Analysis of Thick-Walled Spherical Shells Subjected to Various Temperature Gradients: Thermo-Elasto-Plastic and Residual Stress Studies

Abstract

In this paper, the elastic, elastoplastic, and thermal residual stresses due to autofrettage in a thick-walled spherical structure have been investigated. A steady-state radial temperature gradient has been applied throughout the thickness of the shell structure made of elastic-perfect-plastic constitutive material. This temperature gradient is assumed to be in both directions from inward to outward and vice versa. To calculate the equivalent stress and initial yield point, the Von Mises yield criterion (failure criterion) is used, and all relations are derived analytically. Then, the differences between the elastic–plastic behavior and the residual stresses in the thick-walled structure, caused by loading in two states of the temperature gradient, are investigated. Finally, the conditions for the occurrence of reverse yielding and its relation with the thickness and temperature gradient are carefully studied.