Micromechanical Elastoplastic Damage Mechanics for Elliptical Fiber-Reinforced Composites with Progressive Partial Fiber Debonding

By considering progressive interfacial partial debonding, a multi-level elastoplastic damage formulation is proposed to predict the overall transverse behavior of continuous elliptical fiber-reinforced metal matrix composites within the framework of micromechanics and homogenization. Based on the method of equivalent inclusion and taking the evolutionary interfacial debonding angle into consideration, partially debonded isotropic elliptical fibers are replaced by equivalent orthotropic yet perfectly bonded elliptical fibers. Three interfacial damage modes are considered. The Weibull’s probabilistic function is employed to describe the varying probability of progressive partial fiber debonding. The effective elastic moduli of four-phase composites, consisting of a ductile matrix and randomly located yet unidirectionally aligned elliptical fibers are derived via a micromechanical formulation. Further, the explicit exact exterior-point Eshelby’s tensor for an elliptical fiber is presented to investigate its effects upon inelastic responses of composites due to the cross-sectional shapes of fibers. In order to characterize the overall transverse elastoplastic damage behavior, an effective yield function is derived based on the ensemble-area averaging and the first-order effects of eigenstrains upon the overall yielding. Finally, comparisons between the present predictions and experimental data, and biaxial simulations are performed to illustrate the potential of the proposed framework.