Self-consistent approaches and strain heterogeneities in two-phase elastoplastic materials

The Generalized Self Consistent Scheme [GSCS] extended to the nonlinear case with help of a deformation theory of elastoplasticity is used to predict the strain heterogeneities that spread out in two phase elastoplastic materials submitted to a monotonic uniaxial load. Materials with different microstructural morphologies are considered. The single composite inclusion of the GSCS is an accurate representation of matrix/inclusion microstructures but it does not give a sufficient representation of the considered morphologies. That’s why this model is extended to more general cases by using two or even more different spherical composite inclusions: local concentration fluctuations and local morphological inversions can then be modeled. The nonlinear extension is also modified: the composite inclusions are discretized into several concentric layers in order to take into better account the strain gradient along the radius and a new definition of the work-hardening parameter of each of these layers is proposed. The elastoplastic strain field in the single composite inclusion is also computed numerically by means of finite element methods and compared to the analytical result. Unfortunately, these modifications do not basically modify the strain heterogeneity predictions of the GSCS, which widely underestimate the measured strain heterogeneities in most of the cases. In fact, the inaccuracy of the GSCS in these cases is basically due to the appearance of long range shear bands that cannot be described by a local self-consistent approach.