Linear Elastic Stress Field in Cracked Bodies

Abstract

Fracture mechanics is based on the assumption that all engineering materials contain cracks from which failure starts. The estimation of the remaining life of machine or structural components requires knowledge of the redistribution of stresses caused by the introduction of cracks in conjunction with a crack growth condition. Cracks lead to high stresses near the crack tip; this point should receive particular attention since it is here that further crack growth takes place. Loading of a cracked body is usually accompanied by inelastic deformation and other nonlinear effects near the crack tip, except for ideally brittle materials. There are, however, situations where the extent of inelastic deformation and the nonlinear effects are very small compared to the crack size and any other characteristic length of the body. In such cases the linear theory is adequate to address the problem of stress distribution in the cracked body. Situations where the extent of inelastic deformation is pronounced necessitate the use of nonlinear theories and will be dealt with in the next chapter.