Electric Field Gradient Effects In Anti-plane Crack Problems Of Piezoelectric Ceramics

Due to their intrinsic electro-mechanical coupling behaviors, piezoelectric materials are used widely in high technological devices, such as transducers, sensors, ultrasonic generators and actuators. However, when subjected to electric and mechanical loads, these piezoelectric materials can fail prematurely due to their brittleness and the presence of defects or flaws such as cavities, cracks and dislocations. Therefore, it is important to investigate the electro-elastic interaction and fracture behavior of piezoelectric materials. Because the transversely isotropic piezoelectric ceramics are the most prevalent in the actual application areas of industry engineering, the research on the anti-plane fracture behavior of piezoelectric ceramics has been very active in recent years. In this dissertation, an anti-plane crack problem in piezoelectric ceramics is analyzed with the theory for electroelastic solids including electric field gradient effects, i.e., the electric field gradient theory. First, the derivation of the electric field gradient theory is introduced, including the constitutive equations and the boundary conditions. After this, the electric field gradient theory is used to solve the piezoelectric anti-plane crack problem. Fourier transform is employed to reduce to this mixed boundary value problem to three pairs of dual integral equations; also the new additional boundary conditions are discussed. By using the Copson method, one of these equations is transformed into a Fredholm integral equation of the second kind to obtain the solution. Furthermore, the intensity factors, the total energy release rate and the mechanical strain energy release rate are obtained and compared with the classical results without considering the electric field gradient effects. Finally, using PZT-5H as a numerical example, the influence of the electric field gradient effect on piezoelectric fracture mechanics is examined.