Time-Dependent Deformation and Stress Redistribution Analysis of Thick-Walled Spheres Under Radial Temperature Distribution and an Internal Pressure

This paper describes time-dependent stress and deformation redistribution response of thick–walled spherical vessels made of functionally graded materials (FGM) under radial temperature fields and an internal pressure. The material properties except poisson`s ratio are power functions of radius. Total strains are the sum of mechanical، thermal and creep strains. By using equations of equilibrium، stress-strain and strain-displacement as well as using Norton’s law for creep constitutive model and considering the Prandtl - Reuss relations the stress distributions at loading moment and their rates with respect to time are obtained. Time-dependent redistribution of stresses is calculated as the sum of stress distribution at loading moment and integral of stress rates. Radial temperature distribution، history of stresses، displacements، stress rates and the effect of temperature rise on creep evolution are reported in this paper. It is concluded that the influence of tangential stress variations is more notable than radial stress`s and the creep behavior is more significant at high temperature applications. Also by means of FGM materials one can build vessels so that after passing specified time from loading، the stresses and deformations stand at anticipated rates.