A numerical model for evaluating the residual stress field in an autofrettaged spherical pressure vessel incorporating the bauschinger effect

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel's wall, by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only few such studies exist for spherical ones. There are two principal autofrettage processes for pressure vessels: hydrostatic and swage autofrettage, but spherical vessels can only undergo the hydrostatic one. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a two-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elasto-plastic autofrettage problem using the form of the elastic solution. Substituting Hooke's equations into the equilibrium equation and using the strain-displacement relations, yields a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl-Reuss flow rule and the differential equation is solved by the explicit finite difference method. The previously developed 2-D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The appropriate residual stresses are then evaluated using the new code. The presently obtained residual stress field is then compared to three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field.