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The distributions of residual and working stresses in hollow spheres pre-strengthened using a combination of hydraulic and thermal autofrettage are investigated. The analysis is based on the theory of infinitesimal elastoplastic strains, the Tresca or von Mises yield condition, the associated flow rule and the linear isotropic hardening law. During unloading, the sphere material may exhibit the Bauschinger effect. All mechanical and thermophysical parameters are assumed to be independent of temperature. Exact analytical solutions are found for both loading and unloading stages including secondary plastic flow. The values of technological parameters are established at which the strengthening effect is achieved near the inner surface of the sphere. Analysis of the results shows that the use of a positive temperature gradient makes it possible to increase the absolute value of residual stresses on the inner surface of the sphere. On the other hand, with the help of a negative gradient it is possible to reduce working stresses in the sphere.
A. N. Prokudin (Thu,) studied this question.