Anti-plane elastic wave scattering from a rough volumetric crack

Abstract

The scattering of elastic waves from cracks is a field of study which has a number of important applications in nondestructive testing (NDT) and characterization of materials. So far most theoretical studies have concerned smooth cracks. There is reason to believe that the influence of roughness will scatter the energy in a more diffuse way, thus complicating the interpretation of test results.The problem considered here is the scattering of anti-plane waves, i.e. “horizontally” polarized shear waves, from a crack in an otherwise homogeneous, isotropic, elastic solid. The geometry is taken to be two-dimensional, and the scatterer is a curved volumetric crack with a small random roughness, which is characterized by the RMS height and a correlation length which is related to the average distance between the peaks of the irregularities. The term “volumetric” refers to the fact that the crack surfaces are slightly separated. Effects due to overall curvature as well as effects due to surface roughness and separation of the crack surfaces are thus included in the analysis.The method of solution can be described as an extension of the null field approach where certain matrix elements are expanded in terms of a small parameter describing the deviation from the smooth, nonvolumetric crack. The ensemble averaged amplitude of the scattered field for an incident plane wave has been computed numerically. Some results are given for various values of the frequency, the RMS height, the correlation length and the maximum gap between the crack surfaces.