Crack-tip Diffraction in a Transversely Isotropic Solid

A.N. Norris and J.D. Achenbach The Technological Institute Northwestern University Evanston, IL 60201 Crack diffraction in a transversely isotropic material is analyzed. The solution is given for the diffracted field generated by incidence of a plane time-harmonic wave on a semiinfinite crack located in a plane normal to the axis of symmetry of the material. The exact solution is obtained by Fourier integral methods and the Wiener-Hopf technique. The diffraction coefficients have been used in the context of the geometrical theory of diffraction to compute high-frequency scattering by a crack of finite length. Applications to scattering by delaminations in a medium of periodic layering have been considered for the case that the wavelength and the crack length are of the same order of magnitude, but both are much larger than the larger layer thickness. INTRODUCTION In this paper we consider the problem of diffraction from a stress-free crack in an anisotropic solid. The same problem in an isotropic solid is now well understood, and has been discussed by many authors, see Ref.[l] for a review. However, in practice, most materials exhibit some form of anisotropy. Examples of transversely isotropic solids are laminated media with periodic layering (on a length scale much larger than the characteristic thicknesses of the layers), and metals that have been subjected to certain manufacturing processes (e.g., rolling). Anisotropy may also be induced in an isotropic solid by large pre-stressing or straining [2].