Three-dimensional modeling and simulations of single-crystal and bi-crystal titanium for high-strain-rate loading conditions

Abstract High purity single crystal titanium (Ti) under shock wave loading is modeled under both one-dimensional and three-dimensional cylindrical conditions. Cylinder sizes of 10 μm and 20 μm radius are both considered in order to assess influence of boundary conditions. A thermodynamically consistent single crystal model for application to shock conditions is presented. The model accounts for the coupled non-linear elastic, dislocation slip, deformation twinning, and structural phase transformation response of the titanium material. Plate impact experiment results using a copper flyer are used to compare against the simulations for crystals oriented in [ 0001 ] and [ 10 1 ¯ 1 ] crystallographic directions. The one-dimensional and three-dimensional simulations of the two differently oriented single crystals indicate differences between the one-dimensional and three-dimensional representation, especially for the [ 10 1 ¯ 1 ] oriented single crystal. This orientation breaks the relative orientation symmetry between the crystal and cylinder which otherwise exists for the [ 0001 ] oriented single crystal. A significant amount of heterogeneity in the field response of the [ 10 1 ¯ 1 ] oriented simulation was demonstrated due to the highly coupled nature of the deformation. A bi-crystal model composed of both the [ 0001 ] and [ 10 1 ¯ 1 ] orientations with the boundary between the two along the axis of the cylinder is also considered for a cylinder model size of 10 μm. The results indicate a strong interaction between the two grains that affects the ω phase volume fraction achieved relative to the single crystal calculations.