A mixed boundary value problem in orthotropic strip containing a crack

Abstract

In this study, an orthotropic strip containing a symmetrically located crack whose sides are parallel to the boundaries of strip is considered. It is assumed that the strip is hinged along its boundaries, the crack sides are loaded by distributed pressure and the principal directions of orthotropy are parallel and perpendicular to the boundaries. The problem is solved under plane strain conditions. As a result, the stress concentration characterized by the stress intensity factor (SIF) of mode I arises at the crack tip. By using the boundary conditions and the Fourier transform technique a Cauchy type singular integral equation of first kind is derived to determine the derivative of the function describing vertical displacements of the points on the crack sides. Iterative method is used to construct the approximate solution of this integral equation. A theorem is given to determine the lower bounds of applicable of the iterative method respect to the relative thickness of the strip, which has a geometrical importance. Two loading conditions are considered during the analysis. In this paper, the influence of relative thickness of strip as geometry parameter and the effect of the mechanical orthotropic properties on the SIFs are studied.