Continuum phase field theory was applied to study elastic twinning in calcite and sapphire single crystals subjected to indentation loading by wedge-shaped indenters. An order parameter was associated with the magnitude of stress-free twinning shear. Geometrically linear and nonlinear theories were implemented and compared, the latter incorporating neo-Hookean elasticity. Equilibrium configurations of deformed and twinned crystals were attained numerically via direct energy minimization. Results were in qualitative agreement with experimental observations: a long thin twin forms asymmetrically under one side of the indenter, the tip of the twin was sharp and the length of the twin increases with increasing load. Qualitatively similar results were obtained using isotropic and anisotropic elastic constants, though the difference between isotropic and anisotropic results was greater in sapphire than in calcite. Similar results were also obtained for nanometer-scale specimens and millimeter-scale specimens. Indentation forces were greater in the nonlinear model than the linear model because of the increasing tangent bulk modulus with increasing pressure in the former. Normalized relationships between twin length and indentation force were similar for linear and nonlinear theories at both nanometer and millimeter scales. Twin morphologies were similar for linear and nonlinear theories for indentation with a 90° wedge. However, in the nonlinear model, indentation with a 120° wedge produces a lamellar twin structure between the indenter and the long sharp primary twin. This complex microstructure was not predicted by the linear theory.

Phase Field Modeling of Twinning in Indentation of Transparent Crystals. J.D.Clayton, J.Knap: Modelling and Simulation in Materials Science and Engineering, 2011, 19[8], 085005