A first phase-field model was formulated for the evolution of a multi-dislocation system in an elastically anisotropic crystal under an applied stress. The model was a modification of, and extension to, a previous phase-field micro-elasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations was calculated exactly, and was explicitly incorporated into the phase-field formalism. It also automatically took account of the effects of short-range interactions, such as the multiplication and annihilation of dislocations and the formation of various metastable microstructures which involved dislocations and defects. The proposed 3-dimensional phase-field model for dislocations did not impose any a priori constraints upon possible dislocation structures or their evolution paths.

Nanoscale Phase Field Microelasticity Theory of Dislocations - Model and 3D Simulations. Y.U.Wang, Y.M.Jin, A.M.Cuitiño, A.G.Khachaturyan: Acta Materialia, 2001, 49[10], 1847–57