Dislocation mechanics-based constitutive equations

Abstract

A review of constitutive models based on the mechanics of dislocation motion is presented, with focus on the models of Zerilli and Armstrong and the critical influence of Armstrong on their development. The models were intended to be as simple as possible while still reproducing the behavior of real metals. The key feature of these models is their basis in the thermal activation theory propounded by Eyring in the 1930's. The motion of dislocations is governed by thermal activation over potential barriers produced by obstacles, which may be the crystal lattice itself or other dislocations or defects. Typically, in bcc metals, the dislocation-lattice interaction is predominant, while in fcc metals, the dislocation-dislocation interaction is the most significant. When the dislocation-lattice interaction is predominant, the yield stress is temperature and strain rate sensitive, with essentially athermal strain hardening. When the dislocation-dislocation interaction is predominant, the yield stress is athermal, with a large temperature and rate sensitive strain hardening. In both cases, a significant part of the athermal stress is accounted for by grain size effects, and, in some materials, by the effects of deformation twinning. In addition, some simple strain hardening models are described, starting from a differential equation describing creation and annihilation of mobile dislocations. Finally, an application of thermal activation theory to polymeric materials is described.

Advances in material and friction data for modelling of metal machining

“…They model the flow stress as a summation of athermal and thermal stress terms that are functions of the strain, strain rate, and temperature. Differences in the flow stress behaviours of fcc, bcc, and hcp metals are captured by the equations, which account for the coupling of strain hardening, strain rate hardening, and thermal softening, as appropriate for the crystal structure of the metal under consideration [233,232].…”

“…Zerilli-Armstrong (Z-A) [232]: [66] integrated the effects of the state of stress and dynamic recrystallization in the J-C model to simulate the machined surface integrity in orthogonal cutting of OFHC copper.…”

Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature

“…The Zerilli-Armstrong (ZA) model (Zerilli andArmstrong (1987, 1993); Zerilli (2004)) is based on simplified dislocation mechanics. The general form of the equation for the flow stress is…”

Comparison of dynamic compressive flow behavior of mild and medium steels over wide temperature range

“…The Zerilli-Armstrong equation [33,34] can be expressed in a modified form as [14] where n, C 0 , C 1 , C 3 , C 4 , and C 5 are material constants. For an adiabatic deformation process, it is important that the effect of the temperature rise generated by the plastic deformation be taken into account.…”