A generalized comopsite approach to the flow stress and strain hardening of crystals containing heterogeneous dislocation distributions

A generalization of the composite approach to the flow stress of crystals containing heterogeneous dislocation distributions is proposed. The macroscopic flow stress is calculated assuming that a local flow stress depending on the local dislocation density can be ascribed to each mesoscopic volume element of the crystal. While the conventional composite approach allows for two values of the local flow stress (the local dislocation density) only, allowance is made for an arbitrary distribution of dislocation densities. It is demonstrated how such distributions and their evolution with strain may be calculated from simple models using methods of stochastic dislocation dynamics.