Delay Differential Equation Approach to the Stress-Strain Behavior of Crystalline Materials during Hot Working

摘要

During hot working, deformation of metals such as copper involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates, the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases, the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recrystallization causes the oscillatory nature. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. A delay time due to diffusion is taken into account, which is expressed as the critical strain for nucleation for recrystallization. The results show that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization.