The flow stress of dual-phase, non-hardening solids

A dual-phase composite comprised of an isotropic distribution of two elastic—perfectly plastic phases is considered. Each phase is characterized by a Mises yield surface and its associated tensile flow stress. The limiting tensile flow stress of the composite is computed in terms of the flow stresses of the phases and their respective volume fractions using a fully non-linear self-consistent model which identifies one phase as particulate and the other as matrix. It is found that the uniform strain-rate upper bound, which is just the rule of mixtures in terms of the phase flow stresses, provides an excellent approximation to the composite flow stress as long as the flow stresses of the phases do not differ by more than a factor of two. The results are applied to obtain some insight into the effect of a non-uniform isotropic distribution of rigid particles in reinforcing an elastic-perfectly plastic matrix. By identifying the tensile flow stresses of the two phases with flow stresses of particle-rich and particle-poor regions, one can predict the dependence of the limit flow stress of the composite on certain types of non-uniform distributions of the rigid particle reinforcements.