An Analysis of the Thermodynamics of Dislocation Glide

Abstract A general treatment of thermally activated dislocation motion is presented following the approach first suggested by Basinski and making use of Leibniz's formula to analyze the properties of arbitrarily shaped obstacles. The small region surrounding a dislocation obstacle is shown to be an acceptable thermodynamic system with the effective stress, defined as the difference between the applied stress and the long range internal stress evaluated at the obstacle, as an appropriate thermodynamic variable. All of the thermodynamic properties of such a local system are self consistent. The question of the choice of a thermodynamic system is discussed in connection with the results of prior treatments of the problem. Whether one considers a local system using the effective stress as the operative thermodynamic variable, or the entire crystal as a system using the applied stress, the value of the effective stress and the conditions for which it is zero must be known, in general, in order to relate measured thermodynamic quantities to the properties of an obstacle. The thermodynamic methods are illustrated with the use of a simple sinusoidal model for the backstress produced by an obstacle. The difficult problem of relating the stress and temperature dependence of plastic flow to the results of thermodynamic analysis is treated. The discussion indicates that serious errors can be made either when the effective stress is not precisely known, as is commonly the case for high temperature creep, or when the stress and temperature dependence of the preexponential constant are not taken into account.