Multi-level Elastoplastic Damage Mechanics for Elliptical Fiber-reinforced Composites with Evolutionary Fiber Debonding

Abstract

A micromechanical multi-level elastoplastic evolutionary damage framework is proposed to predict the overall mechanical behavior and interfacial damage evolutions of elliptical fiber-reinforced ductile composites. Progressively debonded fibers are replaced by equivalent microvoids. The effective elastic moduli of three phase composites, composed of a ductile matrix, randomly located yet monotonically aligned elliptical fibers and elliptical microvoids, are derived by using a micromechanical formulation. In order to characterize the homogenized elastoplastic behavior, an effective yield criterion is derived based on the ensemble-area averaging process and the first-order effects of eigenstrains. The resulting effective yield criterion, together with the overall associative plastic flow rule and the hardening law, constitutes the analytical framework for the estimation of effective elastoplastic damage responses of ductile composites containing both perfectly bonded and completely debonded fibers. An evolutionary interfacial fiber debonding process, governed by the internal stresses of fibers and the interfacial strength, is incorporated into the proposed work. The Weibull's probabilistic distribution is employed to describe the varying probability of fiber debonding. Further, systematic numerical simulations are presented to illustrate the potential of the proposed methodology.