Green's function formulation of plane crack problems for general anisotropic materials.

Abstract

The widespread use of composites in structural applications has led to increased interest in the elastic and thermoelastic behavior of anisotropic materials. Problems involving the presence of a slit-like crack in an infinite general anisotropic material arise in the study of fracture mechanics. The isothermal problem of a plane crack in a general anisotropic infinite body subjected to a uniform stress field at infinity is reviewed, using two methods: Fourier transforms and continuously distributed dislocations. In both methods, the crack was assumed to remain open. Here we give the condition under which this assumption is feasible and the problem is resolved for the case where the crack is closed. The method of Fourier transforms has been used to formulate thermoelastic problems in anisotropic materials. In particular, a solution is given in the literature for the plane crack obstructing a uniform heat flux in a homogeneous anisotropic medium, but it is valid only when the material has certain symmetries i.e. where the k$\\sb{12}$ component of the conductivity tensor is zero. This solution assumes that the crack is always open. The mathematical difficulties that arise in adapting this method to formulate problems for the more general kind of anisotropy, can be avoided using the Green's functions formulation. We developed the thermoelastic Green's functions for plane problems in general anisotropy. These functions give stress and displacement fields which are continuous everywhere, but correspond to a discontinuity in temperature along the half-line x$\\sb2$ = 0, x$\\sb1 >$ 0. The Green's functions and the solution due to a dislocation are used to solve the plane crack problem in a homogeneous general anisotropic body perturbing an otherwise uniform heat flow. The formulation initially assumes that the crack remains open, and the condition under which this assumption is physically feasible is obtained. The problem is then solved for the case where the crack is partially closed.