A cracked functionally graded piezoelectric material strip under transient thermal loading

Considered in this paper is a functionally graded piezoelectric material strip (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 under static mechanical loading. 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 the thermal stress distributions in an uncracked strip are calculated by using the Laplace transform. Then, these mechanical and thermal stresses are 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 stress and thermal stress intensity factors are computed as a function of the normalized time, the nonhomogeneous and geometric parameters. The temperature and the thermal stress distributions for the uncracked problem and the results for the crack contact problem are also included.