Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

Abstract

The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this paper using the generalized Almansi's theorem. To make the analysis tractable, it was assumed that the shear modulus varies exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials.

The fracture behaviour of functionally graded piezoelectric materials containing collinear dielectric cracks

“…It is found that the material gradient has significant effect upon the fracture properties of FGPMs. Owing to the fact that brittle FGPMs are susceptible to developing multiple cracks, the interacting crack problems for FGPMs have drawn the interests of research communities recently (Ma et al 2004;Liang 2006;Zhou & Wu 2006;Zhang et al 2008). …”

The nonlocal theory solution of a Mode-I crack in functionally graded materials

“…[35][36][37], it can be seen that the Schmidt method is performed satisfactorily if the first ten terms of infinite series in eqs. and ν =0.28, respectively.…”

Four parallel non-symmetric Mode-III cracks with different lengths in a functionally graded material plane

“…The unknown variables of dual integral equations are the dislocation density functions and the number of cracks is infinite as shown in [16][17][18][19]. Recently, the interactions of two parallel cracks in a functionally graded piezoelectric material plane were investigated in [20,21], where only the symmetric problems were considered. However, relatively fewer studies have been conducted to deal with the interaction of finite multiple cracks in functionally graded materials [20,21].…”

“…Recently, the interactions of two parallel cracks in a functionally graded piezoelectric material plane were investigated in [20,21], where only the symmetric problems were considered. However, relatively fewer studies have been conducted to deal with the interaction of finite multiple cracks in functionally graded materials [20,21]. To our knowledge, understanding of the multicrack interaction problem in a functionally graded material plane is very insufficient compared with homogeneous materials.…”