Thermal effects in dislocation theory

Abstract

The mechanical behaviors of polycrystalline solids are determined by the interplay between phenomena governed by two different thermodynamic temperatures: the configurational effective temperature that controls the density of dislocations, and the ordinary kinetic-vibrational temperature that controls activated depinning mechanisms and thus deformation rates. This paper contains a review of the effective-temperature theory and its relation to conventional dislocation theories. It includes a simple illustration of how these two thermal effects can combine to produce a predictive theory of spatial heterogeneities such as shear-banding instabilities. Its main message is a plea that conventional dislocation theories be reformulated in a thermodynamically consistent way so that the vast array of observed behaviors can be understood systematically.

Thermal effects in dislocation theory. II. Shear banding

“…As in [1], consider a strip of polycrystalline material, of width 2 W , oriented in the x direction, being driven in simple shear at velocities V x and −V x at its top and bottom edges. The total strain rate is V x /W ≡ Q/τ 0 , where…”

“…In the preceding paper [1], I reviewed basic features of a thermodynamic theory of dislocation-mediated plasticity in polycrystalline solids. I showed there, in an oversimplified toy model, how this theory might explain shearbanding instabilities in such materials.…”

“…The thermodynamic dislocation theory described in [1][2][3] has focussed on strain hardening and related strainrate dependent phenomena. It describes those phenomena in terms of a small number of physically meaningful state variables that are consistent with basic principles of nonequilibrium statistical physics [7].…”

“…To work around this difficulty, I will use the same strategy here that I used in [1]. Thanks to the pioneering work of Kocks, Mecking, Follansbee, Meyers and others [8][9][10], we have a first-principles picture of plastic deformation in copper.…”

“…The trouble is that copper is not observed to undergo ASB, probably because its thermal conductivity is too high. In [1], I invented a "pseudo copper" by using the material parameters that I had available for real copper. Then I used artificial values for the thermal parameters so that my pseudo copper exhibited a rudimentary form of ASB.…”