Local stresses in an orthotropic plate with crack-like defect

Abstract

We develop an approach to the determination of the local stress-strain state of an infinite orthotropic plate weakened by a thin cut with small nonzero radius of curvature at the tip. We deduce asymptotic formulas for the distributions of stresses and displacements near the tip of the defect and obtain expressions for the generalized stress intensity factors and parameters determining the next (in the order of smallness) terms of the asymptotic expansions. It is shown that, within the analyzed range of the radii of curvature, the generalized stress intensity factors are expressed via the corresponding quantities for a crack of zero width (to within a constant factor).A method developed in [l] enables one to establish the structure of the fields of stresses and displacements near peaked holes and rigid inclusions in isotropic plates under the action of various kinds of loads without solving a particular problem. In the present work, we generalize this method for anisotropic materials containing defects with imperfectly sharp vertices.Consider an infinite orthotropic plate containing a curvilinear crack-like hole. The points at which the radius of curvature attains local minima (small but nonzero) are called tips. We introduce a Cartesian coordinate system x 10x 2 whose origin is located at the geometric center of the defect and the xt-axis passes through one of its tips. S(ij r) (P;(~r) 2r=l r=l where aij, i, j = 1, 2, and bij, i, j = 4, 5, are, respectively, the compliance and stiffness moduli of the orthotropic material [3].