Fracture of a finite piezoelectric layer with a penny-shaped crack

Abstract

This paper studies a penny-shaped crack in a finite thickness piezoelectric material layer. The piezoelectric medium is subjected to a thermal flux on its top and bottom surfaces. Both thermally insulated crack and heated crack are considered. Numerical solution for the finite layer thickness is obtained through the solution of a pair of dual integral equations. The result reduces to the closed form solution when the thickness of the piezoelectric layer becomes infinite. Exact expressions for the stress and electric displacement at the crack border are given as a function of the stress intensity factor, which is determined by the applied thermal flux. This paper is useful for the reliability design of piezoelectric materials in thermal environments.

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

“…The solving process and method in the present paper are quite different from those adopted in the literatures . The crack‐shaped was assumed to be penny‐shaped , rectangular‐shaped , or cylindrical‐shaped . At the same time, the method (the Schmidt method) of the present paper is different from 3D finite element analyses method , singular integral equations , hypersingular integral equation method , extended displacement discontinuity integral equation method , the potential theory method , and the extended finite element method .…”

“…In recent years, the fracture problems in piezoelectric materials have been discussed under different electrical boundary conditions on the crack surfaces. For example, Li et al carried out to probe into the influences of the cylindrical piezoelectric fiber on the 3D crack‐tip stress fields by detailed 3D finite element analyses.…”

“…Ueda considered the mixed‐mode penny‐shaped crack problem for a functionally graded piezoelectric material strip. Wang et al studied a penny‐shaped crack in a finite thickness piezoelectric material layer under a thermal flux on its top and bottom surfaces. Li et al investigated a penny‐shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer.…”

“…The surfaces of the composite structure are subjected to both mechanical and electrical loads, and the crack surfaces are assumed to be electrically impermeable. In order to obtain the exact solutions, the crack‐shaped was often assumed to be penny‐shaped , rectangular‐shaped , or cylindrical‐shaped . For instances, Chen et al derived an impermeable penny‐shaped crack subjected to a concentrated thermal load (prescribed point temperature) applied arbitrarily at the crack surfaces by using the generalized potential theory method.…”

Analytical solution for the axisymmetric problem of a penny-shaped crack under internal pressure in a multi-layer composite

“…Ding and Li (2008) considered anti-plane problem of FGM coating on an elastic substrate containing a single crack and a periodic array of cracks on the interface between the coating and substrate. Recently, problems of piezoelectric materials with a crack (Tian and Rajapakse, 2006;Viun et al, 2018;Wang et al, 2011;Zhang et al, 2014) have been also attracted interest. Miura et al (2018b) solved the problem of an isotropic elastic layer sandwiched by semi-infinite bodies with an internal penny-shaped crack by expressing the normal displacement at the crack surface by Chebyshev polynomials of the second kind.…”