Issue 9

An. Carpinteri et alii, Frattura ed Integrità Strutturale, 9 (2009) 46 – 54; DOI: 10.3221/IGF-ESIS.09.05 51 The C-S criterion is hereafter applied in terms of nominal stresses. The nominal loading paths analysed are reported in Fig.3, where normal stress x  and shear stress xy  at point P are the stress perpendicular and that tangent to the weld bead, respectively. Figure 3 : Summary of nominal loading paths. In order to determine the mean directions of the principal stress axes at point P , the instantaneous values of the principal Euler angles are averaged by employing the weight function   tW proposed in Eq.(2). Then, the angle  between 1ˆ and w is determined by using Eq.(3). As is mentioned above, such an equation was originally proposed in Ref .[15] for hard metals which are characterised by values of the ratio 1, 1,     af af ranging from 3 1 to 1 . For data set reported in Ref.[21] the ratio 1, 1,     af af is greater than 1. This is to be expected because the fatigue limits 1,   af and 1,   af are derived by testing welded specimens [11, 19-21] and, therefore, the values of such parameters are influenced by the presence of fillet welds. As is stated in Section 2.2, the off angle  is assumed to be equal to 0 when 1 1, 1,      af af . Fig. 4 shows a comparison between experimental fatigue life ( exp N ) and calculated fatigue life ( cal N ) for each experimental data set considered above, where the solid line indicates exp cal N N  , the dashed lines correspond to exp cal N N / equal to 1/2 and 2 (scatter band with coefficient 2) and the dashed-dotted lines correspond to exp cal N N / equal to 1/3 and 3 (scatter band with coefficient 3). Note that the run-out tests are excluded from the present analysis. Tab. 1 reports the number of specimens tested and the percentage of the results of fatigue life estimation included into the scatter band with coefficient 2 and into the scatter band with coefficient 3, for each data set analyzed. The quality of the predictions made by applying the extended C-S criterion can be evaluated through an error index, I (  ), defined as follows:              exp cal cal cal exp exp cal exp cal exp N N N N N N N N N N I for % for % (12)