Several cracks in a functionally graded piezoelectric plane: In-plane steady harmonic loading case solved by dislocation method

Abstract

In this article, the problem of fracture mechanics in an infinite plane made of piezoelectric materials with functionally graded properties containing straight cracks with different orientations and arrangements as well as a curved crack under steady harmonic loading is presented. First, the in-plane dislocation solution in the functionally graded piezoelectric plane (FGPP) under investigation is solved according to the multi-valued conditions of displacement and electric potential, as well as considering the continuity of stress and electric displacement on the dislocation line and using Fourier transform. Then, linear constitutive equations are used and stress and electric displacement fields are presented. In this study, based on a logical assumption and to get closer to simplifying the solution of the equations governing the problem, the gradual and continuous changes of the functional material are considered exponentially and in the x-axis direction. In the following, to analyze the problem of multiple cracks, the dislocation distribution method is used to find singular integral equations. Finally, several graphs are presented to investigate the effect of material properties, electromechanical coupling coefficient, loading conditions and cracks arrangement on the field intensity factors and the results are compared and confirmed by the findings of other researchers.