Size Effects In Plasticity Research Articles

Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide

Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide

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

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.

On size effects in polycrystal plasticity

Two cumulative ‘size’ effects are responsible for the increased strength of a polycrystalline aggregate above the single crystal strength at low temperatures : a ‘specimen size’ effect and a ‘grain size’ effect. The ‘specimen size’ effect occurs when few grains are present in a specimen cross-section (say less than twenty), and this effect is due mainly to the orientation dependence of crystal plastic flow. The ‘grain size’ effect occurs when many grains are in a specimen cross-section (say more than twenty), and this effect results because, in addition to the orientation dependence of plastic flow within grains, internal concentrations of stress are necessary at grain boundaries to cause bulk yielding and subsequent plastic flow of the polycrystalline aggregate.