Probabilistic mesh-independent discrete damage analyses of laminate composites

In this paper, probabilistic failure response and damage patterns in laminate composites was investigated by considering spatially varying and cross-correlated strength properties. The effect of statistical parameters such as the correlation length, variance and correlation coefficient between normal and shear strength within Discrete Damage Modeling (DDM) framework was examined for the first time. For this purpose, an efficient random field modeling framework for multiple cross-correlated random fields is proposed whereby different sets of uncorrelated random variables in Karhunen-Loève (KL) expansion corresponding to independent auto-correlation functions are generated and transformed to sets of correlated random variables. DDM is performed by means of Regularized eXtended-Finite Element Method (Rx-FEM) where multiple matrix cracks in different plies are modeled simultaneously with interplay delaminations in interactive fashion. Two composite laminates a quasi-isotropic carbon/epoxy [45/90/−45/90]s Hexply IM7/8552 and [45/−45/90]s T300/976 were modeled by using probabilistic DDM. Significant effects of the statistical parameters on the failure behavior and ultimate component strength were observed, manifesting importance of accurate definitions of the statistical properties for predicting probabilistic failure behavior and damage tolerance of laminate composites. The average strength values predicted by probabilistic analysis with spatially correlated strength values were closer to experimental data than the predictions with uncorrelated strength values.