A unified micromechanical model for the mechanical properties of two constituent composite materials part II: Plastic behavior

This series of papers reports a new, general, and unified micromechanical model for estimating the three-dimensional mechanical properties of a composite made from two isotropic constituent materials, i.e., continuous fiber and matrix. The present pa per concentrates on the plastic behavior of the composite. Based on a perfect bonding assumption for the fiber and matrix interface during the entire elastic-plastic deformation range under consideration, a bridging relationship connecting the internal stresses generated in the matrix with those in the fiber is dependent only on the constituent geometric and material properties. Thus, the bridging matrix used in Reference [1] for elastic deformation analysis is modified according to the changed material properties of the constituents to account for their plastic deformation effect. With this matrix, the internal stress increments in each constituent material at every load level are explicitly related to the overall stress increments on the composite. The overall instantaneous compliance matrix of the composite follows easily once the constituent compliance matrices have been defined using any existing plastic flow theory of isotropic materials. Such an instantaneous compliance matrix will be of crucial importance in failure analysis of laminated composites. Incorporation of the Prandtl-Reuss flow relations with the explicit formulae proposed for the bridging matrix in Reference [1] has been described in the present paper. Good correlation has been found between predicted and available experimental elastic-plastic stress-strain curves of several unidirectional fibrous composites subjected to both uniaxial and combined load conditions.