Numerical method for calculating the apparent eddy current conductivity loss on randomly rough surfaces

Because of their frequency-dependent penetration depth, eddy current measurements are capable of mapping the near-surface depth profile of the electrical conductivity. This technique is used to nondestructively characterize the subsurface residual stress and cold work distributions in shot-peened metal components. Unfortunately, the spurious surface roughness produced by the shot peening process causes an apparent loss of eddy current conductivity, thereby decreasing the accuracy of the measurements, especially in thermally relaxed specimens where the primary material effects are significantly reduced. In this paper, a numerical method is introduced based on the Rayleigh approximation for calculating the apparent eddy current conductivity loss exhibited by 1D randomly rough surfaces. The relevant boundary conditions are satisfied using the so-called point-by-point technique, and the results are first compared to the previously developed Rayleigh– Fourier technique for a 1D sinusoidal corrugation. Pseudorandom surface profiles of different autocorrelation functions are considered. It is found that the Gaussian model lends itself the best to numerical simulations, but it significantly underestimates the apparent eddy current conductivity loss expected on real shot-peened surfaces, which exhibit essentially exponential correlation function. It is also demonstrated that the Lorentzian model is numerically less stable, but physically closer to the exponential one. The latter could not be simulated reliably by the present numerical technique because of its slowly decaying high-frequency spectral components. © 2004 American Institute of Physics. @DOI: 10.1063/1.1737474#