Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

Abstract

The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure.

Research on Multiple Griffith Cracks at the Interface of Fine‐Grained Piezoelectric Coating/Substrate

“…However, when D 0 increases from zero, G/G cr firstly increases and then begins to decrease. e results show that negative electric displacement loading always prevents crack propagation and positive electric displacement loading may prompt or prevent crack propagation, which are consistent with the conclusions of Pak et al [4,10,13]. However, the peak energy release rate of the fine-grained piezoelectric coating/substrate structure is higher than that of the large-grained piezoelectric coating/ substrate structure.…”

“…erefore, in the practical application of engineering, we can choose the appropriate load to ensure the safety of the structure. (2) For a bimaterial structure, compared with previous works [10,13], we found that the peak of the energy release rate at the crack tips of a fine-grained piezoelectric coating/substrate interface is larger than that at the crack tips of a large-grained piezoelectric material/substrate structure interface, and thus, the fine-grained piezoelectric coating/substrate structure has safer material properties. erefore, in order to better resist fractures, fine-grained piezoelectric materials are a better choice in engineering.…”

“…e integral equations were solved by the integral method, and it was concluded that the material parameters could prevent the transient fracture of the interface crack. Gherrous and Ferdjani [13] investigated a Griffith interface crack of bi-piezoelectric materials, and the singular integral equations were reduced into algebraic equations by using Chebyshev polynomials. Nan and Wang [14] studied the effect of residual surface stress on the stress and electric field strength of conductive cracks in piezoelectric nanomaterials.…”

1-3 Piezoelectric Composite Ferroelectric Materials in Smart Medical Ultrasonic Diagnostic Transducers

“…ANSYS software system is an universal FEM analysis software system that integrates construction, streamline, electromagnetic, and sound field analysis methods. It is widely used in engineering, scientific research and other fields [23]. ANSYS software realizes multiple functions such as structural analysis, electromagnetic analysis, fluid dynamics analysis, collision analysis, and adaptive mesh analysis [24].ANSYS also proposes the addition of macro instruction function for parameter design statements, which provides users with secondary development functions.…”

Interaction between Screw Dislocation and Interfacial Crack in Fine-Grained Piezoelectric Coatings under Steady-State Thermal Loading

“…Lee and Pak [13] used the complex variable function and conformal transformation method was given in linear piezoelectric materials semi-infinite long crack and screw dislocation interaction explicit solution of the problem, after analysis found that the crack tip stress, electric displacement and electric field had a singularity, also discussed under the condition of the limit of power lost, the results were consistent with pure elastic situation. Gherrous et al [14] derived the Griffith crack propagation problem at the interface of dual piezoelectric materials in semi-infinite planar structures. The solution of piezoelectric equation was transformed into singular integral equations by Fourier integral transformation, and the expression of the intensity factor.…”