A simple numerical model of the apparent loss of eddy current conductivity due to surface roughness

Abstract

In light of its frequency-dependent penetration depth, the measurement of eddy current conductivity has been suggested as a possible means to allow the nondestructive evaluation of subsurface residual stresses in shot-peened specimens. This technique is based on the so-called electro-elastic effect, i.e. the stress-dependence of the electrical conductivity. Unfortunately, the relatively small change in electrical conductivity caused by shot peening is often distorted, or even completely overshadowed, by the apparent conductivity loss caused by the accompanying surface roughness. This geometrical artifact is due to the fact that as the frequency increases, and therefore the penetration depth decreases, the path of the eddy current must follow a more tortuous route in the material, which produces a reduction in the observed conductivity. This paper addresses the apparent reduction of the near-surface electrical conductivity measured by the eddy current method in the presence of surface roughness. The rough surface is modeled as a one-dimensional sinusoidal corrugation using the Rayleigh–Fourier method. The apparent conductivity is determined from the resulting change in the plane-wave reflection coefficient of the conducting half-space at normal incidence. In spite of the simplicity of the suggested analytical model, the obtained theoretical results are found to be in good qualitative agreement with recently published experimental data from shot-peened copper specimens.