Green's Function for Orthorhombic Aggregates of Weakly Anisotropic Cubic Crystals

Herein a closed but approximate formula of the Green's function is obtained for orthorhombic aggregates of cubic crystallites. This formula, which includes three material constants and three texture coefficients, accounts for the effects of the orientation distribution function (ODF) up to terms linear in the texture coefficients. Thus it is expected that our formula would be applicable to aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. The approximate formula remains valid and assumes a simpler form when the polycrystal reduces to a weakly anisotropic cubic crystal. Two examples are presented to compare predictions from our formula with those from Nishioka and Lothe's formula and from Synge's contour integral through numerical integration.