A stress distribution remodelling technique

The stress distribution ahead of a notch is of great practical interest when undertaking fatigue and fracture analyses. In particular it is generally the first principal stress close to the notch which is desired. For a sharp notch this can be characterized by the stress field parameter K-N which is referred to as the notch stress intensity factor (or N-SIF). The finite element method is a very powerful tool which is commonly used to determine K-N. However, unless specialized methods are used the finite element mesh must be extremely refined in the region of the notch in order to calculate an accurate value. In practical situations, the degree of mesh refinement necessary is often not possible, due to either time or computer limitations. The following describes a simple technique which can be used to accurately determine the stress distribution close to a sharp notch, by remodelling or reshaping a stress distribution that has been obtained from a finite element analysis using a coarse or inadequate mesh. A theoretical equation for defining the principal stress distribution ahead of a sharp notch, which has been developed by Atzori et al. (2005) is used to do this. It is shown that the theoretical distribution can be explicitly determined from the finite element distribution by using global equilibrium conditions. It is shown that this technique is independent of the finite element mesh size. The method is used to calculate K-N for seven different combinations of geometry and loading condition, using various FE mesh refinement. It is shown that the results are accurate to within 15%.