Primary creep analysis of nanocomposite thick-walled sphere under thermal, magnetic and mechanical loading using viscoelastic Bergurs model

In this study, stresses and strains history of nanocomposite thick walled sphere wich is made of Polyimide reinforced by SiO2 nanoparticles are investigated using the viscoelastic Bergurs model. Loading of sphere includes the thermal and magnetic uniform field under hydrostatic inner pressure. Constitutive model of the problem based on elasticity relationship is obtained. Solving this equation with respect to mechanical boundary conditions leads to stresses and strains at zero time so called thermo-elastic solution in which these stresses are used at beginning creep problem procedure. With differentiating of constitutive differential equation with respect of time and using relationship between Bergurs model and Prandtl–Reuss relations drives a new constitutive equation for creep. History of stresses and strains are provided by solving this equation using numerical strain rate method. Results show that maximum effective stress and creep strains occurs at inner surface. Also the primary creep stage occurs up to 1000 second with quick change of stresses and strains. After this stage the value of stresses and strains change with uniform speed.