An examination of the constitutive equation for elevated temperature plasticity

It was 25 years ago that the symposium on rate processes in plasticity was organized. Since then, advances in transmission electron microscopy, large-scale computation as well as molecular dynamics simulation, etc. have contributed much to our understanding of elevated temperature plasticity. The constitutive relation that links the stress-strain rate-grain size-temperature relation (Mukherjee-Bird-Dorn, MBD correlation) was presented in 1968/1969 to describe the elevated-temperature crystalline plasticity. This equation has held up well during the intervening quarter of a century. It has been applied to metals, alloys, intermetallics, ceramics, and tectonic systems, and it has worked equally well. It made the depiction of deformation mechanism maps in normalized coordinates a reality and provided a rationale for estimating life prediction by giving a quantitative estimate of the steady-state creep rate in creep damage accumulation relationship. In the case of particle-dispersed systems as well as metal matrix composites, the introduction of the concept of a threshold stress was a substantial improvement in creep studies. One of the significant applications of the MBD relation has been in superplasticity. The concept of scaling with either temperature or with strain rate, inherent in this relationship, seems to be obeyed as long as the rate-controlling mechanism is unchanged. The application of this relation to high strain-rate superplasticity and also to low-temperature superplasticity has been illustrated. Experimental data demonstrate that superplasticity of nanocrystalline metals and alloys follows the general trend of the constitutive relation but with important differences in the level of stress and strain hardening rates. It is shown that in the nanocrystalline range, molecular dynamics simulation has the potential to yield data on stress-grain size-temperature dependencies at very low grain size ranges where experimentalists cannot conduct their studies yet. (C) 2002 Elsevier Science B.V. All rights reserved.