Hilbert transform approach to solve a problem of collinear Griffith crack in the mid-plane of an infinite orthotropic strip

Abstract

In this paper, an integral transformation of the displacement is employed to determine the solution of the elastodynamics problem of two collinear Griffith cracks with constant velocity situated in a mid-plane of an infinite orthotropic strip where the boundaries are assumed to be stress-free. By use of the integral transformation of the displacement, the problem is reduced to a solution of the triple integral equations and the finite Hilbert transformation technique is used to solve it. The expressions of stresses are obtained asymptotically for large values of strip depth. An analytical expression of the stress intensity factor at the crack tip is obtained and represented graphically for two different orthotropic materials.

Keywords

Griffith crack Mach number Fredholm integral equation elliptic integral asymptotic expansion stress intensity factor

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