Extended Fatigue Life by Shot Peening Process via Shakedown Analysis

The goal of this work was to quantify the improvement in the fatigue limit of solid structures which have undergone shot peening (SP) by small rigid particles. The work was based on Melan’s shakedown theorem for estimating the allowable safe stress amplitude (in a lower bound sense) of structures that otherwise might fail during fatigue loading by plastic strain accumulation (ratcheting). Aided by geometrical simplification (mainly by assuming that the residual craters of the peened surfaces are shallow and flat), the benefit of SP to increase fatigue limits of structures subjected to fluctuating loads was quantified and compared to experiments. As a by-product, the long-time accepted empirical formulas for decreasing fatigue limits due to an increase of the loading mean tensile stress (Gerber, 1874, Z Bayer Arch Ingenieur-Vereins, 6, pp. 101–110; Goodman, 1899, Mechanics Applied to Engineering, Longmans, Green, London) have received a theoretical justification from shakedown analysis. The suggested empiricism-free solution traces well Gerber and Goodman’s empirical formulas in the positive mean stress regime of the applied load. It has a notable advantage that it also smoothly extends to the negative mean-stress regime (akin to the superimposed residual compressive stresses in a thin layer generated by the SP process) not covered hitherto by formulas. This shakedown analysis manifests the merit of shot peening processes by showing specifically the existence of larger range of fatigue-safe stress amplitudes (or equivalently, exhibiting a prolonged fatigue life) before disruption by ratcheting. Various fatigue experiments which were found in the open literature, are in a satisfactory agreement with the theoretical analysis.