Consistent formulation of the method of cells: Micromechanics model for transversely isotropic metal matrix composites

The predicted elastic and inelastic response of metal matrix composites given by the method of cells micromechanics model is critically examined using the theoretical framework provided by Hill's concentration factors. Concentration matrices for the incremental formulation of the method of cells are evaluated explicitly in terms of phase properties and phase volume fractions. Consistency equations for the concentration matrices are introduced. The parallel structure of the plastic and thermal strain increments of the composite is identified using the plastic-thermal weight matrices.; Using the concentration matrices, a new averaging approach is developed for the method of cells. Unlike the original averaging approach, the new approach ensures consistency of subcell and composite stresses and normality of the composite plastic strain increment to the composite yield surface.; The applicability of the unaveraged (tetragonal) method of cells model and the new averaged (transversely isotropic) method of cells model to composites with elastoplastic phases is established. The inelastic composite response is based solely on the fundamental assumptions of the micromechanics model and the assumed properties of the elastic fibers and the elastoplastic matrix. The predicted response of the unaveraged model and the new averaged model exhibit general structural features of heterogeneous elastoplastic systems. The overall composite yield surface is convex and it has a corner when two or more subvolumes yield concurrently. The composite plastic strain increment is normal to the composite yield surface at smooth points on the yield surface and confined to the cone of outward normals at corners. Composites with stiffening fibers are examined using the unaveraged (tetragonal) model, and nonconvex yield surfaces are generated.; The results are qualitative in nature and ensure the applicability of the method of cells to composites having elastoplastic phases. The derived analytical equations constitute a plasticity theory for fiber reinforced metal matrix composites (assuming that the matrix is an isotropic hardening, elastoplastic metal). The initial and subsequent yield conditions and the composite plastic strain increment are expressed in terms of composite stress, and the predicted mixed hardening behavior of the composite is fully described.