Non-singular anti-plane fracture theory of two parallel cracks within non-local functionally graded piezoelectric materials

Article type: Research Article

Authors: Liu, Hai-Tao^{a; *} | Zhou, Zhen-Gong^b | Wu, Jian-Guo^a

Affiliations: [a] School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, P. R. China | [b] Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, P. R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, the electromechanical behavior of two parallel cracks in functionally graded piezoelectric materials (FGPMs) by using non-local theory is investigated under the electric permeable boundary conditions. To overcome the mathematical difficulty, a one-dimensional non-local kernel is used instead of a two-dimensional one for the fracture problem to obtain the stress and the electric displacement fields near the crack tips. The effects of the crack length, the distance between two parallel cracks, the functionally graded parameter and the lattice parameter of the FGPMs on the stress and the electric displacement fields at the crack tips are discussed. The present solution exhibit no stress and electric displacement singularities at the crack tips. The non-local solutions yield a finite hoop stress and electric displacement at the crack tips.

Keywords: Solid mechanics, two parallel cracks, non-local theory, FGPMs, lattice parameter, electromechanical behavior

DOI: 10.3233/SFC-170198

Journal: Strength, Fracture and Complexity, vol. 10, no. 1, pp. 23-38, 2017