Generalized method of images in the crack analysis

A new and effective method has been developed for the analysis of cracks in elastic bodies, subjected to arbitrary loading, as well as for the analysis of crack interactions. The cases of Bat cracks of arbitrary shape inside a transversely isotropic elastic half-space and inside a layer are considered. Governing integral equations are derived by the introduction of quasi-images of the cracks. The idea of images was originally used at the beginning of the century by Lord Kelvin for the solving of electrostatics problems. The new method allows one to obtain a complete solution, defining all stresses and displacements in the whole body, not only in the plane of the crack. For the first time, an exact formulation of a crack problem in a layer is given for the case where the crack is not located in the middle plane of the layer. The case of circular cracks is considered in detail. The integral equations are inverted analytically, thus allowing an effective numerical or approximate analytical solutions. The case of axisymmetric loading is considered as an example. The relationship between the new method and the integral transform approach is discussed. (C) 1997 Elsevier Science Ltd.