Coarse-grained descriptions of dislocation behaviour

Abstract

Recent computational advances have permitted mesoscale simulations of systems containing of the order of 10⁶ dislocations. While such simulations are beginning to provide a wealth of information about dislocation energetics and dynamics, it is worth noting that the macroscopic deformation response of well-worked materials with dislocation densities ranging between 10¹⁰ and can be accurately described by a smaller number of macrovariables and an appropriate relation between these variables. The large-scale reduction in the number of degrees of freedom required to characterize plastic deformation implies that homogenization, or coarse graining, of variables is appropriate over some range of length and time scales. Here, we describe recent work in which temporal and spatial coarse-graining strategies are identified, which link the mesoscale with the continuum. More specifically, three distinct examples are considered: the impact of solute–dislocation interactions on dislocation mobility (including pinning effects); thermally induced dislocation interactions; dislocation structure and properties at spatially coarse scales, primarily in two dimensions. In this latter example we formulate a continuum Hamiltonian and identify the corresponding macrovariable set (including the dislocation density and its gradients) that is relevant at each level of the coarse-graining hierarchy. Our goal is to show how these seemingly unrelated problems can be viewed as part of a unified picture of coarse-grained dislocation behaviour.

Acknowledgements

The work of R. LeSar was performed under the auspices of the US Department of Energy (US DOE) and was supported by the Office of Science, Office of Basic Energy Sciences, Division of Materials Science of the US DOE. J. M. Rickman would like to thank the National Science Foundation for its support under grant DMR-9975384, and both Princeton University and Los Alamos National Laboratory for their hospitality during his sabbatical. The authors thank Professor David Srolovitz of Princeton University for helpful discussions. They also thank Jason Lewis (University of California, Santa Barbara) for performing the analysis on the dislocations in three dimensions.

Notes

† Email: [email protected].

Additional information

Notes on contributors

R. LeSar†

† Email: [email protected].