Estimation of the error in determining residual stresses under elastic-plastic loading of thick-walled spherical shells during linear hardening of the material

Abstract

The study considers the problem of estimating residual stresses in thick-walled spherical shells under internal pressure during elastic-plastic deformation. A mathematical model of elastic-plastic deformation of a spherical shell was constructed using the provisions of the deformation theory of plasticity. The novelty of the study is due to the consideration of changes in the geometry of the shell during loading when determining residual stresses. For a piecewise linear model of the material, the results of calculating residual stresses using analytical formulas using the "hardening" principle and the method of variable elasticity parameters when changing the geometry of the shell during loading are presented. According to the results of the evaluation of solutions obtained analytically and numerically, with an increase in the wall thickness of the spherical shell, as well as with an increase in the hardening index of the shell material, the relative error in calculating residual stresses increases.