Constrained and unstable expansion of dislocation loops using an invariant formulation of the free energy

Abstract

The expression of the free energy related with the Eshelby-Kröner's inelastic inclusion problem is simplified using the theory of irreductible representations. This formulation simplifies significantly problems requiring energy derivatives and particularly moving boundary problems. As a first application, the stability of a dislocation loop under applied stress is studied and a new interpretation of the critical shear stress in single crystal is obtained. The second application deals with the problem of grain size effect in polycrystalline plasticity: The yield stress σ y follows a relation like σ y ≈ d − n where n = 1 2 holds for low grain size (equivalent to the classical Hall Petch relation) while for large grain size n is equal to unity.