Thin Homogeneous Two-Layered Plates of Cubic Crystals with Different Layer Orientation

Abstract

The paper provides a theoretical analysis of axially stretched rectangular thin plates composed of two differently oriented layers of cubic crystals. In one layer, the crystal has its principal crystallographic orientations parallel to the plate edges, and in the other, the crystal is oriented at a certain angle to the plate plane. The analysis shows that more than fifty cubic crystals with positive anisotropy can form two-layered plates whose effective Young’s modulus is greater than the moduli of both layers, which violates the well-known Voigt’s rule of mixtures. The anomalous behavior of effective Young’s modulus and Poisson’s ratios in the plates depends on the properties of their constituent crystals: the sign and value of anisotropy coefficients and Poisson’s ratio, ratio of Young’s moduli, relative orientation angle, and layer thickness ratio.