Transient Thermoelectromechanical Response of a Functionally Graded Piezoelectric Material Strip with a Normal Crack

Abstract

Considered in this paper is a functionally graded piezoelectric material (FGPM) strip containing an embedded crack or an edge crack perpendicular to its boundaries. The problem is solved for an FGPM strip that is suddenly heated or cooled from the bottom surface. The top surface is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the bottom surface. First, the transient temperature and thermal stress distributions in an uncracked strip are calculated by using the Laplace transform. Then, the thermal stress is used as the crack surface traction with opposite sign to formulate the mixed boundary value problem. By using the Fourier transform, the electromechanical problem is reduced to a singular integral equation which is solved numerically. The numerical results for the thermal stress intensity factors are computed as a function of the normalized time for various values of the nonhomogeneous and geometric parameters. The temperature and thermal stress distributions for the uncracked problem and the results for the crack contact problem are also included.