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

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

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 3

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

MAC/GMC Repeated Unit Cell Architecture 5 Square fiber, square pack Repeated Unit Cell with effective properties Approximately circular fiber, square pack For simplicity, this research used repeated unit cells with effective properties Debonding Faces

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

Mode I Delamination: DCB Test  Material properties of AS4/  Plane-strain finite element model  Unidirectional fibers aligned with the length direction (Y) 7 4” 1.15” 0.12” Applied displacements +/- 0.05” Fixed BC Debond interface MAC/GMC RUC Y X E 1 / ksiE 2 / ksiE 3 / ksi G 12 / ksiG 13 / ksiG 23 / ksi 21, = G IC / in- lb/in 2  S n / psi S s / psiS t / psi K 1 / psi K 2 / psiK 3 / psi e9 Through thickness 0.3”

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

Comparison of Stresses 9 Cohesive ModelVCCT ModelMAC/GMC Model ModelTotal CPU Time/s MAC/GMC Model1423 VCCT Model3241 Cohesive Model14, 806

Mode II Delamination: End-Notch Flexure (ENF) Test 10 U1=U2=U3=0 Displacement 0.2” 2t Crack tip 0.5L F w =0 a0a0 c0c0 u, w =0 U2=U3=0 Ref. 2 Reference 2: Song, et.al, Abaqus User Conference, 2008

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 ” (0.007mm) –Resulting element length ” (0.0025mm) Selection of interfacial strength values along the normal and shear directions are challenging 11

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 12 Ref. 2: Song, et al. Abaqus User Conf. (2008) Ref. 2 Problems Associated with Cohesive/VCCT Model

Effect of Mesh Size on MAC/GMC 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. 13 Refined mesh along the crack front makes debonding more localized Loss of element stiffness will not create a large (unrealistic) crack opening

Eccentrically Loaded 3-Point Bend Test in Reference 3: Rudraraju et. al, 50 th AIAA ASME/ASCE/AHS/ASC SDM Conference, 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

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 15

Prediction of Crack Path with MAC/GMC 16

Crack Propagation 17

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 18

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 19

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