Abstract
Most theoretical work related to the study of the effective properties of polycrystals assume infinite media with randomly oriented grains. Therefore, the bulk material has absolute isotropy. However, real samples always include a finite number of grains such that the inspection volume will have some associated anisotropy. Hence, bounds on the bulk properties can be expected for a given measurement. In this work, the effect of the number of grains on this anisotropy variation is studied using Dream.3D software. The effective elastic modulus tensor is derived using Voigt, Reuss, and self-consistent techniques with 1700 microstructures comprised of equiaxed cubic grains in 17 different volumes. The bond transformation is utilized to quantify the standard deviation of the average elastic modulus. The standard deviations of several materials are shown to be inversely proportional to the square root of the number of grains. Based on the single-crystal anisotropy, a master curve is derived which relates modulus anisotropy to the number of grains. In addition, Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a similar master curve is derived. Such results will have important impacts on ultrasonic models associated with metals. [Research supported by AFRL under prime contract FA8650-15-D-5231.]
Published Version
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