Integral Transform Technique For The Stationary And Dynamic Collinear Cracks Problem In A Piezoelectric Strip

Since Curie brothers discovered the electro-mechanical coupling phenomenon in 1880, piezoeletric material have widely been used as actuators, transducers, and sensors in micro-electro-mechanical systems. Because of their brittleness, it is easy to induce crack propatation in piezoelectric material subjected to mechanical and electric loadings. In recent year, many researchers have studied crack problems of in piezoelectric materials.In this paper, the problem of two collinear cracks in a piezoelectric strip is investigated. There are five chapters. In the first chapter, the studing method and progress of the problem of the cracked piezoelectric materials are introduced all over the world, especially for the problem of cracked piezoelectric mateial subjected to the anti-plane shear.In the second chapter, the basic equations of the piezoelectric matieral are given, including constitute equations, geometric equations, and boundary conditions, and so on.In the third chapter, the problem of two colliner anti-plane shear cracks lying at the piezoelectric strip is studied under the permeable and impermeable electrically crack boundary conditions. By using the Fourier transform, the associated problem is reduced to a singular integral equation. For the case of two eccentric collinear cracks, numerical results are determined via the Labatto-Chebyshev collocation method for solving a resulting singular integral equation. While for the case of two collinear cracks lying at the mid-plane of the piezoelectric strip, closed-form expressions for the energy release rates and stress, strain, and electric displacement intensity factors at the inner and the outer crack tips are obtained, The figues of the numerical example are drawn to show the dependence of crack growth on applied electric field and geometric paramaters.In the fourth chapter, the problem of two collinear cracks moving along a piezoelectric strip is investigated under the permeable and impermeable electrically crack boundary condition. The integral transform technique is employed to redu-cre the mixed-boundary-value problem to a singular integral equation. Numerical results for the dynamic energy release rates and the dynamic intensity factors are obtained, For the case of two impermeable collinear cracks moving at the mid-plane in the piezoelectric strip with the constant velocity, closed-form expression for the dynamic energy release rate and intensity factors near the inner and outer cracks are obtained. The influence of the cracks velocity to the intensity factors is analysed. Numerical example present the influence of the crack velocity on the dynamic energy release rates.In the fifth chapter, the above studied problems are concluded. It shows that the colliner anti-plane mode III crack problem is only theoretical. We anticipate that the obtained theoretical results can be used to some practical applications. Along this idea of thought, the problem of the mutiple collinear crack can be considered.