Semi-analytical solution for electromagnetothermoelastic creep response of functionally graded piezoelectric rotating disk

Abstract

Time-dependent electromagnetothermoelastic creep response of rotating disk made of functionally graded piezoelectric materials (FGPM) is studied. The disk is placed in a uniform magnetic and a distributed temperature field and is subjected to an induced electric potential and a centrifugal body force. The material thermal, mechanical, magnetic and electric properties are represented by power-law distributions in radial direction. The creep constitutive model is Norton's law in which the creep parameters are also power functions of radius. Using equations of equilibrium, strain-displacement and stress–strain relations in conjunction with the potential-displacement equation a non-homogeneous differential equation containing time-dependent creep strains for displacement is derived. A semi-analytical solution followed by a numerical procedure has been developed to obtain history of stresses, strains, electric potential and creep-strain rates by using Prandtl–Reuss relations. History of electric potential, Radial, circumferential and effective stresses and strains as well as the creep stress rates and effective creep strain rate histories are presented. It has been found that tensile radial stress distribution decreases during the life of the FGPM rotating disk which is associated with major electric potential redistributions which can be used as a sensor for condition monitoring of the FGPM rotating disk.