Imposition of Constraints on the Regularized Integral Method of Incremental Hole-Drilling

Background Incremental hole-drilling (IHD) and X-ray diffraction (XRD) are two of the most commonly used methods to measure through-thickness residual stress variation. IHD readily provides interior stress data, but the technique is prone to large uncertainty near the surface when steep stress gradients exist. XRD provides excellent near-surface data but insufficient penetration to readily define the stress distribution below the surface. To exploit the best features of each of these complementary residual stress measurement techniques, a means of combining measurements from XRD and IHD was recently demonstrated through the imposition of constraints on a series expansion solution. The regularized integral method is, however, the industry standard. A need therefore exists for a similar approach using the latter method. Objective Develop and demonstrate an approach to constrain the solution of the regularized integral method using data from complementary measurement techniques. Methods Constraints are enforced using the Lagrange multiplier method. The resulting equations are of closed form and make use of readily available information. The method is demonstrated on an aluminium alloy 7075 specimen of 10 mm thickness subjected to laser shock peening. Results Residual stress distributions obtained using the constrained and standard regularized integral methods compare well throughout the hole depth. The effect of incorporating XRD data into the constrained solution is localized to the near-surface region where the uncertainty is reduced. Conclusions Incorporation of XRD data into IHD results is readily achieved and allows the advantages of both techniques to be utilised while minimizing their shortcomings.