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Elastic constants for tantalum single crystals have been calculated by Orlikowski, et al. [1] for a broad range of temperatures and pressures. These moduli can be utilized directly in continuum crystal simulations or dislocation dynamics calculations where the individual grains of the polycrystalline material are explicitly represented. For simulations on a larger size scale, the volume of material represented by the quadrature points of the simulation codes includes many grains, and average moduli are needed. Analytic bounding and averaging schemes exist, but since these do not account for nonuniform stress and strain within the interacting grains, the upper and lower bounds tend to diverge as the crystal anisotropy increases. Local deformation and stress equilibrium accommodate the anisotropic response of the individual grains. One method of including grain interactions in shear modulus averaging calculations is through a highly-descretized finite element model of a polycrystal volume. This virtual test sample (VTS) can be probed to determine the average response of the polycrystal. The desire to obtain isotropic moduli imposes attributes on the VTS. The grains should be equiax and the crystal orientation distribution function should be random. For these simulations, a cube, 300 {micro}m on a side, was discretized with 1 million finite elements on a regular rectangular mesh. The mesh was seeded with 1000 grains generated using a constrained-random placement algorithm, Figure 1. Since the orientations were simply painted in the mesh, the grain boundaries are irregular. The orientation distribution function is shown as pole figure in Figure 2. It has the appearance of being random. Analysis of the simulation results will be used to determine if the randomness of the texture and number of grains are adequate

Tantalum Shear Modulus from Homogenization of Single Crystal Data