Thermo Elasto-Plastic analysis of functionally graded thick-walled cylindrical shells based on Prandtl-Reuss flow rule

This study deals with thermo-elasto-plastic behaviour of functionally graded thick-walled cylinder that is exposed to internal pressure and temperature gradient. For this purpose, Von-Mises yield criterion and Prandtl-Reuss flow-rule under state of plane strain are utilized. The modulus of elasticity, the thermal conductivity and thermal expansion coefficients are assumed to obey the power function in the radial position according to Erdogan’s model. In this work, the presented approach leads to the definition of new formulation to determine the elastic limit pressure and predict the onset radius of yielding, spread and growth of plastic zone. The governing equilibrium equation of cylindrical shell in axi-symmetrical status is solved in order to determine the distribution of radial, circumferential stresses and radial displacement. Various examples are handled to investigate the effect of FG-power law parameters on the yield pattern and distribution of plastic zone. The distribution of radial displacement, radial and circumferential stresses are expressed as the functions of radial position. The numerical results show that by the appropriate choice of the FG parameters and the specified thermal gradient, the plastic zone can commence simultaneously from inside and outside or intermediate radius.