Transient Response of a Functionally Graded Piezoelectric Rectangular Plane with Multiple Cracks under Electromechanical Impacts

The analytical method is developed to examine the fracture behavior of a functionally graded piezoelectric rectangular plane (FGPRP) with finite geometry under impact loads. The material properties of the FGPRP vary continuously in the transverse direction. Two different types of boundary conditions are examined and discussed in the analyses. The finite Fourier cosine and Laplace transforms are employed to obtain stress and electric displacement fields in the finite plane containing electro-elastic screw dislocation. Based on the distributed dislocation technique, a set of integral equations for the finite plane is weakened by multiple parallel cracks under electromechanical impact loads. By solving numerically, the resulting singular integral equation, the dynamic stress intensity factor (DSIF) is obtained for the electrically impermeable case. The new results are provided to show the applicability of the proposed solution. The effects of the geometric parameters including plate length, width, crack position, crack length, loading parameter, and FG exponent on the dynamic stress intensity factors are shown graphically and discusseThe analytical method is developed to examine the fracture behavior of a functionally graded piezoelectric rectangular plane (FGPRP) with finite geometry under impact loads. The material properties of the FGPRP vary continuously in the transverse direction. Two different types of boundary conditions are examined and discussed in the analyses. The finite Fourier cosine and Laplace transforms are employed to obtain stress and electric displacement fields in the finite plane containing electro-elastic screw dislocation. Based on the distributed dislocation technique, a set of integral equations for the finite plane is weakened by multiple parallel cracks under electromechanical impact loads. By solving numerically, the resulting singular integral equation, the dynamic stress intensity factor (DSIF) is obtained for the electrically impermeable case. The new results are provided to show the applicability of the proposed solution. The effects of the geometric parameters including plate length, width, crack position, crack length, loading parameter, and FG exponent on the dynamic stress intensity factors are shown graphically and discussed.