Issue 33

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 33 (2015) 33-41; DOI: 10.3221/IGF-ESIS.33.05 34 I NTRODUCTION otch 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]. This holds true also for components made of structural materials undergoing high cycle fatigue loading [2] as well as for welded joints [3, 4]. In plane problems, the mode I and mode II NSIFs for sharp V-notches, which quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip, can be expressed by means of the Gross and Mendelson’s definitions [5]:   1 1 1 0 0 2 lim r K r                (1)   2 1 2 0 0 2 lim r r K r                (2)    rr  r     notch bisector r A=R 0 2   R 0 (a) (b) Figure 1 : (a) Polar coordinate system centred at the notch tip. (b) Control volume (area) of radius R 0 surrounding the V-notch tip. where (r,θ) is a polar coordinate system centred at the notch tip (Fig. 1a), σ θθ and τ rθ are the stress components according to the coordinate system and λ 1 and λ 2 are respectively the mode I and mode II first eigenvalues in William’s equations [6]. The condition θ = 0 characterizes all points of the notch bisector line. When the V-notch angle 2α is equal to zero, λ 1 and λ 2 equal 0.5 and K 1 and K 2 match the conventional stress intensity factors of a crack, K I and K II, according to the Linear Elastic Fracture Mechanics (LEFM). The main practical disadvantage in the application of the NSIF-based approach is that very refined meshes are needed to calculate the NSIFs by means of definitions (1) and (2). The modelling procedure becomes particularly time-consuming for components that cannot be analysed by means of two-dimensional models. Recently, Nisitani and Teranishi [7, 8] presented a new numerical procedure suitable for estimating K I for a crack emanating from an ellipsoidal cavity. Such a procedure is based on the usefulness of the linear elastic stress σ peak calculated at the crack tip by means of FE analyses characterized by a mesh pattern having a constant element size and type. In particular Nisitani and Teranishi [7, 8] were able to show that the ratio K I /σ peak depends only on the element size for a given element type, so that the σ peak value can be used to rapidly estimate K I , provided that the adopted mesh pattern has been previously calibrated on geometries for which the exact value of K I is known. This approach has been theoretically justified and extended also to sharp V-shaped notches subject to mode I loading [9] giving rise to the so-called Peak Stress Method (PSM), which can be regarded as an approximate FE-based method to estimate the NSIFs. Later on, the PSM has been extended to cracks subjected to mode I as well as mode II stresses [10]. The element size required to evaluate K 1 and K 2 from σ peak and τ peak , respectively, is several orders of magnitude greater than that required to directly evaluate the local stress field. The second advantage of the use of σ peak and τ peak is that only a single stress value is sufficient to estimate K 1 and K 2 , respectively, instead of a number of stress-distance FE data, as usually made by applying definitions (1) and (2). Since the units of the mode I and mode II NSIFs, K 1 and K 2 , depend on the notch opening angle, generally a direct comparison of the NSIF values cannot be performed. This problem was overcome by Lazzarin and Zambardi [11], who proposed to use the total elastic strain energy density (SED) averaged over a sector of radius R 0 (Fig. 1b) for static [11-14] and fatigue [11,15,16] strength assessments. With reference to plane strain conditions, the SED value can be evaluated as follows: N