The fatigue life tests carried out on two groups of ball bearings confirm the positive influence of the compressive residual stresses induced by a previous loading in the elastic-plastic domain. The values of residual stresses are numerically evaluated by employing a three-dimensional strain deformation analysis model. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. To consider the material behaviour the Ramberg-Osgood stress-strain equation is involved and a nonlinear equation is considered to model the influence of the retained austenite. To attain the final load of each loading cycle the two bodies are brought into contact incrementally, so that for each new load increment the new pressure distribution is obtained as the solution of a constrained system of equation. Conjugate gradients method in conjunction with discrete convolution fast Fourier transform is used to solve the huge system of equations. Both the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both plastic strains and residual stresses is performed until the material shakedowns. Comparisons of the computed residual stresses and deformed profiles with corresponding measured values reveal a good agreement and validate the analysis model. The von Mises equivalent stress, able to include both elastic and residual stresses, is considered in Ioannides-Harris rolling contact fatigue model to obtain theoretical lives of the ball bearings groups. The theoretical analysis reveals also greater fatigue lives for the ball bearings groups with induced residual stresses than the fatigue lives of the group without induced residual stresses.

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