Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation

Based on the framework of Ju and Chen (Ju, J.W., Chen, T.M., 1994. J. Engng. Mater. Tech. ASME 116, 310±318) and Ju and Tseng (Ju, J.W., Tseng, K.H., 1996. Int. J. Solids Struct. 33, 4267±4291; Ju, J.W., Tseng, K.H., 1997. J. Engng. ASCE 123, 260±266), we study the e€ective elastoplastic behavior of two-phase metal matrix composites (MMCs) containing randomly located yet unidirectionally aligned spheroidal inhomogeneities. Speci®cally, the particle phase is assumed to be linearly elastic and the matrix phase is elastoplastic. The ensemble-volume averaging procedure is employed to micromechanically derive the e€ective yield function of MMCs based on the probabilistic spatial distribution of aligned spheroidal particles and the particle-matrix in¯uences. The transversely isotropic e€ective elasticity tensor is explicitly derived. Further, the associative plastic ¯ow rule and the isotropic hardening law are postulated according to the continuum plasticity. As a result, we can characterize the overall elastoplastic stress±strain responses of aligned spheroid-reinforced MMCs under three-dimensional loading and unloading histories. The overall elastoplastic continuum tangent tensor of MMCs is also explicitly presented