Under non-monotonic loading conditions, such as those encountered in metal forming operations, multiphase metallic alloys show particularly complex mechanical responses. Conventional plasticity theories fail to provide useful predictions of such trends because they overlook two important sources of internal stresses: the phase partitioning of the plastic strain and the intra-granular dislocation substructure. Different modeling schemes aim to partition the macroscopic load among the constitutive phases of composite materials. Some of them, based on a discretization of the microstructure into finite elements or voxels, are versatile and often accurate but their computational cost is prohibitive in any real-scale simulation of forming processes. Mean-field theories constitute a computationally cheap alternative, applicable to the typical situation of a primary phase (called the matrix) inside of which one or several secondary phases form randomly dispersed, relatively isolated inclusions. Mean-field theories are derived from the equivalent inclusion problem that Eshelby solved in the case of linear-elastic constitutive phases. Transposing this solution to the nonlinear, elastic-plastic regime is not trivial and, in many cases, the proposed extensions are restricted to radial loadings. The incremental Mori-Tanaka model used here is an exception: it has been adapted in order to tackle general, non-monotonic loading conditions.
展开▼
