Issue 47

Z. Hu et alii, Frattura ed Integrità Strutturale, 47 (2019) 383-393; DOI: 10.3221/IGF-ESIS.47.28 390 j tot i 1 f, i i n D N    (8) Finally, the number of cycles to failure, f,e N , can be estimated from the predicted number of blocks to failure, b,e N , i.e.: cr b,e f,e tot b,e tot D N N n N D     (9) where cr D is the critical value of the damage sum. V ALIDATION BY EXPERIMENTAL DATA he data used to validate the proposed extension of the SED approach are those generated by Susmel and Taylor by testing the notched samples of C40 under both the Concave upwards Spectrum (CUS) and Concave Downwards Spectrum (CDS) [3]. As to the strain energy density analysis, the cylindrical samples were modelled by using axisymmetric bi-dimensional model with coarse meshes inside the volume. By applying the net nominal stress σ An at 10 6 cycles to the FE model, the numerical values of notch W  as a function of the critical radius R 0 were obtained as shown in Fig. 5. It is observed that the value of the critical radius R 0 is about 0.11 mm when the value of the SED for the V-notched specimen equals to that of plain specimen, plain 0 W  . Figure 5 : Numerical values of notch W  as a function of the critical radius R 0 . The value of the SED averaged over the control volume was also calculated numerically by using the FE method. As shown in Fig. 4, a set of stress levels are acquired after calculating the load spectrum by Rain-Flow method. Then, the values of the SED of notched specimens with the sharpest radius are evaluated by applied above stress levels in the FE model. According to Eq. (6), the relationship of the SED W  versus fatigue life N f under CA fatigue loading is -0.5266 f =242.4 W N  (10) where the constants in Eq. (10) are determined by a best fit to a series of calculated data. As to the critical value of the damage sum, D cr , initially the hypothesis was formed that it could be taken equal to its average value experimentally determined from the plain samples, D cr,exp =0.63. The obtained results with different notch T