A phase-field model for deformation twinning

We propose a phase-field model for modeling microstructure evolution during deformation twinning. The order parameters are 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 is obtained using first-principle calculations. The gradient energy coefficients are fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that are perpendicular to the twinning planes. The elastic strain energy of a twinned structure is included using the Khachaturyan's elastic theory. We simulated the twinning process and microstructure evolution under a number of fixed deformations and predicted the twinning plane orientations and microstructures.