Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials

Abstract

The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations in which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.

Dynamic anti-plane behavior for interacting cracks emanating from the edges of the circular cavities in piezoelectric bimaterials

“…Zhong and Li [3] gave a closed-form solution for two collinear cracks in a piezoelectric strip. Zhou and Wang [4] obtained the basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials. We can see that these documents are focus on the crack defects.…”

Effect of sintering temperature and time on densification, microstructure and properties of the PZT/ZnO nanowhisker piezoelectric composites

“…Although PZT ceramics have excellent electrical properties, poor mechanical properties such as fracture strength and toughness have been reported. In some applications at high power and high stress, their poor mechanical and electrical reliability become a critical limitation [19][20][21][22][23]. In the past few years, a few studies have dealt with improving the mechanical properties of PZT ceramics by incorporating polymers, particles, oxides, metals, fibers or whiskers [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”