1. 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

2. Outline Motivation Background Numerical Model Details Results
Blocked quasi-isotropic & cross-ply
Statistical strength effects
Dispersed ply quasi-isotropic
Conclusion & Future

3. Normalized Axial Strain from
Motivation
Normalized Axial Strain from
[0/45/90/-45]s Composite X Y
No damage
Extensive Damage

4. Background Goal: Numerical Modeling Basis
Discrete Modeling of Matrix Cracking and Delamination Networks
Matrix Cracking & Delamination
Interaction of
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] …..

5. 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
H(x) is approximated by the same
shape functions as displacements
Iarve (IJNM 2003)

6. 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

7. Numerical Modeling Basis
Background
Numerical Modeling Basis
General Modeling Flow
Step i=0 is thermal pre-stress
Add axial displacement increment
Perform Newton-Raphson iterations to converge damage variables in delam and MIC cohesive laws
Check matrix failure criteria
Add damage and repeat 2-5
Matrix Failure Criteria - Dávila, Camanho, and Rose, “Failure criteria for FRP laminates,” J. of Composite Materials, Vol
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.

8. Previous Experimental Effort
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

9. Numerical Model Details Table 1. Properties for IM7/8552 Lamina
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
[04/904] 2s
Dispersed Ply Specimen (IM7/8552)
[45/90/-45/0] 2s
Table 1. Properties for IM7/8552 Lamina
Material Property
Value
E11 (GPa) Ref 1
161.0
E22,E33 (GPa) Ref 1
11.38
G12,G13 (GPa) Ref 1
5.17
G23 (GPa) Ref 1
3.98
n12, n13 Ref 1
0.32
n23 Ref 1
0.44
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.

10. Numerical Model Details
X-ray Close-up

11. Matrix Damage Comparison
Blocked Quasi
[452/902/-452/02] s Specimen
Shifted Results
Specimen One
Stacked X-Ray
POD = 2.11 mm

12. 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

13. POD vs Load Comparison
Blocked Quasi
[452/902/-452/02] s Specimen

14. Matrix Damage Evolution
Blocked Quasi
[452/902/-452/02] s Specimen

15. Matrix Damage Blocked Cross-Ply
Simulations are symmetric in-plane as well as out-of-plane to aid damage stability.

16. Matrix Damage Evolution
Blocked Cross Ply
[04/904] 2s Specimen
Movie has been mirrored about symmetry plane

17. Blocked Quasi – with Statistical Variation
Matrix Damage
Blocked Quasi – with Statistical Variation
Five different statistical variations of matrix strengths were simulated.
Case 0
Case 1
Case 2
Case 3
Case 4

18. POD vs Load Comparison Blocked Quasi – with Statistical Variation

19. POD vs Load Comparison Blocked Quasi – with Statistical Variation

20. Continuum Damage Model for Fiber Failure
– characteristic length of the FE
IM7/8552 XT
GXT
fXT
fGT
3136 N/mm2
81.5 n/mm
0.2
0.4
C=(1-d)C0
C0 – initial stiffness
d – damage variable
For 1 mm3 volume
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)
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)

21. simulation damage pattern
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

22. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

23. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

24. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

25. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

26. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

27. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

28. Matrix & Fiber Damage Dispersed Quasi [45/90/-45/0/45/90/-45/0] s
Image from Test Specimen #3

29. Conclusions & Future Concusions: Future Efforts:
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

30. Acknowledgements
Partial funding for this work from NASA AAD-2 (NNX08AB05A-G) and AFRL (FA 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

32. X-Ray Computed Tomography
imaging panel
X-ray
Top View
Side View
Image i
3D “voxel” data visualizing internal specimen structure
OCT Specimen

33. X-Ray Computed Tomography
imaging panel
X-ray
Top View
Side View
Image j
3D “voxel” data visualizing internal specimen structure
OCT Specimen

34. X-Ray Computed Tomography
imaging panel
X-ray
Top View
Side View
Image k
3D “voxel” data visualizing internal specimen structure
OCT Specimen

35. 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

36. 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 mm
Voxel Dimension 0.06 mm
crack
voxel

37. Original Results from Li et al
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

38. Matrix Damage Comparison
Blocked Quasi
Specimen 1
POD ~ 2.12 mm
Blunt Notch
POD ~ 2.11 mm
-452/02 Interface

39. Matrix Damage Comparison
Blocked Quasi
Specimen 1
POD ~ 2.12 mm
Blunt Notch
POD ~ 2.11 mm
452/902 Interface