Axisymmetric Elastoplasticity of a Temperature-Sensitive Functionally Graded Cylindrical Vessel

Based on the small deformation theory and Tresca's yield criterion an axisymmetric, plane strain, elastoplastic, thermal stress analysis for a cylindrical vessel made of functionally graded elastic, perfectly plastic material is offered. Elastic modulus and yield strength coefficients are assumed to be power functions of radius and linear functions of temperature. A cylindrical vessel is taken to be composed of two or more nested fully elastic and perfectly plastic cylinders. By comparing the values of the deformation or stress components in the interfaces of the neighboring cylinders, a system of equations is formed. The interfacial boundary values of the fully elastic or perfectly plastic regions are obtained by simultaneous solution of the resulting interfacial consistency conditions. Having prepared the closed form solutions for the stress fields in purely elastic and purely plastic regions, the distribution of stress throughout the vessel can be obtained. Using this model, in some sample problems, the influences of temperature and pressure on the stress, strain, and plastic zone patterns are studied. The location of plastic zones is obtained for a class of material property compositions.