Monitoring near-surface depth profile of residual stress in weakly anisotropic media by Rayleigh-wave dispersion

TL;DR

This paper presents a method to infer the near-surface residual stress profile in weakly anisotropic media using Rayleigh-wave dispersion measurements, with applications to aluminum alloy samples treated by low plasticity burnishing.

Contribution

It introduces a novel inverse problem solution based on a high-frequency asymptotic formula for Rayleigh-wave dispersion in weakly anisotropic, prestressed media.

Findings

Successful modeling of stress profiles in aluminum alloy samples.

Potential for nondestructive stress measurement in engineering materials.

Application to partially relaxed residual stress after service.

Abstract

Herein we study the inverse problem on inferring depth profile of near-surface residual stress in a weakly anisotropic medium by boundary measurement of Rayleigh-wave dispersion if all other relevant material parameters of the elastic medium are known. Our solution of this inverse problem is based on a recently developed algorithm by which each term of a high-frequency asymptotic formula for dispersion relations can be computed for Rayleigh waves that propagate in various directions along the free surface of a vertically-inhomogeneous, prestressed, and weakly anisotropic half-space. As a prime example of possible applications we focus on a thick-plate sample of AA 7075-T651 aluminum alloy, which has one face treated by low plasticity burnishing (LPB) that induced a depth-dependent prestress at and immediately beneath the treated surface. We model the sample as a prestressed, weakly-textured orthorhombic aggregate of cubic crystallites and assume that by nondestructive and/or destructive measurements we have ascertained everything about the sample, including the LPB-induced prestress, before it is put into service. Under the supposition that the prestress be partially relaxed but other material parameters remain unchanged after the sample undergoes a period of service, we examine the possibility of inferring the depth profile of the partially relaxed stress by boundary measurement of Rayleigh-wave dispersion.