A technique is developed for linking the methods of discrete dislocation dynamics simulation and finite element to treat elasto-plasticity problems. The overall formulation views the plastically deforming crystal as an elastic crystal with continuously changing dislocation microstructure which is tracked by the numerical dynamics simulation. The FEM code needed in this regard is based on linear elasticity only. This formulation presented here is focused on a continuous updating of the outer shape of the crystal, for possible regeneration of the FEM mesh, and adjustment of the surface geometry, in particular the surface normal. The method is expected to be potentially applicable to the nanoindentation experiments, where the zone .,around the indenter-crystal contact undergoes significant permanent deformation, the rigorous determination of which is very important to the calculation of the indentation print area and in turn, the surface hardness. Furthermore, the technique is expected to account for the plastic history of the surface displacement under the indenter. Other potential applications are mentioned in the text.

No abstract

No abstract

A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also found that a type B model reduces to a generalized one-sided classical Stefan problem in the case of a high driving thermodynamic force associated with the void growth stage, while it reduces to a generalized one-sided Mullins-Sekerka problem when the driving force is low in the case of void coarsening. The latter case corresponds to the famous rate theory description of void growth. Type C models, which include point defect concentrations and a non-conserved order parameter to distinguish between the void and solid phases and employ coupled Cahn-Hilliard and Allen-Cahn equations, are shown to represent mixed diffusion and interfacial kinetics. In particular, the Allen-Cahn equation of model C reduces to an interfacial constitutive law representing the attachment and emission kinetics of point defects at the void surface. In the limit of a high driving force associated with the void growth stage, a type C model reduces to a generalized one-sided Stefan problem with kinetic drag. In the limit of low driving forces characterizing the void coarsening stage, however, the model reduces to a generalized one-sided Mullins-Sekerka problem with kinetic drag. The analysis presented here paves the way for constructing quantitative phase field models for the irradiation-driven nucleation and growth of voids in crystalline solids by matching these models to a recently developed sharp interface theory.

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.