can be applied to the tiebreak formulation used

here as well since the tiebreaks follow a traction-separation law similar to that used in

cohesive zone formulations. The proposed solution involves lowering the interlaminar

strengths whilst keeping the fracture toughness constant in order to adapt the length of the

cohesive zone for a given mesh size. The required interfacial strength can be

calculated as [88]:

189

√

(5)




elements needed in the cohesive zone has not been well established. Various studies have

used anywhere from two elements to 10 elements [88]. In this study, the results of a

sensitivity study concluded that five elements were sufficient to simulate the propagation

of delamination. Hence, with , equation (5) was used to solve for the new NFLS

and SFLS values. The new SFLS was substituted into equation (4) to calculate the CCRIT

value.

Since the 9-ply laminate of the tube was modeled as three layers of shell elements

with each layer representing three plies, the tiebreak contact was defined only between

these shell layers, rather than between individual plies. However, in reality, delamination

could occur along any, if not all, ply interfaces during specimen crushing, as was

observed experimentally [81, Chapter 5]. In order to account for the energy dissipated by

these additional delamination interfaces, CCRIT was scaled by the ratio of the number of

ply interfaces to the number of tiebreak interfaces , defined as:

(6)

That is, it is assumed (based on the experimental observations discussed in [81,

Chapter 5]) that delamination occurred among all nine plies.

190

The values used and calculated in equations (4), (5) and (6) are given in Table

8-1. They were used to simulate the crushing of the tube with the chamfered and the

combined failure trigger mechanisms.

Table 8-1: Material properties for IM7/8552

9.08 GPa 0.2 kJ/m2 1.33 kJ/m

2 5 0.635 mm 22.5 MPa 57.3 MPa 0.046 mm 0.185 mm


Both the loading platen and the base of the testing machine were modeled as rigid

surfaces. The tubes were placed standing upright between the loading platen and the

base. The interaction between the loading platen and the tube was modeled using a

surface-to-surface contact definition (contact automatic surface to surface), and the

contact between the base and the tube was defined using rigidwall_planar, which does

not allow node penetration. For the simulation of the chamfered tube with a crush cap,

the crush cap was assumed to be rigid and was defined using the same surface-to-surface

contact definition as the platen-tube contact.

The tiebreak contact definition between the shell layers not only facilitates the

simulation of delamination, but also prevents layers from penetrating each other after the

tiebreak has failed, as the contact definition would remain in effect. It should be noted

that since the crush cap forces the layers to deform inwards, the inner layer would

eventually come in contact with itself, i.e., with the inner wall of tube. Therefore, a single

surface contact definition (contact automatic single surface) was added to the inner shell

elements to prevent any self-penetration.

191




Chang failure criterion [73] to determine failure of each ply (associated with an

integration point). This model allows the user to define a local material coordinate system

to specify the orientation of each ply. There are 21 parameters in MAT54 that need to be

specified, 15 of which are physically based and six are numerical parameters [73]. Out of

the 15 physical parameters, 10 parameters are material constants that were obtained from

[83] and [84], as shown in Table 8-2.


E1 E2 G12/13 G23 ν12

171.42 GPa 9.08 GPa 5.29 GPa 3.92 GPa 0.32

XT XC YT YC SL


The remaining five failure parameters are the tensile and compressive failure

strains in the fiber direction, the matrix and shear failure strains, and the effective failure

strain. The six numerical parameters were either estimated or set to their default values,

depending on the behavior required of the material model. A parametric study was

conducted to determine the optimal values of the unknown parameters. It was found that

the only MAT54 parameter that needed to be adjusted was DFAILM, which is the failure

strain in the matrix direction [90, Chapter 7]. Adjusting the value of DFAILM enabled

matrix splitting to occur, as observed in the experiments. DFAILM values ranging from

5% to 30% were analyzed and it was determined that, for the chamfered tube, a value of

192

10% strain yielded the most accurate representation of the crushing process. For the

combined failure trigger mechanism case there was no need for element deletion, hence

DFAILM was set to the default value which disabled the element deletion feature.


8.5.1. DEFORMATION

The simulations of the crushing behaviors of circular tubes with a chamfered-end

show that the modeling approach described above provided a good depiction of the

failure process. Figure 8-4(a) compares the experimental and simulated crushed end of

the chamfered tube at the completion of chamfer crushing. The simulation predicts that

the outer layer of shell elements (three plies) splayed outwards, while the other two shell

element layers (six plies) folded inwards. This result is very similar to that observed in

the experiments, where two plies splayed outwards and seven folded inwards [81,

Chapter 5]. The difference is attributed to the particular grouping of three plies per shell

layer selected for this simulation.

The number of matrix splits predicted in the simulation is significantly smaller

than the actual number of cracks formed during the crushing process, Figure 8-4(b) to

Figure 8-4(d). While the simulation predicts some 12 matrix splits in the outer layer,

approximately 40 cracks - in the form of matrix splits progressing along the fiber

direction - were observed in experiment. Further, the simulation predicts that the matrix

splits occur through the entire thickness of the outer layer (three plies), while in

experiment matrix splits occurred, randomly and separately, across individual plies or ply

groups. These matrix splits generated 1.0-4.0 mm wide CFRP segments of single plies or

ply groups, which splay and extend progressively along the surface of the testing platen

193

with increasing crushing distance. The smaller number of matrix splits predicted by the

simulation is not sufficient to cause the formation of the numerous narrow ply/ply-group

segments. As a result, the outer three-ply segments are prevented from splaying outward

freely in the simulation. Instead, they fold upwards and slide along the outer tube wall,

progressively throughout the crushing distance of the tube. Furthermore, as the fibers in

the outer plies aligned in the +15° and -15° direction, the matrix splits extend, during the

continuous crosshead displacement, along the fibers directions and the ply/ply-group

segments tend to be displaced sideways, rendering a general appearance of twisting of the

tube, Figure 8-4(d) and Figure 4(e). The simulation also captured the twisting phenomena

in the outer three-ply layer, but not as extensively as observed experimentally. The

majority of the crushed material was folded inward, packed, crushed, and compressed

into the interior of the tube, Figure 8-4(e). It is noted here that during unloading, the two

outward splayed plies straightened (clearly showing the ply/ply-group segments). In

simulations the unloading process was not performed.

It should be noted that matrix splitting, which in the current model is represented

by element deletion, could be better simulated by using a significantly finer mesh with

corresponding change in failure strain, by having the elements within each layer split

along their edges, etc. Further, the twisting of the ply/ply-group segments during the

outward splaying could be more accurately predicted if the mesh was aligned with the

fiber direction; this would require each ply to be modeled as a separate shell element

layer. Therefore, this model cannot predict matrix splitting per se, but the occurrence of

axial cracks in the tube’s wall. The added computational cost incurred by employing any

194

of these possible approaches, however, would have been prohibitively high for

accomplishing such a level of accuracy and details.

For the case of combined failure trigger mechanism, the chamfered end of the

tube was attached to a rigid inward-folding crush cap, which forces the material to be

packed into the core of the tube. Figure 8-5 shows a comparison of the deformations

obtained from experiment and simulation. It can be seen that the simulation replicated the

crushed end quite accurately by forcing all plies to fold inward and pack into interior of

the tube.

Experiment Simulation Experiment Simulation

(a) After chamfer has crushed (d) 40 mm of crushing

(b) 5 mm of crushing

(c) 20 mm of crushing (e) Final deformation

Figure 8-4: Comparison of the experimental and simulated deformation of the tube with a chamfered

trigger mechanism at various loading stages.

195

Experiment Simulation

Final deformation

Figure 8-5: A comparison of the experimental and simulated deformation of a tube with a combined

chamfer and inward-folding crush cap trigger mechanism.

8.5.2. LOAD-CROSSHEAD DISPLACEMENT BEHAVIOR

Figure 8-6 shows the simulated load-crosshead displacement curves of a

chamfered tube, showing both the unfiltered (dotted line) results and the filtered (solid

line) results using SAE 300 Hz filter. The unfiltered plot shows three load spikes,

occurring within the first 2 mm of the crosshead displacement. These three load spikes

correspond to the crushing of the three shell element layers in the chamfered region. It is

noted that by modeling each individual ply as a separate shell element layer, (hence with

a much higher computational cost), the number of load spikes would increase to nine and

the magnitude of each spike would reduce significantly, rendering a much smoother load-

displacement curve. With the current three-layer model, the curve could be smoothed

using various data filtering schemes. Clearly, the ‘smoothness’ of the curve depends on

the degree of data filtering, noting that excessive filtering will reduce the utility of the

results. Applying a range of filters, between SAE 180 Hz to SAE 1,000 Hz, indicated

that SAE 300 Hz filter provided the best continuous initial load-displacement behavior

that also compared well with the experimental data, Figure 8-7. It should be noted that

this filtering process did not affect the average sustained crush load and the overall SEA,

196

Figure 8-7, as these values correlated very well with the experimental results regardless

of the filter applied. All simulation results presented herein are smoothed using the SAE

300 Hz filter.

Figure 8-6: A comparison of the unfiltered and filtered load-crosshead displacement curves from a multi-

layer simulation for a tube with a chamfer failure trigger.

Figure 8-7: Load-crosshead displacement comparison between experiment and simulation for specimens

with a chamfer trigger mechanism.

Simulation results for the tube with the combined failure trigger mechanism are

shown in Figure 8-8, together with experimental data from three tests, showing very good

agreement. The simulation, however, predicts a slightly earlier initial peak load, with a

higher value (by approximately 20%) compared to three test results.

0

10

20

30

40

50

0 5 10 15 20

Load

(kN

)



0

10

20

30

40

50

0 5 10 15 20 25

Load

(kN

)


Chamfer tube test 1Chamfer tube test 2Chamfer tube test 3Simulation filtered (SAE 300Hz)

197

Figure 8-8: Load-crosshead displacement comparison between experiment and simulation for specimens

with a combined chamfer and inward-folding crush cap trigger mechanism.

Comparing simulations with experiments in terms of peak loads, sustained crush

loads, and SEA show good correlation, with the simulation predicting 8% - 20% higher

peak load and essentially identical crush load and SEA (Figure 8-9).

(a)

(b)

Figure 8-9: Comparison of simulated and experimental (a) peak loads and sustained crush loads, and (b)

SEA for the tubes with a chamfer trigger mechanism and a combined trigger mechanism.

0

10

20

30

40

50

0 5 10 15 20 25Lo

ad (

kN)


Tube Combined Test 1Tube Combined Test 2Tube Combined Test 3Simulation (Filtered - SAE 300Hz)

0

10

20

30

40

50

PEAK LOAD CRUSH LOAD

Load

(kN

)

Chamfer - ExperimentChamfer - SimulationCombined - ExperimentCombined - Simulation

0

20

40

60

80

100

120

140

160

180

SEA

SEA

(kJ

/kg)

Chamfer - ExperimentChamfer - SimulationCombined - ExperimentCombined - Simulation

198


The finite element model was further validated by comparing the resulting strain

distribution in the chamfered tubes with the experimental measurements obtained from

the high-speed Digital Image Correlation (DIC) system [81, Chapter 5]. Figure 8-10

shows a comparison of the hoop strain distributions for a chamfered tube at four selected

loading stages prior to reaching the initial peak load. That is, these DIC images show the

strain field in the bottom 20 mm section of the tube, during the crushing of the chamfer.

For clarity, it should be noted that the bottom of each DIC image coincides with the top

of the chamfered region, (i.e., the chamfered region is the dark region beneath the DIC

image). Several “hot spots,” representing areas of high hoop tensile strain, initiated at the

top of chamfered region, and propagate upwards along the tube wall with increasing load.

It should be noted that these ‘hot spots’ initiated prior to the completion of chamfer

crushing and initiated at approximately 18.5 kN, i.e., at 71% of the peak load of 25.8 kN.

The predicted locations and strain magnitudes of these hot spots correlated well with the

DIC results. The axial extension of these hot spots eventually became matrix splits. Thus,

the finite element model is capable of accurately predicting the initiation of such matrix

cracks (or matrix splits). A further development of the model discussed earlier, such as

adding an element splitting capability, would allow a more accurate simulation of

progressive matrix cracking.

199

Sim

ula

tio

n

Ex

per

imen

t

Load (kN): 18.5 19.3 21.1 23.7

Figure 8-10: Comparison of simulated and experimental (DIC) local hoop strain fields on a tube with a

chamfer trigger mechanism.


Two finite element models were developed using LS-DYNA to simulate the

crushing behavior of composite tubes with chamfer and combined failure trigger

mechanisms. A multi-layer shell element approach was used to model the deformation

and damage progression of the composite tubes. Each layer of shell element could

contain either a single ply or multiple plies. Layers were tied together using tiebreak

contact definitions. Delamination between layers was simulated by tiebreak failure,

which was determined using an energy based approach. Material model 54 (MAT54) was

used to represent each ply, and it was found that only the matrix failure strain, DFAILM,

needed to be adjusted in order to obtain good correlations with the experimental results.

Simulation results showed, for both the chamfer and combined failure trigger cases, that

the failure processes, strain fields, peak load, sustained crush loads, and SEAs all

compared very well with the experimental results. The correlation of the peak load

depends, of course, on the filters used. The chamfered region would have to be modeled

200

in greater detail (e.g., modeling each ply separately) than the current approximation in

order to achieve better results. In both cases, filtering the simulation data, using SAE 300

Hz filter, resulted in a better agreement of the initial peak load with the experimental

data, without affecting the sustained crush load. Finally, the modeling methodology

developed in this study has been shown to be capable of capturing quite accurately the

overall crushing behavior of the tubes under axial compressive loading. The extensive

matrix cracking observed experimentally could be better simulated by using a

significantly finer mesh with a corresponding change in failure strain, or by allowing

node splitting in the axial direction. Further, aligning the mesh with the lamina direction

could result in a better representation of the matrix cracking, resulting in a more accurate

deformation and crushing process. This will require modeling each ply as an individual

layer. All these, and other, approaches would add significant computational cost.

201

CHAPTER 9: FINITE ELEMENT MODELING OF THE CRUSHING

BEHAVIOR OF THIN-WALLED OPEN CROSS-SECTION CFRP MEMBERS

UNDER AXIAL COMPRESSION

8

9.1. ABSTRACT


process of graphite/epoxy members with thin-walled open cross-sections having either a

chamfer or a steeple failure trigger mechanisms. The cross-sections studied included C-

channels, angle-stiffeners, and hat-stiffeners. The specimens were modeled by using

multiple layers of shell elements with tiebreak contact definitions between layers. Each

layer contained multiple plies. Delamination was simulated by failure of the tiebreaks,

which was determined using the interlaminar fracture toughness values. Material model

54 (MAT54) in LS-DYNA was used to define the material ply properties. Results were

compared with experiments in terms of the load-displacement curve, specific energy

absorption (SEA), failure process, and surface strain distribution. The multi-layer

approach was capable of accurately predicting the sustained crush load, SEA, and

damage initiation, and provided a good depiction of the failure process.

9.2. INTRODUCTION

Crashworthiness of aircraft and rotorcraft has been identified as a key area of

focus to improve occupant survivability in the event of a crash [1]. The subfloor structure

is a critical component in protecting the occupants against sudden deceleration by

8 Siromani, D., Awerbuch, J., Tan, T.-M., “Finite Element Modeling of the Crushing Behavior of Thin-

Walled Open Cross-Section CFRP Members under Axial Compression,” Submitted to: Journal of

Reinforced Plastics and Composites.

202

dissipating energy during the impact event. Several studies have been performed over the

past three decades to investigate the dynamic response of aircraft structures and the

survivability of occupants subjected to severe but survivable impact conditions. Results

of these studies showed the need for energy absorbing devices, integrated with the

subfloor structure, to mitigate the impact energy. Composite materials are considered as

possible candidates for such integrated energy absorbing devices due to their high

strength-to-weight ratio and their high specific energy absorption (SEA) capacity, e.g.

[24-28], resulting from their particular failure characteristics during the crushing process.

The maximum crush load and SEA depend greatly on the selected cross-sections, wall

thickness-to-diameter ratio, constituents, laminate configuration, end constraints, and the

failure trigger mechanism employed.


capacity and failure characteristics of open thin-walled graphite/epoxy members (C-

channels, right angle-stiffeners, and hat-stiffeners) under quasi-static axial compression

[82, Chapter 6]. The effect of two failure trigger mechanisms (chamfers and steeples) on

initial peak loads, crush loads, and failure progression and crushing was studied. Results

showed that the steeple trigger is more effective than the C-channel and hat-stiffeners in

reducing the initial peak loads, while the chamfer trigger yields a lower initial peak load

for the angle-stiffener as compared with the other two cross-sections. The angle- and hat-

stiffeners absorb similarly high specific energy absorption (SEA) while the C-channels

absorb the least.

Due to the relatively high cost of conducting repeated experimental studies (with

different materials and component geometries) and the need to have a design tool to

203

construct the optimal energy absorption sub-structures, there is a need for reliable

computational models capable of predicting the crushing response of such composite

members. There have been several attempts to develop explicit finite element models

with varying degrees of success for circular tubes [57-60], hollow square tubes [59-63],

C-channels [61,62], angle-stiffeners [61,62], and hat-stiffeners [67]. The composite

structures can be modeled using either solid or shell elements. It has been well-

established that shell element models require less computation time and are more widely

used to model the axial crushing of composite members. The laminate can be modeled

using either a single layer or multiple layers of shell elements. In the ‘single-layer’

model the laminate is modeled by using a single layer of shell elements, with each ply

being represented by an integration point in the thickness direction. In the ‘multi-layer’

model, the laminate is modeled as multiple layers of shell elements, each layer may

represent either a single ply or a group of plies, and the layers are tied together using a

tiebreak contact definition.

The single-layer modeling approach has been used in a number of recent studies

to simulate the crushing behavior of various composite members. For example, in

studying the crushing of thin-walled square tubes [58], it was shown that the single-layer

approach was capable of accurately capturing the local wall buckling and unstable

collapse. However, the approach could not depict the progressive failure process. By

carefully adjusting the values of key material and numerical parameters in the material

model (e.g., the eleven parameters in MAT 54) and the contact characteristic between the

end of the test specimen and the loading fixture, the single-layer model was able to yield

good correlation with experimental load-displacement curves for the cross-sections

204

studied in [61,62]. However, the single-layer representation is not appropriate for

describing the failure and crush behavior. The utility of the single-layer model is further

discussed in [90,Chapter 7].

The multi-layer modeling approach, on the other hand, is capable of

approximately capturing the failure process for tubes undergoing progressive crushing

e.g., [57-60]. However, this approach has not always yielded good correlation with the

experimental load-displacement curves. The crush behavior of a hollow tube was

simulated in [57] using LS-DYNA with MAT 54. A good agreement with the

experimental load-displacement was achieved, but the simulation showed significant

local buckling of the tube, rather than the brittle failure observed experimentally. A

simulation of progressive crushing of a thin-walled square CFRP tube was performed in

[58]. The multi-layer finite element model was able to accurately predict the peak load,

but the overall SEA was underestimated by 33%. The difference in SEA was attributed to

the model’s inability to reproduce the formation of debris wedged between the fronds of

the tube’s wall due to excessive element deletion. In [59,60], the simulations of the

crushing behavior of hollow circular and square tubes were performed using the multi-

layer approach; results did not agree well with the experimental load-displacement

curves, deformation, and failure behavior due to the model’s inability to reproduce the

axial matrix cracks observed experimentally. To overcome the modeling deficiency, pre-

defined seams along the element edges in the axial direction of the tubes were introduced

to simulate the propagation of axial cracks, which yielded better agreement. A continuum

damage mechanics model (CODAM) was used in [64], with multiple layers of shell

elements and a tiebreak contact definition to capture delamination. A “debris wedge”

205

model formed between the delaminated surfaces of neighboring plies during the crushing

process was incorporated to improve the accuracy of the simulation. While this approach

can induce ply splaying in the experimentally-observed direction, it may not be generally

applicable to cases with different failure processes. Further, it was noted in [66] that some

of material parameters in the CODAM model require extensive characterization

processes, which are not readily available. As a result, these parameters have to be

obtained by correlating simulation with experiments. A simulation of the crushing of a

hat-stiffener was performed using multi-layer approach in [67]. It was found that

increasing Mode I and Mode II energy release rates for the cohesive interface yielded

better correlation with experimental results than those obtained by using the conventional

energy release rates.

The primary focus of this study is to adapt the multi-layer finite element modeling

methodology that was developed in [90, Chapter 7] to simulate the crushing behavior of

the thin-wall open cross-section members. The experimental work, reported in [82,

Chapter 6], is briefly summarized first, followed by a description of the finite element

models, the results of the numerical simulations, and comparison with experiments.

9.3. SUMMARY OF EXPERIMENTAL WORK

9.3.1. TEST SETUP AND PROCEDURE

Three thin-walled open cross-sectional geometries (C-channel, angle-stiffener,

and hat-shaped stiffener) fabricated from Hexcel IM7/8552, were tested in [82, Chapter

6] to investigate the effectiveness of two failure triggering mechanisms, chamfered-ends

and steeples (Figure 9-1), on increasing the SEA and reducing the initial peak load and

crush load. To ensure stability during the compressive loading, the specimens were

206

supported by a 25.4 mm (1.0 in.) thick potted base. Laminate lay-up sequences and

specimen dimensions are listed in Table 9-1 and shown in Figure 9-2. The cross-

sectional areas were the same for all cross-sections. As a result, the wall thickness of the

angle-stiffener was twice the thickness (i.e., twice number of plies) of the other two

cross-sections, Table 9-1.

Figure 9-1: Open-cross-sections with two failure trigger mechanisms (chamfers and steeples), all having

the same cross-sectional area and attached to a potted base to ensure stability during the 50.8

mm crush displacement.

Table 9-1: Specimen Configuration.

Cross

Section Geometry Lay-up

Cross-sectional

area

mm2 (in

2)

Length

mm (in)

Wall

thickness

mm (in)

1 C-channel [02/+45/-45/02/-

45/+45/02] 180 (0.28)

101.6

(4) 1.52 (0.06)

2 Angle-Stiffener [02/+45/-45/02/-

45/+45/02]s 180 (0.28)

101.6

(4) 3.04 (0.12)

3 Hat-Stiffener [02/+45/-45/02/-

45/+45/02] 180 (0.28)

101.6

(4) 1.52 (0.06)

207

Figure 9-2: Test specimens cross-sectional dimension (all dimensions in mm)



50.8 mm, which provided sufficient crush data to calculate the SEA. The failure process

was recorded with still and video cameras and the full-field deformation and strain on the

surfaces of all specimens were recorded using a Digital Image Correlation (DIC) system.

9.3.2. EXPERIMENTAL RESULTS

The test results showed that the steeple trigger is more effective at reducing the

initial peak loads of the C-channel and hat-stiffeners, while the chamfer trigger yields a

lower initial peak load for the angle-stiffener. The angle- and hat-stiffeners absorb

similarly high specific energy absorption (SEA) while the C-channels absorb the least.

Figure 9-3 shows the average (of three test results) load-crosshead displacement curves

recorded for the three cross sections and two failure triggers. The corresponding

quantitative data on the initial peak load, the sustained crush load, and SEA are shown in

Figure 9-4. Additional results and discussion are provided in [82, Chapter 6].

208

Figure 9-3: A comparison of load-crosshead displacement curves for each cross-section having a: (a)

chamfer trigger, and (b) steeple trigger. Each curve represents the average of three tests

(except for the angle-stiffener with a chamfer trigger which represents the average of two

tests).

Figure 9-4: A comparison of: (a) initial peak load and crush load; and (b) SEA, for each cross-section

having a chamfer and steeple failure triggers (numbers indicate average of three specimens

except for the angle stiffener with a chamfer trigger which represents the average of two

tests).

9.4. NUMERICAL SIMULATIONS

LS-DYNA finite element models were developed to simulate the crushing

behaviors of the open cross-section specimens. Specimens were modeled using four-

node, fully integrated, shell elements (Type 16) and the crushing behavior of the

composite members under axial compressive loads was modeled using MAT54.

209

9.4.1. MODEL SETUP

In the multi-layer approach, the laminate is divided into multiple layers of shell

elements, where each layer consists of either a single ply or multiple plies, and layers are

tied together using a tiebreak contact definition. To improve the computational

efficiency, the C-channel and hat-stiffener specimens made of [02/+45/-45/02/-45/+45/02]

laminate were modeled by five layers of shell elements with each layer representing two

plies (i.e., layer 1: [02], layer 2: [+45/-45], layer 3: [02], layer 4: [-45/+45], and layer 5:

[02]). The angle-stiffener specimen, which is twice as thick and made of the [02/+45/-

45/02/-45/+45/02]s laminate, was modeled by 10 layers od shell elements. Each layer of

elements was assigned two through-thickness integration points corresponding to the two

plies represented by that layer. An element size of 1.27 x 1.27 mm was used for the flat

sections in the models (i.e., web and flanges). For curved sections (i.e., the corners of the

specimens), a refined element size of 0.635 x 0.635 mm was used for a more accurate

simulation of the damage progression in these regions. For all specimens the total number

of elements was approximately 55,000. The computation time needed to simulate the

entire crushing process, up to 50.8 mm of maximum crosshead displacement, was

approximately 30 hours on a cluster with 24 cores.

The 45° chamfer was modeled by staggering the length of each shell layer such

that the inner layer’s first row of elements represented the start of the chamfer and the

outer layer represented the end of the chamfer, Figure 9-5(a). The steeple trigger was

modeled by making two 15° cuts to the top of the model, Figure 9-5(b).

210

(a)

(b)

Figure 9-5: Representations of the C-Channel cross-section having: (a) chamfer and (b) steeple failure

trigger mechanisms in the finite element models.


The shell element layers were tied to each other using a tiebreak contact definition

(contact one way surface to surface tiebreak) with option 8 in LS-DYNA [73]. This

tiebreak formulation allowed for simulating delamination at the interface between shell

element layers. Damage initiates when the stresses on the interface satisfied the failure

criterion [73]:

(| |

)

(| |

)

(1)

in which and are the normal and shear stresses acting at the interface, and






(2)

211

where:

√ ( ) | | (3)

and is the energy released due to the failure of the interface. A sensitivity

study conducted previously [90, Chapter 7] on simulating the crushing of circular

composite tubes showed that Mode II fracture was the dominant mode of failure during

the tie-break failure process. To simplify the simulations, the same approach was adopted

in this study. Consequently, and , and the critical distance to failure is

given by:

(4)


was obtained from [87] for IM7/8552, as shown in Table 9-2. An investigation performed

in [90, Chapter 7] showed that any lower values would cause the ties to break

prematurely, yielding a high rate of delamination progression.



methodologies discussed in [88] were adopted. The proposed solution involves lowering

the interlaminar strengths whilst keeping the fracture toughness constant in order to adapt

the length of the cohesive zone for a given mesh size. While this approach was intended

for use with cohesive zone models, it can also be applied to the tiebreak formulation used

here since the tiebreaks follow a traction-separation law similar to that used in cohesive

zone formulations. The required interfacial strength can be calculated from [88]:

212

√

(5)




elements needed in the cohesive zone has not been well established. Various studies have

used anywhere from two elements to 10 elements [88]. Although no cohesive elements

are required for the tiebreak formulation applied herein, the same concept used for

cohesive elements has been applied to the tiebreaks. A separate sensitivity study

concluded that five elements were sufficient to simulate the propagation of delamination.

Hence, with , Equation (5) was used to solve for the new NFLS and SFLS values.

The new SFLS was substituted into equation (4) to calculate the CCRIT value.

Since the laminate of the open cross-sections was modeled as either five or 10

layers of shell elements, with each layer representing two plies, the tiebreak contact was

defined only between these shell layers, rather than between individual plies. However,

delamination could occur along any, if not all, ply interfaces during specimen crushing,

as was observed experimentally [82, Chapter 6]. In order to account for the energy

dissipated by these additional delamination interfaces, CCRIT was scaled by the ratio of

the number of ply interfaces to the number of tiebreak interfaces , defined as:

(6)

That is, it is assumed (based on the experimental observations discussed in [82,

Chapter 6]) that delamination occurred among all ten (20 for angle stiffeners) plies. The

values used and calculated in Equations (4), (5) and (6) are listed in Table 9-2. It should

213

be noted that was calculated using the larger element size (1.27 mm) used for the

flat surfaces and was used to simulate delamination in throughout the open cross-section

specimens (including the corners).

Table 9-2: Tiebreak input parameters

[GPa]

[kJ/m2]

[kJ/m2]

[mm]

[MPa]

[MPa]

[mm]

[mm]

C-channel 9.08 0.2 1.33

5 1.27 15.9 40.5 0.065

mm

0.148

Angle-stiffener 9.08 0.2 1.33 5 1.27 15.9 40.5 0.065

mm

0.139

Hat-stiffener 9.08 0.2 1.33 5 1.27 15.9 40.5 0.065

mm

0.148


All boundary conditions used in the models were accurate representations of the

experimental setup. The open cross-sections required the nodes along the flat end of the

models to be fixed in all degrees of freedom to simulate the potted base used for support.

The loading platen of the testing machine was modeled as a rigid surface with a friction

coefficient of 0.3. The members were placed standing upright between the loading platen

and the base. The interaction between the loading platen and the specimen was modeled

using a surface-to-surface contact definition (contact automatic surface to surface).

The tiebreak contact definition between the shell layers not only facilitates the

simulation of delamination, but also prevents layers from penetrating each other after the

tiebreak has failed, as the contact definition would remain in effect. It should be noted

that the splaying of the inner and outer layers and their subsequent folding would force

them to come in contact with the un-deformed inner or outer wall of the specimen.

214

Therefore, a single surface contact definition (contact automatic single surface) was

added to prevent any self-penetration.




Chang failure criterion [73] to determine failure of each ply (associated with an

integration point). This model allows the user to define a local material coordinate system

to specify the orientation of each ply. There are 21 parameters in MAT54 that need to be

specified, 15 of which are physically based and six are numerical parameters [73]. Out of

the 15 physical parameters, 10 parameters are material constants that were obtained from

[83] and [84]. The values of these 10 parameters used in this study are shown in Table

9-3.


E1 E2 G12/13 G23 ν12

171.42 GPa 9.08 GPa 5.29 GPa 3.92 GPa 0.32

XT XC YT YC SL


The remaining five failure parameters are the tensile and compressive failure

strains in the fiber direction, the matrix and shear failure strains, and the effective failure

strain. The six numerical parameters were either estimated or set to their default values,

depending on the behavior required of the material model. In [90, Chapter 7], a separate

parametric study was conducted to determine the optimal values of the unknown

parameters and it was found that the results are insensitive to a wide range of values of

five of these parameters. The only MAT54 parameter that needed to be adjusted was

215

DFAILM, which is the failure strain in the matrix direction [73]. Adjusting the value of

DFAILM enabled a steady matrix splitting to occur, as observed in the experiments. The

parametric study performed in [90, Chapter 7] resulted in a DFAILM value of 10% strain

that provided the most accurate representation of the crushing process of circular

composite tubes. This DFAILM value was used for the elements in the corner regions of

the open cross-section specimens since their size is the same as that of the circular tube

model [90, Chapter 7]. To determine the optimal DFAILM value for the flat surface,

regions where elements are twice the size of the corner elements, a separate parametric

study was conducted. It was found that a DFAILM value of 5% strain would provide the

most accurate representation of the crushing process. These values were used in the

simulations of all three cross-sections and two trigger mechanisms.


9.5.1. DEFORMATION

i) Chamfer Failure Trigger

A comparison of the experimental and simulated crushing process of a C-channel,

angle-stiffener, and hat-stiffener with a chamfer failure trigger at selected crosshead

displacements are shown in Figure 9-6, Figure 9-7, and Figure 9-8, respectively. It should

be noted that the difference in post-test configurations of experiment and simulation was

due to the fact that, in all cases, the simulations terminated at the maximum crosshead

displacement and the unloading process was not performed. For the C-channel, the

simulation accurately predicts the damage initiation as the chamfer crushes and the

buckling in the flanges and web with increasing crosshead displacement, Figure 9-6(b).

216

Similar behavior was recorded for the angle- and hat-stiffeners in Figure 9-7(b) and

Figure 9-8(b), respectively.

As the crushing progresses, the simulation predicts the formation and growth of

matrix cracks at the corners and in the web of the C-channel, as well as outward splaying

of the outer plies, Figure 9-6(c) and Figure 9-6(d). However, the simulation was not able

to predict the number of matrix cracks formed during the crushing process, particularly in

the corners and flanges. These matrix cracks generated 5-10 mm wide CFRP segments of

single plies or ply groups, which splay inwards and outwards progressively along the

surface of the testing platen with increasing crushing distance. Similar behavior was

recorded for the angle- and hat-stiffeners in Figure 9-7(c) to Figure 9-7(d) and Figure

9-8(c) and Figure 9-8(d), respectively.

For the C-channel and hat-stiffener, the inability to form sufficient number of

matrix cracks resulted in some buckling of the web and flanges that was not observed in

the experiment, Figure 9-6(d) and Figure 9-6(e), and Figure 9-8(d) and Figure 9-8(e),

respectively. It should be noted that the experimental results, discussed in [82, Chapter

6], showed that the web of the C-channel and hat-stiffener had the tendency to buckle in

the beginning of the crushing process. However, the formation of matrix splits and cracks

at the corners caused the web to crush and splay inward or outward, and quickly relieved

the buckling.

Comparing the final deformed states of all three cross-sections shows that the

simulation was able to accurately capture the overall crushing behavior, including the

direction of splaying of each layer and the extent of damage, Figure 9-6(e), Figure 9-7(d),

and Figure 9-8(e), respectively. It is noted that during unloading in the experiment, the

217

splayed plies straightened (clearly showing recovery of the splayed ply/ply-group

segments).

Ex

per

imen

t

Sim

ula

tio

n

(a) Pre-test (b) δ ~ 1.5mm (c) δ ~ 10mm (d) δ ~ 40mm (e) Post-test

Figure 9-6: Comparison of the experimental and simulated deformation of the C-channel with a

chamfered trigger mechanism at selected crosshead displacement stages.

Ex

per

imen

t

Sim

ula

tio

n


Figure 9-7: Comparison of the experimental and simulated deformation of the angle-stiffener with a

chamfered trigger mechanism at selected loading stages.

218

Ex

per

imen

t

Sim

ula

tio

n


Figure 9-8: Comparison of the experimental and simulated deformation of the hat-stiffener with a

chamfered trigger mechanism at selected loading stages.

ii) Steeple Failure Trigger

A comparison of the experimental and simulated crushing process of a C-channel,

angle-stiffener, and hat-stiffener with a steeple failure trigger at selected crosshead

displacements are shown in Figure 9-9, Figure 9-10, and Figure 9-11, respectively. As

mentioned before, the difference in post-test configurations of experiment and simulation

was due to the fact that the simulation of unloading process was not performed. For all

three cross-sections, the simulation accurately predicts the crushing of the steeple, the

formation of several matrix cracks in the web and at the corners, and the inward/outward

splaying of the different layers. However, similar to the chamfer case, the lack of

sufficient number of matrix cracks formation in the simulation prevents the development

of the numerous ply/ply-group segments observed in the experiments. This resulted in

significant buckling in the web of the C-channel, Figure 9-9, minor buckling in the left

leg of the angle-stiffener, Figure 9-10, and minor buckling in the flanges of the hat-

stiffeners, Figure 9-11.

219

E

xp

erim

ent

Sim

ula

tio

n

(a) Pre-test (b) δ ~ 10mm (c) δ ~ 15mm (d) δ ~ 40mm (e) Post-test

Figure 9-9: Comparison of the experimental and simulated deformation of the C-channel with a steeple

trigger mechanism at selected loading stages.

Ex

per

imen

t

Sim

ula

tio

n


Figure 9-10: Comparison of the experimental and simulated deformation of the angle-stiffener with a

steeple trigger mechanism at selected loading stages.

220

Ex

per

imen

t

Sim

ula

tio

n


Figure 9-11: Comparison of the experimental and simulated deformation of the hat-stiffener with a steeple

trigger mechanism at selected loading stages.

9.5.2. LOAD-CROSSHEAD DISPLACEMENT BEHAVIOR

Figure 9-12 shows the predicted load-crosshead displacement curves of a C-

channel with a chamfer failure trigger mechanism, showing both the unfiltered (dotted

line) results and the filtered (solid line) results. The unfiltered plot shows initial load

fluctuations, occurring within the first 2 mm of the crosshead displacement. These initial

load fluctuations, consisting of five load spikes, correspond to the crushing of the five

shell element layers in the chamfered region. The three higher load spikes correspond to

the crushing of the three [02] layers (layer 1, 3, and 5), whereas the [+45/-45] layers

(layer 2 and 4) result in lower load spikes that are visible only upon closer examination of

Figure 9-12. By modeling each individual ply as a separate shell element layer, (with a

much higher computational cost), the number of load spikes would increase to ten and the

magnitude of each spike would reduce significantly, rendering a much smoother load-

displacement curve. With the current five-layer model, the curve could be smoothed

using various data filtering schemes. It was found that in this particular case an SAE 600

Hz filter provided the most accurate results. It should be noted that in [90, Chapter 7] an

SAE 300 Hz was found to yield the best results for a three-layer finite element model.

221

This indicates that the degree of filtering required decreases with increasing in the

number of shell element layers used to model the laminate (i.e. the chamfered section).

Figure 9-12: A comparison of unfiltered and filtered load-crosshead displacement curves from a multi-

layer simulation for a C-channel with a chamfer failure trigger.

The predicted load-crosshead displacement curve for the C-channel, angle-

stiffener, and hat-stiffener with chamfer and steeple failure trigger mechanisms is show in

Figure 9-13, Figure 9-14 and Figure 9-15, respectively. It should be noted that the load-

displacement data of the specimens with steeple triggers did not require any filtering as

the steeple geometry could be modeled accurately without any approximation. In most

cases, the simulation was able to predict quite accurately the load-crosshead displacement

behavior in terms of the initial peak load (within -1% to +8%) and sustained crush load

(within ±1%), Figure 9-16. The only exception is the angle-stiffener with a steeple

trigger, where the initial peak load is under predicted by 34%. Recall that in order to

properly simulate the initiation and steady progression of matrix splitting along the

corners of the cross-sections observed experimentally, a finer mesh (0.635 mm element

size) with a higher DFAILM value of 10% failure strain were used to model the corner

0

10

20

30

40

50

0 5 10 15 20 25

Lo

ad (

kN

)



222

regions. For C-channels and hat-stiffeners where the apex of the steeple is located far

away from the corners, this modeling strategy worked very well as the two failure

mechanisms are largely independent of each other. For the angle stiffener, on the other

hand, the apex of the steeple coincided with the corner of the cross-section. The

interaction between matrix splitting mechanism and failure triggering mechanism

considerably weakened the material at the steeple apex, resulted in a much lower initial

peak load. Despite this discrepancy, the SEA predicted by all six simulations showed a

high level of agreement with the experimental results, Figure 9-17. It should be noted that

the data filtering process did not affect the average sustained crush load and the overall

SEA, as these values correlated very well with the experimental results, regardless of the

filter applied.

(a) (b)

Figure 9-13: Load-crosshead displacement comparison between experiment and simulation for C-channels

with (a) a chamfer, and (b) a steeple trigger mechanism.

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


C Chamfer Test 1C Chamfer Test 2C Chamfer Test 3Simulation (Filtered - SAE 600Hz)

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


C Steeple Test 1C Steeple Test 2C Steeple Test 3Simulation (Unfiltered)

223

(a) (b)

Figure 9-14: Load-crosshead displacement comparison between experiment and simulation for angle-

stiffeners with (a) a chamfer, and (b) a steeple trigger mechanism.

(a) (b)

Figure 9-15: Load-crosshead displacement comparison between experiment and simulation for hat-

stiffeners with (a) a chamfer, and (b) a steeple trigger mechanism.

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


Angle Chamf. Test 1Angle Chamf. Test 2Simulation (Filtered - SAE 600Hz)

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


Angle Steeple Test 1Angle Steeple Test 2Angle Steeple Test 3Simulation (Unfiltered)

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


Hat Chamfer Test 1Hat Chamfer Test 2Hat Chamfer Test 3Simulation (Filtered - SAE 600Hz)

0

10

20

30

40

50

0 5 10 15 20 25 30

Load

(kN

)


Hat Steeple Test 1Hat Steeple Test 2Hat Steeple Test 3Simulation (Unfiltered)

224

(a) (b)

Figure 9-16: Comparison of simulated and experimental peak loads and sustained crush loads for the

specimens with (a) a chamfer, and (b) a steeple failure trigger mechanism.

(a) (b)

Figure 9-17: Comparison of simulated and experimental SEA for the specimens with (a) a chamfer, and (b)

a steeple failure trigger mechanism.

0

10

20

30

40

50


Load

(kN

)

C Chamfer ExperimentC Chamfer SimulationAngle Chamfer ExperimentAngle Chamfer SimulationHat Chamfer ExperimentHat Chamfer Simulation

0

10

20

30

40

50


Load

(kN

)

C Steeple ExperimentC Steeple SimulationAngle Steeple ExperimentAngle Steeple SimulationHat Steeple ExperimentHat Steeple Simulation

0

10

20

30

40

50

60

70

80

90

100

SEA

SEA

(kJ

/kg)

C Chamfer ExperimentC Chamfer SimulationAngle Chamfer ExperimentAngle Chamfer SimulationHat Chamfer ExperimentHat Chamfer Simulation

0

10

20

30

40

50

60

70

80

90

100

SEA

SEA

(kJ

/kg)

C Steeple ExperimentC Steeple SimulationAngle Steeple ExperimentAngle Steeple SimulationHat Steeple ExperimentHat Steeple Simulation

225


The finite element models were further validated by comparing the resulting

strain distribution in the specimens with the experimentally measured axial and hoop

strain fields recorded with the Digital Image Correlation (DIC) system [82, Chapter 6].

Since similar results were recorded for all cross-sections, only the results recorded for the

C-channel are presented herein. Figure 9-18 shows a comparison of the axial strain

distributions for a chamfered C-channel at three selected crosshead displacements, all

during the initial crush process of the chamfer: at two crosshead displacements prior to

reaching the initial peak load and the third after progressive crushing begins. The finite

element model is not able to accurately predict the axial strains during the initial stages of

crush due to the load fluctuations caused by the approximate chamfer model, as discussed

in the previous section. After the chamfer was fully crushed, however, the model was

able to predict similar high strain levels as observed in the experiment, at approximately

5 mm of crosshead displacement. The lateral strain fields, Figure 9-19, show that the

model was able to predict some of the high lateral tensile strains in the web of the C-

channel, from approximately 1.0 to 1.4 mm of crush. These high strains are due to some

minor outward buckling in the center of the web, discussed in more detail in [82, Chapter

6]. At 2.5 mm crosshead displacement, both simulation and experiment show high strains

along the corners, indicating the location of matrix splitting.

Figure 9-20 shows a comparison of the axial strain distributions for a steeple C-

channel at three selected crosshead displacement stages. Results show that the simulation

can accurately predict the location and magnitude of the high axial strains in all three

226

stages. A similarly high level of correlation is observed in Figure 9-21 for the lateral

strain fields.

Sim

ula

tio

n

Exp

erim

ent

Displacement [mm]: 1.0 1.2 5.0 Figure 9-18: Comparison of simulated and experimental (DIC) axial strain fields in a C-channel with a

chamfer failure trigger mechanism.

Sim

ula

tio

n

Exp

erim

ent

Displacement [mm]: 1.0 1.4 2.5 Figure 9-19: Comparison of simulated and experimental (DIC) lateral strain fields in a C-channel with a

chamfer failure trigger mechanism.

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Sim

ula

tio

n

Exp

erim

ent

Displacement [mm]: 0.3 2.0 3.5 Figure 9-20: Comparison of simulated and experimental (DIC) of the axial strain fields in a C-channel with

a steeple trigger mechanism.

Sim

ula

tio

n

Exp

erim

ent

Displacement [mm]: 0.3 2.0 3.5 Figure 9-21: Comparison of simulated and experimental (DIC) of the lateral strain fields in a C-channel

with a steeple trigger mechanism.



behavior of open cross-section CFRP composite members with chamfer and steeple

228

failure trigger mechanisms. A multi-layer shell element approach was used to model the

laminates. Each layer of shell element could contain either a single ply or multiple plies.

Layers were tied together using tiebreak contact definitions. Delamination between layers

was simulated by tiebreak failure, which was determined using an energy-based criterion.

LS-DYNA Material model 54 (MAT54) was used to model the crushing behavior. It was

determined that only the matrix failure strain, DFAILM, was needed to be adjusted in

order to obtain good correlations with the experimental results. Simulation results

showed, for both the chamfer and steeple failure trigger cases, that the failure processes,

strain fields, peak load, sustained crush loads, and SEAs all compared very well with the

experimental results. The fluctuation of load-displacement curves in the initial crushing

stage, which was caused by the modeling approximation of the chamfered region, could

be reduced by modeling the chamfer in greater details, such as modeling each ply

separately. In all chamfer cases, filtering the simulation data using an SAE 600 Hz filter

resulted in a better agreement of the initial peak load with the experimental load-

crosshead displacement data, without affecting the sustained crush load and SEA. For the

steeple members, no filtering was required as the steeple was modeled without any

geometrical approximation. Finally, the modeling methodology developed in this study

has been shown to be capable of capturing the overall crushing behavior of the members

under axial compressive loading quite accurately.

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CHAPTER 10: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

10.1. CRASHWORTHINESS STUDY

The investigation into aircraft crashworthiness began with the use of a previously

developed finite element model of a 3 m long Boeing 737 fuselage section, which has

been validated against drop test experimental data, to perform a parametric study on the

effect of the coefficient of friction and angle of impact between the fuselage and a rigid

surface. Four different friction coefficients and six different angles of impact were used

to determine their effect on the dynamic response of the fuselage section in terms of the

structural deformation, energy absorption and acceleration-time histories at selected sites.

The results from the parametric study prompted the development of a full-length

fuselage model of a representative narrow-body transport aircraft to simulate crash-

landing on different terrains, including rigid surfaces, soils, and water. The 3 m long

B737 single-section model was first modified to a more computationally efficient model,

and a verification study, comprised of vertical impact simulations on rigid and water

surfaces, was conducted to ensure that the modified section model was capable of

replicating the deformed configuration and acceleration-time histories similar to that of

the original section model. The results indicated that the modified model, while requiring

one-fifth of the computation time, was able to provide accurate simulation results. The

full-length fuselage model was then constructed by expanding the modified section

model. The full-length model consisted of a primary fuselage section, a nose cone, and a

tail section, the latter two represented by simple shell elements, excluding all structural

subcomponents. The landing gear and wings were excluded from the model due to the

230

lack of necessary design details. The full-length model was then employed to conduct a

series of crash landing simulations on a rigid, soil, and water terrains.

Finally, a simple example demonstrating the effect of integrating energy

absorbing structural members into the subfloor structure of the B737 single-section

model was presented. This study utilized spring elements to represent composite

stanchions using a typical load-displacement curve from the crushing of a graphite/epoxy

member. The results were compared to the B737 simulations with and without luggage in

the subfloor region.

10.1.1. KEY CONCLUSIONS

The major conclusions of this investigation are listed below. Additional details

can be found in the conclusion sections of the corresponding chapters:

i) The overall deformation of the B737 fuselage section was significantly affected

by varying the coefficient of friction and the angle of impact. The lower friction

coefficients and impact angles yielded higher plastic deformation and more

extensive buckling of the bottom frames, particularly on the left-hand side of the

fuselage.

ii) The cargo doorframe reinforcements on the right-hand side of the fuselage had a

dominating effect on deformation and acceleration-time histories on that side of

the fuselage, significantly minimizing the effect of using different friction

coefficients and impact angles.

iii) Regardless of the friction coefficient or the angle of impact, the peak acceleration

pulses were higher on the right-hand side than on the left-hand side due to the

presence of the reinforced cargo doorframe.

231

iv) In all cases, the frames and luggage together accounted for most of the energy

dissipated. For lower friction coefficients and impact angles, the greater

deformation of the lower frames caused the luggage to crush more and, hence,

dissipate more energy.

v) The crash landing simulations with the full-length model on rigid, soil and water

terrains yielded similar peak acceleration pulses, the highest occurring at the

forward sections and the lowest at the aft sections.

vi) In all three cases the frames absorbed more energy than the skin and, in the soil

and water impact cases, the terrain also deformed, dissipating a portion of the

initial kinetic impact energy.

vii) The luggage played an important role as the major energy absorber, as well as

acting as a damping mechanism that rapidly diminished the reverberation of the

fuselage structure.

viii) Using spring elements in the subfloor region of the B737 single section model

demonstrated the feasibility of using energy absorbing structural members to

dissipate the impact energy during a crash.

ix) The results indicated that the stanchions could be used to improve the

crashworthy behavior of an aircraft in terms of deformation, acceleration-time

histories and energy dissipation; however, further research is warranted into this

subject.

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10.1.2. SCIENTIFIC CONTRIBUTIONS

Developed a computational methodology to model a full-length aircraft fuselage.

This modeling methodology has a great potential in the following applications:

i) Support the aircraft industry in optimizing future aircraft designs for

crashworthiness.

ii) Support the Federal Aviation Administration (FAA) in developing a crashworthy

certification program.

iii) Aid in investigating actual aircraft crashes and study potential crash scenarios.

10.2. ENERGY ABSORBING STRUCTURES: EXPERIMENTAL STUDY

The results from the crashworthiness simulations highlighted the importance of

improving the energy absorbing capabilities of the aircraft subfloor structure. Hence, a

two-part study was performed to evaluate the energy absorbing capabilities of composite

members for use as stanchions in the subfloor structure. In the first part of the study,

composite tubes, made of graphite/epoxy laminates, were crushed under quasi-static axial

compression. The objective was to determine the most effective approach to decrease the

initial peak crush load while increasing the sustained crush load and SEA. Tests were

conducted with flat-ended, chamfer-ended, and with inward-folding and outward-

splaying crush-caps failure trigger mechanisms. The effect of the corner radius of the

crush-caps on the crushing process was also evaluated. Based on the results obtained

from the initial study, a new combined chamfered-end and inward-folding crush-cap

trigger mechanism was use to further study the effect of corner radius of the inward-

folding crush-caps.

233

The second part of this study included three different cross-sectional geometries

that are more prevalent in the aerospace industry: C-channels, angle-stiffeners and hat-

stiffeners. Two types of failure trigger mechanisms (chamfered-ends and steeples) were

investigated to determine which approach was most capable of decreasing the initial peak

load while increasing the sustained crush load and SEA.

A digital image correlation (DIC) system was used to monitor the axial and hoop

strain fields in the specimens during the crushing process. The DIC strain fields captured

the initiation and progression of damage, and highlighted several important differences

between the failures processes of the various cross-sections used in this study. Further,

these strain fields provide an additional point of validation for the finite element models.




i) For the circular tubes, the chamfer failure trigger was most effective at reducing

the initial peak load while maintaining a high-sustained crush load and high SEA.

ii) The inward-folding failure trigger approach was not as effective at reducing the

initial peak load in the tubes, but was more effective than using a chamfer for

maintaining a high-sustained crush load and SEA. On the other hand, the

outward-splaying crush-cap was ineffective at reducing the initial peak load or in

maintaining a high-sustained crush load and SEA.

iii) A clear correlation between forcing more crushed material into the center of the

tube (using the inward-folding crush-caps), and an increase in SEA was observed.

234

Further, the results obtained with different corner crush-cap radii showed that the

smaller radii provide better results in terms of sustained crush loads and SEA.

iv) A combined chamfered-end and inward-folding crush-cap failure trigger

mechanism yielded a moderate level initial peak load and the highest sustained

crush load and SEA as compared to any of the other failure triggers.

v) For the open cross-sections, the angle- and hat-stiffeners were the most effective

at absorbing energy, yielding very similar SEA values. The C-channel, on the

other hand, yielded a much lower SEA value.

vi) The steeple failure trigger was able to provide a lower initial peak load than the

chamfer failure trigger for the C-channel and hat-stiffener. For angle-stiffeners,

both failure trigger mechanisms resulted in similar initial peak loads.

vii) Cross-sections that had a larger ratio of curved sections typically resulted in a

higher SEA due to the greater extent of damage and interaction amongst the

inward-splaying plies.


Performed a comprehensive experimental investigation into the energy absorption

mechanisms of specimens with various cross-sections and failure trigger mechanisms.

The results from this investigation can be of significant use when designing energy

absorbing devices, at the following stages:

i) Selection of member cross-sectional geometry based on required load-

displacement behavior, failure process, and SEA.

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ii) Selection of a failure trigger mechanism design that is most appropriate for the

required application and selected member.

10.3. ENERGY ABSORBING STRUCTURES: COMPUTATIONAL STUDY

In this phase of the study, finite element models were developed using LS-DYNA

to simulate the crushing behavior of composite stanchions. Two approaches were

employed to model the crushing process, namely, a single-layer approach and a multi-

layer approach. The single-layer approach used one layer of shell elements to represent

the laminate, with through-the-thickness integration points representing individual plies.

In order to achieve a stable simulation, a contact definition that unrealistically permitted

nodal penetration, following a user-defined load-penetration curve, was used. Further,

this approach involved performing an extensive parametric study to obtain the values of

certain parameters required by material model 54 (MAT54) to correctly fit the simulation

results to the experimental load-crosshead displacement data. It was determined that two

parameters, DFAILC and SOFT, play a key role in predicting the initial peak load and

sustained crush load, respectively. An unsuccessful attempt was made to find a common

set of parameters that could be used across the different cross-sections.

For the multi-layer approach, a comprehensive investigation was performed to

develop a methodology to model the crushing behavior of the composite members. This

included determining the most effective laminate configuration, element size and

formulation, contact definitions, loading rate, delamination interfaces, and material

model. First, it was determined that the laminate needed to be divided into an equal

number of plies per shell element layer, in order to maintain consistent spacing between

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each layer. Fully-integrated, four-node elements were used to generate the mesh, with a

finer mesh required for curved surfaces (circular tube and corners of open cross-sections)

that the flat surfaces (web and flanges of open cross-sections). The quasi-static

experimental loading rate was modeled using a two-step function to ramp us the loading

rate while minimizing the dynamic effects. In order to simulate delamination, two

tiebreak options were investigated and it was determined that option 8 (a simple bilinear

traction-separation law) was capable of accurately simulating delamination using an

energy based approach. Finally, two material models were investigated (MAT54 and

MAT58) and it was determined that MAT54 provided the better results in terms of the

load-crosshead displacement and deformation. However, a parametric study needed to be

performed in order to obtain the values of the unknown parameters. It was determined

that DFAILM was the only parameter that needed to be adjusted in order to obtain good

correlation with the experimental results. A parametric study was performed to determine

an optimal set of input parameters for the circular tube and the C-channel. These

parameters were then used across the remaining case studies.




i) The single-layer approach was able to accurately replicate the load-crosshead

displacement curve of the circular tube and the C-channel with a chamfer trigger

by calibrating the material model input parameters to experimental data.

However, it was not possible to predict the deformation and failure process due to

237

the inability of this model to form delamination between plies, matrix splitting,

etc.

ii) An attempt was made to find a common set of parameters that could be used

across the different cross-sections. However, it was found that each cross-section

required a separate set of values.

iii) When applied to specimens with a steeple trigger mechanism, this method was

unsuccessful due to the lack of the chamfer row of elements to effectively use the

SOFT parameters. These models were mostly unstable and it was not possible to

find a common set of parameters to use between the different cross-sections.

iv) The multi-layer modeling methodology was capable of accurately capturing the

overall crushing behavior of the specimens under axial compressive loading. The

failure processes, strain fields, peak load, sustained crush loads, and SEAs

compared very well with the experimental results.

v) The chamfered region would have to be modeled in greater detail (e.g., modeling

each ply separately) than the current approximation in order to achieve better

initial peak loads. In all cases, filtering the simulation data resulted in a better

agreement of the initial peak load with the experimental data, without affecting

the sustained crush load or SEA.

vi) An energy-based approach was used to determine the input parameters for the

tiebreak formulations to accurately simulate delamination between the plies. A

scaling factor was introduced to account for ply interfaces that were not

represented by a tiebreak definition.

238

vii) The element deletion criterion used has a significant effect on the material models

capability to correctly predict the SEA. Permitting only element deletion in the

matrix direction (i.e., matrix splitting) is key to the successful use of the material

model.


Developed a new multi-layer modeling methodology that addresses key issues

such as the most efficient way to model the laminate and its interfaces, and the most

effective element size and formulation, contact definitions, time-step control, and

material model. This modeling methodology has great potential for the following

applications:

i) Support the design of energy absorbing structures by computationally optimizing

cross-sectional geometry, ply orientation and stacking sequence, and material

selection.

ii) Support the design of crashworthy aircraft by incorporating these models into the

subfloor structure.

10.4. FUTURE WORK RECOMMENDATIONS

10.4.1. FULL-LENGTH AIRCRAFT FUSELAGE MODEL

An extensive investigation into the crashworthiness behavior of aircraft structures

was performed, using a Boeing 737 fuselage section and a representative full-length

aircraft model. In order to further extend this work and improve the accuracy and

reliability of the results, realistic geometry and modeling details of the aircraft structure

239

are required. The current model does not take into account the effect of the landing gear,

wings, nose cone and tail section. These simplifications will undoubtedly have an effect

on the overall crashworthy response of the aircraft and will need to be addressed in the

future.

10.4.2. MULTI-LAYER MODELLING METHODOLOGY

The finite element modeling methodology developed to simulate the crushing

behavior of the composite members yielded excellent results for four different cross-

sections, three different failure trigger mechanisms, and two different lay-ups. However,

there are several issues that could be further investigated to improve the results. For

example, the extensive matrix cracking observed experimentally could be better

simulated by using a significantly finer mesh with a corresponding change in failure

strain, or by allowing node splitting in the axial direction. Further, aligning the mesh

with the lamina direction could result in a better representation of the matrix cracking,

resulting in a more accurate deformation and crushing process. This will require

modeling each ply as an individual layer. These approaches, however, would add

significant computational cost.

Additionally, the tiebreak formulation used to model delamination showed that

the simple bi-linear traction-separation law worked better than the fundamentally more

accurate cohesive zone formulation. The primary difference between the two

formulations is that the cohesive zone formulation takes mode-mixity into account, thus

is expected to provide a more accurate representation of delamination. This issue

deserves further investigation and validation at the coupon level, particularly when using

a single contact interface to simulate delamination between multiple plies. Similarly, the

240

study into the optimal material model to simulate crushing showed that the simpler

progressive failure model (MAT54) was more effective than the continuum damage

mechanics based model (MAT58). The latter typically under-predicted the energy

absorbed which appeared to be due to the effective failure strain calculation performed to

account for ply failure. A possible solution to this could be to integrate separate failure

strain for fiber, matrix and shear directions, similar to the MAT54 implementation.

10.4.3. STANCHION MODEL INTEGRATION

. The incorporation of the finite element models, describing the failure process

and energy absorption capacity of the various types and configurations of the stanchions

studied, into the model of the B737 fuselage warrants further investigation. Several issues

need to be addressed in order to successfully incorporate the stanchion models into the

subfloor structure. From a design perspective, this includes the type of cross-section of

the stanchion, connections to surrounding frames, location and number of stanchions

required, failure trigger mechanism employed, etc. From a computational perspective, the

key issue is determining which modeling methodology can be used to represent the

stanchions without adversely affecting the computational cost.

10.4.4. DYNAMIC EFFECTS

The experimental work performed as part of this dissertation utilized a quasi-

static loading rate to study the crushing behavior of the composite members. Hence, the

finite element models were developed assuming a quasi-static loading rate. For

crashworthy applications, however, it is important to understand the effects a dynamic

loading rate would have on the crushing behavior of these composite specimens. The

241

following sections briefly discuss: i) prior experimental results reported in the literature

on the effect of strain-rate on the compressive behavior of composite laminates; and ii)

the implications of including strain rate effects on the finite element methodology

presented in this dissertation and how the modeling could further be updated in the future

to address rate-dependent behavior.

i) Review of Experimental Studies

The experimental studies performed to investigate the strain-rate effects on

composite materials can broadly be classified into two categories: those performed to

study the material response (i.e., using a split-Hopkinson pressure bar) and those

performed to study the structural response (i.e., using tubular members). The former

provides and understanding of the materials response to different loading rates in terms of

its compressive modulus of elasticity, strength and ultimate strain; while the latter

includes the structural response to different loading rates in terms of crush loads and

energy absorption capacity.

The effect of strain rate on the material properties of carbon/epoxy laminates has

been reported in the literature (e.g. [91] to [96]), yielding mostly consistent results. For

example, the longitudinal compressive properties of unidirectional graphite/epoxy

laminates were characterized at dynamic strain rates of up to 118 s-1

in [91] and 110 s-1

in

[92]. Both studies reported an increased longitudinal compressive strength at the higher

strain rates compared to the static strength (up to 79% in [91] and 40% in [92]) but found

no rate effects on the longitudinal compressive modulus of elasticity. Similarly, both

authors also investigated the transverse compression and in-plane shear properties of the

same composite materials in [93] and [94]. Both studies reported an increased transverse

242

compressive modulus (up to 37% in [93] and 12% in [94]) as well as the transverse

compressive strength (up to 100% in [93] and 45% in [94]). A similar trend was observed

for the in-plane shear modulus and strength in both studies. In [95] and [96], similar

trends for the compressive strengths were reported; however, [96] reported an increased

compressive modulus as well.

The quasi-static and dynamic crush tests on composite members reported in the

literature yielded mixed results. For example, in [24] and [98] no clear rate effect on the

SEA was observed during the crushing of graphite/epoxy [24,98], glass/epoxy [24,98]

and Kevlar/epoxy [98] tubes at quasi-static and dynamic loading rates (up to 8.5 m/s in

[24] and 7.6 m/s in [98]). The load-displacement curves and failure processes observed

were similar for different loading rates in both studies. Contrary to these two studies,

however, a clear rate effect was observed for the same materials in [34], reporting that the

SEA decreased by up to 30% for the dynamic loading rates (of 5.5 m/s), while the failure

processes were relatively similar. Similar trends were reported in [100] and [101] for

graphite/epoxy tubes tested under quasi-static and dynamic loading rates (of 7.5 m/s in

[100] and 8.5 m/s in [101]). On the other hand, the opposite trend was reported in a study

performed using graphite/epoxy and Kevlar/epoxy circular tubes [102], where the SEA

increased by up to 35% for graphite/epoxy and up to 45% for Kevlar/epoxy, at higher

loading rates. Note that Kevlar, being a nylon material, is more rate dependent material.

Similar results were reported in [103] for square graphite/epoxy tubes tested at quasi-

static and dynamic loading rates (of 5.4 m/s). It was noted in [103] that the strain rate

resulting from an impact of 5.4 m/s is equivalent to approximately 20 s-1

.

243

In summary, these studies performed at the coupon level showed a definite

increase in compressive longitudinal, transverse and shear strengths, and the transverse

and shear modulus of elasticity, but no change in the longitudinal modulus. Whereas, the

studies performed at the structural level showed mostly inconclusive results with respect

to the energy absorbed during crushing at different loading rates. The reasons for the

conflicting results, reported in the limited number of studies, cannot be discerned. It

should be further noted that the crush tests were typically performed at much lower strain

rates (~20 to 30 s-1

) than those conducted with coupon specimens (>100 s-1

). Finally, the

influences of ply orientation, cross-sectional geometry, and failure trigger mechanisms on

the crushing behavior and energy absorption have not been studied under dynamic

loading. Therefore, there is a clear need to further investigate the crushing response of

composite members under dynamic loading.

In addition to the material response, as highlighted in the experimental portion of

this dissertation, delamination between the plies played a significant role in the energy

absorption process. Hence, it is important to understand the effect of dynamic loading

rate on the delamination process, specifically on Mode I and Mode II fracture toughness

values. Since these are matrix-dominated failures it should be expected that the higher

loading rate will affect the crushing process of composite members.

ii) Numerical Implications

The finite element modeling methodology developed in this dissertation was

aimed at predicting the quasi-static crushing behavior of composite members. However,

this approach may be adopted to simulate crushing under dynamic loading rates as well,

244

to be accomplished by modifying certain aspects of the model setup and input

parameters, as discussed below.

Firstly, the time-scaling functions used to decrease the computation time for

simulating quasi-static loading cases would become unnecessary for the dynamic loading

cases and the actual dynamic loading functions could be used. Second, the material

model would have to be modified to account for material rate dependency. This issue can

be addressed by simply replacing the current material properties with the corresponding

properties for a predetermined dynamic loading rate, or by utilizing a rate-dependent

material model that is capable of predicting the material response at various loading rates.

The first approach can be implemented into the material model (MAT 54) used in this

study, in a manner similar to [103] where the compressive strength values were increased

in the dynamic model. The second approach would require replacing MAT 54 with rate-

dependent material models such as MAT 158 or MAT 161/162. There are, however,

many more input parameters required by these material models that would need to be

obtained parametrically, by calibrating them with test data. Therefore, if the required

dynamic test data and material properties are available, it will be possible to update the

current modeling methodology to incorporate the effects of material rate-dependency. For

example, in [104] the advantage of using strain rate dependent material properties (using

MAT 158) instead of quasi-static material properties (using MAT 58) to simulate the

behavior of triaxially braided composites under impact loads was demonstrated.

Third, the issue of simulating delamination at dynamic rates would have to be

addressed in a similar fashion. The current tiebreak and cohesive formulations require a

fixed set of input parameters that include, or can be calculated from, the Mode I and

245

Mode II interlaminar fracture toughness values. With known fracture toughness values

for a predetermined loading rate, the tiebreak parameters in the current modeling

methodology can be modified to account for a dynamic loading rate.

246

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255

VITA

DEEPAK SIROMANI

EDUCATION

Ph.D., Mechanical Engineering Drexel University, Philadelphia, PA December 2013

Research: Crashworthy Design and Analysis of Aircraft Structures

M.S., Mechanical Engineering Drexel University, Philadelphia, PA June 2009

Research: Multi-terrain Crashworthiness Studies of a Boeing 737 Fuselage

B.S., Mechanical Engineering Drexel University, Philadelphia, PA June 2007

Concentrations: Aerospace, Design and Manufacturing

RESEARCH AND PROFESSIONAL EXPERIENCE

FAA-Drexel Research Fellow Drexel University, Philadelphia, PA September 2008 –

December 2013

Energy Absorbing Mechanisms of Composite Members

• Investigated the crushing response of composite members for use in rotorcraft subfloor structures • Supervised three senior design teams involved in the design and testing of the composite members • Developed finite element models in LS-DYNA to simulate the initiation and progression of damage

through the crushing process

Crashworthiness Simulations of a Boeing 737 Fuselage

• Investigated the dynamic response of a Boeing 737 fuselage section for different impact scenarios using LS-DYNA

• Developed a full-length representative narrow body transport aircraft finite element model • Simulated the effect of multi-terrain (rigid, soil and water) impact conditions using ALE methods

Process Engineering Intern Rohm and Hass, Newark, DE October 2005 – March 2006

• Assisted with process improvement projects at different stages of production • Implemented a defects tracking system and trained operators to use it • Updated P&ID's to reflect recent changes • Developed and revised Return to Service procedures and other operating procedures for various

equipment

Validation Engineering Intern GlaxoSmithKline, Upper Merion, PA September 2004 –

March 2005

• Performed Validation Maintenance studies and Installation & Operational Qualifications on production and non-production equipment including autoclaves, depyrogenation ovens, vessels and freezers

• Generated protocols for Cleaning Validation on various filter skids

• Developed and revised Standard Operating Procedures for studies and operating calibration equipment

Design Technician CSA Group, Philadelphia, PA July 2004 – September 2004

September 2003 – March 2004

• Assisted in the development of a city-wide Geographic Information Systems (GIS) project for the Philadelphia Water Department

• Developed the first stage of a hydraulic model for a pressure district in the city

256

RESEARCH INTERESTS

Crashworthiness of aircraft structures; Impact, penetration and crush analysis; Damage mechanics of composite materials; Fluid-structure interaction (ALE and SPH methods); Material and damage modeling

TECHNICAL SKILLS

LS-DYNA, LS-PrePost, Hypermesh, ANSYS, ABAQUS, Creo Parametric (formerly Pro/Engineer),

AutoCAD, MatLab, Mathematica

TEACHING EXPERIENCE

Course Coordinator -

Introduction to CAD

Drexel University, Philadelphia, PA June 2009 – December 2012

• Developed and managed a hybrid online and in-class course to introduce all first-year engineering students to computer-aided design

• Created online lectures and tutorials, in-class and take-home assignments to assist students in learning the basics of AutoCAD and Creo Parametric (formerly Pro/ENGINEER)

Teaching Fellow - Freshman

Engineering Design Labs

Drexel University, Philadelphia, PA September 2008 – June 2013

• Responsible for running weekly labs and mentoring freshman design projects • Assisted in the development of a reverse engineering lab module

Teaching Assistant Drexel University, Philadelphia, PA January 2008 – December 2011

• Assisted in teaching several core undergraduate and graduate mechanical engineering courses - mechanics of materials, finite element methods (ANSYS), and theory of elasticity

SELECTED PUBLICATIONS

Siromani, D., Cheng, B., DeLuca, M., Donegan, D., Giberson, P., Murcerino, C., Awerbuch, J. and Tan,

T., “An Experimental and Numerical Study on the Energy Absorption Mechanisms of Axially Loaded Graphite/Epoxy Members with Various Cross-sections,” Proceedings of the 2012 Aircraft Airworthiness & Sustainment Conference, April 2-5, 2012, Baltimore, MD.

Siromani, D., Henderson, G., Mikita, D., Mirarchi, K., Park, R., Smolko, J., Ludin, D., Awerbuch, J. and

Tan, T., “Experimental and Numerical Crashworthiness Investigation into the Energy Absorption Mechanisms of Axially Loaded CFRP Tubes,” Proceedings of the American Society for Composites 26th Technical Conference, September 26-28, 2011, Montreal, QC, Canada.

Siromani, D., Awerbuch, J. and Tan, T., “Multi-terrain Crashworthiness Simulations of a Boeing 737

Fuselage Section,” Proceedings of the 2010 Aircraft Airworthiness & Sustainment Conference, May 10-13, 2010, Austin, TX.

Siromani, D., Byar, A., Awerbuch, J. and Tan, T., “Crashworthiness Simulation of a Boeing 737

Fuselage Section: A Parametric Study on the Effects of Angle of Obliquity and Friction on its Dynamic Response,” Proceedings of Aging Aircraft 2009, May 4-7, 2009, Kansas City, MO.

INVITED PRESENTATIONS

Siromani, D., Awerbuch, J. and Tan, T., “Multi-terrain Crashworthiness Simulations of a Narrow Body

Transport Fuselage under Vertical and Oblique Impact Conditions,” CMH-17 Crashworthiness Working Group Meeting, November, 2011, Wichita, KS.

http://www.linkedin.com/search?search=&title=Course+Coordinator+-+Introduction+to+CAD&sortCriteria=R&keepFacets=true&currentTitle=C

http://www.linkedin.com/search?search=&title=Course+Coordinator+-+Introduction+to+CAD&sortCriteria=R&keepFacets=true&currentTitle=C

257

Siromani, D., Awerbuch, J. and Tan, T., “An Experimental and Numerical Study on Energy Absorption

Mechanisms of CFRP Members,” CMH-17 Crashworthiness Working Group Meeting, November, 2011,

Wichita, KS.

HONORS AND AWARDS

• Engineering Design Education Fellowship (2008 – 2013)

• FAA-Drexel Research Fellowship (2008 – 2013) • Research Award, Drexel University Research Day 2012

• Honorable Mention, Drexel University Research Day 2009

• Dean's Scholar at Drexel University • Dean's List • Member, Drexel University Honors Society • Member, National Society of Collegiate Scholars • Member, Pi Tau Sigma - Mechanical Engineering National Honors Society

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