Arc-shaped interfacial crack in a non-homogeneous electro-elastic hollow cylinder with orthotropic dielectric layer

Abstract

The purpose of this present work is to study the arc-shaped interfacial cracking problem in a hollow cylinder that consists of an inner orthotropic dielectric layer and an outer functionally graded piezoelectric layer. Based on the method of variable separation, the problem is reduced to a Cauchy singular integral equation, which is solved by the Lobatto-Chebyshev quadrature technique. Numerical results of the stress intensity factor are obtained and the effects of geometrical and physical quantities on the fracture parameter are surveyed in details.

Appendix

For the case of open-circuit condition, Q _k (n) (k=1,2,…5) are

(A.1)

(A.2)

(A.3)

(A.4)

(A.5)

For the case of short-circuit condition, Q _k (n) (k=1,2,…5) are

(B.1)

(B.2)

(B.3)

(B.4)

(B.5)

For both the open-circuit and short-circuit conditions, Q ₆(n),Q ₇(n) and q are

(C.1)

(C.2)

(C.3)

where $\gamma= \sqrt{\beta^{2} + 4n^{2}}$, $k_{2} = e_{150}^{(2)}/\sqrt{c_{440}^{(2)}\varepsilon_{110}^{(2)}}$ is the dimensionless piezoelectric stiffening coefficient.