An elastic/plastic solution for a hollow sphere subject to thermo-mechanical loading considering temperature dependent material properties

A semi-analytical solution for an elastic/plastic sphere subject to thermo-mechanical loading is given. Material properties are temperature dependent. The solution is valid for any isotropic pressure-independent yield criterion. Even though the general solution in both elastic and plastic regions is rather simple, the solution of the boundary value is cumbersome. The solution is facilitated by using the dimensionless temperature as an independent variable instead of the radial coordinate. A detailed analysis of the solution of the boundary value problem is provided assuming that the pressure and temperature at the inner radius slowly increase whereas the pressure and temperature at the outer radius are kept constant. In particular, qualitative features of the solution are emphasized. Some of these features are useful for the design of spherical vessels subject to thermos-mechanical loading.