Basic solution of a mode-I permeable crack in functionally graded piezoelectric materials

Article type: Research Article

Authors: Liang, Jun

Affiliations: Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin, P. R. China

Note: [] Address for correspondence: Jun Liang, Center for Composite Materials and Structures, Harbin Institute of Technology, P.O. Box 3010, No. 2 Yikuang Street, Harbin 150001, P. R. China. E-mail: liangj@hit.edu.cn.

Abstract: The basic solution of a mode-I finite length crack in an infinite functionally graded piezoelectric material plane was investigated by using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. 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.

Keywords: Crack, functionally graded piezoelectric materials, mechanics of solids

DOI: 10.3233/SFC-2009-0091

Journal: Strength, Fracture and Complexity, vol. 5, no. 2-3, pp. 63-78, 2009