Creep Stress Redistribution Analysis of Thick-Walled FGM Spheres

Time-dependent creep stress redistribution analysis of thick-walled FGM spheres subjected to an internal pressure and a uniform temperature field is investigated. The material creep and mechanical properties through the radial graded direction are assumed to obey the simple power-law variation throughout the thickness. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time temperature and stress dependent.  Using equations of equilibrium, compatibility and stress-strain relations a differential equation, containing creep strains, for radial stress is obtained. Ignoring creep strains in this differential equation, a closed form solution for initial thermo-elastic stresses at zero time is presented. Initial thermo-elastic stresses are illustrated for different material properties. Using Prandtl-Reuss relation in conjunction with the above differential equation and the Norton’s law for the material uni-axial creep constitutive model, radial and tangential creep stress rates are obtained. These creep stress rates are containing integrals of effective stress and are evaluated numerically. Creep stress rates are plotted against dimensionless radius for different material properties. Using creep stress rates, stress redistributions are calculated iteratively using thermo-elastic stresses as initial values for stress redistributions. It has been found that radial stress redistributions are not significant for different material properties. However, major redistributions occur for tangential and effective stresses.