A review of constitutive models based on the mechanics of dislocation motion was presented, with attention being focussed on the models of Zerilli and Armstrong. The models were intended to be as simple as possible, while still reproducing the behavior of real metals. The key feature of the models was their basis in the thermal activation theory of Eyring. The motion of dislocations was governed by thermal activation over potential barriers produced by obstacles; which could be the crystal lattice itself or dislocations and other defects. In body-centred cubic metals, the dislocation-lattice interaction typically predominated while, in face-centred cubic metals, the dislocation-dislocation interaction was the most significant. When the dislocation-lattice interaction was predominant, the yield stress was temperature and strain-rate sensitive, with essentially athermal strain-hardening. When the dislocation-dislocation interaction was predominant, the yield stress was athermal, with a large temperature and rate-sensitive strain-hardening. In both cases, a significant part of the athermal stress was accounted for by grain-size effects and, in some materials, by the effects of deformation twinning. Some simple strain-hardening models were also described; starting from a differential equation which described the creation and annihilation of mobile dislocations.

Dislocation Mechanics-Based Constitutive Equations. F.J.Zerilli: Metallurgical and Materials Transactions A, 2004, 35[9], 2547-55