Effective Elastoplastic Damage Mechanics for Fiber Reinforced Composites with Evolutionary Partial Fiber Debonding

Abstract

A micromechanical two-level elastoplastic evolutionary damage model is proposed to predict the overall transverse mechanical behavior and interfacial damage evolution of fiber-reinforced ductile matrix composites. Progressive partially debonded cylindrical isotropic long fibers are replaced by equivalent orthotropic yet perfectly bonded elastic cylindrical inclusions. Up to three interfacial fiber debonding damage modes in two dimensions are considered. The effective elastic moduli of five-phase composites, composed of a ductile matrix, randomly located yet unidirectionally aligned cylindrical fibers, and equivalent (damaged) cylindrical fibers, are derived by using a micromechanical formulation. In order to characterize the overall transverse elastoplastic damage behavior, an effective yield criterion is derived based on the statistical ensemble-area averaging process and the first-order effects of eigenstrains upon overall yielding. The proposed effective yield criterion, together with the overall plastic flow rule and the hardening law, constitute the 3-D analytical homogenization framework for the estimation of effective elastoplastic damage responses of metal matrix composites containing both perfectly bonded and partially debonded aligned cylindrical fibers randomly located in the matrix. Further, the Weibull's probabilistic function is employed to describe the varying probability of progressive partial cylindrical fiber debonding. The proposed micromechanical elastoplastic damage formulation is applied to the transverse uniaxial and varied stress ratios of transverse biaxial tensile loading to predict the various stress—strain responses under the plane-strain condition. Efficient computational algorithms are also presented to implement the proposed elastoplastic damage model. Finally, comparison between the present predictions and available experimental data and other simulations are performed to illustrate the potential of the proposed framework.