Shot peening is widely used to improve the fatigue life of engine blades and rotors by inducing compressive residual stress. However, the residual stresses can relax due to exposure at high service temperature and mechanical loading. A physics-motivated analytical solution was developed to predict the residual stress relaxation at high temperature and under mechanical loading. In this thermo-mechanical relaxation model, the plastic strains in shot peening layer and substrate are obtained analytically by using linear kinematic hardening materials law, and then the plastic strain evolution at high temperature is modeled by using a recovery strain term. The final stress as a function of time, temperature and mechanical loading is obtained analytically by combining this recovery strain with equilibrium and compatibility conditions. The whole method can be implemented into Microsoft (MS) Excel, and is easy to use and validate. As a special case, an analytical closed-form solution to predict pure thermal relaxation of shot peening residual stress is developed. The model predictions agree satisfactorily with published experimental data.

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