Abstract
In this article, it is demonstrated that current methods of modelling plasticity as the collective motion of discrete dislocations, such as two-dimensional discrete dislocation plasticity (DDP), are unsuitable for the simulation of very high strain rate processes (10 6 s −1 or more) such as plastic relaxation during shock loading. Current DDP models treat dislocations quasi-statically, ignoring the time-dependent nature of the elastic fields of dislocations. It is shown that this assumption introduces unphysical artefacts into the system when simulating plasticity resulting from shock loading. This deficiency can be overcome only by formulating a fully time-dependent elastodynamic description of the elastic fields of discrete dislocations. Building on the work of Markenscoff & Clifton, the fundamental time-dependent solutions for the injection and non-uniform motion of straight edge dislocations are presented. The numerical implementation of these solutions for a single moving dislocation and for two annihilating dislocations in an infinite plane are presented. The application of these solutions in a two-dimensional model of time-dependent plasticity during shock loading is outlined here and will be presented in detail elsewhere.
Highlights
Plastic deformation in crystalline materials occurs through the motion of defects
The aim of the technique known as discrete dislocation dynamics (DDD) is to simulate plasticity as the result of the collective motion of individual dislocations within an elastic continuum
This paper introduces an elastodynamic formulation of Discrete dislocation plasticity (DDP) in which the time dependence of elastic fields of injected and moving dislocations is treated explicitly
Summary
Plastic deformation in crystalline materials occurs through the motion of defects. Point defects may be involved as in diffusional creep, and interfaces may be involved as in twinning and stressinduced martensitic transformations. Discrete dislocation plasticity (DDP) is a two-dimensional formulation of DDD, describing plasticity as the collective quasi-static motion of dislocations modelled as line singularities in a linear elastic solid. This necessarily limits the scope of the method to infinite straight edge dislocations so that plane strain conditions apply. Orowan’s equation suggests that these relativistic effects may be expected at strain rates of the order of 106 s−1 At those strain rates, the shapes of the elastic fields of moving dislocations may differ from their static counterparts and, the plastic response of the material can be different.
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