The equivalent thermal load was previously shown to be the only feasible method by which the residual stresses due to autofrettage and its redistribution, as a result of cracking, can be implemented in a finite element (FE) analysis of a fully or partially autofrettaged thick-walled cylindrical pressure vessel. The present analysis involves developing a similar methodology for treating an autofrettaged thick-walled spherical pressure vessel. A general procedure for evaluating the equivalent temperature loading for simulating an arbitrary, analytical or numerical spherosymmetric autofrettage residual stress field in a spherical pressure vessel is developed. Once presented, the algorithm is applied to two distinct cases. In the first case, an analytical expression for the equivalent thermal loading is obtained for the ideal autofrettage stress field in a spherical shell. In the second case, the algorithm is applied to the discrete numerical values of a realistic autofrettage residual stress field incorporating the Bauschinger effect. As a result, a discrete equivalent temperature field is obtained. Furthermore, a FE analysis is performed for each of the above cases, applying the respective temperature field to the spherical vessel. The induced stress fields are evaluated for each case and then compared to the original stress. The FE results prove that the proposed procedure yields equivalent temperature fields that in turn simulate very accurately the residual stress fields for both the ideal and the realistic autofrettage cases.

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