Fracture mechanics stress analysis

Abstract

In this chapter the boundary integral equation (BIE) method is discussed with particular reference to its application to fracture mechanics stress analysis. Although the BIE method has been used to treat a variety of boundary value problems, those encountered in fracture mechanics possess certain unique features which require special treatment. There are essentially two distinct difficulties which are encountered when applying standard BIE procedures to fracture models in which a crack is modelled as having a planform of zero thickness (e.g. a line crack in two dimensions). These are:— (1) The indeterminacy encountered when (in plane strain or stress), the direct BIE formulation of a thin ellipse is used to represent a crack when the ellipse degenerates to a line. A similar feature occurs in three-dimensional problems. We describe this degeneracy more fully later in this introduction, attempts to remove this difficulty are described in Section 3.3. (2) The existence of a stress singularity at a sharp crack tip which requires accurate boundary element modelling in order to obtain reliable numerical results. Such modelling is described in detail in Section 3.4. Note however that, although a square root stress singularity occurs in the elastic analysis of a crack in a homogeneous medium, other stress singularities may be encountered (for a review see Atkinson1).