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

High purity single crystal titanium (Ti) under shock wave loading is modeled under both onedimensional and three-dimensional cylindrical conditions. Cylinder sizes of 10 um and 20 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) over bar1] crystallographic directions. The one-dimensional and three-dimensional simulations of the two differently oriented single crystals indicate differences between the onedimensional and three-dimensional representation, especially for the [10 (1) over bar1] 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) over bar1] 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) over bar1] orientations with the boundary between the two along the axis of the cylinder is also considered for cylinder model sizes of 10 and 20 mu m. The results indicate a strong interaction between the two grains that affects the omega phase volume fraction achieved relative to the single crystal calculations.