Progressive Failure Analysis of Laminated Composite · PDF fileProgressive Failure Analysis of...

VT / EADS4/22/2014 1

Progressive Failure Analysis of Laminated

Composite Structures

Arafat I. Khan

Department of Aerospace an Ocean Engineering

Virginia Tech

April 22, 2014

Progressive Failure in Laminated Composites

Presented to

Society for Industrial and Applied Mathematics

at Virginia Tech

VT / EADS4/22/2014 2

Financial support from European Aeronautics

Defense and Space Company N.V. (EADS)

Academic Advisors:

Dr. Rakesh K. Kapania

Dr. Romesh C. Batra

Dr. Eric R. Johnson

AIRBUS Technical Advisor:

Dr. Jean-Mathieu Guimard

Acknowledgements


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Introduction

• Importance includes high specific

strength, light - weight, resistance

to fatigue/corrosion and flexibility

in design

Figure 1 : Use of composite material in A380, Courtesy of Airbus

• Progressive Failure Analysis

(PFA) of composites enables

understanding of the response

of the structure

Figure 2 : Use of composite material in Boeing 787, Courtesy of Boeing

• Failure analysis is an

important design requirement

• Composite material plays a

important role in current aircraft

industry


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Failure in Aircraft Structures


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Constituents

Micromechanics

Ply

Laminate

Structure

Composite Overview


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Understand the role of composite failure mechanisms

for aircraft design

Perform progressive

failure analysis on

laminated structure

Adapt a methodology for

the Finite Element Method

framework

Simulation progressive failure in commercial finite

element software (ABAQUS)

Objectives of Current Study


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A Stress-based failure criteria

Fiber failure modes in tension and

compression are predicted by

non-interacting maximum

allowable stresses

Matrix failure modes are due to

brittle fracture along a plane

parallel to the fibers as originally

proposed by Hashin (1980)

The tension criterion denoted as

Mode A is different from the

compression criteria denoted as

Modes B and C.

Continuum damage mechanics

principles are used to degrade

matrix material properties for

failure in Modes A, B and C.

Mode AMode B

Mode C

Failure Criteria


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Strength Parameters and Inclination slopes for failure envelope in

plane stress:

Inclination Parameters:

α = Fracture AngleFracture Plane Angle:

Strength Parameters:YT = Transverse tensile strengthSL = In-plane shear strength

ST = Shear strength transverse to the fibers

in the fracture plane, the maximum

value of σnt in Fig. 8YC = Transverse compressive strength

σ22

σ21

Mode AMode C Mode B YT-ST-YC 0

tan-1 𝒑𝒏𝟏−

tan-1 𝒑𝒏𝟏+

sL

Figure : (a) Stresses acting on the failure plane, (b) resultant

shear stress on the failure plane

ψα

x3xt

xn

x2x1

σnnσnt

σn1

σnt

σn1

σnψ

(a) (b)Fracture Plane

𝒑𝒏𝟏

+ 𝐚𝐧𝐝 𝒑𝒏𝟏

(−)

Parameters in Matrix Failure


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Matrix Failure Criteria

𝑭𝑰𝑴𝑨 = 𝟏 − 𝒑𝒏𝟏

+ 𝒀𝑻

𝑺𝑳 𝟐

𝝈𝟐𝟐

𝒀𝑻 𝟐

+ 𝝈𝟐𝟏

𝑺𝑳 𝟐

+𝒑𝒏𝟏

+ 𝝈𝟐𝟐

𝑺𝑳 𝝈𝟐𝟐 > 𝟎 (𝟏)

𝑭𝑰𝑴𝑩 = 𝝈𝟐𝟏

𝑺𝑳

𝟐

+ 𝟐 𝒑𝒏𝟏

− 𝝈𝟐𝟐

𝑺𝑳

; −𝑺𝑻 ≤ 𝝈𝟐𝟐 < 𝟎; 𝑺𝑳 < 𝝈𝟐𝟏 ≤ 𝑺𝑳 𝟏 + 𝟐𝒑𝒏𝟏

− (𝟐)

𝑭𝑰𝑴𝑪 =𝟏

𝟐 𝟏 + 𝒑𝒏𝟏

−

𝝈𝟐𝟐

𝑺𝑻 𝟐

+ 𝝈𝟐𝟏

𝑺𝑳 𝟐

𝑺𝑻

−𝝈𝟐𝟐 ; −𝒀𝑪 < 𝝈𝟐𝟐 < −𝑺𝑻 (𝟑)

FIMA, FIMB and FIMC are

dimensionless failure indices,

which are less than one for no

failure and equal to one at failure

initiation

𝑺𝑻 =𝒀𝑪

𝟐 𝟏 + 𝒑𝒏𝟏

−

where

Failure criteria is dependent on state of stress in material principal direction (σ11 , σ22 and σ12 )

Figure 10: Matrix failure envelop in plane stress

σ22

σ21

Mode AMode C Mode B YT-ST-YC 0

tan-1 𝒑𝒏𝟏−

tan-1 𝒑𝒏𝟏+

sL


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Fiber direction

2

1

3Material principal coordinate system

used in current work

Fiber direction considered

the current work

θ-Ply angle

y

θ x

12

Fiber/Matrix in Composites


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Implementation at Global Level

• The failure criteria are

implemented using CLPT in

(MATLAB)

Analytical Approach

• Post failure material degradation

implemented for structures

with homogenous deformation

• Commercial software Abaqus

is used for Finite Element

implementation

• A user subroutine is required

to model the failure criteria

Finite Element Approach

• User Define Field Variable,

USDFLD subroutine is used

• Analytical solution is developed

to understand the progressive

failure analysis process

• The composite layup feature

in Abaqus is used to model

laminates


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𝑭𝑭𝑻 =𝝈𝟏𝟏

𝑿𝑻 𝑻𝒆𝒏𝒔𝒊𝒐𝒏 ; 𝟎 ≤ 𝑭𝑭𝑻 ≤ 𝟏 (𝟒)

𝑭𝑭𝑪 =(−𝝈𝟏𝟏)

𝑿𝑪 𝑪𝒐𝒎𝒑𝒓𝒆𝒔𝒔𝒊𝒐𝒏 ; 𝟎 ≤ 𝑭𝑭𝑪 ≤ 𝟏 (𝟓)

Fiber failure Modes:

Where,

XT = Longitudinal tensile strength

XC = Longitudinal compressive strength

FFT, and FFC are dimensionless failure indices, which

are less than one for no failure and equal to one at fiber

failure

Fiber Failure


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Significant PFA Terminologies

FPF = First Ply Failure which indicates failure initiation

in either matrix or fiber, also referred to as initial failure

For the case of homogenous deformations, fiber failure indicates

final failure or ultimate failure

For the case of non-homogenous deformation fiber failure does

not necessarily indicates the failure of the entire laminate

Failure Indicators

Damage Variable Indicators

For the matrix failure the damage variable is referred to as

the “Degradation Factor” and is represented by η


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PFA in ABAQUS

In the 2D Plane Stress implementation of Puck and

Schürmann’s failure material properties are reduced

corresponding to the modes of failure in Abaqus:

Mode of Failure Properties Reduced

Mode A E2, ν12 and G12

Mode B G12

Mode C G12

Fiber Failure in Tension E1

Fiber Failure in Compression E1

Table 1: Modes of Failures and Corresponding Degradable Material Properties

Abaqus provides stress components to the USDFLD

subroutine in order to compute the degradation factors

(damage variables) and failure flags based on the modes of

failure


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𝑺(𝜼𝒂, 𝜼(−)) =

𝟏

𝑬𝟏−

𝜼𝒂𝝂𝟏𝟐

𝑬𝟏𝟎

−𝜼𝒂𝝂𝟏𝟐

𝑬𝟏

𝟏

𝜼𝒂𝑬𝟐𝟎

𝟎 𝟎𝟏

𝜼𝒂𝜼(−)𝑮𝟏𝟐

(𝟖)

We assume a symmetric compliance matrix,

Where, 0 < ηa < 1 and 0 < η(-) < 1

Failure/Damage: Failure in a particular ply of a laminate is detected

when any of the failure criteria is satisfied (First Ply Failure)

ηa corresponds to degradation factor in Mode A

η(-) corresponds to degradation factors in Mode B or Mode C

For undamaged laminate, ηa =1 and η(-) = 1

After FPF, failure indices are found as functions of material

degradation factor ηa or η(-) depending on mode of failure initiation

Material Degradation in Plane Stress


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Calculating Material Degradation Factor

If the first ply failure occurs in Mode A, then after damage

initiation, Eq.(1) can be expressed as:

𝒈𝟐 𝜼 − =

𝟏

𝟐 𝟏 + 𝒑𝒏𝒕 −

𝝈𝟐𝟐 𝜼 −

𝑺𝑻

𝟐

+ 𝝈𝟐𝟏 𝜼

−

𝑺𝑳

𝟐

𝑺𝑻

−𝝈𝟐𝟐 𝜼 −

− 𝟏 = 𝟎 ; 𝝈𝟐𝟐 < 𝟎,

For damage initiation in Mode B, Eq. (2) can be expressed as:

System of non-linear equations are solved to determine

degradation factor ηa and η(-) after FPF, since failure criteria

are maintained at their critical values for increasing load

𝒈𝟏 𝜼𝒂 = 𝟏 − 𝒑𝒏𝟏

+ 𝒀𝑻

𝑺𝑳

𝟐

𝝈𝟐𝟐 𝜼𝒂

𝒀𝑻

𝟐

+ 𝝈𝟐𝟏 𝜼𝒂

𝑺𝑳

𝟐

+𝒑𝒏𝟏

+ 𝝈𝟐𝟐 𝜼𝒂

𝑺𝑳

− 𝟏 = 𝟎 ; 𝝈𝟐𝟐 ≥ 𝟎

Number of non-linear equations correspond to the number of

integration points which experience failure under particular state

of load

Finally, the degradation factors (damage variables) are calculated

by solving system of non-linear equations


VT / EADS4/22/2014 Society for Industrial and Applied Mathematics 17

σy

σy

y in MPa0 200 400 600 800

Deg

ra

da

tio

n F

acto

r i

n M

od

e A

,

a

0.2

0.4

0.6

0.8

1.0

1.2

a in 0o

Ply

a in -45o

Ply

a in 45o

Ply

a in 90o

Ply

First Ply Failure in 0o PlyIn Mode A Matrix Failure

Fiber Failure in Tension in 90o

Plies

Failure Initiation in ±45o Plies

Figure: [90o/±45o/0o]s laminate under

uniaxial tension

[90o/±45o/0o]s

ABAQUS\USDFLD implementation is

compared with test datay

x Failure initiates in 0o plies in Mode A matrix

failure

Fiber failure occurs in tension in 90o plies

[90o/±45o/0o]s

[90o/±45o/0o]s

%y

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

y

, MP

a

0

200

400

600

800

COMET Implementation by Puck and Schurmann

ABAQUS/USDFLD

Test Results

Comparison with experiment

First Ply Failure in 0o PlyIn Mode A Matrix Failure

Fiber Failure in Tension in 90o Plies

σy

σy

PFA of a Sample Problem

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a

L

b

uy

L= 9 in.b= 1 in.a= 0.25 in.

Figure 21: Schematic for the open hole

tension * Coupon

Parameters Values

SL 13.76 ksi

YT 8.72 ksi

YC 24.3 ksi

XT 412 ksi

XC 225 ksi

Strength Parameters*:

Properties Values

E1 23. 2 Msi

E2 1.3 Msi

ν12 0.278

G12 0.9 Msi

Material Properties for

T300H/3900-2 graphite

epoxy Composite*:

Inclination Slope for Graphite :

Parameter Values

pǁ⊥(+) 0.3

pǁ⊥(-) 0.25

• Ply Thickness: 0.00645 in.

• Total Thickness: 0.1032 in.

[(0o/90o)4]S

x

y

*Knight, N.F., "User-Defined Material Model for Progressive Failure Analysis," NASA/CR-214526, Dec. 2006.

• The fibers in 0o plies are aligned

in the x-direction in Fig. 21

Open Hole Tension Coupon


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S4 Elements Used

Composite layup is

used to define the

stacking sequences

for the laminate 1.8 in.9 in.

800 Elements around

the hole in each ply

in region ABCD

Solution dependent

variables (SDV’s) in

Abaqus refer to

degradation factors

for matrix and failure

flags for fiber failure CD

800 Elements

in each ply

A B

CD

Mesh Density


VT / EADS4/22/2014 20

Applied Displacement, in

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Lo

ad

, L

bs

0

2000

4000

6000

8000

10000

12000Tsai Wu Criteria, from Knight 2008

Max Strain Criteria, from Knight 2008

Max Stress Criteria, from Knight 2008

ABAQUS/USDFLD Using Puckand Schurmann's Criteria

aL

b

uy

Maximum Load

Linear elastic analysis

Symmetric cross-ply of: [(0o/90o)4]S

Global Structural Behavior


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Progression of Failure in Matrix

Mode A degradation factors, ηa are shown

0o Ply 90o Ply

SDV1 = Mode A

Degradation

Factor

SDV1 = Mode A

Degradation

Factor

Animations are attached to show the progression of failure

uy = 0.14 in uy = 0.14 in


VT / EADS4/22/2014 22

Progression of Failure in Fiber

0o Ply 90o Ply

No Fiber Failure Fiber Failure in Tension

SDV6 = Flag

For fiber failure

In Tension

SDV6 = Flag

For fiber failure

In Tension

uy = 0.14 in uy = 0.14 in


VT / EADS4/22/2014 23

Concluding Remarks

Progressive failure analyses of filamentary composite

laminates were performed by degrading lamina material

properties based on the mode of failure

Damage evolution laws are based on the failure modes

and corresponding criteria developed by Puck and

Schürmann. The failure modes are matrix tension,

matrix compression, fiber tension and fiber compression

Developed a USDFLD subroutine in Abaqus to implement

of the progressive failure analysis

Future work involves implementation of Puck’s 3D action

plane criteria in USDFLD and extend the scope of the PFA


VT / EADS4/22/2014 24

Thank You !!!


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