Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Abstract

In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter k, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. IntroductionDue to their intrinsic coupling between mechanical deformation and electric fields, piezoelectric materials are widely used as sensors and actuators to monitor and control the dynamic behavior of intelligent structural systems. Conventional piezoelectric devices are homogeneous or multi-layered, and they are susceptible to cracking and debonding due to uneven stress distributions or metal-to-ceramic bonds at which stress concentration occurs. In order to improve the integrity and reliability of piezoelectric devices, considerable research has been directed toward the development of functionally graded piezoelectric materials (FGPMs), [1][2][3]. In FGPMs, the material properties are continuously varied in one or more directions in order to eliminate mismatch of material properties at the interface and, thus, enhance the bonding strength and significantly improve the fracture toughness.Piezoelectric components are often subjected to impact mechanical and electrical loads in operation. Furthermore, in comparison with static loads, dynamic loads are likely to produce higher stress and electric fields in piezoelectric devices. It is of great importance to investigate the transient response of cracked piezoelectric materials and structures, therefore many studies investigated the fracture behavior of conventional piezoelectric materials and structures. The dynamic crack problem in a piezoelectric strip subjected to electro-mechanical impact was considered in [4], [5] and [6], while [7] analyzed a cracked piezoelectric laminate subjected to electromechanical impact loads. Paper [8] analyzed the interface crack between two piezoelectric layers under mechanical and electrical impacts, whereas [9] analyzed the interface crack of bonded piezoelectric and elastic half-space under transient electromechanical loads. Transient response of a smart laminate was investigated in [10] in which two piezoelectric layers were bonded to an elastic layer. In [11], the mode III Yoffe-type moving crack in a FGPM strip was considered, while in [12] a transient mode I crack in a FGPM plate, was investigated.

Stress intensity factor of an anti-plane crack parallel to the weak/micro-discontinuous interface in a bi-FGM composite

“…Ueda and Mukai [11] investigated the plane fracture problem of a layered medium with graded interfacial zone. Chen et al [12] analyzed the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a graded interfacial zone. Wang et al [13] put forth a linear multi-layered model for fracture analysis of a graded interfacial zone.…”

Mode III eccentric crack in a functionally graded piezoelectric strip

“…Jin et al (2003) solved the propagation problem of an antiplane moving crack in a function graded piezoelectric strip. Chen et al (2003a) studied the dynamics response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes. They found that the presence of the dynamic electric field could impede or enhance the crack propagation depending on the time elapsed and the direction of the applied electric impact.…”

A moving crack in a nonhomogeneous material strip

“…The investigation in Ref. [5] was the dynamic fracture of a crack in a nonhomogeneous interface. All of these papers considered the time-dependent crack tip field in nonhomogeneous materials.…”