A Physically Based Internal Variable Model for Rate Dependent Plasticity

Abstract

In 1978 Krieg et al. published a ‘unified creep-plasticity’ model for rate-dependent deformation of metals, incorporating a power-law relationship between inelastic strain rate, applied stress, and instantaneous value of two internal variables.¹ The internal variables were permitted to evolve by a Bailey—Orowan process, including strain hardening and recovery. Hardening was taken to be linear and to increase the internal variables rather than the flow stress directly; recovery was treated as thermal (as opposed to dynamic strain-activated) only, where the kinetics were derived from dislocation mechanics for the process in question. The physical basis was established because (a) the power-law flow rule was taken to be a mathematically convenient approximation to rate-process theory at fixed microstructural state, (b) linear strain hardening in polycrystals is usually viewed as an aggregate manifestation of the linear (stage II) hardening behavior of fcc single crystals oriented initially for single slip and in the absence of dynamic recovery,^2,3 and (c) the recovery kinetics were derived from dislocation models. The value of physical bases follows, of course, from the confidence (indeed the meaning) that is given to extrapolation of the relationship beyond the range of measured data.