Three-dimensional crack problems

Abstract

The present chapter is devoted to the investigation of the growth characteristics of arbitrary cracks embedded in three-dimensional bodies. The general equations of the strain energy density criterion developed in chapter one are used to determine the critical loads for crack extension, as well as the new shape of the crack after propagation. The determination of the stress field along the crack front in three-dimensional crack problems is more complicated than in two-dimensional problems. A thorough study of three-dimensional crack problems was provided by Sih and his coworkers [1–6] who expressed the local stress field along the crack front in a form analogous to the two-dimensional case. Three stress intensity factors were used, all of which are independent of the local coordinates, depending only on the crack geometry, the form of loading and the location of the point along the crack border. This result is fundamental, in analyzing the fracture behavior of cracks, and provides uniform expressions for the local stresses under various geometrical and loading conditions where only the values of stress intensity factors differ. Kassir and Sih [7] analyzed three-dimensional crack problems under a variety of loads. They presented the stress field around embedded and external elliptical or circular cracks in a uniform form and gave the values of stress intensity factors under various loading forms. The variety of problems considered covers most of the corresponding cases of two-dimensional problems as presented by Sih [8], including single or interacting circular and elliptical cracks under normal, shear, torsional and thermal loads; semi-infinite plane cracks under a variety of loads; cracks along the interface of dissimilar materials; cracks in anisotropic and nonhomogeneous materials; and penny-shaped cracks under dynamic loads.