Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 79-89; DOI: 10.3221/IGF-ESIS.41.12 85 following closed-form expression:                        2 2 3 1 1 3 2 1 2 1 1 3 1 3 1 K K W e e E R R (8) Figure 3 : Local shear stress field along the notch bisector line (Mode III loading). In previous expression,  K 1 and  K 3 are the Mode I and Mode III NSIF ranges, respectively, R 1 and R 3 represent the control volume sizes related to Mode I and Mode III loadings, respectively, while e 1 and e 3 are known coefficients which take into account the local notch geometry. These parameters are tied to the integrals over the control volume of the angular stress functions and they can be evaluated a-priori by means of closed-form expressions, as a function of the notch opening angle. Being the tested samples characterized by an opening angle 2  of 90 degrees, e 1 and e 3 result to be 0.146 and 0.310, respectively, with reference to a Poisson’s ratio  = 0.3. Very refined FE meshes must be adopted in the close vicinity of the singularity point to evaluate the NSIFs on the basis of definitions (3) and (4). On the other hand, the local SED results to be insensitive to the mesh refinement. Indeed, it can be accurately calculated also from FE analyses with coarse meshes, since it directly depends on nodal displacements. The most important and useful advantages tied to the use of the averaged strain energy density parameter are analysed and discussed in detail in Ref. [30]. The expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged SED relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (NSIFs) and the control radius, in correspondence of 2·10 6 cycles. By taking into consideration, instead, cracked samples, the critical NSIFs should be substituted by the threshold values of the stress intensity factors. By considering the Mode I and Mode III loading conditions as independent, the control radii R 1 and R 3 (as shown in Fig. 4) can be estimated. In particular, they result to be dependent on the high-cycle fatigue strengths of un-notched specimens,  1A = 950 MPa and  3A = 776 MPa, and on the mean values of the NSIFs,  K 1A and  K 3A , with reference to a given number of cycles, N A = 2·10 6 :              1 1 1 1 1 1 1 2 A A K R e (9a)                1 1 3 3 3 3 3 1 A A e K R (9b) 0,1 1 10 100 0,001 0,010 0,100 1,000   z /  nom Distance from the notch tip, [mm]