Issue 50

P. Livieri et alii, Frattura ed Integrità Strutturale, 50 (2019) 613-622; DOI: 10.3221/IGF-ESIS.50.52 619 Figure 5 : Circular crack at the weld toe of Fig. 4. Tab. 1 shows the comparison on the Stress Intensity Factor prediction by means of Eqn. (13) and the results obtained with FE analysis. An accurate mesh is considered and the strand of the principal stress along the crack direction is shown in Fig. 6. The dimensions of smaller elements at the tip of the crack were in the order of 10 -5 mm. Fig. 7, as an example, shows the mesh used for point C. The difference between the analytical and numerical results is less than 7%. So that, from an engineering point of view, the simple Eqn. (13) can be used for SIF assessments of a small defect in the neighbourhood of the weld toe as made in references [8–9] for semi-circular cracks. If the crack has an irregular shape not approximable to a disc, Eqn. (25) can be used. In order to estimate the fatigue limit for small cracks or defects under a uniform tensile stress, Murakami and Endo [25–27] proposed 4 area as an empirical parameter to estimate the maximum SIF value of a convex-shaped crack. On the basis of numerous numerical analyses, Murakami and Nemat-Nasser proposed a synthesis relation for the maximum value of the SIF of superficial cracks in the form: ,max I K Y area    , where Y is a dimensionless factor that assumes the value of 0.629 for lateral cracks [25]. In the case of internal cracks, the value of Y is approximated to 0.5 [25]. Figure 6 : Principal stress σ 1 along the bisector for point A of Fig. 4 (a=0.1 mm; d=0.15 mm, opening angle 2α=135°).