Elastic Properties of Statistically Equivalent Materials With Varying Individual Grain Orientations

The elastic properties of copper metal with different individual grain orientations exhibiting the same texture are determined. We simulate the real material by two different types of clusters. The first one consists of 365 cubic grains, the second cluster is an arrangement of 181 Wigner-Seitz cells of a body centred cubic (bcc)-lattice. For each type of cluster we let the local grain orientations vary. The displacement field inside these aggregates as a result of a homogeneous deformation acting on the surface of the clusters is calculated. Although the resulting local deformation field for different individual grain orientations varies strongly, the macroscopic elastic moduli are in the frame of this simulation identical for any cluster of the same type, as it has to be for statistically equivalent materials.