M. Ozturk et F. Erdogan, MODE-I CRACK PROBLEM IN AN INHOMOGENEOUS ORTHOTROPIC MEDIUM, International journal of engineering science, 35(9), 1997, pp. 869-883
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.