2004 Volume 53 Issue 3Appendix Pages 1-11
Three kinds of approach from macro-, meso- and micro-scopic viewpoints are summarized, in this paper, relevant to simulating the phase transformation incorporating processes. Since the fields of material structure, temperature and stress/strain induced in a body in such process are coupled each other, the ordinal way to solve independent (or, uncoupled) governing equations for transformation kinetics, heat conduction and stress analysis is insufficient, but thermodynamics-based consideration is needed to obtain the coupled equations among three fields. A transformation parameter indicating progressive phase change is introduced as one of internal parameters representing volume fraction of each phase or phase field parameter, and governing three kinds of equation for the parameter, Fourier law and stress-strain constitutive equation are derived. Thus obtained equations are applied to formulate the macroscopic finite element scheme and also the phase field method in meso-scopic sense in the framework of continuum thermodynamics. The molecular dynamics approach is also carried out to evaluate microscopic, or physical aspect of the fields. Some examples of the computer simulated processes with phase transformation are illustrated based on such three kinds of approach.
