Issue 41

K. Slámečka et alii, Frattura ed Integrità Strutturale, 41 (2017) 123-128; DOI: 10.3221/IGF-ESIS.47.17 125 This method (Eqs. 1-4) was compared to the von Mises (Eq. 5) and Tresca (Eq. 6) criteria and to the Gough-Pollard criterion for ductile metals (Eq. 7), which are similar quadratic formulas:   2 2 f σ σ eq,a σ σ a a 1 log log log 3 2 N A m A m         , (5) 2 2 f τ τ eq,a τ τ a a 1 1 log log log 2 4 N A m A m               , (6) 2 2 a a c c 1                   . (7) In Eq. (7),  c and  c are the axial and torsion fatigue strengths that, conceptually, correspond to the same fatigue life. Therefore, this criterion reflects the non-parallelism of the S-N curves (variation of the  c /  c ratio), as the middle curve criterion does, but is more difficult to apply, e.g. [7]. The middle-curve criterion is more general than the von Mises and Tresca criteria. Indeed, when  c /  c = √3 (or  c /  c = 2) holds in the whole range of fatigue life, the middle-curve criterion becomes equivalent to the von Mises (or Tresca) criterion. Furthermore, the middle-curve becomes equal to the Gough- Pollard criterion for materials with parallel S-N curves but gives better results for materials with non-parallel S-N curves (see hereafter). E XPERIMENTAL DATA he studied methods were evaluated using plane-bending/torsion data on 2017A-T4 aluminium alloy, S355J2WP and S355J2G3 alloy steels, 30CrNiMo8 medium alloy steels, and Inconel 713LC nickel-base superalloy, see Refs. [6-9] and references therein for more detailed information on these fatigue experiments. Tab. 1 summarizes the ultimate strength σ u and the yield strength σ y of all materials and the parameters of bending and torsion S-N curves. The angle  is the angle between the two curves and its positive value means that the axial curve is steeper. Except for 2017A- T4 aluminum alloy, the S-N curves are clearly not parallel. Material σ u (MPa) σ y (MPa) σ y /σ u σ A τ m τ A  (°) 2017A-T4 [8] 545 395 0.72 -7.0 21.8 -7.1 20.3 0.1 S355J2WP [6] 556 414 0.74 -12.5 37.6 -5.8 18.6 -5.3 S355J2G3 [6,7] 611 394 0.64 -7.2 23.9 -11.7 32.8 3.0 Inc713LC [9] 982 801 0.82 -4.5 17.4 -7.5 23.9 4.8 30CrNiMo8 [6] 1014 812 0.80 -8.1 27.6 -24.7 69.7 4.7 Table 1 : Basic material properties and the parameters related to the bending and torsion S-N curves. R ESULTS AND DISCUSSION ab. 2 summarizes parameters related to the middle-curve criterion. Note that the constant k 0 lies in the range from 2.22 to 4.29. Since k 0 = 3 for the von Mises criterion, this criterion can be expected to provide a plausible prediction for all materials except for S355J2WP steel, which should comply with the predictions obtained from the Tresca criterion. Fig. 2 compares the experimental and calculated fatigue lives, N f,exp and N f,calc , in the log-log space. A full diagonal line signifies a perfect agreement between predicted and observed values. The dashed and dash-dot lines constitute factors of two and three bandwidths. Fig. 3 plots the distribution of deviations from the perfect-agreement line for all materials T T