Stability Analysis of Microstructure Evolution Processes

"Various stability criteria are introduced and thermo-kinetic models for metallurgical processes are used as concrete examples for evaluation. Kinetic criteria for the process of dynamic recrystallization are proposed. These criteria are compared to the non-equilibrium thermodynamic approaches discussed in the literature. The application of macroscopic stability criteria to materials processing is then discussed.IntroductionThe mechanical behavior of metals at elevated temperature is very well predicted by any of several empirical constitutive relations. Typical is the power-law (or Swift's) form,Equationwhere r-is the stress, y is the strain and m, n , t0, y0 and Q are material constants. This form has been used with some success in the metals processing area [1]. In general, though, all of the empirical constitutive equations are static, failing to account for any dynamical properties of the system they seek to describe.The physics of warm deformation is qualitatively well understood. An example is power-law creep, where the dominant mechanism is assumed to be lattice diffusion limited climb of dislocations, which allows the strain-rate to be determined by the applied stress through"