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A B S T R A C T The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V-notch tip is needed and no longer the whole stress-distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V-notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V-notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles.Keywords elasticity; finite element analysis; notch stress intensity factor; stress intensity factor; V-notches. N O M E N C L A T U R Ea = crack length, V-notch depth or component's reference dimension d = adopted finite element size ρ = notch tip radius ρ * = virtual notch tip radius r, θ = polar coordinates K I = mode I Stress Intensity Factor K V I = mode I Notch Stress Intensity Factor for a sharp V-notch σ r , σ θ = stress components in a polar frame of reference σ g = nominal stress on the gross section σ max = linear elastic maximum principal stress at the tip of a rounded notch (exact stress) σ peak = linear elastic peak stress calculated by FEM at the sharp V-notch tip by means of a given mesh pattern 2α = opening angle of the V-shaped notch I N T R O D U C T I O NNotch stress intensity factors (NSIFs) play an important role in static strength assessments of components made of brittle or quasi-brittle materials and weakened by sharp V-shaped notches. 1-8 This holds true also for components made of structural materials undergoing high cycle fatigue Correspondence: P. Lazzarin. loading 9,10 as well as for welded joints both under tension or bending loading 11-16 and multiaxial loading. 17 In plane problems, the Mode I NSIF for sharp V-notches can be expressed by means of the Gross and Mendelson's definition 18 :where (r, θ ) is a polar coordinate system centred at the notch tip as shown by Fig. 1, σ θ is the stress component c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 30, 95-106 95

A diagram valid for the analysis of the fatigue limit of cracks and notches centred in an infinite plate was recently proposed by the authors of the present work with the aim to make explicit the bridging at the fatigue limit between defect sensitivity (correlated to the length parameter a0, according to El Haddad–Topper–Smith's definition) and notch sensitivity (correlated to a*, where a* is a particular notch depth corresponding to the intersection between the ΔKth and Δσ0/Kt curves). The expression being valid, defect sensitivity and notch sensitivity were seen as two sides of the same medal. Such a diagram is now extended to finite size components by simply introducing the shape factor α commonly used in fracture mechanics. The obtained critical defect size is termed aD, which is a material and geometry dependent parameter, in order to distinguish it from a0, which is a material parameter. As a consequence the critical notch depth aN is introduced, such that . This results in the proposal of a ‘universal’ diagram able to summarize experimental data related to different materials, geometry and loading conditions. The diagram, the validity of which is checked by means of several results available in the literature, is applied both to the interpretation of the scale effect and to the surface finishing effect.

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