Cracked Infinite Transversely Isotropic Piezoelectric Material Plate Fracture Analysis

Piezoelectric material is a kind of functional materials which can transformmechanical energy and electrical energy. It can be used to make piezoelectricbouchon, shells detonating device, etc. Due to advantages of piezoelectricmaterial, which are low cost and simple production and changing to higherefficiency, it is widely used in many industrial sectors and high-tech fields,especially in the aerospace, vehicle engineering, civil engineering and other fields.But in the process of making and using piezoelectric material, there are a lot ofbrittleness, it inevitably appears defects (such as,cracks, inclusions, voids, etc.)under the action of a mechanical and electrical loading, Which can lead to apremature failure occurred even destroyed and affect the performance andreliability of smart structures. So the fracture problem of piezoelectric material isof great significance.Complex function method is one of the effective methods to study fracturemechanics. By using the complex function method and undetermined coefficientsmethod, we can study composite material fracture problem, double compositematerials interface crack, periodic cracks and a series of problems. We find thatcomplex function method can also be applied to solve the problem of fracture ofpiezoelectric material, so we can use complex function method to analyse thefracture problems of piezoelectric material.Using the complex function method and undetermined coefficients method,the anti-plane fracture problems of an infinite transversely isotropic piezoelectricplate respectively with a central crack or collinear periodic cracks and the planefracture problems of an infinite transversely isotropic piezoelectric plate with acentral crack are studied. Using the complex function method, the mechanicsproblems are converted into boundary value problems of partial differentialequations. Combined with boundary conditions to select the appropriate functionsand use undetermined coefficients method, the solutions of boundary valueproblems of partial differential equations are gotten. Then defining the stressintensity factor and electric displacement intensity factor near the crack tip, the stress intensity factors, electric displacement intensity factors, stress fields, theelectric displacement fields and displacement fields and electric potential fieldsand mechanical strain energy release rate can be obtained. Finally we analyzeinterference effect and scale effect of collinear periodic cracks and crack length,stress and electric displacement effect on the mechanical strain energy release rateare discussed.