A phase-field model was proposed for modelling microstructural evolution during deformation twinning. The order parameters were proportional to the shear strains defined in terms of twin plane orientations and twinning directions. Using a face-centered cubic Al as an example, the deformation energy as a function of shear strain was obtained using first-principle calculations. The gradient energy coefficients were fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that were perpendicular to the twinning planes. The elastic strain energy of a twinned structure was included using the Khachaturyan's elastic theory. The twinning process and microstructural evolution were simulated for a number of fixed deformations and the twinning-plane orientations and microstructures were predicted.

A Phase-Field Model for Deformation Twinning. T.W.Heo, Y.Wang, S.Bhattacharya, X.Sun, S.Hu, L.Q.Chen: Philosophical Magazine Letters, 2011, 91[2], 110-21