Mesoscale model of plasticity

A framework for investigating plasticity phenomena and their dependence on the underlying physical and size-dependent mechanisms is developed. The framework is based on crystal plasticity and three-dimensional discrete dislocation dynamics analyses. Particularly, the mesoscale model couples continuum crystal plasticity framework with a set of spatio-temporal evolution equations for dislocation densities representing mobile and immobile species. The evolution laws consists of a set of components each corresponding to a physical mechanism that can be explicitly evaluated and quantifi ed from the discrete dislocation dynamics analyses. This includes dislocation glide, pile-ups, growth, annihilation, junction formation and breaking, dislocation–defect interaction, and cross-slip. It is shown that the discrete events of cross-slip of screw dislocations can be explicitly incorporated in the continuum theory based on a probability distribution function defi ned by activation energy and activation volume of cross-slip, which is analogous to the one used for the discrete system. This enables the redistribution of dislocations, making it possible to better predict the behavior for various loading conditions. Moreover, it is shown that in the presence of stress gradients the formation of dislocation pileups leads naturally to size-dependent fl ow stress with no artifi cial length scales. The result is a physically based mesoscale model for plasticity which can predict not only the macroscopic material mechanical behavior, but also the corresponding microscale deformation and the formation of dislocation patterns.