Stress analysis of a hyperbolic elastic-plastic disk under thermomechanical loading

Abstract

   A general solution is constructed for the distribution of stresses within a thin, hyperbolic elastic-plastic disk subjected to external and internal pressures while in a steady-state temperature field and under plane stress conditions. The pressures applied to the disk are assumed not to induce any plastic flow at the initial, uniformly distributed temperature. The disk is loaded by increasing the temperature of its inner radius. The temperature of the outer radius is kept constant. Elastic and temperature strains are related to stresses by the Duhamel–Neumann law. In the plastic region, the von Mises yield criterion is valid. The tensile yield stress is taken as constant. The boundary value problem is statically determinate. Therefore, the plastic flow rule is not required to determine the stress field. The final part of the general solution depends on the parameters classifying the boundary value problem, including whether the plastic flow initiates at the inner or outer radius of the disk. The solution is presented in dimensionless form. The loading parameter comprises the inner surface temperature of the disk, the coefficient of linear thermal expansion, the initial temperature of the disk, the dimensionless inner radius of the disk, the yield stress under uniaxial tension, and Young’s modulus. The general solution is obtained for both cases (for a plastic region appearing at the inner or outer radius of the disk). A specific numerical solution is constructed for a disk subjected to external pressure and a steady-state temperature field. The temperature of the inner radius at which the plastic region first appears is calculated. As it increases, the plastic region extends. At a certain temperature value, another plastic region appears near the outer radius of the disk. This value is determined as part of solving the boundary value problem. The influence of the parameters classifying the boundary value problem on the development of the plastic region and the stress distribution along the radius of the disk is shown. The qualitative differences between the new and existing solutions for a disk of constant thickness under the action of a uniform temperature field are discussed.