On the Inversion of Subsurface Residual Stresses from Surface Stress Measurements
X-ray diffraction provides an efficient method to measure the stress tensor at a surface point of a polycrystalline body. When the stress at an interior point of the body is to be measured, it is common to remove matter in order to reach the considered point. However, this matter removal induces, in general, a stress redistribution so that the measured stress is different from the original residual stress. This paper addresses the problem of reconstructing the original stress field from the measurements. The problem is solved by a general method which leads to explicit inversion formulae for the case of simple geometries. Closed-form expressions are obtained for the two-dimensional and three-dimensional half-space. For bodies of arbitrary shape, an existence and uniqueness theorem is proved. The existence proof is constructive and a numerical algorithm may be derived.
KeywordsResidual Stress Stress Field Surface Traction Residual Stress Field Curvilinear Coordinate System
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- Moore, M.G. and Evans, W.P. (1958) Mathematical correction for stress in removed layers in X-ray diffraction residual stress analysis, SAE Trans., Vol. no. 66, pp 340–345.Google Scholar