Simulation of Discrete Damage in
Composite Overheight Compact
Tension Specimens
David Mollenhauer, Logan Ward
Air Force Research Laboratory, USA
Endel Iarve, Sirina Putthanarat, Kevin Hoos
University of Dayton Research Institute, USA
Stephen Hallett, Xiangqian Li
University of Bristol, United Kingdom
CompTest 2011
Lausanne, Switzerland
14-16 February 2011
Outline
• Motivation
• Background
• Numerical Model Details
• Results
• Blocked quasi-isotropic & cross-ply
• Statistical strength effects
• Dispersed ply quasi-isotropic
• Conclusion & Future
Motivation
Normalized Axial Strain from
[0/45/90/-45]s Composite
Y
X
No damage
Extensive Damage
Background
Numerical Modeling Basis
Goal:
Discrete Modeling of Matrix Cracking
and Delamination Networks
• General approach based
on X-FEM ideas
• Moes, et. al., 1999, IJNME
• Must accommodate
cracking & delamination
interaction
[1] Van der Meer F P and Sluys L J, (2nd ECCOMAS, 2009)
[2] Qingda Yang and Brian Cox, (CompTest, 2008)
[3] Iarve (AIAA 1998), Iarve (IJNM, 2003), Iarve et al. (Composites A, 2005; IJMS, 2007)
[4] …..
Background
Numerical Modeling Basis
Mesh Independent Crack (MIC) Modeling
- A Regularization of X-FEM
• Crack is modeled by adding degrees of
freedom (element enrichment)
• Regularization means that the crack face
step function is approximated by FEM
H=0
H=1
H(x) is Heaviside step function
With a jump over the crack surface
Iarve (IJNM 2003)
H(x) is approximated by the same
shape functions as displacements
Background
Numerical Modeling Basis
MIC & Delamination Interaction and Propagation
• The original Gauss
integration schema is
preserved for any crack
orientation
• Adjacent plies tied
through node/and or
surface element
integration contact
• Propagation is through
cohesive zone method
Background
Numerical Modeling Basis
General Modeling Flow
1. Step i=0 is thermal pre-stress
2. Add axial displacement
increment
3. Perform Newton-Raphson
iterations to converge damage
variables in delam and MIC
cohesive laws
4. Check matrix failure criteria
5. Add damage and repeat 2-5
Matrix Failure Criteria - Dávila, Camanho, and Rose, “Failure criteria for FRP
laminates,” J. of Composite Materials, Vol.39 2005.
Cohesive Zone Propagation - Turon, Camanho, Costa, and Dávila, “A damage
model for the simulation of delamination in
advanced composites under variable-mode
loading,” Mechanics of Materials, Vol.38, 2006.
Mesh Independent Cracks - Iarve, “Mesh independent modeling of cracks by
using higher order shape functions,” Int. J. Num.
Meth. Eng., Vol.56, 2003.
Background
Previous Experimental Effort
• Overheight Compact Tension specimens tested at the University
of Bristol in the UK (Li et al, Composites Part A 40, 2009)
• Multiple stacking sequences of both dispersed & blocked plies
• Displacement-load, 2D X-ray, & c-scan measurements
Numerical Model Details
• In-house code BSAM (B-spline analysis method) used
• Geometry matched to Bristol’s test specimens
• Blocked Ply Specimens (IM7/8552)
• [452/902/-452/02] s
Table 1. Properties for IM7/8552 Lamina
• [04/904] 2s
Material Property
Value
• Dispersed Ply Specimen (IM7/8552)
E11 (GPa)
161.0
E22,E33 (GPa)
11.38
• [45/90/-45/0] 2s
Ref 1
Ref 1
Ref 1
G12,G13 (GPa)
G23 (GPa)
n12, n13
n23
Ref 1
Ref 1
5.17
3.98
0.32
0.44
Ref 1
a1 (1/◦C)
0.00
a2 (1/◦C)
3.00e-05
GIC (N/mm)
Ref 1
0.2
GIIC (N/mm)
Ref 1
1.0
YT (MPa)
60.0
YC (MPa)
275.0
S (MPa)
90.0
[1] Hallett, S.R., Jiang, W.G., Khan, B., and Wisnom, M.R., “Modeling the
interaction between matrix cracks and delamination damage in scaled
quasi-isotropic specimens,” Compos Sci Technol, 68(1): pp.80-89, 2008.
Numerical Model Details
X-ray Close-up
Matrix Damage Comparison
Blocked Quasi
[452/902/-452/02] s
Specimen
Shifted Results
POD = 2.11 mm
Specimen One
Stacked X-Ray
Matrix Damage Comparison
Blocked Quasi
Specimen 1
POD ~ 2.12 mm
Specimen 1
POD ~ 2.12 mm
Specimen 1
POD ~ 2.12 mm
POD ~ 2.11 mm
POD ~ 2.11 mm
POD ~ 2.11 mm
452/902 Interface
902/-452 Interface
-452/02 Interface
POD vs Load Comparison
Blocked Quasi
[452/902/-452/02] s Specimen
Matrix Damage Evolution
Blocked Quasi
[452/902/-452/02] s Specimen
Matrix Damage
Blocked Cross-Ply
Simulations are
symmetric in-plane as
well as out-of-plane to
aid damage stability.
25
20
15
10
Experiment
Experiment 2
Current Simulation
5
0
0
1
2
3
4
5
6
Matrix Damage Evolution
Blocked Cross Ply
[04/904] 2s Specimen
• Movie has been mirrored about symmetry plane
Matrix Damage
Blocked Quasi – with Statistical Variation
Case 0
Five different statistical variations of
matrix strengths were simulated.
Case 1
Case 2
Case 3
Case 4
POD vs Load Comparison Blocked
Quasi – with Statistical Variation
POD vs Load Comparison Blocked
Quasi – with Statistical Variation
Continuum Damage Model for Fiber Failure
– characteristic length of the FE
IM7/8552
For 1 mm3
volume
C=(1-d)C0
XT
GXT
fXT
fGT
3136 N/mm2
81.5 n/mm
0.2
0.4
C0 – initial stiffness
d – damage variable
P. Maimi, P. P. Camanho, J. A. Mayugo, C. G. Davila, A continuum damage model for composite laminates: Part I
constitutive model, Mechanics of Materials,39 (10) (2007) 897-908.
P. Maimi, P. P. Camanho, J. A. Mayugo, C. G. Davila, A continuum damage model for composite laminates: Part II
computational implementation and validation, Mechanics of Materials 39 (10) (2007) 909-919.
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0] 2s Specimen
experimental
X-ray
simulation
damage pattern
• Continuum damage mechanics
routine used for fiber damage
courtesy of Carlos Davila of
NASA LaRC
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Matrix & Fiber Damage
Dispersed Quasi
[45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3
Conclusions & Future
• Concusions:
• Simulated load-displacement behavior correlates
well with actual specimen behavior
• Simulated discrete damage patterns correlate
extremely well with X-ray CT images
• At similar applied load levels
• Predicted complex specimen behavior obtained
using only lamina-level, measurable properties and
application of “simple” descriptions of damage.
• Future Efforts:
• Validate current fiber failure methodology
• Implement alternative fiber failure methodology
Acknowledgements
• Partial funding for this work from NASA AAD-2
(NNX08AB05A-G) and AFRL (FA8650-05-D-5052)
• Many thanks to Dr Cheryl Rose and Dr Carlos Davila
of NASA LaRC for collaboration and advice.
• The authors also wish to acknowledge their
collaboration with Anoush Poursartip, Reza Vaziri, and
Navid Zobeiry at the University of British Columbia in
conducting the OCT experimental testing
X-Ray Computed Tomography
X-ray
imaging panel
Image i
X-ray
imaging panel
Top View
Side View
OCT Specimen
3D “voxel” data
visualizing internal
specimen structure
X-Ray Computed Tomography
X-ray
imaging panel
Image j
X-ray
imaging panel
Top View
Side View
OCT Specimen
3D “voxel” data
visualizing internal
specimen structure
X-Ray Computed Tomography
X-ray
imaging panel
Image k
X-ray
imaging panel
Top View
Side View
OCT Specimen
3D “voxel” data
visualizing internal
specimen structure
X-Ray Computed Tomography
•
•
•
•
Specimens sectioned to increase magnification
Damage enhanced with zinc iodide solution
Cracks appear as discrete white lines
Delaminations appear as lightening of background
• Delamination front is brighter
X-Ray Computed Tomography
• A “voxel averages the X-ray
density across its volume
• Some will span ply interfaces
• Beam hardening effects further
smear results
delam
Ply Thickness
crack
0.125 mm
voxel
Voxel Dimension
0.06 mm
Experimental Results
•
•
•
•
Load Displacement Results from the [452/902/-452/02] s Specimen
Data shifted to extrapolate linear portion to zero
Coarse X-ray CT results at POD = 1.74, 2.12, & 2.26 mm
Detailed X-ray CT results at POD = 1.74 mm & 2.26 mm
Original Results from Li et al
Shifted Results
Matrix Damage Comparison
Blocked Quasi
Specimen 1
POD ~ 2.12 mm
-452/02 Interface
Blunt Notch
POD ~ 2.11 mm
Matrix Damage Comparison
Blocked Quasi
Specimen 1
POD ~ 2.12 mm
452/902 Interface
Blunt Notch
POD ~ 2.11 mm