MODE-I CRACK PROBLEM IN AN INHOMOGENEOUS ORTHOTROPIC MEDIUM

In the symmetric crack problem considered the material is both oriente d and graded. The properties of the medium is assumed to vary monotono usly in the x(1)-direction, x(1) and x(2) are the principal axes of or thotropy, and the crack is located along the x(1)-axis. The loading is such that x(2) = 0 is a plane of symmetry. The mode I crack problem f or the inhomogeneous orthotropic plane is formulated and the solution is obtained for various loading conditions and material parameters In the formulation four independent engineering constants, E-11, E-22, G( 12) and v(12), are replaced by a stiffness parameter E = root E11E22, a stiffness ratio c = (E-11/E-22)(1/4), a Poisson's ratio v = root v(1 2)v(21) and a shear parameter K = (E/2G(12)) - v. The results show tha t the stress intensity factors are independent of E and c and generall y the effect of K and v on the stress intensity factors is not very si gnificant. The exception is the values of K approaching - 1, where the physical range of K is - 1K < infinity. In the isotropic case the ker nel of the related integral equation is evaluated in closed form, whic h simplifies the numerical solution and improves the accuracy of the r esults. (C) 1997 Elsevier Science Ltd.