Reflection and transmission of plane waves at a shear-twin interface

Abstract

This paper is concerned with the effect of simple shear on the reflection and transmission of plane waves at the boundary between two half-spaces of incompressible elastic material, and, in particular, two half-spaces which form a twin in the sense that equal and opposite simple shears are applied to the two half-spaces. The objective is to simulate the (plastic) deformation associated with the twinning of crystals and thereby to provide a theoretical framework for the non-destructive evaluation of twinned interfaces. For a special class of constitutive laws it is shown that an incident plane harmonic (shear) wave propagating in the plane of shear in one half-space gives rise to an interfacial wave in each half-space in addition to a reflected and a transmitted plane wave in the respective half-spaces for every angle of incidence, although the amplitudes of the waves may vanish at certain discrete angles (different for each type of wave) depending on the state of deformation. For a specific material not in this special class, corresponding calculations for a particular value of shear show that the nature of the resulting waves is similar to that for the special class of materials. On the other hand, we note that for values of the shear beyond a certain critical value there are certain ranges of angles of incidence for which, instead, two homogeneous plane (shear) waves are reflected and also two transmitted. The dependence of the amplitudes of the reflected, transmitted and interfacial waves on the angle of incidence, the magnitude of the shear strain and the material properties is illustrated graphically.