Modeling dislocation storage rates and mean free paths in face-centered cubic crystals

The first part of a dislocation-based constitutive formulation for strain hardening in face-centered cubic crystals is presented. This multiscale approach is based on the storage–recovery framework expanded at the scale of slip systems. A parameter-free formulation is established for the critical stress and the storage rate, taking advantage of recent results yielded by dislocation dynamics simulations. The storage rate of dislocations in the presence of forest obstacles is modeled for the first time at the level of dislocation intersections and reactions. The mean free path per slip system is found to be inversely proportional to the critical stress. It also depends on the number of active slip systems, which leads to an orientation dependence of stage II strain hardening in agreement with experimental data. The total storage rate is obtained by including three additional contributions, notably that of the self-interaction, which leads to a model for stage I hardening.