Based on Tresca’s yield criterion and small deformation theory, an axi-symmetric thermal elasto-plastic stress analysis in cylindrical vessels made of Functionally Graded Material (FGM) is presented. Primarily the separate distribution of elastic and plastic stress and deformation for an inhomogeneous cylinder is introduced. The elasto-plastic cylinder is assumed to be composed of several nested elastic and fully plastic cylinders. The deformation of each cylinder is correlated to its neighboring cylinders and consequently a system of equations is formed. Using this model, in some problems, the influence of temperature on the stress, strain and plastic zone patterns are studied. Elastic modulus and yield stress are assumed temperature-independent power functions of radius. Especially, the influence of temperature upon the evolution and growth of plastic zone is studied. It is shown that depending on the composition of thermo-mechanical properties of FG material, the interface line between elastic and plastic regions may take shape in different radii. The rate and direction of the growth of plastic zone are studied. For a wide range of material properties, the patterns of yielded zones are plotted.

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