Simple analytical approximations for eddy current profiling of the near-surface residual stress in shot-peened metals

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 can be used to nondestructively characterize the subsurface residual stress distribution in certain types of shot-peened metals, e.g., in nickel-base superalloys. For quantitative evaluation of the experimental results, analytical and computational techniques are needed to solve the direct and inverse problems, i.e., to predict the frequency-dependent apparent eddy current conductivity from the depth profile of the frequency-independent intrinsic electrical conductivity of the specimen and vice versa. Simple analytical approximations are presented for both the direct and inverse eddy current problems by exploiting two specific features of the subsurface electrical conductivity variation caused by near-surface residual stresses in shot-peened metals. First, compressive residual stresses are limited to a shallow surface region of depth, much less than typical probe coil diameters. Second, the change in electrical conductivity due to residual stresses is always very small, typically less than 1%. The proposed approximations are verified by numerical comparison to much more complicated numerical solutions.