Thermodynamic treatment of cyclic amorphization during ball milling

Thermodynamic balance equations are written to describe the time evolution of a two-phase, crystal-amorphous element of material undergoing ball milling. The state of the microstructure is determined by the phase fraction, deformation state of each phase, and the temperature. Three steady-state solutions are obtained. The stability of the solutions are analyzed and it is shown that, for various combinations of materials parameters and rate constants, the solutions can be asymptotically stable spiral points which indicate cyclic amorphization behavior. Results are presented in terms of bifurcation diagrams for the phase fraction as a function of milling power. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.