Indirect determination of yield strength gradient from shot peening residual stress response and its application to predicting high-cycle fatigue relaxation

Shot peening significantly enhances the fatigue resistance of engineering components by introducing compressive residual stress (CRS) fields into the material surface layers. However, the relaxation of residual stresses under cyclic loading critically undermines the accuracy of fatigue life predictions. Existing predictive models predominantly rely on empirical formulas and extensive experimental data fitting, which neither elucidate the mechanical essence of stress relaxation nor provide practical engineering applicability. In this study, a residual stress relaxation prediction method is proposed based on the Equivalent Yield Strength Gradient (EYSG). To this end, systematic experiments were conducted, including shot peening treatment, microhardness testing, residual stress measurements, cyclic loading tests, and residual stress relaxation assessments. The stabilized residual stress field formed after mechanical loading was used as the benchmark, and the loading spectrum characteristics were incorporated into a mechanics-driven framework to inversely solve for the EYSG, thereby enabling the prediction of residual stress field distributions under high-cycle fatigue (HCF) conditions. Results demonstrate that the EYSG effectively characterizes gradient mechanical responses. The developed method achieves a prediction accuracy of 91.7% for the tested material under cyclic loading, and 90.0% accuracy for a reference material reported in the literature. Experimental validation confirms the method’s capability for engineering-level residual stress relaxation prediction.