A comparison of Mode I and Mode III results for the elastic stress distribution in the immediate vicinity of a blunt notch

Abstract

Fracture mechanics of sharp cracks is a well-established methodology, and is based on the elastic stress distribution in the immediate vicinity of a sharp crack tip being described by the stress intensity factor K. The author is involved in a wide ranging research programme, with the long term objective of extending the sharp crack methodology to the behaviour of notches, so that credit can be taken for their non-sharpness. A key feature of this programme has been the search for a parametric representation of the elastic stress distribution in the immediate vicinity of a blunt notch with radius of curvature ρ, paralleling the K description for a sharp crack. Thus it is shown, via a general model analysis, that for Mode III deformation, the elastic stress at a distance x≪ ρ ahead of the notch root depends only on x, ρ and the peak stress σ p, irrespective of the notch shape and the loading characteristics. However, a similar approach for Mode I deformation shows that the elastic stress, as well as depending on x, ρ and σ p, also depends on the overall notch shape and the loading characteristics though, as observed by other researchers, it approximately depends only on x, ρ and σ p within restricted ranges of notch shapes and loading characteristics. The implications of the findings, particularly with respect to the difference between the Modes I and III situations are discussed as regards the fracture mechanics of notches.