Modeling Progressive Damage in Composites via Continuum Displacement Discontinuities

1. Modeling Progressive Damage in Composites via Continuum Displacement Discontinuities Vipul Ranatunga Miami University Brett A. Bednarcyk Steven M. Arnold NASA Glenn Research Center, Cleveland, OH

2. Objective of the Research Investigate an existing MAC/GMC debonding model as a method for simulating delamination with bonded composite joints

3. Outline Overview of the displacement discontinuity model and MAC/GMC unit-cell architecture Comparison of VCCT, Cohesive, and MAC/GMC simulation results for opening and shearing crack propagation modes Prediction of the crack propagation path for an eccentrically loaded 3-point bend specimen Conclusion and future work

4. Delamination Modes Ref. 1 Mode II (Shearing) Mode I (Opening) Mode III (Tearing) End-notch flexure (ENF) test Double cantilever beam (DCB) test Ref. 1 Ref. 1 Reference 1: Villaverde, PhD Dissertation, Unv. Girona, Spain.

5. MAC/GMC Repeated Unit Cell Architecture www.bren.ucsb.edu/facilities/MEIAF/images.html Debonding Faces Approximately circular fiber, square pack Square fiber, square pack Repeated Unit Cell with effective properties For simplicity, this research used repeated unit cells with effective properties

6. Displacement Discontinuity Model - model parameters which define the unloading of the interfacial stresses - Normal and shear debond strength • Debonding interface is modeled by imposing discontinuity in a given displacement component across the interface • j - normal or transverse direction • Rjis a proportionality constant that may consider as a flexibility for the interface • Explicit time-dependence of the Rj parameter in the model is expressed in an exponential form

7. MAC/GMC RUC Fixed BC Debond interface Applied displacements +/- 0.05” Y 0.12” X 1.15” 4” Mode I Delamination: DCB Test Through thickness 0.3” • Material properties of AS4/3501-6 • Plane-strain finite element model • Unidirectional fibers aligned with the length direction (Y)

8. VCCT and MAC/GMC Models • An excellent agreement between VCCT & MAC/GMC is observed • Extended crack length: • VCCT: 0.28” • MAC/GMC: 0.30”

9. Comparison of Stresses

10. F 0.5L Crack tip 2t a0 c0 w =0 u, w =0 Mode II Delamination: End-Notch Flexure (ENF) Test U1=U2=U3=0 Ref. 2 Displacement 0.2” U2=U3=0 Reference 2: Song, et.al, Abaqus User Conference, 2008

11. Problems Associated with Cohesive/VCCT Model • Length of the cohesive zone under Mode-I loading • Need minimum of 3 elements in the cohesive zone to represent the fracture energy accurately • Cohesive zone length of 0.0003” (0.007mm) • Resulting element length 0.0001” (0.0025mm) • Selection of interfacial strength values along the normal and shear directions are challenging

12. Problems Associated with Cohesive/VCCT Model Ref. 2 Ref. 2: Song, et al. Abaqus User Conf. (2008) • Selection of Interfacial Penalty Stiffness (K) • High enough to prevent introducing artificial compliance • High value can lead to numerical problems • Softening behavior and stiffness degradation leads to severe convergence difficulties • Viscous regularization: introduces localized damping to overcome convergence difficulties • Automatic stabilization of unstable quasi-static problems through volume-proportional damping • Need to compare the energy consumed as the ‘damping energy’ with total strain energy to ensure that the damping energy is not too high

13. Effect of Mesh Size on MAC/GMC • Refined mesh along the crack front makes debonding more localized • Loss of element stiffness will not create a large (unrealistic) crack opening Stiffness of the entire element reduces as the crack progresses between the two layers A larger crack opening (compared to a crack tip) is created and the mesh has to be fine enough to represent the propagating crack front.

14. Eccentrically Loaded 3-Point Bend Test 1.8 in Ref. 3 Ref. 3 In FEA simulations, effective properties are used with fibers going in the thickness direction • Combined shear and normal loading on the bend specimen • Crack path is not know a priori • VCCT or cohesive elements are not suitable for modeling this problem Reference 3: Rudraraju et. al, 50th AIAA ASME/ASCE/AHS/ASC SDM Conference, 2009.

15. Uncoupled Normal and Shear Found that the normal and shear debonding are uncoupled Introduced Hashin’s failure criterion for coupling interface normal and shear stresses Element stiffness degrades if the stresses at the interface satisfy this condition

16. Prediction of Crack Path with MAC/GMC

17. Crack Propagation

18. Conclusion An approach based on a continuum level interfacial displacement discontinuities has been compared to the VCCT and cohesive element approaches MAC/GMC debonding model is considerably more robust and simpler to apply than VCCT and cohesive elements, while producing similar results This approach is far less sensitive to the finite element model control parameters Significant advantage over number of elements used in cohesive approach and the computational time required MAC/GMC has the potential to predict the crack path

19. Issues and Future Work Mesh dependence and the blunting of the crack tip Explicit time dependence of the debonding model Fiber-matrix debonding coupled with matrix cracking Application to bonded composite joints

20. Acknowledgments Thank You! NASA Summer Faculty Fellowship Program, supported through Advanced Composite Technology (ACT) program. Software and hardware resources from Research Computing Support Group at Miami University