Finite element analysis of notched bars subjected to elastic-plastic deformation

For many years engineers and scientists have speculated about the relationship between the load carrying capacity of notched bars and their stress concentration factors. However, past attempts to quantify this relationship have failed and the problem remains largely unresolved. This study strongly supports the view that this relationship exists, and that there are correlations between load carrying capacity and stress concentration for notched bars subjected to tension. The study was done with the use of computer aided technology and finite element analysis, which allowed for more rigorous testing procedures when compared with conventional tensile testing methods. Two studies were conducted: firstly, an analysis which assumed perfectly elastic conditions, and secondly, an analysis which assumed realistic elastic-plastic conditions. Variables of interest included maximum strain energy density, plastic collapse load, elastic stress concentration factor, elastic-plastic stress concentration factor, root radius and the distance between the notch surface to the maximum load. It was found that these variables correlate to one another and that most of them are dependent on material properties. Both linear and non-linear relationships were found. Linear relationships were quantifiable and were represented by equations. Equations for most of the non-linear relationships could not be substantiated, as there were not enough data points present.