Static assessment of brittle/ductile notched materials: an engineering approach based on the Theory of Critical Distances

Engineering components often contain notches, keyways or other stress concentration features. These features raise the stress state in the vicinity of their apex which can lead to unexpected failure of the component. The Theory of Critical Distances has been proven to predict accurate results, but, conventionally, requires two key ingredients to be implemented: the first is a stress-distance curve which can be obtained relatively easily by means of any finite element software, the second is two additional material parameters which are determined by running appropriate experiments. In this novel reformulation, one of these additional parameters, namely the critical distance, can be determined a priori, allowing design engineers to assess components whilst reducing the time and cost of the design process. This paper investigates reformulating the Theory of Critical Distances to be based on two readily available material parameters, i.e., the Ultimate Tensile Strength and the Fracture Toughness. An experimental data base was compiled from the technical literature. The investigated samples had a range of stress concentration features including sharp V-notches to blunt U-notches, and a range of materials that exhibit brittle, quasi-brittle and ductile mechanical behaviour. Each data set was assessed and the prediction error was calculated. The failure predictions were on average 30% conservative, whilst the non-conservative predictions account for less than 10% of the tested data and less than 2% of the non-conservative error results exceed -20%. It is therefore recommended that a safety factor of at least 1.2 is used in the implementation of this version of the Theory of Critical Distances.