A generalised approach to rapid finite element design of notched materials against static loading using the Theory of Critical Distances

The aim of this paper is promoting a simple approach whose use - together with conventional linear-elastic Finite Element (FE) analysis - results in estimates that are more accurate than those obtained by applying the classic Hot-Spot Stress Method. The generalised formulation of the Theory of Critical Distances (TCD) being proposed calculates the required critical distance from two readily available material properties, namely, the ultimate tensile strength, and the plane strain fracture toughness. This alleviates the need for further testing normally required in the conventional TCD methods which can be costly. An extensive search through the technical literature has resulted in a data base storing approximately 800 experimental results, which have been used to validate this simplified TCD methodology. The investigated test samples contained a range of notch root radii from 0.01 mm up to 7 mm. The specimens were made of a variety of engineering materials, exhibiting brittle, quasi-brittle and ductile mechanical behaviour, and were tested under uniaxial as well as multiaxial static loading. This extensive validation exercise demonstrates that the proposed simplified methodology is a powerful engineering tool which allows static strength to be estimated more accurately than with the classic Hot-Spot Stress Method.