In-plane stress analysis in a cracked functionally graded piezoelectric plane

Abstract

The fracture behavior of a cracked functionally graded piezoelectric plane was investigated under in-plane mechanical and electrical loading. The electro-elastic properties of the plane exponentially varied along the y-axis. Employing the Fourier transform, stress analysis containing a Volterra edge dislocation in a functionally graded piezoelectric plane was carried out. These solutions were used to derive a system of Cauchy singular integral equations for analyzing the straight and curved cracks. Linear, arc, parabolic and sine wave-shaped cracks were evaluated. The integral equations were numerically solved using the Lobatto–Chebyshev integration formula for dislocation density functions on the crack face which were employed to calculate field intensity factors. The effects of the shaped crack, loading parameters, and non-homogeneity parameter on the stress and electric intensity factors were considered.

Keywords:

• Mixed mode stress/electric intensity factors
• functionally graded piezoelectric plane
• curved crack
• Volterra edge dislocations
• Lobatto–Chebyshev integration formula