Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 79-89; DOI: 10.3221/IGF-ESIS.41.12 84 Figure 2 : Polar coordinate system for V-shaped notches, with z normal to the plane; Mode I NSIF linked to the stress component   evaluated along the notch bisector line (  =0); under mode III the shear stress component  z  is oriented as   . Considering an opening angle of 90 degrees, the eigenvalues  1 and  3 result to be 0.545 and 0.667, respectively. Moreover, under linear elastic conditions, the NSIFs can be linked to the nominal stress components as follow:       1 1 1 1 nom K k d (5a)       1 3 3 3 nom K k d (5b) In previous expressions, d represents the notch depth (d = 6.0 mm), while k 1 and k 3 are the non-dimensional factors obtained by means of proper FE analyses. They represent the shape factors, similarly to the expressions of stress intensity factors in Linear Elastic Fracture Mechanics. The quadrilateral eight-node harmonic element PLANE 83 of the Ansys  element library has been adopted in the FE analyses. Taking advantage of the symmetry conditions, only one quarter of the sample geometry has been modelled. According to the FE analyses carried out, k 1 is equal to 1.000, while k 3 equals 1.154. The trend of the Mode III stress field, normalized with respect to the nominally applied shear stress and evaluated on the notch bisector line, is reported in Fig. 3 as a function of the distance from the notch tip. It can be observed that the stress field is controlled by the first singular term (NSIF) up to a distance from the notch tip about equal to 1.0 mm. Taking into account the notch depth of the tested samples, namely d = 6 mm, in previous Eqs (5a) and (5b), the following simple expressions can be obtained:      1 2.260 nom K (in MPa ·mm 0.445 ) (6a)      3 2.096 nom K (in MPa ·mm 0.333 ) (6b) By substituting into Eqs. (6a) and (6b) the ranges of the nominal stresses at N A = 2·10 6 cycles relevant to notched samples subjected to pure tension and pure torsion loadings at a nominal load ratio R = -1 (see Tab. 1), one can obtain:      0.445 1 2.260 200 452 A K MPa mm (7a)      0.333 3 2.096 580 1216 A K MPa mm (7b) Dealing with a sharp V-notched component subjected to combined tension and torsion loadings under linear elastic conditions, the strain energy density averaged over a control volume surrounding the notch tip can be evaluated from the