The effect of time-dependent creep on electro-thermo-mechanical behaviors of piezoelectric sphere using Mendelsonʹs method

This paper describes a numerical model which is used for the computation of stresses, electric potential and displacement histories in a hollow piezoelectric sphere subjected to an internal pressure and a distributed temperature field. The mentioned model is on the basis of the Mendelsonʹs method which predicts the variation of the stresses, electric potential and displacement with time through the thickness. The creep constitutive model for the effective strain is on the basis of the Bailey–Nortonʹs law. Since, creep strains are time, temperature and stress dependent, the closed form solution cannot be represented for this constitutive differential equation. Therefore, a semi-analytical method in conjunction with the method of successive approximation has been proposed for this analysis. The results indicate that in mechanical boundary condition which the sphere acts as an actuator, the effect of time-dependent creep causes to change radial stresses from compressive to tensile after 15 years. Hence, the actuator is not usable after 15 years. It has been found that in electrical boundary condition which the sphere acts as a sensor, the radial stresses are compressive during the life of the sphere. This state is suitable, because the sensor can be used for long time.