Thermal Stresses in an Elastic, Work-Hardening Sphere

In this paper, a method is presented for obtaining the transient thermal-stress distribution and the residual stresses in a spherical body where the time-dependent temperature distribution is symmetrical with respect to the center of the sphere. The material is assumed to be elastoplastic, while in the plastic range it work-hardens isotropically. The von Mises yield condition is used. The thermal and mechanical properties of the material are assumed to be temperature independent. The problem is reduced to a single nonlinear differential equation which is solved numerically on the NCR 304 digital computer. Several sets of numerical data representing various degrees of work-hardening in the spherical bodies during a cooling process are presented.