A Deconvolution Method for the Mapping of Residual Stresses by X-Ray Diffraction

Background Inherent averaging effects in X-ray diffraction measurement of residual stresses, related to the finite size of the irradiated area, lead to inaccurate measurements in the presence of high surface stress gradients. Objective This paper develops a reconstruction method which allows the mapping of heterogeneous residual stresses from X-ray diffraction averaged measurements. Methods The stress reconstruction is based on a deconvolution of the average XRD measurements. The combination of a fine measurement grid and the use of two collimators lead to an overdetermined linear system on the average stress measured experimentally whose inversion provides the values of the local stress field. Results First, the method is successfully assessed in a reference problem solved by FEM in which the local distribution and average datasets are known. Then, it is applied to the reconstruction of residual stress mapping from experimental XRD measurements of a specimen processed by repetitive corrugation and straightening. The reconstructed field is in agreement with numerical (local) results of the process. Conclusion The method developed in this work permits the reconstruction of accurate distributions of heterogeneous near-surface residual-stresses.