Modeling the mechanical behavior of heterogeneous ultrafine grained polycrystalline and nanocrystalline FCC metals

A model is developed to describe the grain size effect on elastoplastic behavior of ultrafine grained (ufg) and nanocrystalline (nc) materials using a self-consistent approach. The grain size effect is modeled using two different length scales, the microscale (crystallographic slip system) and the mesoscale (granular level via the grain/matrix interaction law). The difference between the new extension and that previously proposed in AbdulLatif et al., (2009) is based on the fact that the current extension describes not only the ufg materials with grain size diameter (d) range of (100-1,000nm), but also the nc materials having a range of diameters of (limit value100 nm) which is defined by a lower slope of the linear Hall-Petch relation compared to the ufg regime. Note that such a limit value lv varies between about 15 nm and 30 nm. As a model limitation, the nc metals with grain sizes below lv which behave in the case of copper (lv = 25 nm) either as a plateau or as a decrease of the yield strength cannot be described by the model. In this extension, the grain-boundary attribution is assumed to be globally and implicitly described particularly with further grain refinement (i.e., nc materials). The used self-consistent scheme deals with a non-incremental inclusion/matrix interaction law of softened nature. It describes the non-linear elastic-plastic behavior of fcc polycrystals. The overall kinematic hardening effect can be naturally produced by the interaction law. Within the framework of small strain hypothesis, the elastic isotropic behavior is defined at the granular level. The heterogeneous inelastic deformation is locally determined using the slip theory. The model describes fairly well the effect of grain size on the strain-stress responses of copper and nickel.