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Integral method coefficients for the ring-core technique to evaluate non-uniform residual stresses

The ring-core technique allows for the determination of non-uniform residual stresses from the surface up to relatively higher depths as compared to the hole-drilling technique. The integral method, which is usually applied to hole-drilling, can also be used for elaborating the results of the ring-core test since these two experimental techniques share the axisymmetric geometry and the 0°–45°–90° layout of the strain gage rosette. The aim of this article is to provide accurate coefficients which can be used for evaluating the residual stress distribution by the ring-core integral method. The coefficients have been obtained by elaborating the results of a very refined plane harmonic axisymmetric finite element model and verified with an independent three-dimensional model. The coefficients for small depth steps were initially provided, and then the values for multiple integer step depths were also derived by manipulating the high-resolution coefficient matrices, thus showing how the present results can be practically used for obtaining the residual stresses according to different depth sequences, even non-uniform. This analysis also allowed the evaluation of the eccentricity effect which turned out to be negligible due to the symmetry of the problem. An applicative example was reported in which the input of the experimentally measured relaxed strains was elaborated with different depth resolutions, and the obtained residual stress distributions were compared.