Uncertainty of residual stresses measurement by layer removal

A model to evaluate the uncertainty in the measurement of the through-thickness residual stress distribution in plates by the layer removal technique is presented. Thin layers were chemically etched from a stripe on rectangular specimens cut from a low carbon cold-rolled steel sheet. Phase shifting laser interferometry was used to measure the ensuing curvature. Polynomials were least-squares adjusted to the curvatures as a function of the etched depth. The polynomials were inserted into an integro-differential equation relating the curvature to the residual stresses, which were assumed to be a function of depth only. A comparison with X-ray diffraction measurement of the surface residual stresses showed good agreement. The uncertainty was found to increase steeply at the surfaces and to depend mainly on the assumed value for the modulus of elasticity, on the curvature fit, and on the depth of etching.