Local and overall flow in composites predicted by micromechanics

Rate-dependent inelastic flow in metal matrix composites subjected to multiaxial stress states is quantified by flow surfaces, which are geometrically analogous to yield surfaces. The definition of flow is important because the most meaningful definition from a theoretical viewpoint, dissipation, is not measurable in the laboratory. Inelastic power is measurable, but differs from the dissipation due to residual stresses and evolution of the material state. Since experiments are necessary for development and validation of models, both definitions are important and considered here. The relationship between local flow in the matrix and overall flow of the composite is explored using finite element and generalized method of cells micromechanical analyses. The loci of flow surfaces in the axial-transverse and transverse-transverse stress planes are plotted. At the threshold, the overall flow surface is the intersection of all the local flow surfaces. Beyond the threshold, the intersection of all the local flow surfaces is smaller than the overall flow surface and differences between the dissipation and inelastic power are notable. Most importantly, the directions of the overall inelastic strain rate vectors are generally not normal to the overall surface of constant dissipation after the material state has begun to evolve. Thus, an associative macroscale continuum model will be, at best, approximate. Interestingly, local flow surfaces beyond the threshold are not necessarily convex when plotted in the overall stress plane. This is due to the existence of residual stresses. In addition, the generalized method of cells was found to accurately estimate the inner and outer envelopes of the local flow surface cluster with a surprisingly small number of subcells.