In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual change of the shear moduli and mass density is assumed to be same. At first, the Volterra edge dislocation solutions are employed to derive singular integral equations in the form of Cauchy singularity for an FGP plane containing multiple horizontal moving cracks. Then, these equations are solved numerically to obtain dislocation density functions on moving crack surfaces. Finally, the effects of the crack moving velocity, material properties, electromechanical coupling factor and cracks arrangement on the normalized mode I and mode II stress intensity factors and electric displacement intensity factor are studied. Manuscript profile

In this paper, the mechanical fracture problem of a half-plane made of functionally graded material (FGM) with a coating of a homogeneous layer containing multiple interface cracks is investigated in order to determine the dynamic stress intensity factors (DSIFs) under transient in-plane loading. According to exponential law, the properties of functionally graded material change continuously along y-direction. Initially, integral transformations and dislocation of the Volterra type of climbing and sliding edges on the interface of a FG half-plane with a homogeneous coating leads to the numerical solution of a system with singular integral equations. These equations which have the Cauchy type-singularity are then obtained using the distributed dislocation technique (DDT). Using the inversion technique in the Laplace domain, the dislocation density on the crack faces is obtained which has led to the determination of the DSIFs. Finally, in order to show the accuracy and validity of this research, the final results in the form of graphs have been compared with other references and a very acceptable conformity has been observed. The influences of the FG parameter, coating thickness, crack length, the variation of time and the interaction between of cracks on the DSIFs are studied. Manuscript profile