Computational Modelling of Single Crystals

The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Following Franciosi and co-workers, the strength of the short-range obstacles introduced by the forest dislocations is allowed to depend of the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading, with transients in the density of forest dislocations accounted for. This solution, coupled with suitable equations of evolution for the dislocation densities, provides a complete description of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in Cu single crystals illustrate the versatility of the method.