The arbitrarily loaded single-edge cracked circular disc; accurate weight function solutions

A general solution for the stresses and displacements of collinear cracks in an infinite homogeneous anisotropic medium subjected to uniform loading at infinity has been given in this paper by using the Stroh's formulation. The solutions are valid not only for plane problems but also for antiplane problems and the problems whose inplane and antiplane deformations couple each other. Two special collinear crack problems are solved explicitly: (1) two collinear cracks, (2) an infinite row of evenly spaced collinear cracks. A closed form solution of the stresses and displacements in the entire domain is obtained. Through the use of identities developed in the literature, the stress intensity factors, crack opening displacements and energy release rate are expressed in real form, which are valid for any kind of anisotropic materials including the degenerate materials such as isotropic materials. The simple explicit form solutions for the crack opening displacements and energy release rate reveal that the effect of anisotropy is totally determined by the fundamental elasticity matrix L. The relation between the stress intensity factors and energy release rate is obtained in quadratic form and related to L.