Shot peening is widely used to improve the fatigue life of engine blades and rotors by inducing compressive residual stress on component surfaces. However, the residual stresses can relax due to exposure at high service temperature and mechanical loading. A physics-motivated analytical solution is developed to predict the residual stress relaxation at high temperature and under mechanical loading. In this thermomechanical relaxation model, the plastic strains in the shot peening layer and the substrate are obtained analytically by using linear kinematic hardening material law, and the plastic strain evolution at high temperature is modeled by using a recovery strain term. The final residual 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 Excel, and is easy to use and validate. As a special case, an analytical closed-form solution to predict the pure thermal relaxation of a shot peening residual stress is developed. The model predictions agree satisfactorily with published experimental measurements.

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