An alternative three-term decomposition for single crystal deformation motivated by non-linear elastic dislocation solutions

Abstract

Abstract : A new third term is incorporated within the multiplicative decomposition of the deformation gradient in the context of geometrically non-linear mechanics of defective elastic-plastic crystals. This enhanced description, when applied to an element of material of finite volume, accounts explicitly for average local residual lattice distortion due to defects within that volume. The magnitude of the distortion from this third term, determined analytically for an elastic cylindrical volume of outer radius R containing a single dislocation line threading its centre, is estimated as {[b/( R)]2 + f 2 + g2}1/2, where b is Burgers vector magnitude, f accounts for elastic non-linearity, and g accounts for core effects. For a straight screw dislocation in a third-order isotropic elastic medium, at a dislocation density of 10 per cent of theoretical maximum, b/( R) is on the order of 0.1, f on the order of 0.01 and g is proportional to pressure exerted by the core and can be significant. Predictions of stresses and dislocation density under simple shear and uniaxial compression demonstrate differences from those of usual crystal plasticity at large strain and for high hardening. Besides offering a natural and precise delineation of contributions from dislocation velocity and dislocation generation to irreversible deformation, the three-term model allows for residual elastic strains including dilatation observed in experiments and atomic simulations not addressed by conventional two-term crystal plasticity.