CRASH SIMULATION OF FIBRE METAL LAMINATE FUSELAGE
166
CRASH SIMULATION OF FIBRE METAL LAMINATE FUSELAGE A THESIS SUBMITTED TO THE UNIVERSITY OF MANCHESTER FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (PhD) IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES 2014 AHMAD SUFIAN ABDULLAH SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
Transcript of CRASH SIMULATION OF FIBRE METAL LAMINATE FUSELAGE
CRASH SIMULATION OF FIBRE METAL LAMINATE FUSELAGE
A THESIS SUBMITTED TO
THE UNIVERSITY OF MANCHESTER
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (PhD)
IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES
2014
AHMAD SUFIAN ABDULLAH
SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
Table of Contents
Contents 2
List of Figures 6
List of Tables 9
Abstract 10
Declaration 11
Copyright Statements 12
Acknowledgement 13
Chapter 1 INTRODUCTION ................................................................................................. 14
1.1. Background and Motivation ............................................................................... 14
1.2. Aim of Research ................................................................................................. 16
1.3. Outline of Structure ........................................................................................... 16
Chapter 2 LITERATURE REVIEW ......................................................................................... 18
2.1 Crash Simulation of Aircraft ............................................................................... 18
2.1.1 Introduction of Aircraft Crash Simulation ................................................... 18
2.1.2 Methodology of Aircraft Crash simulation .................................................. 18
2.1.3 Crash Simulation of Composite Aircraft Fuselage ........................................ 21
2.2 Failure and Impact Response of Fibre Metal Laminate and its Constituents ...... 24
2.2.1 Introduction to Failure and Impact Response of Fibre Metal Laminate ....... 24
2.2.2 General Review on Mechanical Properties of Fibre Metal Laminate ........... 24
2.2.3 Bending and Buckling Behaviour of Fibre Metal Laminate .......................... 26
2.2.4 Impact Response and Damage of Fibre Metal Laminate under Low Velocity
Impact …………………………………………………………………………………………………………………..27
2.2.5 Review on Failure and Impact Response of Fibre Reinforced Composite
Laminate under Low Velocity Impact ......................................................................... 30
2.2.6 Review on Failure and Impact Response of Metal under Low Velocity Impact
…………………………………………………………………………………………………………………..34
2.2.7 Finite Element Modelling of Impact and Damage on Fibre Metal Laminate
and Its Constituents................................................................................................... 35
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2.3 Summary of the Literature Review ..................................................................... 38
Chapter 3 BACKGROUND THEORY OF FIBRE METAL LAMINATE ......................................... 39
3.1 Introduction on Fibre Metal Laminate ................................................................ 39
3.1.1 GLARE: A Glass Fibre Reinforced Based Fibre Metal Laminate .................... 39
3.1.2 Impact Behaviour of GLARE ........................................................................ 40
3.2 Aluminium Alloys ............................................................................................... 42
3.2.1 Stress-strain Relationship of Isotropic and Homogeneous Materials ........... 42
3.2.2 Impact Behaviour of Aluminium Alloys Structure ........................................ 45
3.3 Fibre Reinforced Composite Laminate................................................................ 48
3.3.1 Stress-strain Relationships of Fibre Reinforced Composite Laminate .......... 48
3.3.2 Analysis of a Composite Lamina ................................................................. 49
3.3.3 Failure of Fibre-reinforced Composite Laminate ......................................... 52
3.3.4 Impact Behaviour of Fibre-Reinforced Composite Laminate under Low
Velocity Impact ......................................................................................................... 56
Chapter 4 FINITE ELEMENT METHOD................................................................................. 59
4.1. Introduction....................................................................................................... 59
4.1.1. Introduction of Finite Element Method in Aircraft Crash Analysis ............... 59
4.1.2. General Description of Finite Element Method ........................................... 60
4.1.3. Abaqus Finite Element (FE) Software .......................................................... 61
4.2. Nonlinear Dynamic Analysis ............................................................................... 62
4.2.1. Nonlinear Analysis of Aircraft Structure ...................................................... 62
4.2.2. Dynamic Analysis of Aircraft Structure........................................................ 64
4.3. Selection of Elements for Discretisation ............................................................. 66
4.3.1. Shell element ............................................................................................. 66
4.3.2. Incompatible Mode Solid Element .............................................................. 69
4.3.3. Reduced Integration Element ..................................................................... 69
4.3.4. Hourglass Control ....................................................................................... 70
4.3.5. Cohesive Element ....................................................................................... 71
4.4. Material and Damage Model of Aluminium Alloy ............................................... 76
4.4.1. Material Model of Aluminium Alloy ............................................................ 76
4.4.2. Damage model of Aluminium Alloy ............................................................ 77
4.4.3. Onset of damage in Aluminium Alloy .......................................................... 77
4.4.4. Damage Evolution of Aluminium Alloy........................................................ 77
4.5. Material and Damage Model of Fibre-Reinforced Composite Laminate .............. 79
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4.5.1. Material Model of Fibre-Reinforced Composite Laminate ........................... 79
4.5.2. Onset of damage in Fibre-Reinforce Composite Lamina .............................. 80
4.5.3. Damage Evolution of Fibre-Reinforced Composite Lamina .......................... 82
4.6. Interaction and Contact Modelling ..................................................................... 85
4.7. Constraint and Connection Modelling ................................................................ 88
4.7.1. Mesh Tie Constraints .................................................................................. 88
4.7.2. Mesh Independent Fasteners ..................................................................... 88
4.8. Computational Facilities in The University of Manchester .................................. 89
Chapter 5 DEVELOPMENT OF FIBRE METAL LAMINATE FUSELAGE CRASH MODEL ............. 90
5.1. Introduction of Aircraft Crash Methodology ....................................................... 90
5.2. Methodology of Crash Modelling of Fibre Metal Laminate Fuselage................... 91
5.3. Validation of Material and Damage Model Subjected to Impact Loading ............ 93
5.3.1. Validation of Aluminium Alloy Material and Damage Model ....................... 93
5.3.2. Validation of Composite Laminate Material and Damage Model .............. 102
5.4. Validation of General Impact Modelling ........................................................... 112
5.5. Verification of Fuselage Frame Impact Modelling ............................................. 119
5.5.1. Finite Element Modelling of Fuselage Frame ............................................ 119
5.5.2. Verification Results of Fuselage Frame Impact Model ............................... 122
5.6. Development of Crash Impact FE Model of Aluminium Alloy Fuselage Section . 126
5.6.1. Geometric Information and Assumptions ................................................. 126
5.6.2. Discretisation of the Fuselage Section ...................................................... 127
5.6.3. Material Assignment ................................................................................ 127
5.6.4. Impact and Contact Modelling ................................................................. 127
5.6.5. Location of Mass ...................................................................................... 128
5.7. Development of Crash Impact FE Model of GLARE Fuselage Section ................ 129
5.8. Evaluation of Acceleration Response at Floor-Level.......................................... 130
5.8.1. Data collection and processing of the acceleration response during crash
event …………………………………………………………………………………………………………………130
5.8.2. Human tolerance towards acceleration .................................................... 130
Chapter 6 RESULTS AND DISCUSSIONS ............................................................................ 133
6.1. Introduction..................................................................................................... 133
6.2. Energy Dissipation during Crash ....................................................................... 133
6.3. Structural Deformation of Fuselage Structure .................................................. 141
6.4. Acceleration at Floor Level ............................................................................... 150
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Chapter 7 Conclusions and Future Work.......................................................................... 153
7.1. Conclusions...................................................................................................... 153
7.2. Recommendation for Future Work .................................................................. 155
References ...................................................................................................................... 156
Appendix 1 ...................................................................................................................... 162
Appendix 2 ...................................................................................................................... 165
Word Count: 33,868
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List of Figures
Figure 1-1: A typical fibre metal laminate (Remmers 2006) ............................................... 15
Figure 2-1: Variation of mechanical properties of fibre metal laminate with volume fraction
of its composite, (a) elastic modulus, (b) tensile strength (Reyes & Cantwell 2000). .......... 25
Figure 3-1: Typical stress-strain curve of isotropic material (Gere & Timoshenko 1990) ..... 43
Figure 3-2: Equivalent stress evolution versus equivalent plastic strain for different strain
rates for aluminium alloy 2024-T3 (Rodríguez-Martínez et al. 2011). ................................. 44
Figure 3-3.Buckling of aluminium can under axial loading (Palanivelu et al. 2011). ............ 46
Figure 3-4. Local coordinates of a lamina........................................................................... 50
Figure 3-5 Failure modes of composite laminate (Gay and Hoa 2007). ............................... 52
Figure 3-6. Sketch of crack propagation mode (Farley & Jones 1992). ................................ 58
Figure 4-1. Conventional shell element and continuum shell element (Abaqus
Documentation version 6.12) ............................................................................................ 68
Figure 4-2. Element deforms in hourglass mode (Westerberg 2002). ................................. 70
Figure 4-3. Schematic representation of FML with interface elements (dark-grey) applied
between layers (Remmers & de Borst 2001). ..................................................................... 71
Figure 4-4. Typical traction-separation response (Abaqus Documentation version 6.12).... 73
Figure 4-5. Traction-separation response with exponential softening (Abaqus
Documentation version 6.12). ........................................................................................... 74
Figure 4-6. Stress-strain curve with progressive damage degradation (Abaqus
Documentation version 6.12). ........................................................................................... 78
Figure 4-7. A linear damage evolution based on effective plastic displacement (Abaqus
Documentation version 6.12) ............................................................................................ 79
Figure 4-8. Linear damage evolution of a lamina structure(Abaqus Documentation version
6.12) ................................................................................................................................. 84
Figure 4-9. Hard contact pressure-overclosure relationship diagram (Abaqus
Documentation version 6.12). ........................................................................................... 87
Figure 5-1. Methodology of developing crash simulation of FML fuselage section ............. 92
Figure 5-2. Mesh of aluminium alloy plate with finer mesh at the impact area .................. 96
Figure 5-3. Different stages of the perforation process for an aluminium alloy 2024-T3
sheet, V0 4.0 m/s. (a) Localisation of deformation and onset of crack. (b) Cracks progression
and formation of petals. (c) Development and bending of petals. (d) Complete passage of
the impactor and petalling failure mode. .......................................................................... 98
Figure 5-4. Flow stress evolution versus strain for Johnson-Cook material model ............ 100
Figure 5-5. Impact force as a function of the impactor displacement ............................... 101
Figure 5-6 Permanent deflection of the target for FE model and experiment ................... 101
Figure 5-7. Numerical model of the impact on composite laminate. ................................ 104
Figure 5-8. Impact force-time histories of impacted composite laminate ......................... 107
Figure 5-9. Impact force-displacement histories of impacted composite laminate ........... 108
Figure 5-10. Deformation in impacted plate for FE model without adhesive. ................... 108
Figure 5-11. Deformation in impacted plate for FE model with adhesive. ........................ 109
Figure 5-12. Energy absorption-time histories for impacted composite laminate ............. 110
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Figure 5-13. A quarter symmetric model of cask drop onto a rigid surface (Abaqus
Documentation, 6.12) ..................................................................................................... 112
Figure 5-14. Deformation of side wall of bottom containment at 5 ms, (a) axisymmetric
model, (b) shell element model, (c) C3D8R element with default hourglass control model,
(d) C3D8R element with enhanced hourglass control model and (e) C3D8I element model.
....................................................................................................................................... 116
Figure 5-15. Crushing distance of the containment for all models .................................... 117
Figure 5-16. Plastic dissipation and elastic strain energy time histories............................ 118
Figure 5-17. Fuselage frame configuration and discretisation. ......................................... 120
Figure 5-18. Z cross-section of fuselage frame ................................................................ 120
Figure 5-19. Deformation of frame (a) at time 50 ms, (b) at time 125 ms, (c) at time 175 ms
....................................................................................................................................... 123
Figure 5-20. Crushing distance of frame with various mesh sizes. .................................... 124
Figure 5-21. Plastic energy dissipation of frame finite element models with various mesh
sizes. ............................................................................................................................... 125
Figure 5-22. Energy balance of frame model with mesh size 32 mm. ............................... 125
Figure 5-23. Human coordinate system (Shanahan 2004b) .............................................. 131
Figure 5-24. Acceleration crash pulse in assumed triangular pulse (Shanahan 2004)........ 132
Figure 6-1. Energy balance within the aluminium fuselage for 10 ms-1 impact velocity crash.
....................................................................................................................................... 135
Figure 6-2. Energy balance within the GLARE 5-2/1 fuselage for 10 ms-1 impact velocity
crash. .............................................................................................................................. 135
Figure 6-3. Dissipation of impact energy and its distribution within the aluminium fuselage
for 10 ms-1 impact velocity crash. .................................................................................... 136
Figure 6-4. Dissipation of impact energy and its distribution within the FML GLARE 5-2/1
fuselage for 10 ms-1 impact velocity crash. ...................................................................... 137
Figure 6-5. Energy absorbed by frame structure and its decomposition in aluminium
fuselage .......................................................................................................................... 138
Figure 6-6. Energy absorbed by skin structure its plastic dissipation in aluminium fuselage
....................................................................................................................................... 139
Figure 6-7. Energy absorbed by skin structure and its decomposition in GLARE 5-2/1
fuselage. ......................................................................................................................... 140
Figure 6-8. Deformation histories with plastic strain contour plot of the aluminium fuselage
during crash with impact velocity 10 ms-1. ....................................................................... 143
Figure 6-9. Deformation histories with plastic strain contour plot of the GLARE 5-2/1
fuselage during crash with impact velocity 10 ms-1. ......................................................... 144
Figure 6-10. Crushing distance of aluminium and GLARE 5-2/1 fuselages in 10 ms-1 impact
velocity crash. ................................................................................................................. 146
Figure 6-11. Location of plastic hinge at the bottom half of the fuselage section ............. 146
Figure 6-12. Tensile and compressive matrix failure at composite layers in GLARE 5-2/1 skin
structure at hinge location B. t = 24 ms ........................................................................... 148
Figure 6-13. Matrix tensile failure in glass-fibre laminate (90⁰) outer lamina at t = 78 ms. 149
Figure 6-14. Fibre tensile failure in glass-fibre laminate (0⁰) inner and outer lamina at t = 78
ms. .................................................................................................................................. 149
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Figure 6-15. Acceleration response at passengers’ location in aluminium fuselage during 10
m/s vertical crash. ........................................................................................................... 152
Figure 6-16. Acceleration response at passengers’ location in GLARE 5-2/1 fuselage during
10 m/s vertical crash. ...................................................................................................... 152
Figure A1-1. Schematic representation of the drop weight tower (Rodriguez-Martinez et al,
2011)....................................................................................................................................162
Figure A1-2. The device used to clamp the specimen (a) clamping (b) specimen support
(Rodriguez-Martinez et al,
2011)....................................................................................................................................163
Figure A1-3. Conical striker used in the Rodriguez-Martinez’s experiment (Rodriguez-
Martinez et al,
2011)....................................................................................................................................163
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List of Tables
Table 3-1 Commercially available ARALL laminates (Khan et al. 2009). .............................. 40
Table 3-2 Mechanical properties of aluminium alloy 2024-T3 (Lesuer 2000; Buyuk et al.
2008) ................................................................................................................................ 43
Table 5-1. Material properties of 2024-T3 and 7075-T6 aluminium alloy (Lesuer 2000; Buyuk
et al. 2008). ....................................................................................................................... 95
Table 5-2. Results comparison between FE models and experimental works in terms of
artificial energy percentage, maximum impact force and energy absorption. .................... 97
Table 5-3. Amount of energy absorbed during impact of composite plate ....................... 110
Table 5-4. Cask drop with solid elements modelling to be verified ................................... 113
Table 5-5. Material and damage model parameters of aluminium alloy 7075-T6 (Brar et al.
2009). ............................................................................................................................. 121
Table 5-6. Frame finite element models with various mesh sizes ..................................... 122
Table 5-7. Contact surface pairs modelled within the fuselage ........................................ 128
Table 5-8. Human tolerance limits (Shanahan 2004b). ..................................................... 131
Table 6-1. Percentage of energy distribution within fuselage structure during impact ..... 137
Table A2-1. Material properties of the carbon fibre/epoxy unidirectional
laminate...............................................................................................................................165
Table A2-2. Material properties of the interface cohesive element (Shi et al,
2012)................................................................................................................................. ...166
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Abstract
A finite element model of fibre metal laminate (FML) fuselage was developed in order to
evaluate its impact response under survivable crash event. To create a reliable crash finite
element (FE) model of FML fuselage, a ‘building block approach’ is adapted. It involves a
series of validation and verification tasks in order to establish reliable material and damage
models, verified impact model with structural instability and large displacement and
verified individual fuselage structure under crash event. This novel development
methodology successfully produced an FE model to simulate crash of both aluminium alloy
and FML fuselage under survivable crash event using ABAQUS/Explicit. On the other hand,
this allows the author to have privilege to evaluate crashworthiness of fuselage that
implements FML fuselage skin for the whole fuselage section for the first time in aircraft
research field and industry. The FE models consist of a two station fuselage section with
one meter longitudinal length which is based on commercial Boeing 737 aircraft. For FML
fuselage, the classical aluminium alloy skin was replaced by GLARE grade 5-2/1. The impact
response of both fuselages was compared to each other and the results were discussed in
terms of energy dissipation, crushing distance, failure modes, failure mechanisms and
acceleration response at floor-level. Overall, it was observed that FML fuselage responded
similarly to aluminium alloy fuselage with some minor differences which conclusively gives
great confidence to aircraft designer to use FML as fuselage skin for the whole fuselage
section. In terms of crushing distance, FML fuselage skin contributed to the failure
mechanisms of the fuselage section that lead to higher crushing distance than in aluminium
alloy fuselage. The existence of various failure modes within FML caused slight differences
from the aluminium fuselage in terms of deformation process and energy dissipation.
These complex failure modes could potentially be manipulated to produce future aircraft
structure with better crashworthiness performance.
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Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning.
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COPYRIGHT STATEMENT
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property (the “Intellectual Property”) and any reproductions of copyright works in the
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Intellectual Property and Reproductions cannot and must not be made available for use
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Acknowledgements
First and foremost, I am grateful to The God Allah S.W.T. for His continuous blessings and
for allowing me to complete this thesis despite of having various challenges throughout my
Ph.D journey.
I would like to express my gratitude to my research supervisor Dr. Azam Tafreshi for her
advice and support during my years in The University of Manchester as a postgraduate
student.
Many special thanks go to The Ministry of Education Malaysia as the main sponsor of my
tuition fees and provided financial support during my research years in Manchester and
also many thanks to Universiti Teknologi Mara (UiTM) for their support in various aspects.
I would like to thank to all technical staffs in The University of Manchester that may have
given direct and indirect support in order for me to complete various stages of this
research. Not forget to mention supportive colleagues especially those in Floor D and F of
Pariser Building that always keen to help each other in completing our courses.
Finally but most importantly, thank you to my lovely wife Sakeena in which we got married
during my second year of my research. Her understanding towards the challenges faced by
me, her patience and supports were very much needed and tremendously appreciated.
Thank you to Ali too, our beautiful one year old son, who always keep me smile and feel
blessed. Thank you to my parents and sisters who keep supporting me and always be my
source of motivation and inspiration.
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Chapter 1 INTRODUCTION
1.1. Background and Motivation
The number of flights travelling across continents, countries and cities is growing rapidly
year by year which is motivated by the increasing number of customers demand for air
travel. In parallel, there are demands from the environmentalists and governments to cut
down the fuel emission. There were few measures taken to fulfil the environmentalist and
governments demand which include the research, development and manufacturing of
high-performance lightweight aircraft by the aircraft manufacturers. This trend can be
observed on the new released Boeing 787 Dreamliner which the lightweight composite
materials are widely used for the aircraft’s main structure (Boeing). On the other side, by
incorporating GLARE and other composite laminate into large proportion of the aircraft’s
skin, Airbus A380 manage to cut down production and operating costs and increases the
safety level of the aircraft significantly. Additionally, with the capability of carrying 560 to
660 passengers, the A380 should answer the Boeing’s 747 monopoly (Vlot et al.1999). In
designing the new lightweight aircraft structure, the aircraft manufacturers cannot
compromise the safety of the occupants as well as the integrity of the structure. Thus,
crashworthiness of an aircraft is an important issue in designing the future lightweight
aircrafts.
Crashworthiness of an aircraft can be investigated using experimental method and
numerical method. Evaluating crashworthiness of an aircraft by using experimental method
or crash test is expensive and it can only be executed at the end of the designing stage.
Jackson et al and Adam et al (Jackson et al. 1997; Adams & Lankarani 2010) are among the
researchers that carried crashworthiness evaluation of aircraft using experimental method.
On the other side, numerical analysis and finite element analysis are more cost-effective
compare to crash test. In current state of crashworthiness analysis, most of finite element
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model for crashworthiness evaluation is verified by experiment of the same model such
being implemented in several published papers by Adams et al, Meng et al, Jackson and
Fasanella and Hashemi (Adams & Lankarani 2010; Jackson & Fasanella 2005; Meng et al.
2009; Hashemi et al. 1996).
The crashworthiness of aircraft that uses fibre metal laminate (FML) as the fuselage skin is
the main interest in this thesis. The idea of fibre metal laminates are by stacking metal and
fibre reinforced composite layers in order to gain the superiority fatigue and fracture
characteristics of fibre reinforced composite materials and to combine with the plastic
behaviour and durability of the metal (Remmers 2006) A typical FML configuration is as
shown in Figure 1-1. Three main families of fibre metal laminate in aerospace industry are
ARALL, GLARE and CARALL (ECSS 2011a; ECSS 2011b). Other less commercialised FML are
titanium based and magnesium based FMLs (Sinmazçelik et al. 2011). Vlot et al (Vlot et al.
1999) also anticipated that the application of FML in the entire top half of the A380’s
fuselage around the passengers’ cabin and in cargo floors, cargo liners, bulkheads and flap
skins of the other aircraft.
Figure 1-1: A typical fibre metal laminate (Remmers 2006)
Fibre-reinforced composite
Metal
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1.2. Aim of Research
The aim of the research is to evaluate the crashworthiness performance of fibre metal
laminate (FML) fuselage under survivable crash event. In order to achieve this aim, a
reliable crash finite element (FE) model of FML fuselage has to be developed through a
series of validation and verification tasks.
1.3. Outline of Structure
This thesis consists of seven chapters with each chapter discusses relevant materials and
works towards reaching the aim of research. The outline of the thesis structure is
summarised as below.
Chapter 1 presents the background and motivation that produced the research objective.
Chapter 2 presents the literature review on relevant materials mainly on crash simulation
of aircraft structure and impact response of fibre metal laminate and its constituents.
Chapter 3 presents the background theories on mechanical response of aluminium alloy
and composite laminate in order to establish firm understanding on the mechanical
response of fibre metal laminate.
Chapter 4 presents the finite element method in modelling various material and structural
behaviour in order to establish the foundation of modelling crash simulation of fibre metal
laminate fuselage
Chapter 5 presents the methodology and its process in developing a reliable crash model of
fibre metal laminate fuselage. This includes the results of the validation and verification
works.
Chapter 6 presents the results of crash simulation of aluminium alloy fuselage and fibre
metal laminate fuselage. This chapter also discusses the impact response, failure
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mechanisms and crashworthiness of fibre metal laminate fuselage in comparison to
aluminium alloy fuselage.
Chapter 7 concludes the research work presented in this thesis and future
recommendation works are outlined.
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Chapter 2 LITERATURE REVIEW
2.1 Crash Simulation of Aircraft
2.1.1 Introduction of Aircraft Crash Simulation
The concept of crash survivability of aircrafts has been established over 50 years ago.
However, its implementation into operational aircraft has been remarkably slow until U.S
Army committed to improve the crash survivability of its helicopters during the conflict in
South East Asia (Xue et al. 2014). The NASA Langley research centre is one of the earliest
crash testing facilities which was originally built for simulating lunar landing. Numbers of
crash test on aircrafts and rotorcrafts have been performed there. Their main objective was
to improve crashworthiness by analysing the dynamic response of aircraft structure, seats
and occupants during crash events (Jackson et al. 2004).
Due to the complexity of the dynamic response of aircraft structure and its expensive crash
tests, computational simulations have been developed and quickly become an effective
tool (Xue et al. 2014). In 1995, the validation of numerical simulation was identified as one
of the key technology that needs to be extensively developed to enhance research on
crashworthiness (Noor and Carden 1993).
2.1.2 Methodology of Aircraft Crash simulation
Implementation of numerical methods in crashworthiness research enables researchers to
evaluate the impact behaviour of aircraft structures during crash events and to evaluate a
new crashworthy design approaches with relatively lower cost (Xue et al. 2014).
Throughout the years, several numerical software codes that specifically and non-
specifically developed for crash simulation of air transports have been established and
implemented including LS-Dyna, KRASH, MSC.Dytran and Abaqus (Jackson & Fasanella
2005)(Fasanella & Jackson 2000)(Meng et al. 2009).
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As early as 1980, Pifko and Winter (Pifko & WInter 1980) outlined the computational
formulations and methods for crash simulations in DYCAST program and discussed the use
of that formulation in finite element solution of crash analysis of automobile and on
helicopter cockpits. They described that the implementation of computational nonlinear
dynamic analysis on crash of vehicle is a complex and challenging task. It requires the user
of crash simulation code to clearly understand the underlying theories so that the model
created is reliable. The users are also required to exercise their engineering judgement in
order to interpret results meaningfully.
In 1996, Hashemi et al (Hashemi et al. 1996) presented a modelling verification
methodology of an aircraft subfloor fuselage component under survivable impact
condition. The FE crash simulation of that particular component was modelled and
analysed by PAM-CRASH FE code. To verify the reliability of the FE model, results from FE
analysis is compared with dynamic test in terms of failure mechanisms. The verified FE
model then is used as an established baseline model for the parametric studies.
Throughout this modelling process, they concluded that an established FE modelling
approach at aircraft’s component level is an effective method to verify the full-scale finite
element modelling of aircraft crash simulation. This method is simply the ‘building block’
approach that typically used in the design and certification of aerospace structures.
Building block approach is a method that consists of tests on increasingly complex structure
in order to develop design allowable and to account structural details. It can be adopted to
develop verified full-scale aircraft crash simulation as suggested by Kindervater et al
(Kindervater et al. 2011). Several other authors also used building block approach including
Heimbs in which he verified the FE model at coupon and structural element levels before
simulate the crash of full-scale composite aircraft (Hashemi & Walton 2006; Kindervater et
al. 2011; Heimbs et al. 2013).
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In 2002, Kumakura (Kumakura 2002) and his colleagues developed a crash simulation of YS-
11A aircraft using LS-Dyna3D as part of the project on structural crashworthiness of aircraft
by NAL Structures and Materials Research Center. The computer model consisted of small-
scaled under-floor fuselage structures that crash vertically onto a rigid impact surface. The
impact response was compared with a vertical drop test of a fuselage section from a YS-
11A aircraft. The simulation results fairly correlate with test in terms of deformation of the
under-floor fuselage structure. In 2013, Feng et al (Feng et al. 2013) al also modelled only
the under-floor section of the fuselage that consists of fuselage frame, fuselage skin below
the cabin floor, floor beams, floor panels, stringers and struts. This simplification is based
on assumption that deformation during crash mainly occurred in the fuselage sub-floor
structure. This simplification method is attractive in terms of reducing computational cost,
but it need to be implemented with caution under certain impact condition such as a crash
on a non-symmetry impact surface or inclining roll angle. Besides, under higher velocity
crash, the stress wave propagation would play a significant role on the impact behaviour. In
2001, Fasanella et al (Fasanella & Jackson 2001) modelled a crash simulation of a fuselage
section of Boeing 737 with a relatively rigid auxiliary fuel tank beneath the occupant’s floor.
Adams and Lankarani (Adams & Lankarani 2010) and Tan et al (Tan et al. 2012) also
separately simulated the crash of the same structure. The FE models in their works consist
of a full circle of fuselage section, unlike models simulated by Kumakura (Kumakura 2002)
and Feng et al (Feng et al. 2013). The impact responses being investigated in the
simulations are the acceleration at passengers’ floor, the failure mechanism and the
deformation of the structure. These results were compared with the drop test of Boeing
737 fuselage section with the same configuration which was run and analysed by
Abromowitz et al earlier in year 2000 (Abromowitz et al. 2000).
All the papers reviewed above have mainly focused on the crash simulation of in-service
real aircraft. There are also crash simulations of future aircrafts performed by a few
21
researchers. The objective of their work is to propose new design concepts for aircrafts that
have better crashworthiness performance. These concepts include having new form of
lower fuselage floor, incorporating energy absorbing sub-floor structure also using
composite-foam sandwich materials as the fuselage skin (Jackson et al. 1997; Jackson 2001;
Fasanella et al. 2002; Bisagni 2003; Meng et al. 2009). As their crash simulations could not
be validated by the experimental drop tests, the methodology to verify their respective
crash simulations have been the key aspects in validating their models.
2.1.3 Crash Simulation of Composite Aircraft Fuselage
Aluminium alloys are the most commonly used materials for the construction of aircraft
fuselages. They are capable of absorbing large amount of energy through plastic
deformation during crash event. However, due to their high specific strength and high
specific stiffness ratios, composites have gradually replaced aluminium alloys in the
aerospace industry. Obviously, composites have different mechanical properties and
characteristics. It is generally brittle in nature, unlike aluminium alloys. Thus, composite’s
capability in absorbing energy during crash becomes a new issue for researchers and air
transport designers (Wiggenraad et al. 2001). Therefore, the crashworthiness of composite
fuselage structures has been studied by many academics and aerospace designers in recent
years as reviewed below. However, crash simulations of aircraft structure that related to
composite are based on new design concept aircraft. They are simulated as part of the
design process in order to achieve new design concept with better crashworthiness
performance.
In 1997, Jackson et al (Jackson et al. 1997) simulated the crash performance of a 1/5-scale
aircraft model that had energy absorbing capabilities fuselage skin, floor and sub-floor
structure. The fuselage skin and floor were made of composite laminate with polyurethane
foam core meanwhile the energy absorbing sub-floor structure was made of Rohacell foam.
22
The fuselage skin was made of fibre reinforced laminated composite with various fibre
orientations but they are modelled as a homogenous material. In terms of deformation and
acceleration at passenger’s floor level, the results of their scaled numerical model agreed
well with a crash test of full-scale model. In 2002, Fasanella and Jackson simulated the full
scale model of the same design concept fuselage.
In 2001, Wiggenraad et al (Wiggenraad et al. 2001) simulated crash event of a new design
concept for a composite sub-floor. The new design concept consisted of under-floor
composite fuselage frame and energy-absorber sine-wave beams. However it was proven
that this new concept did not improve crashworthiness unless certain adjustments were
made. In 2013, Feng et al (Feng et al. 2013) numerically studied the effect of composite ply
number and composite ply angle on crashworthiness of aircraft subfloor structure in which
its fuselage skin was made of composite. They concluded that composite skin ply numbers
and ply angles have a great influence on the crashworthiness of a composite fuselage and
these can be tailored for better crashworthiness. However, the modelling technique and
verification for the composite structure was not informed in their crash simulations.
For the ease of modelling and analysis of crash events, in some of the papers reviewed,
laminated composites were modelled as isotropic and homogeneous materials. This
technique requires a coupon test in order to obtain the material properties and failure
strains of the laminate. This technique is also known as macro-level approach. Another
technique in modelling laminated composites is meso-level approach in which each lamina
is modelled as a unidirectional fibre composite. It is obvious that the latter is
computationally more expensive but its implementation in crash simulation of composite
aircraft enables the researcher to capture more accurate failure mechanisms and failure
modes. Besides, the capability to capture the failure mechanisms may also significantly
affect the evaluation of energy absorbance within composite fuselage structure. In the end,
23
it depends on the understanding of the global impact response of the aircraft and objective
of the analysis in choosing the best modelling approach to model the composite laminate.
24
2.2 Failure and Impact Response of Fibre Metal Laminate and its
Constituents
2.2.1 Introduction to Failure and Impact Response of Fibre Metal Laminate
The concept of fibre metal laminates (FML) is to combine metal and fibre reinforced
composite layers in order to improve certain mechanical properties of the material that to
be used in engineering applications especially in aerospace industry. Three most common
families of FML in aerospace industry are ARALL, GLARE and CARE (CARALL), defined by
their fibre-reinforce laminate’s constituent. Improved damage tolerance and superior
impact properties are among the main advantages benefited from FMLs compare to their
parents’ materials. Within these two decades, various studies were reported investigating
the failure mechanics and impact response of FML. Understanding of failure and impact
response of FML in aerospace application is essential as aerospace structure is always
exposed to impact conditions.
2.2.2 General Review on Mechanical Properties of Fibre Metal Laminate
Discussion on failure and impact response of fibre metal laminate (FML) fairly requires
general understanding of the mechanical properties of fibre metal laminate. Obviously
mechanical property of FML depends on the mechanical properties of its constituents.
As early as 1994, Wu et al (Wu et al. 1994) investigated the effect of specimen size and
geometry on the mechanical properties of FML. Based on tension tests on various FML
specimens with various size and geometry, he proved that these parameters do not affect
the elastic modulus, yield stress and ultimate tensile strength of FML. In year 2000, Reyes
and Cantwell (Reyes & Cantwell 2000) carried a general study on the mechanical properties
of FML based on glass-fibre reinforced polypropylene. They observed that by increasing the
volume fraction of composite will cause the FML to have higher ultimate strength but lower
elastic modulus as shown in Figure 2-1.
25
Figure 2-1: Variation of mechanical properties of fibre metal laminate with volume fraction of its composite,
(a) elastic modulus, (b) tensile strength (Reyes & Cantwell 2000).
Kawai et al (Kawai & Hachinohe 2002) in his study on fatigue property of GLARE observed
that the high strength properties of aluminium alloy enhanced the specific stiffness and
strength of GLARE in the fibre direction. In the same paper, Kawai et al also stated that
fibre bridging mechanism in GLARE impedes the growth and propagation of cracks in the
aluminium alloy under tensile loading conditions. The presence of fibre bridging
mechanism in GLARE is also reported by Hagenbeek (Hagenbeek 2005) and previously
proven by Marissen (Marissen 1988) in his study on fatigue crack growth in ARALL.
0
10
20
30
40
50
60
70
80
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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sile
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lus
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a)
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0
100
200
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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engt
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Pa)
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(b)
(a)
26
In 2006, Cocchieri et al (Cocchieri et al. 2006) discussed the interlaminar shear strength of
FML which depends on the adhesion between fibres and matrix and adhesion between
metal and composite laminate. Several researchers are reported of making use of single
cantilever beam test (SCB) and three and five point bending test to determine the
interlaminar shear strength of FML (Reyes & Cantwell 2000; Khalili et al. 2005).
2.2.3 Bending and Buckling Behaviour of Fibre Metal Laminate
Bending and buckling are one of the failure modes of fibre metal laminate (FML). In year
2005, Khalili et al (Khalili et al. 2005) studied the bending of various FML configurations and
compared with monolithic metals and fibre-reinforced composite laminate. He stated in his
paper that bending strength and stiffness of FML would not increase by placing aluminium
alloy away from the neutral axis. Additionally he observed that the use of aluminium in FML
would cause higher deflection in bending compare to FML that use steel. He also observed
that in bending, the failure that may occur is either delamination alone or combination of
delamination and tensile failure that starts from the external layers.
In year 2001, Remmers et al (Remmers & de Borst 2001) studied the delamination buckling
of GLARE and he represented the mechanism of the failure in which the failure starts with
initial delamination, followed by local buckling, then growth of delamination until failure.
Mesoscopic-level numerical model was developed by him based on mechanism he
presented and cohesive element was used to model the delamination. He concluded that
buckling of FML cannot be predicted by elastic buckling analysis due to the presence of
buckling delamination and plastic deformation within the aluminium alloy layer. This
conclusion is also supported by Bi et al (Bi et al. 2014) in his study on buckling and post-
buckling of FML.
27
2.2.4 Impact Response and Damage of Fibre Metal Laminate under Low Velocity
Impact
Sinmazçelik et al (Sinmazçelik et al. 2011) in his review on test methods on Fibre Metal
Laminate (FML) categorised impact test on FML into three; low velocity, high velocity and
blast loading impact tests. In this thesis, review are only made on impact response and
damage of FML under low velocity impact as the main work in this thesis is limited to
velocity impact ranging between 1 and 20 ms-1. Recently in 2014, Chai and Manikandan
(Chai & Manikandan 2014) reviewed low velocity impact response of FML and he classified
various parameters that influence impact response of FML into two main groups; material-
based parameters and geometry-based parameters. Materials based parameters include
types of metals, types of fibre-reinforced composite, lay-up configuration and constituent’s
volume fraction.
Impact test is not the only methodology in investigating impact response of FML. A number
of researchers developed finite element modelling of dynamic impact and damage for FML
due to several advantages including capability to analyse barely visible impact damage
(BVID) in composite, capability to quantify the degradation of the materials, inexpensive
and quicker method compare to experiment. Thus, impact response and damage analysis
of FML that carried by numerical studies are also reviewed and discussed in this section.
Moriniere et al (Morinière et al. 2013) in his paper discussed the failure mechanisms of
GLARE that make it a superior impact resistance. When subjected to lateral impact loading,
the composite laminate core that has higher bending stiffness than aluminium modifies the
flexural deformation profile of the aluminium alloy. As a result, the crack initiation of the
aluminium is delayed. In the same time the impacted aluminium layer would dampen the
impact on the composite laminate core. Meanwhile the outer non-impacted aluminium
28
layer delays the delamination growth. These mechanisms results in damage being
contained in the vicinity of the impacted zone.
In 2002, Laliberte et al (Laliberté et al. 2002) studied the low velocity impact response of
FML via experiment and numerical method. It is observed that delamination plays
insignificant role in absorbing impact energy under localised lateral impact condition unlike
under bending and buckling as discussed previously. Thus it is up to the understanding of
the impact event in order to determine either or not to incorporate delamination if to
model impact response of FML. Obviously incorporating delamination model will increase
computational cost especially when involving large models.
All studies on FML impact response discussed above are mainly based on vertical drop
weight impact. In 2005, Khalili et al (Khalili et al. 2005) investigated the impact response of
FML via Charpy impact test. In fact it is observed that Khalili et al is the only author that
studied dyanic impact behaviour of FML by not using the vertical drop weight impact that
produces much localised impact area. In his paper, Khalili et al observed that energy per
unit area required to fracture for GLARE with unidirectional fibre orientation is 5% lower
than its parent glass fibre composite due to the deficiency of aluminium layers in tolerating
tensile loads.
2.2.4.1 Effect of Metal/Composite Volume Fraction on Impact Response of Fibre
Metal Laminate
From 1991 to 1997, Vlot and his colleagues studied the impact properties and impact
damage of FML. In one of his study of impact damage on various FML, he observed that
increasing the volume fraction of glass-fibre reinforced laminate in GLARE will increase the
damage resistance. It also increases the minimum cracking energy at low velocity and high
velocity impact higher than its monolithic constituent aluminium alloy. Besides the
contribution of high stiffness of the composite laminate, the improvement in impact
29
resistance is because the presence of delamination. Delamination causes the FML to be
loaded in a more efficient membrane manner, unlike monolithic metal that dominated by
bending deformation (Vlot 1993; Vlot 1996; Vlot & Krull 1997).
2.2.4.2 Effect of Metal Type on Impact Response of Fibre Metal Laminate
In 2009, Liu and Liaw (Liu & Liaw 2009) studied the impact resistance of different FML
families and grades including GLARE1, 2 and 3. Aluminium alloy 2024-T3 is the metal used
in all GLAREs except in GLARE 1 that utilises stronger aluminium alloy 7475-T6. Due to
tougher and slightly stiffer properties of 2024-T3, GLARE 2 and 3 has better impact
resistance than GLARE 1. In their study, the failure mechanism is observed to start from
indention around the impact area. Then delamination is induced between the outer non-
impacted aluminium and its adjacent fibre-reinforced laminate followed by the non-
impacted aluminium crack. In higher energy impact, the aluminium crack will be followed
by severe damage in the fibre-reinforced laminate layers. Global bending during impact
causes the FML to suffer more damage at the non-impacted side.
Several other researchers are reported to investigate other metal such as magnesium and
titanium as potential replacement of aluminium in FML due to their superior properties
that aluminium alloys does not have. However magnesium and titanium based FML were
proven not as good as aluminium based FML in terms of impact resistance. Details on their
works can be referred at respective references (Cortés & Cantwell 2005; Nakatani et al.
2011).
2.2.4.3 Effect of Stacking Sequence on Impact Response of Fibre Metal Laminate
Several researchers are reported to compare the damage resistance between various
grades of GLARE under low velocity impact which their full work can be referred in their
respective papers (Lalibert 2005; Wu et al. 2007; Liu & Liaw 2009). From their works, it can
be concluded that GLARE 5 shows the best damage resistance as smaller damage observed
30
and less impact energy is absorbed. Meanwhile GLARE 3-3/2 perform better than GLARE
1,2-3/2 in terms of damage resistance. This observation is simply resulted by the higher
volume fraction of fibre-reinforced laminate in GLARE 5. The other reason of having GLARE
5 as the best damage resistance is because of the use of cross-ply composite as studied
later by Yaghoubi et al (Seyed Yaghoubi et al. 2011).
In 2011, Yaghoubi et al (Seyed Yaghoubi et al. 2011) did parametric studies on impact
response of GLARE 5-3/2 by varying the stacking sequence of the composite laminate
which includes cross-ply, unidirectional, angle-ply and quasi-isotropic orientations. He
observed that quasi-isotropic orientation (0⁰/45⁰/90⁰) provides highest stiffness thus
results in good impact resistance with low permanent deflection and conversely
unidirectional orientation (0⁰4) gives the worse impact resistance.
Fan et al (2011) in his numerical modelling of FML under low velocity impact discussed the
effect of FML laminate sequence and composite thickness on impact resistance. Changing
the laminate sequence from 2/1 to 3/2 resulted in increase in perforation energy. Several
other authors that investigate the effect of laminate sequence also provided the same
observation which can be referred in their papers respectively (Sadighi et al. 2012;
Morinière et al. 2013).
2.2.5 Review on Failure and Impact Response of Fibre Reinforced Composite
Laminate under Low Velocity Impact
Failure in fibre-reinforced composite laminate and its impact response significantly affect
the failure and impact response of fibre metal laminate (FML) as presented in previous
section. Good understanding on the failure mechanisms and failure modes of fibre-
reinforced composite is required in analysing impact response of FML. Besides, the
available literature on failure and impact response of FML mostly is based on drop weight
impact that has very localised contact area. Literature on failure and response of FML
31
under dynamic axial loading is non-existence and only limited number of researchers
studied on buckling and bending response of FML as reported previously. Thus general
review is made on literatures that discuss the failure and impact response of the
constituents of FML. This section is on failure and impact response of fibre-reinforced
composite and the next section is on metal.
In general, scientific studies on impact response of composite can be classified into two
main categories. The first one is lateral impact which the impact occurs in the direction of
the composite thickness (Robinson & Davies 1992)(Kim et al. 1997)(Aslan et al. 2003)(Shyr
& Pan 2003). The second one is axial impact which the impact occurs in the direction of the
length of the composite(Robinson et al. 1997; Farley & Jones 1992; Bisagni 2009).
In 1992, Robinson and Davies (Robinson & Davies 1992)studied a lateral low velocity
impact on composite and examined the effect of impactor’s mass on the impact response
of various woven fibre-reinforced composite laminate. They observed that the impact
damage is a function of impact energy alone and independent from mass or velocity of the
impactor. Two approaches were introduced by them on predicting energy absorbed
through damage process by the specimen. The first one is simply by subtracting the elastic
energy at maximum impact force from the incident impact energy and the second one is by
integrating the force-time history. Further discussion on reliability of these encouraging
approaches can be referred in their paper (Robinson and Davies, 1992).
Aslan et al in 2003 (Aslan et al. 2003) experimentally and numerically studied the response
of rectangular E-glass/epoxy laminate (0⁰/90⁰/90⁰/0⁰)s under low velocity lateral impact.
Numerically, it is observed that the out-of-plane stresses are significantly smaller than the
in-plane stresses but they may lead to delamination within the laminate. Meanwhile the
maximum stress in fibre direction is larger than in its in-plane orthogonal direction because
the flexural wave moves faster in the fibre direction as explained by them. They also
32
observed that larger delamination occurs at the outer non-impacted layer due to bending
stresses compare to the upper impacted layers (Aslan et al. 2003). Shyr and Pan (Shyr &
Pan 2003) in studying impact resistance and damage for various E-glass reinforced
composite also reported the same observation on the delamination location which is due
to bending stresses at the non-impacted layers. In the same paper, they also observed that
fibre fracture dominates the impact failure in thick laminate meanwhile delamination plays
a major role in thinner laminate.
As most of the impact response investigations were carried numerically on a flat composite
plate, Kim et al (Kim et al. 1997) observed that failure coupling between matrix cracking
and delamination occur in curved composite laminate under low velocity impact loading.
They also observed that as curvature of laminate increases, the delaminated area is also
widens under the same impact energy.
Impact response of composite laminate under axial loading is studied by several authors. In
1992, Farley and Jones (Farley & Jones 1992) studied the crushing characteristics of
composite tubes which they described the response is complex due to interactions of
various failure mechanisms that control the crushing process. They explicitly described
three unique crushing modes of composite tube under axial loading are; transverse
shearing, lamina bending and local buckling which were controlled by various failure
mechanisms. The failure mechanisms that involved in determining the failure mode might
be combination of delamination, lamina bundle fracture, matrix fracture and fibre fracture.
In 2009, Bisagni (Bisagni 2009) also studied on axial impact on composite tube and
discussed the failure mode of the tube. Despite of using different terms for the composite
collapse mode such as socking mode, tearing mode and splaying mode, the fundamental
concept of the failure mode are just the same as described by Farley and Jones (Farley &
Jones 1992).
33
Robinson et al (Robinson et al. 1997) studied the parameters affecting the crashworthiness
of composite material structure under axial, bending and combined loading. He observed
that composite material do not undergo plastic deformation like metal due to its brittle
nature of both fibres and matrix. The parameters that affect the energy absorption
capabilities of composite include the materials of the composite, structural geometry and
loading condition
One of the failure mechanisms that consistently appear in discussing impact response of
composite is delamination. Delamination is also the main failure mechanism of composite
under buckling mode. In 1993, Jih and Sun (Jih & Sun 1993) studied delamination as an
impact response of composite under low velocity impact and they concluded that
delamination could be predicted by using the static interlaminar fracture toughness.
In 1993, Shaw and Shen (Shaw & Shen 1993) studied dynamic buckling of a composite
circular cylindrical shell that geometrically imperfect. He observed that the sensitivity of
critical load over size of imperfection under dynamic load increases significantly compare
to under static loading. Delaminated composite is also a type of imperfection that control
buckling of composite. In 2006, Tafreshi studied delamination buckling in composite
cylindrical shells under combined axial compression and external pressure by using finite
element method. Critical load does not decrease by the existence of very small area of
delamination but the critical load is sensitive to the location of the delamination in the case
of larger area of delamination. The critical load is observed to be very small when the
delamination moves closer to the free surface of the composite laminate. Besides, stacking
sequence of laminate also plays significant role on critical buckling, thus there are stacking
sequence that can be tailored to favour higher resistance on buckling (Tafreshi 2006).
34
2.2.6 Review on Failure and Impact Response of Metal under Low Velocity
Impact
In 2000, Karagiozova (Karagiozova & Jones 2000) studied the dynamic effects on buckling
and energy absorption of steel and aluminium cylindrical shells. He revealed that a shell
that subjected to axial impact is both mass and velocity sensitive. The inertia characteristics
and material properties of the shell would determine the patterns of the axial stress wave
propagation resulting different type of dynamic buckling. His studies continue in 2001
(Karagiozova & Norman Jones 2001; Karagiozova & N Jones 2001) on the same topic gives a
good insight on mechanism of buckling initiation in a transient mode where combination of
plastic and elastic stress wave speed and propagation determined the type and shape of
the buckling. In his numerical studies on dynamic impact, Karagiozova and Jones
(Karagiozova & N Jones 2001; Karagiozova & Jones 2002; Karagiozova & Norman Jones
2001) observed that dynamic effects are larger in strain-rate sensitive material compare to
the one with less sensitivity. The effects include initial instability pattern, energy absorption
during the deformation process and the deformation shapes.
In 2004, Marais et (Marais et al. 2004) al studied two material models that incorporate
strain-rate plasticity model which are Cowper-Symonds and Johnson-Cook model. He
tested these two material models by compare them with experimental results. He
concluded that the selection of correct parameter values for both constitutive models is
vital in obtaining good correlation with experimental results. Earlier in 2000, Lesuer (Lesuer
2000) studied the dynamic effect on Johnson-Cook material model and failure model in
which he suggested a new material and failure parameter values to be implemented for
high strain rate impact analysis. With the new parameters provided by Lesuer, Buyuk and
Loikkanen (Buyuk et al. 2008) studied the effect of different Johnson-Cook parameters
including the original material parameters provided by Johnson and his colleagues (Johnson
1983; Johnson & Cook 1985). He concluded that it is necessary to recalibrate the Johnson-
35
Cook parameters to obtain a better consistency between simulations. For implementation
of Johnson-Cook model in low velocity impact regime, Mohotti et al (Mohotti et al. 2013)
tested the model for low impact velocity ranging between 9.02 to 13.20 ms-1. Results from
the numerical model that used Johnson-Cook material and failure models correlate well
with experimental results but has a small time lag observed in its deflection-time histories.
2.2.7 Finite Element Modelling of Impact and Damage on Fibre Metal Laminate
and Its Constituents
2.2.7.1 Plane stress assumption and choice of element
In 2014, Chai and Manikandan (Chai & Manikandan 2014) et al reviewed works on low
velocity impact response of fibre metal laminate (FML) and concluded that a full
unambiguous continuum finite element model with appropriate interface elements is
required to simulate impact response of FML. In the same year, Morinière et al (Morinière
et al. 2014) also highlighted that plane stress assumption in composite failure criterion
within FML impact response model is invalid and he suggested full three-dimensional
composite failure criterion is used instead. There is a number or researchers that
implement full three-dimensional composite failure in their impact models. The
development of their FE impact model of composite can be referred in their respective
papers (Seo et al. 2010; Donadon et al. 2008; Tita et al. 2008; Lee & Huang 2003). All of
them concluded that model with full three-dimensional material and damage model
produced very good correlations with experimental results in almost all aspects. Important
to be mentioned that in modelling impact response of composite laminate, plane stress
material and failure model still produced reasonable results as proved by Seo et al (Seo et
al. 2010). This claim is also supported initially by Hashagen in 1995 (Hashagen et al. 1995)
in which solid-like shell element that implement plane stress analysis is capable of
computing laminate structure behaviour and its consequences. In Abaqus FE code, solid-
36
like shell element is known as continuum shell element (Abaqus Documentation, version
6.10). Other researchers that also implemented plane stress failure criterion for composite
and FML also proved that their results correlate well up to certain degree with
experimental results (Sadighi et al. 2012; Song et al. 2010; Fan et al. 2011; Seo et al. 2010;
Zhu & Joyce 2012). With all due respect, understanding of the impact mechanics of
particular impact event is essential in order to determine the requirement of full three-
dimensional material and damage model for composite constituent in FML. Localised
impact event is the most likely case to implement full three-dimensional model as the
impact occurs in through thickness direction, meanwhile impact condition that might cause
buckling and bending as the main responses could adequately modelled with plane stress
assumption in its composite constituents. It is obvious that by upgrading plane stress model
to full three-dimensional model will cause increase in computational cost.
In modelling metal constituent of the FML, eight nodes solid element is mainly used by
researchers including Zhu and Joyce (Zhu & Joyce 2012), Seo et al (Seo et al. 2010) and Fan
et al (Fan et al. 2011). Buyuk and Loikkanen (Buyuk et al. 2008) and Kay (Kay 2003) that
studied impact behaviour of aluminium alloy 2024-T3 also discretized the metal plate using
solid element in which produced results that well correlate with experiment.
Computational efficiency in their finite element models is achieved by implementing
reduced integration solid element with suitable hourglass control without compromising
the accuracy of the results.
2.2.7.2 Interface layer for delamination model
In 2004, Linde (Linde et al. 2004) et al develop an FE model of the inter rivet buckling
behaviour in a stiffened FML fuselage shell. He described that delamination is not expected
only to occur between metal and composite surfaces, but it is also likely to occur within the
composite layers themselves.
37
Morinière et al (Morinière et al. 2014) claimed that delamination in low velocity localised
impact event has lower contribution compare to high velocity localised impact event and it
is proven by Laliberte et al (Laliberté et al. 2002)in his comparative study between FML
impact model with and without delamination. This claim is valid for localised impact event
but invalid for impact event in the axial direction that may cause buckling. Earlier in 2001,
Remmers (Remmers & de Borst 2001) presented that buckling delamination is the main
failure mode in FML buckling. Thus the impact condition on FML should determine the
significance of modelling interface layer between layers.
38
2.3 Summary of the Literature Review
The importance of evaluating crashworthiness of fibre metal laminate (FML) fuselage has
been discussed previously. In the early work in the literature review, it is proven that
numerical modelling is progressively becoming a practical method in evaluating
crashworthiness of an aircraft. The capability of computational facilities nowadays makes
numerical modelling less expensive and more efficient than crash test in evaluating
crashworthiness of an aircraft. In addition to the non-existence crash test of FML fuselage,
a fully computational development of reliable numerical model of FML fuselage are taking
place in this thesis. In order to do this, it is suggested by several authors that building block
approach that mainly used in aircraft design industry can be adapted into pure
computational modelling of aircraft crash numerical model. This building block adaptation
is well explained in Chapter 5. It involves validation of material and damage model of both
aluminium alloy and composite laminate, validation of impact modelling that causes large
displacement and instability and verification of a fuselage frame under impact condition.
This adaptation technique is modelled based on the understanding obtained from the
mechanical and impact properties of fibre metal laminates and its constituents. Papers
reviewed suggested several material models that suit impact and damage for aluminium
and composite laminate which is valuable in modelling reliable numerical model of FML
fuselage. The discussion on the necessity of modelling interface layer within composite
laminate concluded that the author has to exercise its engineering judgement based on the
general structure of interest, impact condition and anticipation on the failure mechanisms
of the FML structure.
39
Chapter 3 BACKGROUND THEORY OF FIBRE METAL LAMINATE
3.1 Introduction on Fibre Metal Laminate
Fibre metal laminates (FML) are made of a combination of fibre reinforced laminated
composites and thin layers of metals. These hybrid materials provide superior mechanical
properties compared to the polymer matrix composites or aluminium alloys. FMLs have
better tolerance to fatigue crack growth and impact damage especially for aircraft
applications. Different combinations of metal alloys and composite laminates produce
different families of FMLs. The most common types of FMLs are Glass Reinforced
Aluminium Laminate (GLARE), Aramid Reinforced Aluminium Laminate (ARALL) and Carbon
Reinforced Aluminium Laminate (CARALL). This chapter reviews and discusses the material
properties, constitutive equations and impact characteristics of aluminium alloys, fibre
reinforced laminated composites and GLARE.
3.1.1 GLARE: A Glass Fibre Reinforced Based Fibre Metal Laminate
GLARE is a glass fibre reinforced aluminium laminate which is commercialized in six
different grades as shown in Table 3-1. Composite in GLARE is all based on advanced
unidirectional glass fibres which are embedded within epoxy FM94 adhesive with a nominal
fibre volume fraction of 60% (Cocchieri et al. 2006; Sadighi et al. 2012). Metal in GLARE is
aluminium alloy 2024-T3 except for GLARE 1 that uses aluminium alloy 7475-T761. Prepreg
is stacked symmetrically in GLARE except for GLARE 3 and GLARE 6. In standard practice, a
coding system is used to specify GLARE and other FML. For example GLARE 2B-4/3-0.4 is a
GLARE 2B (Table 3-1) that has four layers of aluminium with 0.4 mm thick each and three
90⁰/90⁰ prepreg layers (Cocchieri et al. 2006).
GLARE that has already been used to construct the top half fuselage skin in Airbus A380 has
a potential to be used as bottom half of the fuselage skin in the near future as it has
excellent impact resistance (Sinmazçelik et al. 2011). In fact it is being evaluated for use as
40
cockpit crown, forward bulkheads and leading edges in which they are the area that require
most excellent impact resistance material (Asundi & Choi 1997).
In comparison to ARALL, GLARE has advantages in terms of higher tensile strength, higher
compressive strength, higher failure strain, superior impact resistance and does not absorb
moisture. However GLARE has higher specific weight and lower stiffness than ARALL.
Grade Sub Metal type
Metal thickness (mm)
Fibre layer (mm)
Prepeg orientation in each fibre layer (⁰)
Characteristics
GLARE 1 - 7475-T761
0.3-0.4 0.266 0/0 Fatigue, strength, yield stress
GLARE 2 GLARE 2A
2024-T3 0.2-0.5 0.266 0/0 Fatigue, strength
GLARE 2B
2024-T3 0.2-0.5 0.266 90/90 Fatigue, strength
GLARE 3 - 2024-T3 0.2-0.5 0.266 0/90 Fatigue, impact
GLARE 4 GLARE 4A
2024-T3 0.2-0.5 0.266 0/90/0 Fatigue, strength, in 0⁰ direction
GLARE 4B
2024-T3 0.2-0.5 0.266 90/0/90 Fatigue, strength, in 90⁰ direction
GLARE 5 - 2024-T3 0.2-0.5 0.266 0/90/90/0 Impact, shear, off-axis properties
GLARE 6 GLARE 6A
2024-T3 0.2-0.5 0.266 +45/-45 Shear, off-axis properties
GLARE 6B
2024-T3 0.2-0.5 0.266 -45/+45 Shear, off-axis properties
Table 3-1 Commercially available ARALL laminates (Khan et al. 2009).
3.1.2 Impact Behaviour of GLARE
Extensive review on impact behaviour of FML has been presented in Chapter 2 and it is
conclusive that mechanical property and impact response of fibre metal laminate (FML)
41
depends on the mechanical properties and impact response of the constituents itself. In
addition to the impact response of FML’s constituent as the basis, the interaction between
their impact response to each other including various failure mechanisms and modes have
to be taken into account.
42
3.2 Aluminium Alloys
Aluminium alloys have been used in aircraft industry since World War One and they still
remain one of the most important materials in aerospace industry. Aluminium alloy is an
isotropic and homogeneous material where by definition the material properties are
independent of direction.
3.2.1 Stress-strain Relationship of Isotropic and Homogeneous Materials
The stress-strains relations for a linear elastic, isotropic and homogeneous material can be
written as
(3.1)
where and , E and are the stress tensor, strain tensor, Young’s Modulus and
Poisson’s ratio, respectively. The above equation can also be written in matrix form as,
(3.2)
where is called the stiffness matrix. As shown in equation 3.1, only two material
properties or elastic constants are required to form the stiffness matrix of a homogeneous
and isotropic material. The stress-strain relations can also be written in terms of the
compliance matrix (S) where
(3.3)
or
43
Similar to other metal, aluminium alloy exhibits elastic-plastic behaviour in which it
undergoes irreversible plastic strain when the stress within the material reaches yield
stress, . The stress-strain curve that illustrates elastic-plastic behaviour of a typical
aluminium alloy bar subject to static loading is shown in Figure 3-1. Beyond yield stress the
plastic deformation occurs with strain hardening up to ultimate tensile strength (UTS).
Beyond UTS, the strain softens until fracture or total fail. Aluminium alloy 2024-T3 that
used in GLARE also follows the same stress-strain behaviour. Mechanical properties of
aluminium alloy 2024-T3 are tabulated in Table 3-2.
Figure 3-1: Typical stress-strain curve of isotropic material (Gere & Timoshenko 1990)
Density, ρ (kg/m3) 2700
Melting temperature, Tm (Kelvin) 775
Elastic properties
Young’s modulus, E (GPa) 73.1
ν 0.33
Yield stress, (MPa) 345
Ultimate tensile strength, UTS 483
Failure strain, 0.18
Table 3-2 Mechanical properties of aluminium alloy 2024-T3 (Lesuer 2000; Buyuk et al. 2008)
Stress,
Strain,
E
UTS
0
44
Metallic material can be sensitive or insensitive to the strain-rate when subject to loading
and this sensitivity depends on the type of alloy. The stress-strain relationships of a strain-
rate sensitive material under static loading cannot accurately predict the stress-strain
relationships of the same material when is subject to impact loading (Rodríguez-Martínez
et al. 2011). Figure 3-2 shows the stress-strain curves of aluminium alloy 2024-T3 for
subjected to loading with three different strain rates. It is observed that strain rate affect
the yield stress, hardening and ultimate tensile strength of the material.
Figure 3-2: Equivalent stress evolution versus equivalent plastic strain for different strain rates for
aluminium alloy 2024-T3 (Rodríguez-Martínez et al. 2011).
Stress-strain curves under different strain rate can be obtained by tensile test carried on
the strain rate desired. Several models are available to estimate the strain response of
metal under various loading rate including Johnson-Cook material model that contain the
estimation of rate-dependent yield stress and rate-dependent hardening as in Equation 3.4
to 3.5 (Johnson & Cook 1983; Abaqus Documentation version 6.12). In a non-thermo-
coupled analysis, the homologous temperature so the final term consists of the
0
100
200
300
400
500
600
0.00 0.05 0.10 0.15 0.20
Equ
ival
ent s
tres
s (M
Pa)
Equivalent plastic strain
0.01s-1
10s-1
100s-1
45
homologous temperature will be equal to 1. So the expression can be rewritten without the
final term as in Equation 3.5.
(3.4)
(3.5)
where , , , and are material properties of the aluminium alloy, is equivalent
plastic strain, is equivalent plastic strain rate, is reference strain rate and is
homologous temperature.
3.2.2 Impact Behaviour of Aluminium Alloys Structure
An aluminium alloy structure which is subjected to axial impact may fail due to buckling
when the impact load exceeds its dynamic critical buckling load. Figure 3-3 shows
aluminium alloy structure that fail under axial impact loading due to buckling. The critical
buckling load of an aluminium alloy structure under dynamic impact mainly depends on its
material properties, mass, the impact velocity and most importantly the impact energy.
These parameters determine the patterns of the axial stress wave propagation which result
in different type of buckling modes. The axial stress wave can be divided into elastic stress
wave and plastic stress wave. The above parameters also affect the energy absorption of
the aluminium alloy structure during impact. The aluminium alloy structure which is subject
to axial impact may experience elastic-plastic deformation only or may crack as well. As
mentioned earlier, this mainly depends on the geometry of the structure, its material
properties, impact energy and impact velocity (Karagiozova et al. 2000; Karagiozova &
Jones 2000; Karagiozova & Jones 2001a, Hooputra et al 2004).
46
Figure 3-3.Buckling of aluminium can under axial loading (Palanivelu et al. 2011).
An aluminium alloy plate subjected to the lateral low velocity impact may be subjected to
indention damage or perforation. Again, this mainly depends on the plate’s material
properties, the impact energy and the impact velocity. The plate that exhibits indention
initially experiences localised plastic deformation, with or without cracks. If perforation
occurs, it usually starts with a local plastic deformation. Thus cracks initiate and then
followed by crack propagations (Rodriguez-Martinez et al. 2011).
Crack or fracture in aluminium alloy in any type of impact loading may occur due to
stresses within the aluminium alloy that surpass its critical limit. The stresses could be
tensile stress or shear stress. Tensile failure or fracture occurs due to nucleation growth
and coalescence voids within the structure. Meanwhile shear fracture is caused by shear
band localisation (Abaqus Documentation version 6.12). Johnson-Cook failure criterion is
one of the ductile fracture criterions as expressed in Equation 3.6.
(3.6)
where is the equivalent plastic strain at failure, are failure parameters
measured at or below the transition temperature, , p is the pressure stress, q is
the Mises stress. is the plastic strain rate and is the reference strain rate (Johnson &
Cook 1985; Abaqus Documentation version 6.12).
47
Damage mechanics would determine the effect of damage on the stiffness of the damaged
material up to its total failure condition. The strain response in damaged material is
generally defined by Equation 3.7
(3.7)
where the damage variable represents the damage within the material point which
controlled by stiffness degradation rules based on fracture mechanics. The damage variable
may have values between 0 to 1 in which denotes that the material has totally
damaged; leaving no residual stiffness and that element is removed from the global finite
element equation of the body problem.
48
3.3 Fibre Reinforced Composite Laminate
Fibre reinforced laminates are composite materials that have strong continuous or non-
continuous fibres surrounded by a weaker material called matrix. The most common types
of fibre materials are glass, aramid (Kevlar), carbon, boron and silicon carbide. Meanwhile
matrix materials could be grouped into three categories; polymer matrix such as
thermoplastic resins, ceramic matrix such as carbon and metallic matrix such as aluminium
alloys. Fibres and matrix are bonded during a manufacturing process called curing (Gay &
Hoa 2007).
3.3.1 Stress-strain Relationships of Fibre Reinforced Composite Laminate
Unlike aluminium alloy, composite materials are anisotropic in nature which make
composite to have 21 independent engineering constants in its stress-strain relationship as
expressed in Equation 3.8.
(3.8)
where is the stiffness matrix ( ). The stress and strain tensors
are symmetric, and since the stress-strain relations in linear elasticity can be derived from
a strain energy density function, the following symmetries hold for linear elastic materials
for .
An orthotropic material has two orthogonal planes of symmetry. Therefore, only 9
independent engineering constants are required to construct the material’s stiffness
matrix. Stress-strain relations for a linear elastic orthotropic material can be as expressed
(Gay & Hoa, 2007).
49
(3.9)
As shown, there is no interaction between normal stresses , , and shear strains
, , . Similarly there is no interaction between shear stresses and normal strains.
The stress-strain relationships of orthotropic composite laminates can also be expressed in
terms of the compliance matrix (Gay & Hoa, 2007),
(3.10)
or
(3.11)
with
, ,
3.3.2 Analysis of a Composite Lamina
A unit block of a composite laminated structure is a lamina. Superposition of a number of
laminas or layers made of unidirectional layers form a composite laminate. A lamina is very
thin in relation to its transverse dimensions and it is usually considered to be in plane stress
50
state when subjected to in-plane loadings. Figure 3-4 illustrates the local coordinates of
lamina under state of plane stress analysis.
Figure 3-4. Local coordinates of a lamina
Under this plane stress state, is assumed to be zero. The stress-strain relationships are
now expressed as in equation 3.12 to 3.17 which reduces the independent constants to
only four (Gay & Hoa, 2007). The stress-strain relationship of an orthotropic composite
lamina in terms of stiffness coefficients is;
(3.12)
(3.13)
with
,
, (3.14)
,
,
and its compliance;
(3.15)
1
2
x
y
Direction of fibres
51
(3.16)
,
, (3.17)
,
,
All expressions defining stress and strain relationship are in local 1,2 directions of the
lamina. If the local direction is not coincident with global axis, transformation matrix must
be applied such that;
and (3.18)
(3.19)
where
(3.20)
with and with is the angle between the local axis and global axis.
Finally forming the relation between global stresses and strains as
(3.21)
with is global stiffness matrix of the composite lamina where
(3.22)
Subscripts and in Equation 3.18 to 3.21 indicate the global axis and local axis
respectively.
52
3.3.3 Failure of Fibre-reinforced Composite Laminate
Fibre-reinforced composite laminates experience different types of failure such as fibre
rupture, matrix rupture and delamination. Figure 3-5 illustrates schematically main modes
of damage when the loads exceed the critical limits.
Figure 3-5 Failure modes of composite laminate (Gay and Hoa 2007).
In composite design, various failure criteria have been proposed by several researchers in
order to predict the onset of composite laminate failure. The most popular failure criteria
are the Hashin’s criterion Puck’s criterion, Tsai-Hill criterion, Chang and Chang’s criterion,
maximum stress criterion and maximum strain criterion. Hashin’s failure criterion has been
used by many researchers and it is one of the most reliable methods to predict the strength
of laminated composites (Sun & Tao 1998). In this thesis, Hashin’s failure criterion (Hashin
& Rotem 1973; Hashin 1980) is employed and both three-dimensional and two-dimensional
or plane stress cases are presented.
Hashin’s failure criterion was originally developed for unidirectional fibre-reinforced
laminate. Even though a three-dimensional failure criterion is available, but it is limited to
the scope of unidirectional laminates (Hashin and Rotem 1973; Hashin 1980). The criterion
53
is based on two failure mechanisms which are associated with failure in fibre and failure in
matrix, distinguishing in both cases between tension and compression. Two sets of Hashin’s
failure criterion are presented here; one with a plane stress assumption and the second
one is three-dimensional failure criterion.
3.3.3.1 Hashin’s Failure Criterion under State of Plane Stress
Failure mechanisms of fibre are governed by the longitudinal stress with reference to the
fibre orientation. Meanwhile failure mechanisms of matrix are governed by the transversal
and tangential stresses to the fibre. Failure is said to occur or damage is initiated at any
failure mode if the failure criterion of that failure mode is equal or greater than one
(Abaqus Documentation version 6.12). It must be noted that the original Hashin’s failure
criterion based on his paper in 1998 for compressive fibre mode is a non-quadratic
expression. Modification to quadratic term in fibre compressive mode possibly due to
maximum stress criterion would underestimate the strength of the laminate.
For failure in tensile fibre mode ( ),
(3.23)
For failure in compressive fibre mode ( ),
(3.24)
For failure in tensile matrix mode ( ),
(3.25)
For failure in tensile matrix mode ( ),
(3.26)
54
where XT, XC, YC, YT, S12, S23 and are the longitudinal tensile strength, longitudinal
compressive strength, transverse tensile strength, transverse compressive strength,
longitudinal shear strength, transverse shear strength in 2-3 direction and coefficient that
determines the contribution of the shear stress to the fibre tensile failure criterion,
respectively. is a function that describes the failure criterion.
3.3.3.2 Three-Dimensional Hashin’s Failure Criterion
Three-dimensional Hashin’s failure criterion is based on Hashin’s work in 1980. The same
basis as Hashin’s failure criterion under plane stress state is used where two separate
failure mechanisms are described in both tensile and compressive stress states. The
additional term that does not appear in failure criterion under plane stress state is the
transverse shear strength of 1-3 direction, .
For failure in tensile fibre mode ( ),
(3.27)
For failure in compressive fibre mode ( ),
(3.28)
For failure in tensile matrix mode ( ),
(3.29)
For failure in tensile matrix mode ( ),
(3.30)
55
3.3.3.3 Delamination of Fibre-Reinforced Composite Laminate
Delamination or interlaminar crack occurs when the lamina that form the laminate
structure separate from each other due to interlaminar shear stresses. It may also be
triggered by matrix cracking close to the surface of the laminas with different fibre
orientation or close to a matrix rich area between two plies. Composite structures that fail
under buckling mode always suffer delamination. Composite structure may also suffer
delamination at the outer layers that experiences tensile stress gradient along its thickness
when subjected to bending. Delamination in composite laminate is also part of the failure
mechanisms that control the failure mode when a composite laminate structure is axially
crushed. In laminate and delamination analysis, the surface where the delamination can
occur is always referred as interface layer.
Delamination degrades the stiffness and strength of laminate, alters the damping
coefficient in impact and can cause local buckling if compression load is applied. The
analysis of delamination in composite laminate is divided into two steps; delamination
initiation and delamination propagation.
A stressed based quadratic failure criterion for delamination initiation is expressed in
equation 3.31 (Brewer & Lagace 1988; Zhou & Sun 1990).
(3.31)
where in the above equations is tensile strength in the thickness direction at the
interface layer, is interlaminar shear strength in the direction at the interface layer
and is interlaminar shear strength in the direction at the interface layer.
Stresses in Equation 3.31 are the average interlaminar stresses defined as in Equation 3.32
where is the thickness of the interface layer.
56
(3.32)
In analysing delamination propagation, fracture mechanics is always used as this approach
may avoids difficulties caused by stress singularity at crack point. Delamination growth is
mainly controlled by the properties of the matrix (Farley & Jones; 1992).
3.3.4 Impact Behaviour of Fibre-Reinforced Composite Laminate under Low
Velocity Impact
Impact behaviour of fibre-reinforced composite laminate is mainly analysed under two
categories. The first one is lateral impact onto the laminate by drop weight alike and the
second one is dynamic axial crushing. Both analyses involve analysing the impact damage,
failure mechanisms, failure modes and energy absorption due to the damage process.
3.3.4.1 Lateral Impact
Under lateral impact on composite laminate, out-of-plane stresses are significantly smaller
than in-plane stress even though the impact is in the thickness direction. In the same time,
maximum stress in fibre-direction is always larger than in its in-plane orthogonal direction
because the flexural wave moves faster in the fibre direction compare to the other
direction (Aslan et al, 2003). Failure in composite laminate under low velocity lateral impact
can be caused fibre fracture or matrix fracture or delamination or combination of them.
Thick and thin composite laminates response differently under lateral loading. In thick
laminate, impact failure is always dominated by fibre fracture meanwhile in thin laminate,
delamination plays a major role in the impact failure. High bending stiffness in thick
laminate causes high out-of-plane stresses within the localised impacted area thus causes
high indention effect which results the fibre fracture dominate the impact damage in thick
laminate. In thin laminate, low bending stiffness causes the high bending or tensile stress at
the outer layer (non-impacted). This high in-plane tensile stress causes matrix cracking at
the surface of the outer lamina and may trigger delamination at that surface. The impact
57
response of thin laminate is almost like an efficient membrane response especially in the
presence of delamination. Due to this, researcher that model impact response of laminate
that consists of unidirectional laminas always simply consider the composite laminate as a
combination of lamina under plane stress state but with incorporation of interface layer
modelling in order to take into account the delamination.
3.3.4.2 Axial Impact
Impact response of composite laminate under axial crushing exhibits complex response due
to the interaction of various failure mechanisms. Three crushing modes of composite
laminate tube under dynamic axial loading are;
i. Transverse shearing mode
Failure mechanisms that control transverse shearing mode are interlaminar crack growth
and lamina bundle fracture. Interlaminar crack growth or delamination can occur as
opening mode (Mode I) or as forward shear mode (Mode II) as illustrated in Figure 3-6. Its
growth is mainly controlled by the properties of the matrix, but in the same time
circumferentially oriented fibre can have a major influence. Then the delaminated lamina
or laminates are subjected to the bending force, causing the lamina bundles to fracture
once the stress at the tensile side of the bended bundle exceeds its strength.
58
Figure 3-6. Sketch of crack propagation mode (Farley & Jones 1992).
ii. Lamina bending crushing mode
The failure mechanisms that control this failure mode is almost the same as in transverse
shearing mode except that when the lamina bends, the transverse shear crack does not
take place but the bending keep its progress and interlaminar crack progressively
propagate. Besides interlaminar crack, energy is absorbed due to friction work between the
loading surface and crushing surface of the composite. Thus it is important to take into
account the contribution of friction work in modelling such failure mode.
iii. Local buckling crushing mode
This mode is controlled by yielding of matrix or combination of both matrix and fibres.
59
Chapter 4 FINITE ELEMENT METHOD
4.1. Introduction
4.1.1. Introduction of Finite Element Method in Aircraft Crash Analysis
Finite element method is a numerical technique for finding approximate solutions to
boundary value problems for differential equations. Since the basic idea is to find the
solution of a complex problem by replacing it with a simpler one, the solution will be an
approximation rather than the exact one. The region of the problem to be solved is
discretised to many small interconnected subregions which are called as finite elements. By
assuming approximate solutions of each finite element, conditions of overall equilibrium of
the region are derived. In this study, region of the problem is referred to aircraft structure
such as fuselage frames, fuselage skin, stringers and floor beams.
Originally, finite element method was developed for the aircraft structure’s analysis either
on component level, structural level, section level or full-scale fuselage level. Substantial
amount of static and dynamic analyses have been carried using finite element method
either by researchers or aircraft designers (Hashemi et al. 1996; Hashemi & Walton 2000;
Fasanella and Jackson 2000; Jackson & Fasanella 2005; Meng et al. 2009). One of the
departments in aircraft structural analysis benefited from finite element method is aircraft
crash analysis in order to analyse the impact response of the aircraft including structural
integrity of the aircraft, collapse mechanisms and crashworthiness. In the emergence of
new materials for aircraft structure such as composites and fibre metal laminate (FML), the
impact response of the aircraft especially in terms of crashworthiness becomes new issue
for the aircraft designers. Impact test might provide extensive data on impact response
under crash but it is limited to a number of impact conditions only. Additionally, impact
test is very expensive. The use of finite element method enables researchers to analyse
crash of aircraft not just with lower cost but with almost unlimited impact conditions can
60
be simulated. In order to simulate aircraft crash, certain methodology must be developed
in order to obtain reliable crash simulation results. This might includes material
characterisation and modelling verifications. Methodology and verification process of crash
simulation model for fibre metal laminate (FML) fuselage is presented in the next chapter.
This chapter discusses about finite element method and its background theory used in
developing crash simulation of FML fuselage section.
4.1.2. General Description of Finite Element Method
A structure to be analysed by finite element method has to be discretised to form
interconnected finite elements in which the connections between elements occurs at
specified joints call nodes. Field variables at the nodes are the unknowns to be solved from
the finite element problems which are generally in the form of matrix equations. Once the
unknowns at the nodes are solved, the field variables inside the elements are
approximated by a simple function called interpolation models. As a result, the field
variables throughout the assemblage of elements or the whole region will be known.
Generally, solving a continuum problem by the finite element method is an orderly step by
step process. The step by step process is described below (Rao 1999).
Step 1: Discretization of the structure
Step 2: Selection of a proper interpolation model or displacement model
Step 3: Formation of element stiffness matrix
Step 4: Formation of global stiffness matrix and load vector
Step 5: Solution of the unknown nodal displacements
Step 6: Computation of element strains and stresses
Step 7: Post-processing
61
These steps are carried carefully throughout the process in developing a finite element
model of fibre metal laminate (FML) fuselage section. While using commercial finite
element (FE) code software, these steps are not necessarily distinctive because they could
be mixed between them while the user select the type of elements to be used, the
formulations used to control the section of elements, the material models, type of analysis
and many more. For in-depth understanding on these six steps, one can refer to text books
that discuss about finite element model from the fundamentals to specific analysis
(Zienkiewicz & Taylor 1991a; Zienkiewicz & Taylor 1991b; Rao 1999).
In general, a finite element equation system is form for the body region to be analysed as
(4.1)
, and denote the load vectors, stiffness matrix and displacement vectors of the
complete structural body or system. The finite element equation is solved by various
methods depends on the body problem and type of analysis.
4.1.3. Abaqus Finite Element (FE) Software
All finite element modelling and analysis in this thesis is done in Abaqus/Explicit version
6.10 and 6.12 but all the final results of the FML crash simulation are solved in version 6.12.
Abaqus/Explicit is used in order to take advantage its capabilities in solving nonlinear
transient analysis and its computational efficiency. The analysis was carried successfully
even though there were challenges in terms of computational stability in explicit solver
which may cause the solution to diverge and terminated immaturely. The author used both
CAE and keyword modelling (input files) for pre-processing and fully used CAE for post-
processing.
62
4.2. Nonlinear Dynamic Analysis
4.2.1. Nonlinear Analysis of Aircraft Structure
In many practical engineering problems including fuselage deformation in crash analysis,
the linearity of the problems does not preserved. In structural analysis, the nonlinearity of
the problem exists might be due to either by the nonlinearity of the constitutive relations
or by the nonlinearity of the structure geometry. Both nonlinearities exist in crash
simulation of fibre metal laminate (FML) fuselage. Fuselage section that made of FML
consists of aluminium alloy that will undergo plastic deformation when the stresses surpass
its yield criterion. Due to this, nonlinear constitutive relations are considered in the metallic
part of the fuselage structure. Meanwhile nonlinearity of the structure geometry occurs in
this study when the fuselage structure undergoes large displacement and structure
instability.
4.2.1.1. Plasticity Analysis
In nonlinear plasticity analysis, the stress-strain relationship within the material is
expressed in incremental form. The nonlinearity requires the stress-strain relationship and
both local and global finite element equation to be solved and satisfied incrementally
(Zienkiewicz & Taylor 1991b). The constitutive stress-strain relationship in nonlinear plastic
analysis is in form of
(4.2)
where is the nonlinear stiffness matrix. Incremental strain is decomposed into
incremental elastic strain, and incremental plastic strain as expressed in Equation
4.3.
(4.3)
63
To solve the finite element equation of plastic analysis, first one needs to solve the
incremental stress in Equation 4.2. There are several methods to solve the equation.
Method that used by Abaqus FE code is by solving few related equations with the
constitutive stress-strain equations using backward Euler method and central difference
operator (Abaqus Documentation version 6.12). Following the incremental procedure of
the stress-strain constitutive equation, the finite element equation (Equation 4.1) for the
plasticity analysis is also in incremental form and solved by applying incremental load
(Zienkiewicz & Taylor 1991b).
4.2.1.2. Geometrically Nonlinear Analysis
In aircraft crash analysis, the structure might undergo large displacements and strains such
as deformation due to instability of the structure. Large displacement or deformation can
occur even the elastic limits are still not exceeded. Geometry nonlinearity must be
considered in aircraft crash analysis. In crash simulation of FML fuselage, geometric
nonlinearity is combined with material nonlinearity.
In geometrical nonlinear analysis, the stress-strain constitutive equation is linear but the
strain-displacement relationship is non-linear unlike strain-displacement relationship in
ordinary linear stress-strain analysis. Besides that, geometrical nonlinear analysis equations
are in incremental form, similar to equations in plastic analysis. If the analysis is a
combination of geometrical nonlinear and plastic analysis, the linear stress-strain
constitutive equation is replaced with the nonlinear stress-strain equation as in plasticity
analysis (Zienkiewicz & Taylor 1991b).
Once the finite element equation for the geometrically nonlinear analysis is formed, the
same procedure as plasticity analysis is used to solve the equation.
64
4.2.2. Dynamic Analysis of Aircraft Structure
Aircraft crash analysis is a nonlinear dynamic analysis problem which is a time-dependent
or transient process. Such nonlinear analysis can be solved either implicitly or explicitly in
Abaqus FE code. In implicit analysis (Abaqus/Standard), the problems are solved by
iterating the nonlinear equations at every increment in order to solve them. It solves the
equilibrium state of the whole problem domain at every increment. As it iterates at every
increment, implicit procedure can be performed relatively at fewer number of time
increments compare to explicit procedure but it has a large set of linear equations to be
solved. On the other hand, explicit procedure solves the problem without iterations by
explicitly advancing the kinematic state of the body problem from the previous increment.
Due to this, it requires a large number of small time increments, but relatively inexpensive
as it does not have to solve large number of linear equations as in implicit (Zienkiewicz &
Taylor 1991b, Abaqus Documentation version 6.12).
Explicit procedure is efficient for problem that involves wave propagation. Besides, it is very
attractive in terms of computational cost as it requires less disk space and memory and it
solves dynamic problems quicker than implicit procedure for the same simulation. This is
because implicit procedure has to store and solve large amount of linear equations within
each iteration. With all due respect, explicit procedure is used in this project in simulating
crash of fibre metal laminate (FML) fuselage.
The key element in explicit dynamic analysis in Abaqus/Explicit is the implementation of an
explicit integration rule and the use of diagonal element mass matrices. The finite element
equation of dynamic is based on the dynamic equation of motion of a body thus the field
problems in dynamic equation are not just in form of stresses, strains and displacements
but also in form of velocities and accelerations. This equation of motion is integrated using
the explicit central difference integration rule. Explicit procedure is conditionally stable due
65
to the use of central difference operator, unlike implicit procedure that unconditionally
stable. The stability is controlled by introducing small amount of damping which reduces
the stable time increment. The time increment scheme in Abaqus/Explicit is automatic thus
it will automatically determine the stable time increment for the solution to proceed
successfully (Abaqus Documentation version 6.12; Zienkiewicz & Taylor 1991b).
66
4.3. Selection of Elements for Discretisation
There are few considerations need to be made in order to select the proper element in
discretising the structure of the problems. The considerations include type of analysis, the
geometry of the structure, the dimension of the problem and the application of the
structure within the problem. Computational efficiency and cost would also become the
reason of one to choose a specific type of element to discretise the problem. For example,
in aircraft fuselage section, the structure consists of fuselage frames, stringers and floor
beams that act as the main stiffeners of the fuselage section which can be represented as
sets of beams. The fuselage skin alone is like a massive cylindrical shell structure.
Meanwhile the interface layer in between composite laminate and aluminium alloy within
FML acts as the adhesive between these two layers. Thus suitable element has to be
selected to model all those structures.
4.3.1. Shell element
Shell element is used to model a three dimensional body structure which its thickness is
significantly smaller than the other dimensions. It is actually an improvisation of the flat or
plate element that originally developed to analyse flat plate. Plate is a flat structure that
subjected to bending. Meanwhile shell is an extension of plate by initially forming the
middle plane to a singly or doubly curved surface in which its stress resultant parallel to
middle plane now have components normal to the surface (Zienkiewicz & Taylor 1991b).
Shell element is categorized as structural element in finite element analysis as it possesses
common configuration in many physical structures and bodies.
4.3.1.1. Thin and Thick Shell Theories
Shell element formulation could be based on Kirchhoff thin shell theory or Reissner-Mindlin
thick shell theory. Both theories have a mutual basic assumption which is the middle plane
of the shell remains plane during and after deformation.
67
For thin shell theory, two additional assumptions are made as the basis of the theory. The
assumptions are the normal of the middle plane remain normal to the middle plane and
the thickness of the shell does not change during and after deformation (Timoshenko &
Woinowsky-Krieger 1959). As a result, there is no transverse shear deformation in thin shell
theory. This type of shell element is suitable for structure that has thickness less than 1/15
of the characteristic length of the structure and the transverse shear deformation can be
neglected (Abaqus Documentation version 6.12).
Meanwhile in thick shell theory, the two additional assumptions are not incorporated so
the shell can have transverse shear deformation. There will be stress gradient across the
shell thickness and the thickness of the shell may change. This element is suitable for thick
shell structure in which the transverse shear stress and deformation are essential in
capturing the structure’s response accurately (Abaqus Documentation version 6.12).
4.3.1.2. Conventional Shell Element and Continuum Shell Element
Two types of shell element are available which are conventional shell element which the
body is discretised as a reference surface and continuum shell element which the body is
discretised as three-dimensional body. Figure 4-1 illustrates conventional shell element and
continuum shell element. Conventional shell element is specified at the reference surface
in which its thickness does not appear in its geometry but defined in the constitutive
equation that define its section behaviour. It has both rotational and displacement degree
of freedom at each node. Meanwhile continuum shell element discretised the whole
geometry where its thickness depends on the defined geometry. Its nodes have only
displacement degree of freedom.
68
Figure 4-1. Conventional shell element and continuum shell element (Abaqus Documentation version 6.12)
In this thesis, both conventional and continuum shell elements that are categorised as
general-purpose shell elements where they use thick shell theory as the thickness increases
and use thin shell theory as the thickness decreases. Kirchhoff constraint is applied in their
formulation in which the constraint becomes fully effective when the thickness is very thin
and gradually released up to full thick shell theory as the thickness increases. The use of
such shell element is capable of providing robust and accurate solution for many
applications (Abaqus Documentation version 6.12).
Interpolation model in an element is used to interpolate the field variables output at its
node to the space within its element. Interpolation model within shell element can be
linear or polynomial (Rao 1999). In Abaqus, only linear and quadratic interpolation
formulations are available for shell elements and there is only linear interpolation
formulation available for explicit analysis. The number of nodes within an element shall
describe the interpolation model used within an element. An element that uses linear
interpolation formulation has only corner nodes and it should not have middle node at any
of its edge. Consequently, a linear quadrilateral conventional and continuum shell element
has four and eight nodes within their element respectively.
69
4.3.2. Incompatible Mode Solid Element
In finite element model of fuselage section, the fuselage skin can be modelled either by
shell element or continuum element. It is adequate to use shell element if the fuselage skin
is a single layer metallic material such as aluminium alloy. In a case of fuselage skin made of
fibre metal laminates (FML) which consisted of at least two aluminium alloy layer and few
layers of glass fibre composite laminate, it is more suitable to use continuum elements to
discretise the structure. The interactions between lamina by using interface layers and the
requirement of stresses continuity between them suggest that continuum element is more
suitable. Solid continuum element is the most suitable element to model the aluminium
alloy layer because it is modelled as elastic-plastic material, gets involve with contact and
might undergoes large deformation during the analysis.
Incompatible mode solid element is a fully integrated first-order solid element in which
incompatible mode is being incorporated in its formulation in order to improve its bending
behaviour. The incompatible mode is responsible to eliminate the parasitic shear stresses.
Parasitic shear stresses are the stresses and artificial stiffening due to Poisson’s effect that
cause ordinary first-order solid element to have stiff response towards bending. The use of
incompatible mode in first order solid element requires incorporation of internal degree of
freedom which causes this element more expensive than ordinary fully integrated solid
element. However, it is favourable as it can produce results as good as second order fully
integrated solid element (Abaqus Documentation version 6.12).
4.3.3. Reduced Integration Element
Integration point is the location where the integration evaluates various values including
the stiffness matrix of the element. In fully integrated element, there are four integration
points meanwhile in reduced integration element there is only one integration point. The
field output calculated from these integration points than extrapolated within the element.
70
Intuitively, fully integrated element should produce more accurate results. However fully
integrated element may suffer shear locking and in the same time reduced integration
element may suffer hourglassing. By incorporating proper hourglassing control, accurate
results can be obtained by using reduced integration element which sometimes better than
its full integration element.
4.3.4. Hourglass Control
Most of the reduced integration element has only integration point being placed at the
centroid of the element. Under certain condition, nodes that form the shape of the
element may have displacement but the integration point at the centroid registers no
energy and no straining. This zero-energy mode caused a phenomenon called hourglassing
which finally leads to inaccurate results. Figure 4-2 shows the deformation of the element
in an hourglassing mode with the integration point experience no displacement or
straining.
Figure 4-2. Element deforms in hourglass mode (Westerberg 2002).
Hourglass control is introduced to prevent hourglassing problem within reduced integration
element. This is done by adding a small artificial stiffness that associated with the zero-
energy deformation. Several hourglass control formulations are available in Abaqus FE to
suppress hourglass modes. Enhanced hourglass control is the best approach as it can
produce good results with coarse mesh, provides increased resistance to hourglassing for
nonlinear materials and works well with reduced integration shell element in both in-plane
71
and out-of-plane bending. This approach is actually a refinement of pure stiffness method
in which the stiffness coefficients are based on the enhanced assumed strain method
(Abaqus Documentation version 6.12). The pure stiffness method is based on Kelvin
viscoelastic approach defined as in Equation 4.4.
(4.4)
where is the hourglass mode magnitude, is the force conjugate to , is the scaling
factors and is the hourglass stiffness. So in enhanced hourglass control, the scaling
factors is removed but the formulation would alter the hourglass stiffness based on its
enhanced assumed strain method.
4.3.5. Cohesive Element
Interface layer has to be modelled in between FML layers. Interface layer can be
represented by cohesive element (Linde et al. 2004). It is a special type element in Abaqus
designated to model discontinuities like adhesives and interfacial layers in composite.
Figure 4-3 illustrates a schematic representation of a finite element model of FML with
cohesive element (dark-grey) being applied between layers.
Figure 4-3. Schematic representation of FML with interface elements (dark-grey) applied between layers (Remmers & de Borst 2001).
72
Interface layer in FML is very thin and its thickness is relatively negligible to the thickness of
the FML. So traction-separation constitutive approach to model the mechanical
constitutive response of the cohesive element is implemented. This approach is simply an
application of fracture mechanics in which amount of energy to create a new surface is
being considered and it can be applied in three-dimensional problems (Abaqus
Documentation version 6.12).
4.3.5.1. Mechanical Constitutive Response of Traction-Separation Cohesive Element
The traction-separation model assumes initially linear elastic behaviour followed by
damage initiation and damage evolution. The elastic constitutive matrix that relates the
nominal stresses to the nominal strains governs the elastic behaviour of the cohesive
element. To ensure that the nominal strain is equal to the separation, the constitutive
thickness is set to be equal to 1.0. It must be reminded that constitutive thickness in this
model is not the same with the actual thickness of the interface layer which is typically
equal or close to zero (Abaqus Documentation version 6.12). The nominal stress vector
consists of three components; the normal stress , shear traction on 1-local direction
and shear traction in 2-local direction . The elastic behaviour then is written as
(4.5)
where
,
and
(4.6)
,
,
.
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with , and are the corresponding separations and is the original thickness of the
cohesive element. Figure 4-4 illustrates typical traction-separation response with failure
mechanisms in a cohesive element.
Figure 4-4. Typical traction-separation response (Abaqus Documentation version 6.12)
4.3.5.2. Damage of Traction-Separation Cohesive Element
Damage initiation of interface layer is determined by the damage criterion. Several option
of damage criterion for cohesive element is available in Abaqus. Quadratic nominal stress
criterion assumes damage is initiated when a quadratic interaction function involving all
nominal stress component ratios reaches a value of one. The quadratic nominal stress
criterion is adapted from Brewer & Lagace (1988) and Zhou & Sun (1990) as in equation
3.31 and rewritten as in Equation 4.7.
(4.7)
where , , are the normal and two transverse shear tractions, ,
, are the normal
and two transverse shear strengths and the symbol denotes that a pure compressive
deformation or stress state does not initiate damage.
74
In order to fully model the damage of cohesive element, damage evolution model has to be
incorporated to describe the propagation of the damage through degradation of the
material stiffness corresponds to the damage initiation that has been satisfied.
Damage evolution is defined based on the fracture energy or amount of energy being
dissipated due to the damage process (Abaqus Documentation version 6.12). Fracture
energy is the area under the traction-separation curve as shown in Figure 4.5. Figure 4.5
illustrates the traction-separation response with exponential damage model. The term
exponential mentioned indicates that the material softening occurs exponentially once the
material point passes the effective separation at damage initiation, as shown in Figure
4-5. Meanwhile is the effective separation at total failure.
Figure 4-5. Traction-separation response with exponential softening (Abaqus Documentation version 6.12).
Evolution of damage variable in exponential softening is expressed as in Equation 4.8
where and are effective traction and displacement respectively and is elastic
strain energy at damage initiation (Abaqus Documentation version 6.12).
(4.8)
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Fracture energy is defined separately for each traction components, but it can be modelled
as mixed mode in which the deformation fields are dependent proportionally with all the
traction components. The power law fracture criterion defines that failure under mixed-
mode conditions is governed by a power law interaction of the energies required to cause
failure in each individual traction mode. The criterion is expressed as
(4.9)
where , , are the work done by the tractions and their conjugate relative
displacements and ,
, are the fracture energies of each mode (Abaqus
Documentation version 6.12). In this criterion, the power of the law is 2.
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4.4. Material and Damage Model of Aluminium Alloy
This section presents the material and damage model of the aluminium alloy used in
modelling the metallic part of the FML fuselage. Some of the constitutive equations have
been presented in previous chapter so it will not be rewritten here but reference of the
equation number will be given. Material and damage properties of both aluminium alloy
2024-T3 and 7075-T6 are presented in Chapter 5 while specifically discussing on validation
of their material models.
4.4.1. Material Model of Aluminium Alloy
Aluminium alloy fuselage structure is modelled as an elastic-plastic material. The elastic
part of the model is described as isotropic elastic which possess only two elastic constants;
Young’s modulus and Poisson’s ratio. The constitutive three-dimensional stress-strain
relationship that governs the elastic response of the aluminium alloy is expressed in
Equation 3.2.
The plastic response that defines the yielding and hardening of aluminium alloy is modelled
using Johnson-Cook plasticity model as expressed in Equation 3.5. Johnson-Cook plasticity
model is capable of determining the rate dependent yield stress and rate dependent
hardening so it is very suitable to model the aluminium alloy under impact loading. It is also
very suitable for high strain rate deformation modelling (Abaqus Documentation version
6.12). Four material parameters are required to use this plasticity model which can be
obtained by sets of material test. These parameters for aluminium alloy 2024-T3 and 7075-
T6 that used in FML fuselage section are available in several published papers. The
numerical solution procedure of plasticity is as described in section 4.2.1.1 on plasticity
analysis.
77
4.4.2. Damage model of Aluminium Alloy
Failure onset, damage evolution and the total failure are used to model damage and failure
in aluminium alloy. This damage models are suitable for both quasi-static and dynamic
conditions. Following is the description of the damage initiation model to determine the
onset of failure or damage in aluminium alloy. The damage evolution that describes the
progression of the initiated damage and the total failure in which the element’s stiffness
has fully degraded are also described.
4.4.3. Onset of damage in Aluminium Alloy
The onset of damage in Aluminium Alloy is determined by a special ductile criterion named
Johnson-Cook criterion. The criterion determines the equivalent plastic strain at the
onset of damage as expressed in Equation 3.6 and rewritten as Equation 4.10 by removing
the thermo-coupled term in the equation.
(4.10)
This criterion is a function of plastic strain rate , stress triaxiality
and parameters to
. p is the pressure stress, q is the Mises stress which are measured at the instantaneous
time meanwhile the to are failure parameters obtained from experiment. These
parameters for aluminium alloy 2024-T3 and 7075-T6 that used in FML fuselage section are
available in several published papers (Lesuer, 2000; Murat Buyuk, Matti Loikkanen 2008).
4.4.4. Damage Evolution of Aluminium Alloy
Damage evolution defines the stiffness degradation of the material in which the damage
has initiated based on the Johnson-Cook failure criterion. Figure 4-6 illustrates the typical
stress-strain curve of aluminium alloy with progressive damage and stiffness degradation.
The softening curve is controlled by the damage evolution model. The dash line is simply
the path of the straining if damage evolution is not modelled. The stiffness of the material
78
is degraded and controlled by the damage parameter . Effective plastic displacement
is introduced once damage is initiated with
(4.11)
where is the characteristic length of an element. In a first-order solid element, is simply
the length of a line across that element. is used to form a new stress-displacement
relationship in order to evaluate damage, as the use of ordinary stress-strain relationship
can no longer accurately present the behaviour of the material once damage occurs
(Abaqus Documentation, version 6.12). Figure 4-7 illustrates the linear damage-effective
plastic displacement relationship where
is the effective plastic displacement at total
failure. The damage-effective plastic displacement follows this relationship
(4.12)
Figure 4-6. Stress-strain curve with progressive damage degradation (Abaqus Documentation version 6.12).
79
Figure 4-7. A linear damage evolution based on effective plastic displacement (Abaqus Documentation version 6.12)
4.5. Material and Damage Model of Fibre-Reinforced Composite
Laminate
This section presents the material and damage model of the fibre-reinforce composite
laminate used in modelling the composite laminate part of the FML fuselage. Some of the
constitutive equations have been presented in previous chapter so it will not be rewritten
here but reference of the equation number will be given.
4.5.1. Material Model of Fibre-Reinforced Composite Laminate
Fibre-reinforce composite laminate alloy fuselage structure is modelled as elastic material
with damage model incorporated at lamina level. Plasticity is not modelled as this material
is brittle in nature. Modelling the material response at lamina level allow us to represent
each lamina as in a state of plane stress, thus there is only five elastic constants in its
stress-strain constitutive equation. The plane stress-strain relationship is expressed
previously in Equation 3.13 and its compliance form as in Equation 3.15. The through
thickness response of the laminate is modelled by stacking each lamina and incorporating
interface layer in between.
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4.5.2. Onset of damage in Fibre-Reinforce Composite Lamina
Failure onset, damage evolution and the total failure are used to model damage and failure
in fibre-reinforced composite laminate. Again, damage model is incorporated at lamina
level same as how the undamaged mechanical response is modelled. Damage through
thickness is represented by the damage of the cohesive element as the interface layer
which has been discussed in section 4.3.5. Following is the description of the damage
initiation model to determine the onset of damage, the damage evolution that describes
the progression of the initiated damage and the total failure in which the element’s
stiffness has fully degraded in composite laminate.
In general, damage in the lamina degrades the stiffness of the material and it modifies the
constitutive elastic stress-strain relationship as in Equation 4.14 (Abaqus Documentation
version 6.12).
(4.13)
with
(4.14)
where , is the current damage state of fiber, is the
current damage state of the matrix and is the current damage state of shear damage.
Onset of damage in fibre-reinforce composite lamina is based on Hashin’s failure criterion.
The criterion differentiates four failure modes; fibre mode in tension, fibre mode in
compression, matrix mode in tension and matrix mode in compression (Hashin & Rotem
1973; Hashin 1980). It is a stress based failure criterion in which the effective stress is used
to express the failure surface. Effective stress is the stress acting over the area that
efficiently resists the stress. The material that resists the stress within the lamina might
81
have been damaged by other failure mode. So the undamaged part within the damaged
material is presented as the area left to resists the stress applied. Equation 4.15 expresses
the relationship of stresses and the effective stresses.
(4.15)
where is the effective stress, is the true stress and is the damage operator in which
(4.16)
with
,
,
Shear damage is in the function of all other damage mode that occurring within the
lamina (Abaqus Documentation version 6.12). The Hashin’s failure criterion for each mode
is presented in Equation 3.23 to 3.26. With all the stress components are replaced with
their effective stresses respectively, the damage initiation criterion is rewritten as in
Equation 4.17 to 4.20 below. It should be noted that the criterion used here assumes plane
stress state following that the plane stress state is assumed in the stress-strain constitutive
equation of the lamina.
For failure in tensile fibre mode ( ),
(4.17)
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For failure in compressive fibre mode ( ),
(4.18)
For failure in tensile matrix mode ( ),
(4.19)
For failure in tensile matrix mode ( ),
(4.20)
In the above equations
where XT, XC, YC, YT, S12, S23 and are the longitudinal tensile strength, longitudinal
compressive strength, transverse tensile strength, transverse compressive strength,
longitudinal shear strength, transverse shear strength in 2-3 direction and coefficient that
determines the contribution of the shear stress to the fibre tensile failure criterion,
respectively. F is a function that describes the failure criterion.
4.5.3. Damage Evolution of Fibre-Reinforced Composite Lamina
Similar to damage evolution in aluminium alloy, stress-displacement relationship is
established to avoid mesh-dependency problem during softening if using ordinary stress-
strain relationship. The equivalent displacement and stress are defined for each failure
mode gives
For failure in tensile fibre mode ( ),
(4.21)
(4.22)
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For failure in compressive fibre mode ( ),
(4.23)
(4.24)
For failure in tensile matrix mode ( ),
(4.25)
(4.26)
For failure in tensile matrix mode ( ),
(4.27)
(4.28)
Symbol in above equations indicate that for every as . Once
the damage has initiated, the following expression define the damage of each failure mode
(Abaqus Documentation version 6.12).
(4.29)
where is the equivalent displacement at damage initiation for particular mode and
is the equivalent displacement at total failure for that particular mode. Damage evolution
of each mode is independent to each other unlike damage evolution in cohesive element
that exhibit mixed mode damage. Figure 4-8 illustrates the equivalent stress-equivalent
displacement relationship with linear softening represented by line AC. If damage material
is unload back to origin state such from point B to 0, the same path will be followed back to
point B and then continue with the softening. Area under the curve is the energy required
84
to cause a total damage to a material point. So the fracture energy of each mode is
specified which will then determine the equivalent displacement at failure at each mode.
The fracture energy can be related to strain to failure as in Equation 4.30 to 4.33 (Shi et al.
2012) in which strain to failure is material parameters that can be determined through
material tests.
(4.30)
(4.31)
(4.32)
(4.33)
where , , , are fracture energy of each mode and
are
strain at total failure of each mode with subscript represents fibre tensile
mode, fibre compression mode, matrix tensile mode and matrix compression mode
respectively.
Figure 4-8. Linear damage evolution of a lamina structure(Abaqus Documentation version 6.12)
85
4.6. Interaction and Contact Modelling
General contact algorithm in Abaqus/Explicit is used in this study. It only has few
restrictions in its algorithm compare to contact pair algorithm. This advantage makes it
very suitable for crash analysis of FML fuselage which involves complex interaction within
various bodies. General contact also allows the use of element based surface in order to
model surface erosion during analysis. Thus the faces of any failed element will be removed
from the contact domain which means the contact domain evolves during the analysis.
General contact algorithm is enforced with penalty constraint enforcement.
For computing efficiency, the pair of the surfaces involve in the contact are defined. This
includes the two adjacent layer surfaces in FML fuselage skin that separated by cohesive
elements so that contact will occur once the cohesive element in between has failed and
deleted. If contact and interaction are not defined between these adjacent layers, the
structure would not exhibit proper structural response including excessive element
distortion and surface penetration. As a result, the job analysis might be terminated or
diverging results are produced. In this thesis, any possible contact surface was predicted by
observing results of crash tests and crash simulation of Boeing 737 fuselage section
previously done by other authors. Besides, the author himself makes an attempt to
anticipate any other possible contact surface. If the anticipated contact surfaces never
make any contact during the simulation, it would not affect the results of the simulation
except adding some computation time due to the contact algorithm within the software
package. The details of the possible contact surfaces are discussed in Chapter 5.
General contact algorithm refers to interaction property between surfaces in order to
model the tangential behaviour and normal behaviour. Tangential behaviour is defined by
friction formulation meanwhile normal behaviour is defined by contact pressure-
overclosure relationship (Abaqus Documentation version 6.12).
86
The classical isotropic Coulomb friction model is used as the friction formulation. The
model assumes that no relative motion occurs if the equivalent frictional stress is less
than the critical stress, in which the critical stress is proportional to the contact
pressure as in Equation 4.34.
(4.34)
where is the friction coefficient. The equivalent frictional stress is defined as
(4.35)
where it is a function of transmitted shear forces across the interacting surfaces.
The contact pressure-overclosure relationship governs the motion of the interacting
surfaces in the contact domain. In this work, hard contact pressure-overclosure
relationship is enforced. Figure 4-9 shows the hard contact pressure-overclosure
relationship. The relationship defines that when the contact pressure between surfaces
reduces to zero, the surfaces will separate and when the clearance between the surfaces
becomes zero, the surfaces will come into contact. Any contact pressure can be
transmitted between the contacted surfaces during contact. Meanwhile Transfer of tensile
stress across the contact interface is not allowed in this model (Abaqus Documentation
version 6.12).
87
Figure 4-9. Hard contact pressure-overclosure relationship diagram (Abaqus Documentation version 6.12).
88
4.7. Constraint and Connection Modelling
Fuselage section is an assemblage of few structures that connected either by adhesive,
fasteners and spot welds. Finite element allows modelling such connection with various
approaches such as applying constraint between two parts or fastens the two parts with
additional connecting elements. Two main concepts in such modelling are constraints and
connections.
4.7.1. Mesh Tie Constraints
Mesh tie constraint is one of the constraining approaches that dependent to the mesh of
the constrained bodies. Constraint means that it eliminate degrees of freedom of a group
of nodes called slave nodes and couple their motion to the motion of master nodes. The
constraint bonds the two surfaces through their nodes permanently even though the
element of the surface has fully degraded due to material failure.
4.7.2. Mesh Independent Fasteners
Mesh independent fasteners are independent from the mesh of the connected bodies. It
can be used to model spot welds, rivets and adhesive and failure model can be
incorporated within its formulation. Connector elements defined within the fasteners
definition provide point-to-point connection between two or more surfaces. Mesh
independent fasteners provide distributing coupling constraint in which the distribution
weight between the two surfaces can be controlled.
89
4.8. Computational Facilities in The University of Manchester
Abaqus FE code version 6.10 and 6.12 has been used to solve all the finite element models
related to this thesis. Three main computing facilities that contributed to the finite element
analysis of this research are:
1. Personal desktop with Abaqus 6.10 and 6.10 licensed to The University of
Manchester
2. Condor or previously known as Epsilon; a high throughput computing (HTC) owned
and managed by Engineering and Physical Science Faculty of The University of
Manchester. The maximum number of processor can be used for a job is 4 cores
with 4 to 8GB RAM for each core.
3. Computer Shared Facilities (CSF): A cluster of machines that include Intel and AMD
processors with various specs that owned by The University of Manchester.
Mechanical, Aerospace and Civil Engineering School in total can submit up to 288
cores in the multiple nodes that connected with Infiniband at one time.
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Chapter 5 DEVELOPMENT OF FIBRE METAL LAMINATE
FUSELAGE CRASH MODEL
5.1. Introduction of Aircraft Crash Methodology
Crash simulations of aircraft have been carried by many researchers mainly for the purpose
of investigating the impact response. Various methodologies they used to ensure the
results produced from their simulations are reliable. Several researchers used ‘building
block’ approach to develop a fuselage section crash model. Building block approach is a
typical approach in design and certification of aerospace structure. It involves step-by-step
tests from coupon test for material characterization, followed by structural element tests,
then components and finally the full scale fuselage structure. This approach is adapted to
finite element modelling by following the same step-by-step procedure but with fully
computational works or combination of both computations and tests (Hashemi and
Walton, 2000; Kindervater, 2011; Heimbs et al, 2013). Other methodology is by simulating
crash of a scaled fuselage model accompanied by validations from a scaled fuselage test in
which the results of the scaled fuselage test have been pre-correlate with a full scale
fuselage test (Jackson et al, 1997). Scaling effects are being considered in order to produce
reliable results. Modelling method by simulating only a section of the aircraft is a popular
method. This method is always applicable if the impact condition is limited to vertical
impact only which is a component of the impact direction in a real aircraft crash. Subjected
by a vertical impact loading, aircraft is always sectioned into the area that the researchers
are interested in such as fuselage section that contain three rows of passengers’ seats.
Based on the simulation objectives, some researchers assumed that the aircraft crash
response only dominated by the fuselage structure underneath the floor level, thus only
structure below the floor are modelled and investigated (Kumakura et al, 2002; Feng et al,
2013)..
91
5.2. Methodology of Crash Modelling of Fibre Metal Laminate
Fuselage
As the development of fibre metal laminate (FML) fuselage crash simulation is fully
computational work, verification and validations of the model at material modelling level,
failure mechanisms level and structural response level are essential. These verification and
validation works are incorporated into the building block approach thus making it as the
main frame of the development methodology. Fully verified and validated model at each
level should produce a reliable full scale FML fuselage crash model. Crash simulation of FML
fuselage in this thesis is limited to the vertical component of the impact due to the size and
complexity of the model especially in its material level. Combined with the one of the
objective of the thesis which is to evaluate crashworthiness, only a fuselage section with
two rows of passengers’ seats is modelled. Figure 5-1 summarise the methodology adopted
in developing the crash simulation of FML fuselage.
Development of crash simulation of FML fuselage starts with validation of material and
damage modelling for materials used in FML fuselage. Materials used in FML fuselage in
this thesis are classified into two which are aluminium alloy and fibre-reinforced composite
laminate. In modelling fibre-reinforced composite laminate, adhesive material is also
modelled to represent the interface layer between laminas. Material and damage model
for both categories are validated as the preliminary work and presented in section 5.3. The
development process continues with the verification of impact model that possesses
dynamic instability and large displacement which is presented in section 5.4. The last stage
before modelling the full scale fuselage section is the verification of the main individual
structure of the fuselage section as presented in section 5.6. The main individual structure
being verified is the fuselage frame. Finally, the verified and validated models at every
92
level, the structures are assembled to form a full-scale fuselage section and ready for its
crash simulation and analysis.
Figure 5-1. Methodology of developing crash simulation of FML fuselage section
93
5.3. Validation of Material and Damage Model Subjected to Impact
Loading
Fibre metal laminate (FML) fuselage section consists of three categories of material which
are aluminium alloy that exhibits elastic-plastic response, composite laminate that exhibits
elastic-brittle response and balsa wood that only exhibits elastic response. Fuselage
structures that are made of aluminium alloy are metallic part of the FML fuselage skin,
fuselage frames, floor beams, longitudinal stringers and seat tracks. Meanwhile composite
laminate is the constituent of the FML fuselage skin. The balsa wood with elastic response
only is used as the floor panel but its material model is not necessary as it is assumed that it
is not actively involved in the global impact response of the fuselage section. In fact some
of the researchers did not model the floor panel in its aircraft crash simulation model
(Meng et al, 2009; Yu et al, 2013). Following section discusses about validation model of
material and damage model for aluminium alloy and composite laminate.
5.3.1. Validation of Aluminium Alloy Material and Damage Model
The geometry and material of the fuselage section in this thesis is based on commercial
aircraft Boeing 737. The only difference is that the FML fuselage uses FML material instead
of aluminium alloy alone in the real Boeing 737. Boeing 737 uses aluminium 7075-T6 for its
fuselage frames, floor beams, stringers and seat tracks and aluminium alloy 2024-T3 for its
fuselage skin. In GLARE FML fuselage skin, the metallic constituent is also 2024-T3
aluminium alloy. The material and damage model for both are the same in which they
exhibit elastic-plastic response and undergo damage once the criterion is satisfied followed
by damage progression up to total failure.
Validation of material and damage model is carried by subjecting an FE plate model made
of this material with a rigid impactor under low velocity impact. The impact loading and the
plate structure of this FE model is based on an experimental work done by Rodriguez-
94
Martinez who was originally studying a 2024-T3 aluminium alloy plate under thermo-
mechanical impact loading (Rodriguez-Martinez et al, 2011). The results of the
experimental work under room temperature are then compared to the results from the FE
model. The Rodriguez-Martinez’s experimental set-up is shown in Appendix 1.
Material and Damage Model Formulation
The elastic response of aluminium alloy is based on the stress-strain constitutive equation
of isotropic material in Equation 3.1, Chapter 3. Two engineering constants are required,
Young’s modulus, and Poisson’s ratio, . The yield stress and plastic hardening model
with strain-rate dependent is modelled by using Johnson-Cook plastic model as expressed
in Equation 3.5, Chapter 3 and failure criterion of the alloy is prediction by Johnson-Cook
damage model as in Equation 4.10, Chapter 4. The material properties including
parameters that required for Johnson-Cook plasticity and damage model are tabulated in
Table 5-1 for both 2024-T3 and 7075-T6 aluminium alloy. However, only FE plate model
with 2024-T3 aluminium alloy only is being modelled in this thesis. Meanwhile aluminium
alloy 7075-T6 will be used for few structural parts once the fuselage section has been
assembled, Section 5.6 and 5.7.
95
Parameter Notation 2024-T3 7075-T6
Density (kg/m3) ρ 2700 2810
Young’s modulus (MPa) 70000 71700
Poisson’s ratio 0.33 0.33
Strain failure 0.18 0.11
Plasticity parameters of Johnson-Cook Plasticity Model
Static yield stress (MPa) 369 546
Strain hardening modulus (MPa) 684 678
Strain hardening exponent 0.73 0.71
Strain rate coefficient 0.0083 0.024
Damage parameters of Johnson-Cook Damage Model
0.112 -0.068
0.123 0.451
-1.5 -0.952
0.007 0.036
Table 5-1. Material properties of 2024-T3 and 7075-T6 aluminium alloy (Lesuer 2000; Buyuk et al. 2008).
5.3.1.1. Finite Element Model under Low-Velocity Impact for Aluminium Alloy 2024-
T3
The model consists of an aluminium alloy plate with thickness of mm and size of A =
80 x 80 mm2. As the plate is clamped at all sides in the experimental set up, all degree of
freedom for nodes at all edges in the numerical model are set to zero. The plate is
impacted by a discrete rigid impactor that has conical shape at impact velocity 4 m/s. The
larger diameter of the striker is 20 mm, radius of nose is 3 mm and angle of its conical nose
is 18⁰. Total mass of the stiker, Mtotal is 18.787 kg.
The meshing of the plate is shown in Figure 5-2. Mesh of aluminium alloy plate with finer
mesh at the impact area where the mesh is finer at the impacted area. The geometry of the
plate is meshed by a reduced integration linear solid element C3D8R. Four elements are
defined across the plate’s thickness.
96
Figure 5-2. Mesh of aluminium alloy plate with finer mesh at the impact area
5.3.1.2. Validation on Model with Various Hourglass Controls
Preliminary, five cases using different hourglass control option are analysed. The first case
uses enhanced hourglass control option; the second uses relax stiffness hourglass control
option; and the rests are pure stiffness, pure viscous and combined stiffness and viscous
hourglass control options.
Table 5-2 shows that model with viscous hourglass control has the lowest value of artificial
strain energy meanwhile model with enhanced hourglass control has the highest. Amount
of artificial strain energy observed from any numerical model is directly associated with
constraints used to remove singular modes including hourglass control (Abaqus
Documentation, version 6.12). It is recommended that the artificial strain energy (ALLAE) is
less or equal to 2% from the total internal energy (ALLIE) but overall the artificial strain
energy for all numerical model is still low (below than 5%).
97
Model with different
Hourglass Control
Artificial strain
energy, ALLAE (%)
Maximum impact
force (kN)
Energy absorbed,
Et (J)
Experiment (Rodriguez-
Martinez) - 3.75 14.64 (10%)
Enhanced 4.103% 3.57303 10.105
Relax stiffness 0.696% 2.99191 9.192
Stiffness 2.611% 3.33666 9.395
Viscous 0.265% 2.49626 9.127
Combined 1.313% 3.08959 9.239
* All values are evaluated at failure time tf
Table 5-2. Results comparison between FE models and experimental works in terms of artificial energy percentage, maximum impact force and energy absorption.
Numerical model with enhanced hourglass control has maximum impact force closest to
experiment results. Model with viscous hourglass control is the worst, 33% lower than
experiment results. Meanwhile in term of amount of energy absorbed, Et at failure time, tf
indicates that model with enhanced hourglass control produced the best results when
compare to experiment results followed by stiffness, combined, relax stiffness and viscous
hourglass control models. Failure time, tf is the time when the impact force is maximum,
where . Overall, energy absorbed, Et predicted by all numerical model is still
lower than the energy absorbed recorded from the experiment. Based on these
observations, the rest of the results are analysed from FE model with enhanced hourglass
control.
5.3.1.3. Results Correlation
Sequence of images of the perforation and failure process is shown in Figure 5-3. A dishing
phase is found at the beginning of the loading process that involves both elastic and plastic
deflection of the plate as can be seen in Figure 5-3a. Subsequently, strain localises on the
contact surface which leads to the onset of cracks. From this point on, high circumferential
strains caused by the passage of the striker lead to radial crack propagation as can be seen
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in Figure 5-3b. Figure 5-3c-d illustrates a number of symmetric petals are formed and bent
until complete perforation of the target.
Figure 5-3. Different stages of the perforation process for an aluminium alloy 2024-T3 sheet, V0 4.0 m/s. (a) Localisation of deformation and onset of crack. (b) Cracks progression and formation of petals. (c) Development and bending of petals. (d) Complete passage of the impactor and petalling failure mode.
Next is to compare energy absorbed, by the target from the first contact up to the
failure time, . In the experiment by Rodriguez-Martinez, energy absorbed is expressed by
Equation 5.1
(5.1)
(a) (b)
(c) (d)
99
where is residual velocity at failure time. Numerically, energy absorbed by the target is
simply evaluated by subtracting the kinetic energy of the striker at failure time from the
impact energy. It is understood that the process of strain localisation and subsequent
plastic instabilities are responsible for the target collapse during impact (Rodriguez-
Martinez, 2011). Most of the energy is dissipated through these plastic works. The FE
model under predicted the energy absorbed by the 2024-T3 plate by 21%. This behaviour is
well explained by the comparative stress-strain curves between experimental results
(Rodriguez-Martinez, 2011) and Johnson Cook material model as shown in Figure 5.4. The
comparison is made for 100 s-1 strain rate. Strain rate in FE model is evaluated by dividing
the equivalent plastic strain at failure, 0.18 by the failure time, tf which is 1.62 ms (Fan
et al, 2011) resulting 111 s-1 strain rate. Failure time, tf is the time when the impact force
reaches its maximum value or
in which is the displacement of the impactor
(Rodríguez-Martínez et al. 2011). Plastic flow exhibited in experiment is higher than plastic
flow in Johnson-Cook plastic model as shown in Figure 5-4 which indicates that the ‘real’
aluminium alloy absorbed more energy per unit volume compared to Johnson-Cook plastic
model. So the energy absorbed by material based on stress-strain curve from experiment is
higher than by material modelled by Johnson-Cook for the similar yielding and straining.
This explains why FE model under predict the energy absorption by the aluminium plate
subjected to impact loading. Energy absorbed per unit volume, is the area under the
stress strain curve (Rodriguez-Martinez et al, 2011) as expressed in Equation 5.2.
(5.2)
100
Figure 5-4. Flow stress evolution versus strain for Johnson-Cook material model
Impact force versus striker displacement is examined up to 15 ms where the whole body of
the striker has perforated through the aluminium alloy plate. Figure 5-5 shows that FE
model correlates well with experiment in terms of maximum impact force. However, the
predicted maximum impact occurred at lower striker displacement compare to experiment.
In terms of permanent deflection of the plate, FE model predicted higher deflection than
experiment by 20% as illustrated in Figure 5-6.
5.3.1.4. Conclusion on the Validation Work on Material and Damage Model of
Aluminium Alloy
Despite of having highest artificial strain energy within the model which was greater than
recommended 2% value, enhanced hourglass control method provide the best results
compared with experimental results in terms of the force evolution and energy absorbed
during impact. Artificial strain energy to total internal energy ratio of 4% is still considered
low and relatively being compromised as its results correlate well with experiment.
0
100
200
300
400
500
600
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
Equ
ival
en
t str
ess
(MP
a)
Equivalent plastic strain
Experiment
FE material model
101
Overall, FE material and damage model predicted well the impact response and damage
process of aluminium alloy where it starts with strain localisation at the impacted area,
crack onset, progress of perforation and petalling. It is observed that the material strain
rate is in magnitude of 100 s-1 when impacted by impactor under 4 m/s impact velocity.
However, FE models under predicted the amount of energy dissipated through damage by
21%.
Figure 5-5. Impact force as a function of the impactor displacement
Figure 5-6 Permanent deflection of the target for FE model and experiment
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Forc
e (N
)
Striker displacement (mm)
Experiment
FE model
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Pe
rman
ent d
efl
ecti
on
on
th
e t
arge
t (m
m)
Target length, Lt (mm)
experiment
FE Model
102
5.3.2. Validation of Composite Laminate Material and Damage Model
Composite laminate within the FML fuselage skin consists of unidirectional composite
lamina stacked and bonded in an orderly orientation. Validation of material and damage
model for composite is carried by subjecting an FE plate model made of fibre-reinforce
composite laminate with a rigid impactor under low velocity impact. The impact loading
and the composite laminate structure of this model is based on experimental work and FE
model developed by Shi et al (2011) who was investigating impact response of composite
laminate subjected to low velocity impact (Shi et al, 2011). Then the results from this FE
model are compared to experiment and FE model produced by Shi et al (2011).
In Shi et al (2011) work, he investigated the impact response of a carbon fibre composite
laminate. Even though carbon fibre composite laminate is not used in this thesis, but the
response of this material as a laminate consists of orderly stacked fibre-reinforced
unidirectional lamina should possess the same characteristic with the one made of glass-
fibre that used in GLARE FML. Thus it assumed that this work is adequate to validate the
material and damage model of fibre reinforced composite laminate. The only difference
between carbon-based and fibre-based reinforced composite laminate is the value of their
material properties.
5.3.2.1. Material and Damage Model Formulation
The composite laminate is modelled as a compilation of individual laminas in which
interface layer is incorporate between each laminas in order the lamina to interact with
each other and to form continuities along the thickness direction as previously illustrated in
Figure 4.3, Chapter 4. Effectively, two separate material and damage models are used to
model the individual lamina and the interface layer or we call it as adhesive. Theoretically,
the adhesive between unidirectional lamina is the matrix of the composite itself in which
that bonding was formed during curing. However a richer matrix composition is formed at
103
the surface plane between adjacent laminas with different fibre orientation, effectively
being regarded as adhesive or interface layer. Thus the material properties of the adhesive
are actually the material properties of the matrix of the lamina itself.
i. Composite lamina
Composite lamina exhibits elastic-brittle mechanical response which is based on the stress-
strain constitutive orthotropic material in Equation 3.12 to 3.17 in Chapter 3. This stress-
strain relationship considers a state of plane stress. Only four engineering constants
required to model the mechanical response of the undamaged lamina respectively Young’s
modulus in the direction of fibre , Young’s modulus in the direction orthogonal to the
fibre , the Poisson’s ratio and the in-plane shear modulus .
No plasticity is modelled due to the elastic-brittle nature of composite lamina. Damage is
initiated once the lamina stress condition satisfies the failure criterion. Failure criterion of
the composite lamina is Hashin’s failure criterion that defines criteria for each failure mode
separately; fibre tensile, fibre compressive, matrix tensile and matrix compressive as
explain in section 3.3.3. The plane stress Hashin’s failure criterion is used as expressed in
Equation 3.23 to 3.26. However the effect of the damage from other mode to the damage
initiation of other mode does exist via relationship in Equation 4.13 to 4.16. The damage
evolution of composite lamina as discussed in section 4.5.3 is modelled with a linear
stiffness degradation with fracture energy of each failure mode determines the equivalent
displacement at total failure. The material properties of carbon fibre reinforced composite
laminate in this validation work are tabulated in Appendix 2.
ii. Adhesive (Interface layer)
Adhesive between lamina is modelled using a special-purposed element regarded as
cohesive element in Abaqus which is governed by a linear mechanical constitutive traction-
104
separation relationship as in Equation 4.5 to 4.6 in Chapter 4. Damage initiation is based on
quadratic nominal stress criterion (Equation 4.7). Mixed-mode damage between all traction
components are used with power law is used to interact the fracture energy for each mode
as expressed previously in Equation 4.8. The power of the law used is 2 and the damage
evolution response is exponential. The material properties of the adhesive in carbon fibre
reinforced composite laminate in this validation work are tabulated in Appendix 2.
5.3.2.2. Finite Element Model under Low-Velocity Impact for Fibre-Reinforced
Composite Laminate
The impact target is made of 2 mm composite plate consisted of eight plies with a ply
thickness of 0.25 mm in the stacking sequence [0,90]2s. Diameter of the composite laminate
plate is 75 mm with all displacement and rotational degree of freedom at all nodes of the
edge is set equal to zero in order to have a clamped boundary condition. The impactor has
hemispherical head of 15 mm in diameter and its weight is 2 kg. The impactor hits the
target with impact velocity of 3.834 ms-1 resulting in impact energy of 14.7 J. Figure 5-7
illustrates the geometry of the model and the boundary condition at the edge of the plate.
Figure 5-7. Numerical model of the impact on composite laminate.
z
y
x Fixed edge
mm
mm
105
In this validation task, two different models are developed, one with cohesive element and
the other without cohesive element. The purpose of modelling two techniques is to
investigate the significance of adhesive layer as delamination model in modelling impact
response of composite laminate.
Continuum shell element, SC8R is used to model the unidirectional lamina. Cohesive
element, COH3D8 is used to model the interface layer with its geometrical thickness of
0.001 mm. As mentioned previously, geometrical thickness is not the constitutive thickness
used in the traction-separation constitutive equation. The computing time is reduced by
introducing different mesh size/density in different regions of the FE model; higher density
mesh at the impacted zone as can be seen in Figure 5-7. The degradation parameters were
set as maximum and failed elements were removed from the FE model once the failure
criteria are satisfied.
5.3.2.3. Results Correlation
Impact force and energy versus time curves from finite element model in this validation
model is compared to Shi’s experimental and numerical work in order to assess the
accuracy of the proposed model.
i. Impact force
In Figure 5-8 shows the force-time histories for the 14.7 J impact test.. In general the
impact force time histories start with vibration induced by initial contact between the
striker and the composite laminate. Then the impact force will increase up to the peak
value which when the damage within the laminate is initiated. The striker then bounces
upward and the load is reduced to zero. All finite element models in this study follow this
general impact force time histories pattern.
106
The maximum force recorded in Shi’s experiment and his finite element model are 4605 N
and 3917 N respectively. Finite element models without and with adhesive developed for
validation estimated maximum force of 6359 N and 4663 N respectively. Easily notified that
finite element model with adhesive estimated more accurate results than the FE model
without adhesive. In FE model without adhesive, it overestimates the strength between the
composite lamina or actually the composite lamina will never delaminate. Effectively, this
model is stiffer than FE model with adhesive. Meanwhile in FE model with adhesive,
delamination failure provides additional energy dissipation mechanism thus decreasing the
striker’s deceleration and maximum impact forces on the composite laminate. As a result, it
is predictable that FE without adhesive causes higher maximum impact force compare to
the experiment and FE models with adhesive.
After the peak load is reached and the striker starts to rebound, the numerical results take
longer time to reach zero compare to experimental results except for FE model without
adhesive. As mentioned by Shi et al (2011), this phenomenon might occur due to contact
forces between delaminated plies after the cohesive elements have been removed from
the simulation as the composite plate returns to its original shape. However, Shi’s
explanation should not be the case in this validation models because the impact force
output is obtained from the impact surface pairs which is between impactor and the
composite laminate.
The impact force-time results in Figure 5-8 are then translated into force-displacement
curves shown in Figure 5-9. In the initial phase of the impact event, there is similar slope
until the maximum impact force reached. It is the same case as force-time curves where FE
model without adhesive estimated relatively higher maximum force impact compare to the
rest of FE models predictions and experiment results. However, all numerical models
predicted smaller or zero indention when the contact force has reduced to zero compared
107
to experimental results. This is simply due to the linearity of the material in FE model in
which in experiment, the composite possessed little inelastic strain which caused
permanent deformation. FE model without adhesive predicted that the composite plate
returns to its initial pre-impact state which indicates that there is no permanent
displacement except some elements are deleted as they have fully degraded. Figure 5-10
and Figure 5-11 show impacted composite plates and their cross-section of the FE mode.
For FE model without adhesive, it shows no permanent deflection and few elements are
deleted due to material failure. FE model with adhesive shows the existence of
delamination. The delamination causes the lamina to undergo large displacement and have
more elements to fail compare to FE model without adhesive, thus gives more damping
and absorbs more impact energy.
Figure 5-8. Impact force-time histories of impacted composite laminate
0 500
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 7,000
0 1 2 3 4 5 6
Forc
e (N
)
Time (ms)
Experiment (Shi)
FE model (Shi)
FE model with no adhesive
FE model with adhesive
108
Figure 5-9. Impact force-displacement histories of impacted composite laminate
Figure 5-10. Deformation in impacted plate for FE model without adhesive.
0 500
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500
0 1 2 3 4 5 6 7
Forc
e (N
)
Displacement (mm)
experiment FE model (Shi)
FE model with no adhesive FE model with adhesive
109
Figure 5-11. Deformation in impacted plate for FE model with adhesive.
ii. Impact energy
The impact energy of the striker is transferred to the composite laminate once contact is
made. Figure 5-12 illustrates the energy absorption-time histories. During the impact
event, part of the energy is absorbed by composite laminate in the form of elastic energy
which will not cause any permanent deformation, while a larger amount of energy is
dissipated through damage in the composite lamina, delamination and friction between
contact surfaces. Once the striker’s velocity reaches zero, the elastic energy stored in the
laminate will be transferred back to the striker causing it to rebound in opposite direction.
FE models predicted that the impact energy are transferred to the composite laminate at
higher rate compare to experiment results and to FE model developed by Shi.
FE model without adhesive quickly lose its energy as large amount of it that has been
absorbed initially were transferred back to the striker. The composite laminate absorbed
the initial kinetic energy mainly as elastic energy. Only little of them were absorbed which
caused the intra-lamina damage in the composite laminate. The rest of the model absorbed
110
more energy than FE model without adhesive as the energy was also dissipated through
delamination. Table 5.3 presents the amount of energy absorbed by the laminate and its
prediction from numerical models. FE model with adhesive predicts better in terms of
energy absorption compare to other models including model developed by Shi himself.
Figure 5-12. Energy absorption-time histories for impacted composite laminate
Impact energy (J) Absorbed energy
Experiment (J) FE by Shi (J) FE model without
interface layer (J)
FE model with
interface layer (J)
14.7 9.52 9.08 5.67 9.49
Table 5-3. Amount of energy absorbed during impact of composite plate
5.3.2.4. Conclusion on the Validation Work on Material and Damage Model of Fibre-
Reinforced Composite Laminate
FE model without adhesive experiences highest impact energy than the rest of the FE
model. This is because delamination as one of the main energy dissipation mode is not
modelled. So the impact energy is mainly absorbed by elastic strain and only small portion
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16
0 1 2 3 4 5 6
Ene
rgy
(J)
time (ms)
Experiment (Shi et al)
FE model (Shi)
FE model without adhesive
FE model with adhesive
111
of the impact energy is absorbed by intralaminar damage which causes under-prediction of
energy absorption. In strength-sense, FE model of composite laminate without adhesive
will overestimate the strength of the laminate especially if delamination mode is one of its
main energy absorption in that particular impact condition.
Results of FE model with adhesive correlates well with experiment results in terms of
impact force between the contacted surfaces. It predicts the maximum impact force and
the duration of the impact force close to experiment.
As a conclusion, the material model used in this work is able to predict the impact response
and damage of fibre-reinforced composite laminate. The incorporation of cohesive element
as interface layer which is used to model delamination improve the material and damage
response of the laminate under impact loading as it provide better prediction in terms of
failure mechanisms and energy dissipation mechanisms.
112
5.4. Validation of General Impact Modelling
This section is to validate a general impact modelling that involves geometrically nonlinear
response of the structure due instability and large deformation. Validation of finite element
model of dynamic buckling of structure made of isotropic element suits this objective.
The validation task involves modelling of a non-modified and modified finite element
model of cask drop analysis using axisymmetric solid element, shell element and three-
dimensional solid element which. This impact model is based on one of the impact model
example in Abaqus Documentations (version 6.12). The configuration of the cask drop
analysis is as shown in Figure 5-13.
Figure 5-13. A quarter symmetric model of cask drop onto a rigid surface (Abaqus Documentation, 6.12)
Example of cask drop with foam impact limiter in Abaqus Documentation is based on
Sauve’s work (Sauve et al, 1993). A containment cask is partially filled with fluid and a foam
113
impact limiter as illustrated in Figure 5-13. The drop impact onto a rigid surface is modelled
by assigning the whole cask including the water and foam in it with initial velocity, V0 of
13.35 m/s which equivalent to the same cask being dropped from a height of 9.09 meter.
The dropping is this case is not modelled by impacting the cask onto a rigid surface but it is
modelled by setting zero degree of freedom (ENCASTRE) to all nodes at the containment
base.
Contact conditions are defined for interaction between the fluid and the inside part of the
upper compartment and for interaction between foam impact limiter and the inside of the
bottom compartment of the cask. Self contact is also defined in the structure. The
examples in Abaqus Manual present the results of model using axisymmetric shell element
(SAX1) and three-dimensional shell element (S4R) for the side wall of the containment.
Three models using solid element are also simulated in this test in order to verify the
reliability of solid element in modelling impact by comparing to the results of axisymmetric
shell element model and shell element model provided by the manual. These three solid
element model parameters are listed in Table 5.4.
Model Element used to model side wall of the
containment
Hourglass control
1 Reduced integration solid element, C3D8R Relax stiffness (default)
2 Reduced integration solid element, C3D8R Enhanced
3 Incompatible mode solid element, C3D8I -
Table 5-4. Cask drop with solid elements modelling to be verified
For this particular validation work, the field of interest is to analyse the deformation of the
side wall of the lower containment, the displacement of the steel that separate the fluid
and the foam and the energy balance during the impact. Figure 5-14 shows the
deformation shape of the side wall of bottom containment which is the rounded part for all
models at 5 ms. The bottom wall buckled in a similar way for all models except solid
114
element with default hourglass control model which exhibits stiff response. The
deformation shape for incompatible mode solid element model is totally similar to
axisymmetric model as C3D8I element has good bending behaviour. Meanwhile model with
enhanced hourglass control solid element buckled with smaller deflection compare to both
axisymmetric model and shell element model. As nodes of shell element have rotational
degree of freedom, it is expected that the buckled wall contains hinged deflection between
each element affected within model with shell elements.
115
(a) (b)
(c) (d)
116
Figure 5-14. Deformation of side wall of bottom containment at 5 ms, (a) axisymmetric model, (b) shell element model, (c) C3D8R element with default hourglass control model, (d) C3D8R element with enhanced hourglass control model and (e) C3D8I element model.
Displacement of the bottom side wall is measured at dotted location in Figure 5-14a for all
models. Displacement at this location represents crushing distance of the structure during
impact. Figure 5-15 illustrates the crushing distance histories of all models meanwhile
Figure 5-16 illustrates the elastic strain energy and energy dissipated through plastic
dissipation during impact. Crushing time history and final crushing distance of incompatible
mode element model correlates well with results from Abaqus example. The results
correlation is consistent with the deformation shape and magnitude of deflection of the
side wall by referring to Figure 5-14.
The amount of energy dissipated through plastic deformation for all models correlates well
with axisymmetric model with the largest difference of 7.5% by solid element with default
hourglass control model. Incompatible mode element model differs with axisymmetric
model with 5% meanwhile enhanced hourglass control solid element gives the best
correlation with axisymmetric model in terms of plastic energy dissipation.
(e)
117
In terms of crushing distance and plastic energy dissipation, incompatible mode element is
seen as better option to model isotropic element that undergoes crushing due to impact
compare to enhanced hourglass control solid element. This is due to good bending
capability of incompatible mode element. Meanwhile enhanced hourglass control solid
element C3D8R comes second possibly because part of the impact energy is dissipated
through its artificial strain energy due to hourglassing control. There is no hourglassing in
full integrated incompatible mode element C3D8I.
Figure 5-15. Crushing distance of the containment for all models
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25
Dis
pla
cem
ent
(mm
)
Time (ms)
axisymmetric model
shell element model
solid element with default hourglass control model
solid element with enhanced hourglass control model
incompatible mode solid element model
118
Figure 5-16. Plastic dissipation and elastic strain energy time histories
0
5
10
15
20
25
0 5 10 15 20 25
Ener
gy (
kJ)
Time (ms)
ALLPD - axisymmetric model ALLPD - shell element model ALLPD - default hourglass control solid element model ALLPD - enhanced hourglass control solid element model ALLPD - incompatible mode solid element model ALLSE - axisymmetric model ALLSE - shell element model ALLSE - default hourglass control solid element model ALLSE - enhanced hourglass control solid element model ALLSE - incompatible mode solid element model
119
5.5. Verification of Fuselage Frame Impact Modelling
Fuselage frames are the main structure in an aircraft fuselage section that keep the shape
of the fuselage structure and hold the weights of the aircrafts body section. As fuselage
frame is the main source of strength within the fuselage section, reliable finite element
modelling of fuselage frame is essential in order to simulate crash of aircraft fuselage.
5.5.1. Finite Element Modelling of Fuselage Frame
Verification of fuselage frame under crash event is essential in developing crash simulation
of full-scale fuselage section. A semi-monocoque frame based on Boeing 737’s frame
geometry is discretised as shown in Figure 5-17. The upper outer radius and lower outer
radius of the frame are 1.88 meter and 1.80 meter. Details of the frame’s geometry are
obtained from Boeing Company website and Niu’s textbook (Boeing Website; Niu 1988).
Frame is made of aluminium alloy 7075-T6 which is stiffer then aluminium alloy 2024-T3
used for fuselage skin. Density of AA 7075-T6 is 2934.07 kg/m3 with Young’s modulus of
71.7 GPa and Poisson’s ratio of 0.33. Full material properties and damage parameters of
aluminium alloy 7075-T6 used in this model are provided in Table 5-5. Plastic hardening
and damage of AA 7075-T6 are defined by Johnson-Cook material and damage models, the
one that has been validated in section 5.3.1.
120
Figure 5-17. Fuselage frame configuration and discretisation.
Figure 5-18. Z cross-section of fuselage frame
121
Parameter Notation
Hardening parameters
Static yield stress [MPa] A 546
Strain hardening modulus [MPa] B 678
Strain hardening exponent n 0.71
Strain rate coeeficient C 0.024
Thermal softening exponent m 1.56
Melting temperature [K] 750
Damage parameters
-0.068
0.451
-0.952
0.036
0.697
Table 5-5. Material and damage model parameters of aluminium alloy 7075-T6 (Brar et al. 2009).
Shell element S4R with enhanced hourglass control is used for the entire fuselage frame.
Mass element is modelled at two locations as highlighted as red dots in Figure 5-17 in order
to replicate the weight of floor beam. Red dots are a simplified location of where the floor
beam is attached to the frame. In order to avoid deflection in longitudinal z-direction, inner
flange of the frame is restrained from moving into z-direction. In full fuselage section,
fuselage frames are restrained to move in z-direction by the stringers and the rigid fixes.
Initial velocity of 9 m/s is defined at all nodes of the frame causing to have 3.5 kJ of impact
energy onto a rigid impact surface. General contact that implements penalty contact
method is used to define contact between frame and rigid surface. Self-contact on frame
structure is also defined. Friction coefficient of 0.15 is set between frame and rigid surface.
Element is set to be deleted if its damage degradation reaches maximum value, Dmax = 1.
Energy balance during impact is the main output to be analysed in order to check the
reliability of the models. Meanwhile the crushing distance of the frame which is measured
122
at location that is highlighted with black dot in Figure 5-17 is also analysed. Three finite
element models with three different mesh sizes are modelled as described in Table 5-6.
Model Mean Characteristic length (Element size) Number of elements
frame_64 64 mm 734
frame_32 32 mm 2018
frame_20 20 mm 3899
Table 5-6. Frame finite element models with various mesh sizes
5.5.2. Verification Results of Fuselage Frame Impact Model
Figure 5-19 shows the deformation at time 50 ms which the bottom of the fuselage started
to buckle in upward direction. Another major buckling occurred at two locations which
geometrically symmetric to each other at impact time 125 ms as shown in Figure 5-19b.
Figure 5-19c shows the deformation of the frame just before it rebounded in upward
direction due to elastic strain stored within the structure. All these major buckling
produced permanent plastic strain that dissipated most of the impact energy beside the
elastic strain energy that causes the frame to rebound. This deformation mode
corresponds to the buckling verification of isotropic structure made of shell element
discussed previously.
123
Figure 5-19. Deformation of frame (a) at time 50 ms, (b) at time 125 ms, (c) at time 175 ms
(a)
(b)
(c)
124
Crushing distance of the frame is illustrated in Figure 5-20. All models with various mesh
sizes have almost similar crushing pattern. Displacement of model with most refine mesh is
1.237 meter which the difference with model with coarsest mesh is only 1%. The
displacement is only analysed up to 225 ms as the frame rebounded right after that and the
impact force has reduced to zero.
Figure 5-20. Crushing distance of frame with various mesh sizes.
Figure 5-21 shows plastic energy dissipation of models with various mesh sizes. Mesh
convergence is observed when mesh size is reduced from 32 mm to 20 mm with energy
dissipated through plastic strain is 1.7 kJ. Energy balance of finite element model with
element size 32 mm is further shown in Figure 5-22 which indicates consistency of kinetic
energy loss with plastic strain energy dissipation and elastic strain energy stored.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 20 40 60 80 100 120 140 160 180 200 220 240
Cru
shin
g d
ista
nce
(m
eter
)
Time (ms)
Crushing distance 64 mm
Crushing distance 32 mm
Crushing distance 20 mm
125
Figure 5-21. Plastic energy dissipation of frame finite element models with various mesh sizes.
Figure 5-22. Energy balance of frame model with mesh size 32 mm.
0
500
1000
1500
2000
2500
0 20 40 60 80 100 120 140 160 180
ALL
PD
(J)
Time (ms)
ALLPD 64 mm
ALLPD 32 mm
ALLPD 20 mm
0
500
1000
1500
2000
2500
3000
3500
4000
0 20 40 60 80 100 120 140 160 180 200 220
Ener
gy (
J)
Time (ms)
ALLKE
ALLPD
ALLSE
126
5.6. Development of Crash Impact FE Model of Aluminium Alloy
Fuselage Section
5.6.1. Geometric Information and Assumptions
The fuselage section is based on commercial Boeing 737 fuselage. The front fuselage
section with no cargo door and auxiliary fuel tank was modelled. The geometry
measurements of the fuselage section were obtained from the technical data owned by
Boeing Company. The cross-section of the fuselage is a double-lob structure with lower lob
and upper lob radius of 1.8 meter and 1.88 meter respectively. Only two fuselage stations
were modelled with a total longitudinal length of 1.016 meter which includes two window
cutouts at both sides.
The fuselage section consist of three fuselage frames, a cylindrical fuselage skin with
windows cutouts, three floor beams, floor panel, seat tracks and longitudinal stringers. The
same fuselage frame model that has been verified in section 5.5.2 was used in this model.
The cylindrical fuselage skin is attached to the fuselage frames by mesh tie constraint.
Meanwhile longitudinal stringers are fastened to fuselage skin using mesh independent
fastener. There is no failure being modelled in joints that formed by both mesh tie and
mesh independent fastener. The rest of the joints to assemble all structures into a
complete fuselage section is also modelled by mesh tie constraints. The impact surface
where the fuselage section will impacted onto is modelled as rigid impact surface. Thus no
deformation would occur at the impact surface. Another simplification is that seats and
occupants were modelled by point mass element. These assumptions and simplifications
are necessary to keep the model simple without compromising the reliability of the results
(Adams and Lankarani, 2003).
Development of model is performed by Abaqus. The fuselage section is discretized,
assigned with proper elements and material models. Contact is defined between bottom
127
part of the fuselage and the rigid impact surface. Contact is also defined in between
fuselage structures that may come into contact.
5.6.2. Discretisation of the Fuselage Section
The verified fuselage frame was modelled by shell element, S4R with enhanced hourglass
control. Meanwhile the aluminium alloy 2024-T3 fuselage skin was modelled by
incompatible mode solid element, C3D8I. This element was chosen based on the
verification of impact modelling of isotropic structure in section 5.4. Meanwhile seat tracks
were modelled by beam elements, B31. The rest of the structures were discretised by shell
elemet S4R including stringers, floor beams and floor panels.
5.6.3. Material Assignment
All structures in aluminium alloy fuselage section are made of aluminium alloy 7075-T6
except fuselage skin and floor panel. Fuselage skin is made of aluminium alloy 2024-T3
meanwhile floor panel is made of balsa wood that only possessed elastic response.
5.6.4. Impact and Contact Modelling
General contact algorithm was used to model contact between fuselage section and the
rigid impact surface. Contact between structures within fuselage was also modelled using
general contact algorithm. All nodes within the fuselage structure were given initial velocity
10 ms-1 in downward direction in order to simulate the impact velocity of the fuselage.
Gravitational force was also assigned to the fuselage structure. Friction coefficient of 0.15
was assigned between fuselage and the rigid impact surface. Table 5-7 shows the possible
contact surfaces and pairs during the crash of the fuselage.
128
Pair Surface 1 Surface 2
1 Ground (Rigid impact surface) Fuselage skin (outer and inner)
2 Ground (Rigid impact surface) Fuselage frame
3 Fuselage frame (bottom half) Floor beams
4 Fuselage frame (bottom half) Floor panels
5 Fuselage frame (bottom half) Seat tracks
6 Fuselage skin (bottom half) Floor beams
7 Fuselage skin (bottom half) Floor panels
8 Fuselage skin (bottom half) Seat tracks
9 Longitudinal stringers Floor beams
10 Longitudinal stringers Floor panels
11 Longitudinal stringers Seat tracks
12 Longitudinal stringers Fuselage skin
13 Fuselage frame Fuselage Frame (self-contact)
14 Fuselage skin Fuselage skin (self-contact)
Table 5-7. Contact surface pairs modelled within the fuselage
5.6.5. Location of Mass
Mass element is modelled to represent the mass of the seats and the passengers. This
fuselage model has six seats in a row which three at each side. 100 kg is specified for the
total mass of a passenger and a seat. Thus in total 300 kg seats with passengers at each
side. These mass is distributed between two seat tracks at each side where each seat tracks
supports 150 kg. The 150 kg mass is further distributed at nodes within a single seat track.
129
5.7. Development of Crash Impact FE Model of GLARE Fuselage
Section
The only difference between aluminium alloy fuselage section and GLARE fuselage section
is the modelling of their fuselage skin. This section discuss the development of the GLARE
fuselage skin meanwhile the rest of the fuselage structure were modelled with the same
technique as discussed in section 5.6.
GLARE fuselage skin is made of GLARE grade 5-2/1 which has two outer layer of aluminium
alloy 2024-T3 and four layers of unidirectional glass-fibre reinforce lamina with stacking
orientation of 0⁰/90⁰/90⁰/0⁰.
The aluminium alloy 2024-T3 is modelled by incompatible model solid element C3D8I and
Johnson-Cook plastic and damage model. Meanwhile the laminate is modelled by
continuum shell element, SC8R with Hashin’s failure criterion to model the damage
initiation. Interface layer is incorporated in between layers including in between lamina and
aluminium alloy. All the constituents within GLARE are modelled based on the validated
and verified models in previous section. However, maximum material degradation of
composite laminate is set as 0.99 and no element deletion is modelled. The reason of not
modelling element deletion at maximum degradation is to ensure that the elements of the
laminate did not distorted excessively due to complex contact interaction between lamina,
cohesive element and aluminium alloy within the GLARE skin.
130
5.8. Evaluation of Acceleration Response at Floor-Level
5.8.1. Data collection and processing of the acceleration response during crash
event
Acceleration response of the fuselage during crash was evaluated at two nodes for both
fuselages; the node at the outer right seat track and at the inner right seat track. This is to
represent the acceleration response experienced by the passengers seating inside the
fuselage cabin during crash. As the fuselage section is geometrically symmetry, only
acceleration at the right side was evaluated. The acceleration response on the left side is
assumed to be mirror image response of the right side. Noises in the acceleration-time
history data were filtered with a 60 Hz low pass filter using Matlab. Cutoff frequency 60 Hz
was applied as it is the cutoff frequency that commonly used by aircraft crash researchers
in analysing acceleration response including Adams and Lankarani (Adams & Lankarani
2010). The filtered response has pulse duration that match the apparent pulse duration of
the unfiltered acceleration response.
5.8.2. Human tolerance towards acceleration
The acceleration responses experienced by the passengers in crash analysis of aluminium
alloy and fibre metal laminate fuselage are analysed based on the human tolerance
towards acceleration. Two factors of human tolerance towards abrupt acceleration
(Shanahan 2004a) are evaluated; magnitude of the acceleration and direction of the
acceleration.
Due to the different tolerance level in different direction, the acceleration tolerance level
of human is described in term of coordinate axes which comprises of magnitude and
direction as in Figure 5-23 and Table 5-8. In vertical crash test or crash simulation, only
headward and tailward acceleration direction is considered.
131
Figure 5-23. Human coordinate system (Shanahan 2004b)
Table 5-8. Human tolerance limits (Shanahan 2004b).
Table 5-8 shows the summary of tolerance level of human towards acceleration in their
respective directions for 0.1 second crash pulse. In general, human can tolerate better
towards shorter crash pulse of the same acceleration magnitude. The acceleration
tolerance level in this table is specified in terms of G, where 1 G is the gravitational
acceleration at sea level which is 9.81 m/s2.
Acceleration-time history of a crash may consist of pulses with very complex shapes. For
practical purposes, the crash pulse is considered as triangular in shape as suggested by
Shanahan (Shanahan 2004b) as in Figure 5-24. The maximum acceleration experienced is
132
denoted by the peak of the pulse and the average acceleration of the pulse is one-half of
the peak acceleration.
Figure 5-24. Acceleration crash pulse in assumed triangular pulse (Shanahan 2004).
133
Chapter 6 RESULTS AND DISCUSSIONS
6.1. Introduction
The crash simulation was carried on two types of fuselage section models. The first model
was fuselage section that made of aluminium alloy fuselage skin representing the original
Boeing 737 fuselage section. The second model was fuselage section that made of the fibre
metal laminate (FML) GLARE 5-2/1 fuselage skin. Beside the fuselage skin, all other
structures within fuselage with FML fuselage skin are the same with the fuselage with
aluminium alloy fuselage skin. From now on in Chapter 6, fuselage section with aluminium
alloy fuselage skin is simply referred as aluminium fuselage meanwhile fuselage section
with fibre metal laminate (FML) GLARE 5-2/1 fuselage skin is simply referred as GLARE 5-
2/1 fuselage.
Two main objectives to be achieved in this chapter are to analyse the impact response of
GLARE 5-2/1 fuselage and how impact response of GLARE 5-2/1 fuselage differs from the
aluminium fuselage during crash event. Discussion on these results should develop
understanding on failure and deformation, energy dissipation and acceleration response at
floor level within future FML fuselage during survivable crash event.
6.2. Energy Dissipation during Crash
Aluminium fuselage and GLARE 5-2/1 fuselage were both executed with at 10 ms-1 in their
vertical direction. The duration of the simulation was 180 ms. With 10 ms-1 impact velocity,
the impact energy of aluminium fuselage and GLARE 5-2/1 fuselage was 35.41 kJ and 39.05
kJ respectively. The mass difference is due to the difference in the mass of their fuselage
skin alone. Apparently, GLARE 5-2/1 fuselage in this thesis is 5.8% heavier than the
aluminium fuselage. Worth to mention that GLARE 5-2/1 could have different specific mass
134
depends on the thickness of the aluminium alloy layer as commercially it varies between
0.2 to 0.5 mm.
During crash, fuselage structure absorbs the impact energy and distributed among the
structural components such as fuselage frames, fuselage floor, fuselage skin, seat tracks
and stringers. Analysing the percentage of energy transferred to and dissipated through the
structural components should gives understanding on energy dissipation mode within the
aircraft structure. With this technique, the energy absorption capability of GLARE 5-2/1
fuselage skin can be evaluated.
Figure 6-1 and Figure 6-2 show the energy balance of aluminium and GLARE 5-2/1 fuselage
crash simulations under velocity impact 10 ms-1. Both energy balances show similar
characteristic in terms of their energy dissipation. The energy is absorbed by the fuselages
initially by their elastic response and then followed by plastic deformation that dominates
energy dissipation in both fuselages. Energy dissipated through material damage is almost
negligible in both fuselages but it is too early to conclude that damage material model can
be neglected in modelling aircraft crash simulation under this impact velocity. As can be
seen in Figure 6.1 and 6.2, the total kinetic energy do not reach zero after declining
gradually due to plastic deformation and elastic strain energy within the first 150 ms in
both fuselages. Beyond 180 ms, all major deformation would have been completed and the
fuselage has started to bounce upward due to elastic strain energy stored in the structure
especially within the frames.
135
Figure 6-1. Energy balance within the aluminium fuselage for 10 ms-1 impact velocity crash.
Figure 6-2. Energy balance within the GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash.
Figure 6-3 and Figure 6-4 show the distribution of impact energy within the main
aluminium fuselage structure and GLARE 5-2/1 fuselage structure respectively meanwhile
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
Ene
rgy
(kJ)
Time (ms)
Total kinetic energy
Plastic dissipation
Elastic strain energy
Damage dissipation
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
Ene
rgy
(kJ)
Time (ms)
Total kinetic energy
Plastic dissipation
Elastic strain energy
Damage dissipation
136
Table 6-1 summarises the percentage of energy distributed within fuselage structures.
Frame structure absorbs highest percentage of the impact energy in both fuselage with
54.91% for aluminium fuselage and 59.50% for GLARE 5-2/1 fuselage. Frame structure in
fuselage is designed not just to maintain the shape of the fuselage, but it is also designed to
have a strong structure in order to protect the occupants in the fuselage space. Thus it is
desirable and expected to see that it absorbs the most of the impact energy in form of
elastic strain energy, plastic strain deformation and damage in both type of fuselage.
Figure 6-3.Dissipation of impact energy and its distribution within the aluminium fuselage for 10 ms-1
impact velocity crash.
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
Ener
gy (k
J)
Time (ms)
Total kinetic energy Total energy dissipated Frames (energy distribution) Skin (energy distribution) Floor beams (energy distribution) Stringers (energy distribution)
137
Figure 6-4. Dissipation of impact energy and its distribution within the FML GLARE 5-2/1 fuselage for 10 ms-1 impact velocity crash.
% of energy distribution at
maximum total energy dissipation
Structure
Aluminium
fuselage
GLARE 5-2/1
fuselage
Frame 54.91% 59.50%
Skin 14.23% 24.15%
Stringer 13.08% 4.61%
Floor beam 12.17% 9.21%
Seat tracks 0.49% 0.49%
Table 6-1. Percentage of energy distribution within fuselage structure during impact
Figure 6-5 shows the decomposition of energy distributed to frame in aluminium fuselage.
Great amount of the energy dissipated through plastic deformation in which it significantly
reduces the energy within the fuselage. Effectively, frame structure in aluminium fuselage
dissipates 52.9% of the impact energy through plastic deformation. Small amount of the
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
Ene
rgy
(kJ)
Time (ms)
Total kinetic energy Total energy dissipation Frames (energy distribution) Skin (energy distribution) Floor beam (energy distribution) Stringer (energy distribution)
138
absorbed energy is in the form of elastic strain energy that gives the frame some
recoverable deformation at the end of the crash. Energy dissipated through material
damage is very small and almost negligible in aluminium fuselage, only in range of 6 mJ.
This suggests that frame in aluminium fuselage can be modelled without incorporating
damage model for such impact condition. Orderly after frame, energy distribution within
aluminium fuselage structure is followed by skin, stringer and floor beam with each of
them absorbed energy in between 12.17 to 14.23% only. The rest of the energy is
distributed within seat tracks and floor panels.
Figure 6-5. Energy absorbed by frame structure and its decomposition in aluminium fuselage
Figure 6-6 shows the energy dissipated through plastic strain and amount of energy
absorbed by skin structure in aluminium fuselage. 57% of the energy absorbed by the skin
in aluminium fuselage is dissipated through plastic deformation. Effectively, skin structure
dissipates the impact energy of the whole fuselage structure through plastic deformation
by 9.8%.
0
5
10
15
20
25
0 20 40 60 80 100 120 140 160 180
Ener
gy (k
J)
Time (ms)
Energy absorbed
Plastic dissipation
139
Figure 6-6. Energy absorbed by skin structure its plastic dissipation in aluminium fuselage
In GLARE 5-2/1 fuselage, higher percentage of energy is absorbed by skin structure
compare to energy absorbed by skin in aluminium fuselage as shown in Figure 6-7 and
Table 6.1. Skin structure in GLARE 5-2/1 fuselage dissipates impact energy by 9.49% and
0.22% through plastic dissipation and damage due to material degradation respectively.
With total energy dissipated of 9.71% of the impact energy through its skin, this made the
GLARE 5-2/1 skin structure is as effective as aluminium alloy skin in terms of energy
absorption during impact. However, this is not conclusive in terms of improvement on
crashworthiness as acceleration at passengers’ level and global deformation must be taken
into account as well.
0
5
10
15
20
25
0 20 40 60 80 100 120 140 160 180
En
erg
y (k
J)
Time (ms)
Energy absorbed Plastic dissipation
140
Figure 6-7. Energy absorbed by skin structure and its decomposition in GLARE 5-2/1 fuselage.
0
5
10
15
20
25
0 20 40 60 80 100 120 140 160 180
Ener
gy (J
)
Time (ms)
Energy absorbed
Elastic strain energy
Plastic dissipation
Damage dissipation
141
6.3. Structural Deformation of Fuselage Structure
Analysing the deformation should give more understanding on the failure mechanisms and
failure modes of the fuselage structure during crash. By reflecting the deformation
behaviour with the energy balance, the impact behaviour of GLARE 5-2/1 fuselage section
during crash can be established. First of all, deformation of frame structure is analysed as
the main structure that absorbed the impact energy and sustain the shape of the fuselage.
After that, we will discuss on the deformation of the fuselage skin structure. Figure 6-8 and
Figure 6-9 show the deformation or crushing process of the aluminium and GLARE 5-2/1
fuselage during crash respectively. The deformation histories are shown in selected time
steps up to 180 ms.
In aluminium fuselage, the plastic strain localisation started at the bottom impacted frame
structure due to impact force reaction. This exerted large lateral force and caused the
frame at the bottom to have bending response. Another two locations possessed localised
plastic strain as early as 10 ms in the frame at the inner side that has non-smooth circular
shape. The immediate plastic strain response shown in the deformation history is also
supported by the energy balance diagram in Figure 6.1 where energy was quickly dissipated
by plastic straining immediately after impact. Around 10 ms, the localised plastic strain at
the bottom of frame started to buckle upward as the inertia of the fuselage section
provided a compressive force along the frame circumference and the reaction force at the
impacted side guided the direction of the deflection. The buckling progressed and caused
large plastic deformation at the bottom part of the frame between 20 to 150 ms. This large
plastic deformation within this period also can be observed in the energy balance of frame
during impact in Figure 6-5. During this period, the frame at the bottom is also observed to
be twisted at the high localised strain locations mentioned earlier. The non-symmetry
cross-section of the z-shaped frame caused instability at that area which finally caused the
142
deflections. At 85 ms, the buckled frames made contact with and exerted impact force to
the floor beams which caused the floor beams displaced in upward direction and
experienced plastic deformation at the impacted area. The contact between the frames
and the floor beams continued up to 180 ms and as a result, seat tracks that attached to
floor beam experienced plastic deformation as well. For crash simulation of aluminium
fuselage, the fuselage structure started to bounce upward at 148 ms as the elastic strain
energy within the fuselage section was released into kinetic energy meanwhile it occurred
at impact time 151 ms for GLARE 5-2/1 fuselage. As mentioned earlier, all major
deformation would have been completed once the impact time reached 180 ms and the
fuselage has started to bounce upward due to the release of the elastic strain energy
stored in the structure especially within the frames.
Deformation history of frames in GLARE 5-2/1 fuselage exhibits the same character as in
aluminium fuselage as shown in Figure 6-9 in terms of deformation process and the
deformation shapes. One observable difference is that the third fuselage frame at the back
deflected upward higher than the frame in aluminium fuselage as can be seen in both
fuselage, for example in Figure 6-8 at time 50 ms for aluminium fuselage. The frame
deflection is due to the non-symmetry cross-section of the frame about the fuselage
vertical plane as shown in Chapter 5. Supposedly, such deflection is minimal in real full
body fuselage due to the continuation of the fuselage frame, skin and stringers along the
fuselage length. As no additional stiffener was modelled around the open ends of the
fuselage section FE model, such deflection is inevitable. It is believed that the deflection
played a minor role in terms of the crushing of the bottom of the fuselage and the response
experience at the passenger’s floor level. However, the difference in deflection magnitude
at the top of the frame between aluminium fuselage and GLARE 5-2/1 fuselage is assumed
to be the couple effect of impact energy distribution between frames and skin. The ratio of
energy distributed between frame and skin in aluminium fuselage and GLARE 5-2/1
143
fuselage is around 3.9:1 and 2.5:1 respectively. The deformation of the frame far from the
impacted area which mainly depends on the stress wave propagation might be affected by
the deformation of skin at the top which also mainly depends on the same mechanisms.
Thus the difference of stiffness and strength of the two skins effected the deformation at
the top part of the fuselage section.
Figure 6-8. Deformation histories with plastic strain contour plot of the aluminium fuselage during crash with impact velocity 10 ms-1.
144
Figure 6-9. Deformation histories with plastic strain contour plot of the GLARE 5-2/1 fuselage during crash with impact velocity 10 ms
-1.
Material in frame did not degrade up to the total failure in both aluminium and GLARE 5-
2/1 fuselage as there was no element deletion occurred. However there were few
elements deleted in stringer for both fuselages. The elements deleted in both fuselages
were at different location but both occurred at area that fastened to the fuselage frames.
The skin of the fuselage is constrained to the frames and stringers. The modelling used
does not allow the skin to detach from the frames and stringers. However skin still may
detach if the element at the connection point itself is deleted due to material degradation.
145
With this assumption in the constraint modelling, skin structure is expected to follow the
deformation of the more dominant frame structure during crash event. Figure 6-10 shows
the crushing distance time history meanwhile Figure 6-11 shows the deformation shape of
fuselage skin for both aluminium and GLARE 5-2/1 fuselages at impact time 180 ms. The
same buckling deformation and plastic hinge as frames occurred at the bottom part of the
fuselage. Plastic hinges at the side bottom frame did not occur in skin structure as that
hinges occurred at the inner side of the frames as shown earlier in Figure 6-8. Even though
the deformation of both skins was alike in general view, the response and damage within
the GLARE 5-2/1 skin structure must be studied. Worth to mention that although frames
were the dominant structure in responding to the impact force, but the bottom part of the
fuselage skin was the main structure that transferred the impact force from the rigid
impact surface to the frames through the thickness of the skin
Observation on deformation of the fuselage structure continues by analysing the crushing
distance of the fuselage. Figure 6-10 shows that GLARE 5-2/1 fuselage possessed larger
crushing distance than aluminium fuselage by 6.27 cm. The crushing distance was mainly
determined by the large bending and rotation that occurred at the plastic hinges within the
frames and skin as shown in Figure 6-11. Although the difference is relatively small, it is our
interest to investigate how it happened.
146
Figure 6-10. Crushing distance of aluminium and GLARE 5-2/1 fuselages in 10 ms-1 impact velocity crash.
Figure 6-11. Location of plastic hinge at the bottom half of the fuselage section
As crushing distance was mainly determined by the magnitude of the rotation and bending
at the plastic hinges, attempts are made to find the cause of the magnitude change
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 20 40 60 80 100 120 140 160 180
Cru
shin
g d
ista
nce
(m
)
Time (ms)
Aluminium fuselage 10 m/s
GLARE 5-2/1 fuselage 10 m/s
A
B
C
147
between aluminium fuselage and GLARE 5-2/1. As the frames for both fuselages were the
same in every sense, the bending stiffness and critical buckling load of the skin at plastic
hinges location could be the source of differences.
Plastic hinges occurred in skin because skin and frames are tied together thus skin that
attached to frames would deform according to deformation of frames. In the same time,
the stiffness and strength in skin structure provided some resistance to the deformation
that taking place at the proximity of the tied frame. Figure 6-12 shows damage that
occurred within composite laminate in GLARE 5-2/1 skin structure at hinge location B at 24
ms. Element in red indicates that the composite material has reached its maximum
damage, either in matrix tensile mode or matrix compressive mode. As the material
stiffness of the skin degraded especially along the line of hinge location B, the damaged
skin gave minimal resistance towards deflection progression due to bending in frames.
However there is no failure in fibre mode at hinge location B at that impact time. Figure
6-13 shows the matrix tensile failure in the outer lamina at step time 78 ms where the
frames buckling and bending were progressing. At hinge location A, B and C, it is observed
that the outer and inner 0⁰ laminas were damaged in their fibre tensile mode as shown in
Figure 6-14. Based on these observations, it is understood that the material stiffness
degradation in various failure modes within GLARE 5-2/1 contributed to the crushing
process of the GLARE 5-2/1 fuselage during crash.
Critical loading for buckling is sensitive to delamination especially delamination that occur
further from the composite of FML surface. However, there was no total material
degradation within adhesive layer observed, thus there was no delamination occurred in
this crash analysis that can contribute to the failure mechanisms of the GLARE 5-2/1
fuselage during crash under 10 ms-1 velocity impact.
148
Figure 6-12. Tensile and compressive matrix failure at composite layers in GLARE 5-2/1 skin structure at hinge location B. t = 24 ms
0⁰ fibre orientation, inner layer 90⁰ fibre orientation, inner layer
Outer layer (90⁰) Outer layer (0⁰)
149
Figure 6-13. Matrix tensile failure in glass-fibre laminate (90⁰) outer lamina at t = 78 ms.
Figure 6-14. Fibre tensile failure in glass-fibre laminate (0⁰) inner and outer lamina at t = 78 ms.
Inner lamina (0⁰) Outer lamina (0⁰)
150
6.4. Acceleration at Floor Level
One of the main crashworthiness evaluations of aircraft is the acceleration experienced by
the passengers or occupants during crash event. The acceleration-time histories were
measured at two locations on the seat tracks; the outer right seat track and the inner right
seat track. The acceleration-time histories were filtered with 60 Hz low pass filter as
discussed in previous chapter. The peak acceleration on headward and tailward direction
for both locations were used to compare with the amount of acceleration that human can
tolerate in order to evaluate the survivability of the passengers during crash.
Figure 6-15 shows the acceleration-time histories at the outer and inner right seat tracks of
the aluminium fuselage. Both acceleration responses started with headward direction
(eyeballs down) and then followed by tailward direction (eyeballs up) and continued with
this cycle until the impact energy was dissipated through plastic deformation and through
global change of velocity due to elastic energy released within the structure. Headward
peak acceleration at the outer right seat track of aluminium fuselage was 24.31 G which
occurred as early as 8 ms of the impact time. Meanwhile tailward peak acceleration of
19.24 G occurred at 162 ms impact time. However, both headward and tailward peak
accelerations at inner right seat track were larger than the peak accelerations at outer right
seat track with 43.37 G and 42.02 G respectively. High headward peak acceleration
(eyeballs down) at inner right seat track occurred right after the buckled bottom part of the
fuselage frame made contact with the floor beam as can be seen in Figure 6-8 (t = 100ms).
By comparing these peak acceleration values to the tolerable values by human, headward
acceleration pulse at the outer right seat track was the only value lower than the tolerable
value, i.e.: uninjured passenger. The rest of the peak acceleration values indicated that the
passengers in both outer and inner seat tracks may have suffered severe injury during the
crash. However, in real crash event, the passengers are well restrained by safety belt,
151
seated on cushioned seats and the seats themselves may have structures that capable of
absorbing some of the impact energy. Thus, the acceleration response of the passengers in
real event should be lower than shown in Figure 6-15. To put things into perspective, the
magnitude of the peak acceleration experienced by passengers during aircraft crash which
was carried by Adams and Lankarani (Adams & Lankarani 2003) was used for comparison.
In Adams and Lankarani’s work, acceleration response was measured at seat tracks for
both experimental crash test and crash simulation, similar to the measurement’s location in
this thesis. Similar fuselage section B737 was used in Adams and Lankarani’s but with lower
impact velocity of 9 ms-1. The peak acceleration measured at the inner seat track in Adams
and Lankarani’s work was 38 G which is comparable to peak acceleration measured in this
thesis in terms of order of magnitude. Even though the acceleration values evaluated in
this thesis are incapable of determining exactly whether or not the passengers will sustain
severe injury (restrain and seat were not modelled), their order of magnitudes are very
valuable in which they will be compared to the acceleration response in a GLARE 5-2/1
fuselage crash event.
Figure 6-16 shows the acceleration response of both outer and inner seat tracks of GLARE
5-2/1 fuselage. At outer seat track, both headward and tailward peak acceleration values
were larger than peak acceleration values in aluminium fuselage. Contrarily, peak
acceleration at the inner seat track in GLARE 5-2/1 fuselage was smaller than in aluminium
fuselage for both headward and tailward directions. This difference might be due to the
differences in crushing distance and failure mechanisms at the plastic hinges and buckled
structures between aluminium and GLARE 5-2/1 fuselage. Overall, the peak acceleration
responses for both fuselages exhibited similar magnitude which indicates that the
crashworthiness performance in terms of acceleration experience by passengers in GLARE
5-2/1 fuselage is in the same order with the original aluminium fuselage.
152
Figure 6-15. Acceleration response at passengers’ location in aluminium fuselage during 10 m/s vertical crash.
Figure 6-16. Acceleration response at passengers’ location in GLARE 5-2/1 fuselage during 10 m/s vertical crash.
24.31
-19.24
-42.02
43.47
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
Acc
eler
atio
n (G
)
Time (ms)
outer right aluminium
inner right aluminium
-29.21
29.49 32.44
-40.66
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 20 40 60 80 100 120 140 160 180
Acc
eler
atio
n (G
)
Time (ms)
outer right fml
inner right fml
153
Chapter 7 Conclusions and Future Work
7.1. Conclusions
Crash simulation of fibre metal laminate (FML) fuselage went through a series of
development process. The development of FML fuselage FE crash model includes the
establishment of material and damage model for all FML’s material constituents, validation
of the material and damage models, verification of impact model with buckling failure and
large displacement and verification of frame FE model. This long development process was
continued by assembling all the validated and verified works to form a reliable FML
fuselage crash model.
The aim of the research was to develop a reliable FE crash model of fibre metal laminate
(FML) fuselage and to evaluate the crashworthiness of this new future aircraft. A building
block approach which was originally and only previously used in aircraft design industry
was adapted in order to fully computationally develop a reliable FE model of aircraft crash.
The success in adapting this approach is one of the novel achievements and contributions
in this field of research. Throughout the process of developing FML fuselage via building
block approach, various modelling techniques were performed in order to model a reliable
impact response of aluminium alloy, composite laminate and fibre metal laminate
especially when subjected to axial impact condition. It is learnt that there are few critical
aspects to be considered in modelling the impact response of FML. Conclusively, first
aspect is to develop a reliable material model for each of the constituents that suit the
desired impact condition. Secondly, one needs to understand the failure mechanisms of
FML under various impact conditions so that an efficient FE models can be develop. Thirdly,
consideration of how the constituents of FML interact with each other in response to
impact enables one to correctly model the failure of FML structure. With all due respect,
capability to exercise these three aspects was another achievement in this research.
154
However, the greatest and novel finding in this research was to be able to analyse the
impact response of FML fuselage under survivable impact condition by pure computational
work. By comparing the impact response of FML fuselage to the original Boeing 737
aluminium fuselage, few key findings were concluded. During impact, FML fuselage skin
affected the impact response of the main fuselage structure which is the fuselage frame
especially in terms of crushing process of the bottom part of the fuselage. The damage in
laminate played a significant role in the failure mechanisms of the fuselage subfloor
structure. There was no delamination observed within the FML fuselage which may suggest
that delamination model could be ignored by eliminating the need of cohesive element as
interface layers in modelling crash analysis of FML fuselage under low velocity impact. In
terms of acceleration responses experienced by passengers which were measured at the
seat tracks, FML fuselage exhibited the same order of peak acceleration compared to the
aluminium fuselage.
Overall, the response of the FML fuselage based on presented observations indicates that
its crashworthiness performance have the same order and magnitude as the aluminium
fuselage. This finding gives great confidence to aircraft designer to use FML as the fuselage
skin for the whole fuselage instead of being used as the top fuselage skin only as
implemented in Airbus A380. This conclusive crashworthiness performance of FML fuselage
when compared to aluminium fuselage is essential and also a novel contribution into the
research field of an aircraft crash.
155
7.2. Recommendation for Future Work
Enormous amount spent in developing the reliable crash model of FML fuselage left the
author little time to study further on the impact response of FML fuselage. The first and
foremost future work is to process the acceleration data in order to evaluate thoroughly
the crashworthiness of the FML fuselage. Other future works recommended by the author
are:
a. Crash simulation of FML fuselage without delamination model incorporated within the
FML fuselage skin.
b. Parametric studies on impact response of FML fuselage under various impact
conditions.
c. Parametric studies on impact response of FML fuselage based on different grades of
GLARE.
d. Parametric studies on impact response of FML fuselage on various roll angles of impact
surface.
156
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Appendix 1
Experimental set-up for low velocity perforation test by Rodriguez-Martinez
Rodriguez-Martinez studied a low velocity perforation tests on AA 2024-T3 thin plates at
two different initial temperatures 213 K and 288 K by conducting it using a drop test tower.
This configuration allows a perpendicular impact on the specimen with controllable impact
velocity, V0 by adjusting the height from which the striker is dropped.
Figure A1-1. Schematic representation of the drop weight tower (Rodriguez-Martinez et al, 2011)
In Rodriguez-Martinez experiment, several impact velocities were chosen including 4 m/s
which will be modelled numerically in this paper. The specimens have thickness of h = 1
mm and size of At = 100x100 mm2. They were clamped by screws that were symmetrically
fixed all around its active surface of Af = 80 x 80 mm2.
163
Figure A1-2. The device used to clamp the specimen (a) clamping (b) specimen support (Rodriguez-
Martinez et al, 2011)
The steel striker has conical shape as shown in Fig. 3. The larger diameter of the striker is
20 mm, radius of nose is 3 mm and angle of its conical nose is 18⁰. Mass of the striker is
Mp=0.105 kg but it is attached to the instrumented bar of the drop weigh tower and to
additional mass giving its accumulative mass 0.866 kg and 18.787 kg. The Mtotal = 18.787 is
known as effective mass.
Figure A1-3. Conical striker used in the Rodriguez-Martinez’s experiment (Rodriguez-Martinez et al,
2011)
The set-up allows to record impact forces history within 16 ms impact duration with
acquisition frequency of 250 kHz. The time dependent velocity V(t) and displacement δs(t)
of the striker are calculated by integration from the impact force history.
;
(A1-1)
(A1-2)
164
(A1-3)
In above equation, a(t) is the deceleration of the striker during perforation.
165
Appendix 2
Density, ρ (tonne/mm3) 1600 x 10-12
Elastic properties
E1 153 GPa
E2 = E1 10.3 Gpa
ν12 = ν13 0.3
ν23 0.4
G12 = G13 6 GPa
G23 3.7 GPa
Strength
XT 2537 MPa
XC 1580 MPa
YT 82 MPa
YC 236 MPa
S12 90 MPa
S23 40 MPa
In plane fracture toughness
91.6 kJ/m2
79.9 kJ/m2
0.22 kJ/m2
1.1 kJ/m2
Table A2-1: Material properties of the carbon fibre/epoxy unidirectional laminate (Shi et al, 2012)
166
Density, ρ (tonne/mm3) 1200 x 10-12
Elastic properties
E 1373.3 MPa
G 493.3 MPa
Failure stresses
62.3 MPa
92.3 MPa
92.3 Mpa
Fracture energies
Gn 0.28 N/mm
Gs 0.79 N/mm
Gt 0.79 N/mm
Table A2-2. Material properties of the interface cohesive element (Shi et al, 2012)
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