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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
Society for Industrial and Applied Mathematics
VT / EADS4/22/2014 3
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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VT / EADS4/22/2014 4
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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VT / EADS4/22/2014 7
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
Society for Industrial and Applied Mathematics
VT / EADS4/22/2014 9
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
Society for Industrial and Applied Mathematics
VT / EADS4/22/2014 10
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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VT / EADS4/22/2014 11
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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VT / EADS4/22/2014 13
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
Society for Industrial and Applied Mathematics
VT / EADS4/22/2014 14
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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VT / EADS4/22/2014 15
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
Society for Industrial and Applied Mathematics
VT / EADS4/22/2014 16
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
Society for Industrial and Applied Mathematics
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
VT / EADS4/22/2014 18
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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VT / EADS4/22/2014 19
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
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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
Society for Industrial and Applied Mathematics
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
Society for Industrial and Applied Mathematics
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
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VT / EADS4/22/2014 24
Thank You !!!
Society for Industrial and Applied Mathematics