Mechanical and Thermal Stresses In a Linear Plastic FGM Hollow Cylinder Due to Axisymmetric Loads

In this paper, an analytical solution for computing the linear plastic stresses, critical temperature and pressure in an FGM hollow cylinder under the internal pressure and temperature is developed. It has been assumed that the modulus of elasticity and thermal coefficient of expansion were varying through thickness of the FGM material according to a power law relationship. The Poisson s ratio was considered constant throughout the thickness. The general forms of thermal and mechanical boundary conditions were considered on the inner surface. In the analysis section, the effect of nonhomogeneity in FGM cylinder was implemented by choosing a dimensionless parameter, named m, which could be assigned an arbitrary value affecting the stresses in the cylinder. Distribution of stresses in radial and circumferential direction for FGM cylinders under the influence of internal pressure and temperature gradient were obtained. Graphs of critical temperature and pressure versus radius of the cylinder were plotted. Cases of pressure and temperature loadings were considered separately. The direct method has been considered to solve the heat conduction and Navier equations. The outer pressure for all over the cylinder goes to the plastic region when Ti=To=Pi=0 and by increasing the modules of elasticity the pressure will increase. By substituting M=0 in radial linear plastic stress formula, the perfect plastic equation will yield. By putting є p rr = є p rr r = 0 in radial linear plastic stress formula, it turns to the radial elastic stress.