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C. Ronchei et alii, Frattura ed Integrità Strutturale, 34 (2015) 74-79; DOI: 10.3221/IGF-ESIS.34.07 76 Then, the fatigue strength is assessed through an equivalent stress amplitude expressed by a quadratic combination of the equivalent normal stress amplitude ( ' , a eq N ) and the shear stress amplitude ( a C ) acting on the critical plane. Finally, the number of loading cycles to failure, f N , can be found by solving the following equation through an iterative procedure:     2 2 * 2 2 2 , 1 ' 0 , , 1 , 1 0 0 m m m af f f a eq a af af f N N N N C N N N                                     (2) where 0 N is the reference number of loading cycles (for example 6 0 2 10 N   ), and m and * m are the slopes of S-N curve for fully reversed normal and shear stress, respectively. Recently, Łagoda et al. [12] have proposed some modifications to the original  expression. In accordance with the idea originally developed by Carpinteri et al. [9-10] to assume that  is function of the ratio , 1 , 1 af af     (such an expression can be employed for metals ranging from mild to very hard fatigue behaviour), the relationships reported in Ref. [12] are the following:   4 2 , 1 , 1 9 1 45 8 af af               (3)   3 3 , 1 , 1 3 3 1 45 3 3 1 af af                (4)   4 , 1 , 1 3 3 1 45 3 3 3 af af              (5)     2 5 , 1 , 1 2 3 1 45 3 1 af af              (6) E XPERIMENTAL VALIDATION n the present paper, the different relationships of the rotational angle  previously described are implemented in the modified C-S criterion in order to verify whether they are able to improve the above criterion in terms of lifetime estimation of some experimental test results available in the literature. The examined data are related to samples made of 30CrNiMo8 Steel [13,14], 6082-T6 Aluminum Alloy [15,16] and S335J0 Alloy Steel [17] subjected to synchronous, sinusoidal, in-phase loading (with zero and non-zero mean value). The relevant mechanical properties for each examined material are reported in Tab. 1. Material u  [MPa] , 1 af   [MPa] m [-] , 1 af   [MPa] * m [-] 30CrNiMo8 Steel 1014 427.37 -0.13 371.52 -0.04 6082 - T6 Aluminium Alloy 290 152.83 -0.11 87.90 -0.15 S355J0 Alloy Steel 611 276.58 -0.15 183.70 -0.09 Table 1 : Static and fatigue properties for each examined material. I