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When cylindrical and spherical vessels are subjected to the internal pressure, tensile tangential stresses are created throughout the thickness, the maximum of which are located at the inner surface of the vessels. To improve the performance of these vessels, autofrettage process has been devised to produce beneficial compressive residual stresses at the inner part of such vessels. The question arises whether the process such as autofrettage can be useful for vessels such as submarines or other thick walled tanks, which are used in deep sea waters and, therefore, subjected to high external hydrostatic pressure causing both radial and tangential stresses to be compressive across the thickness. On the other hand, is the residual stresses created by unloading from an external pressure beyond elastic limit beneficial and enhance their performances? In this study, elastoplastic and residual stresses in a thick-walled spherical vessel under external hydrostatic pressure has been investigated. The material behavior is considered to be elastic-perfectly plastic. Von Misses yield criterion is used to obtain initial yield point and for the ideal elastoplastic regime analytical relations are presented. It has been found that by applying external hydrostatic pressure yielding process will start from inside of the sphere. Finally after unloading, residual tensile stresses are created at the inner part of the vessel which is useful for the vessel. The residual stresses and the condition of reverse yielding is studied in this paper.

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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.