Plastic collapse of a thin annular disk of variable thickness subject to thermo-mechanical loading

A semi-analytic solution for plastic collapse of a thin annular disk of variable thickness subject to thermo-mechanical loading is presented. It is assumed that the yield criterion depends on the hydrostatic stress. A distinguished feature of the boundary value problem considered is that there are two loading parameters. One of these parameters is temperature and the other is pressure over the inner radius of the disk. The general qualitative structure of the solution at plastic collapse is discussed in detail. It is shown that two different plastic collapse mechanisms are possible. One of these mechanisms is characterized by strain localization at the inner radius of the disk. The entire disk becomes plastic according to the other plastic collapse mechanism. In addition, two special regimes of plastic collapse are identified. According to one of these regimes, plastic collapse occurs when the entire disk is elastic, except its inner radius. According to the other regime, the entire disk becomes plastic at the same values of the loading parameters at which plastic yielding starts to develop.