A Micromechanical Constitutive Model of Progressive Crushing in Random Carbon Fiber Polymer Matrix Composites

A micromechanical damage constitutive model is presented to predict the overall elastoplastic behavior and damage evolution in random carbon fiber polymer matrix composites (RFPCs). To estimate the overall elastoplastic damage responses, an effective yield criterion is derived based on the ensemble-volume averaging process and first-order effects of eigenstrains due to the existence of spheroidal (prolate) fibers. The proposed effective yield criterion, together with the assumed overall associative plastic flow rule and hardening law, constitutes the analytical foundation for the estimation of effective elastoplastic behavior of ductile matrix composites. First, an effective elastoplastic constitutive damage model for aligned fiber-reinforced composites is proposed. A micromechanical damage constitutive model for RFPCs is then developed. The average process over all orientations upon governing constitutive field equations and overall yield function for aligned fiber-reinforced composites is performed to obtain the constitutive relations and effective yield function of RFPCs. The discrete numerical integration algorithms and the continuum tangent operator are also presented to implement the proposed damage constitutive model. The damage constitutive model forms the basis for the progressive crushing in composite structures under impact loading.