Phase-field analysis of fracture-induced twinning in single crystals

Deformation twinning at the tip of a straight crack or notch is analyzed using a phase-field method that seeks equilibrium twin morphologies via direct minimization of a free energy functional. For isotropic solids, the tendency to twin under mode I or mode II loading is found to depend weakly on Poisson’s ratio and elastic nonlinearity and strongly on surface energy and twinning shear (i.e. eigenstrain). Depending on the coherent twin boundary energy, anisotropy of surface energy is important for mode I loading but less so for mode II. Model predictions for several single crystals are in agreement with experimental observations. Calcite demonstrates a preference for mode I cleavage crack extension over crack tip twinning. Magnesium shows a likelihood for tensile twinning from a pre-existing crack on the basal plane. In sapphire, a preference for rhombohedral twins over basal twins is apparent, with the latter thinner in shape than the former.