Based on Tresca’s yield criterion and small deformation theory, an axi-symmetric elasto-plastic thermal stress analysis for a cylindrical vessel made of functionally graded elastic perfectly plastic material is offered. Elastic modulus, yield strength and thermal expansion coefficients are assumed to be power functions of radius and linear functions of temperature. To perform this analysis, primarily both the elastic and the plastic stress and deformation analysis of an inhomogeneous pressure cylindrical vessel are provided. It is assumed that an overloaded cylindrical vessel is composed of two or more nested elastic and fully plastic cylinders. By comparing the interfacial deformations of the neighboring cylinders a system of equations is formed. Simultaneous solution of the resulting nonlinear system of equations provides different distributions of stress and strain fields. Using this model, in some problems, the influence of temperature on the stress, strain and plastic zone patterns are studied. The influence of temperature and pressure upon the evolution and growth of plastic zone is studied. It is shown that depending on the composition of thermo-mechanical properties of the functionally graded cylinder, the interface line between the elastic and the plastic regions may place anywhere across the thickness. The rate and the direction of plastic zone expansion are studied. For a wide range of material properties, the patterns of yielded zones are represented.

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