Fracture analysis of piezoelectric composites using scaled boundary finite element method

Abstract

Piezoelectric materials are widely used as sensors, actuators and transducers owing to the intrinsic mechanical and electrical coupling behavior. In most applications, piezoelectric materials are usually layered with substrates or embedded in a host material. Due to the brittleness and low fracture toughness, they have high tendency to develop cracks, especially under complex mechanical, electrical and thermal loads. In piezoelectric composites, interface cracks and interface debonding may be induced by the high stress concentrations occurring as a result of the mismatch of mechanical and electrical properties between different layers. The increasing use of these materials in modern intelligent material systems emphasizes the importance of the fracture analysis of piezoelectric materials.

This thesis develops a novel technique based on the scaled boundary finite element method to analyze fracture problems of piezoelectric composites under static, dynamic and thermal loadings. The scaled boundary finite element equations are derived for piezoelectric materials. In statics, a solution procedure based on matrix functions and the real Schur decomposition is used to solve the scaled boundary finite element equations. The singular stress and electric displacement fields around a crack tip are expressed analytically in the radial direction. Consequently, the generalized stress and electric displacement intensity factors are determined directly from the solution.

In dynamics, a continued fraction solution for the scaled boundary finite element equation is presented. The dynamic properties are represented by high order stiffness and mass matrices. This allows the use of efficient time-marching algorithms.

Under the thermal loadings, the change in temperature field is obtained using the scaled boundary finite element method. The nodal loads due to the temperature change are treated as a non-homogeneous term in the resulting ordinary differential equations. The particular solution for the non-homogeneous term is expressed as integral in the radial direction. This integral is evaluated analytically leading to a semi-analytical solution for the electromechanical behaviour.

Numerical examples are presented to verify the proposed technique with the results from the literature and the numerical results obtained using the commercial software ANSYS. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.