Time-dependent magnetothermoelastic creep modeling of FGM spheres using method of successive elastic solution

Abstract

Magnetothermoelastic creep behavior of thick-walled spheres made of functionally graded materials (FGM) placed in uniform magnetic and distributed temperature fields and subjected to an internal pressure is investigated using method of successive elastic solution. The material creep, magnetic and mechanical properties through the radial graded direction are assumed to obey the simple power law variation. Using equations of equilibrium, stress–strain and strain–displacement a differential equation, containing creep strains, for displacement is obtained. A semi-analytical method in conjunction with the Mendelson’s method of successive elastic solution has been developed to obtain history of stresses and strains. History of stresses, strains and effective creep strain rate from their initial elastic distribution at zero time up to 55 years are presented in this paper. Stresses, strains and effective creep strain rate are changing in time with a decreasing rate so that after almost 50 years the time-dependent solution approaches the steady state condition when there is no distinction between stresses and strains at 50 and 55 years.