PSI - Issue 77

Bastian Roidl et al. / Procedia Structural Integrity 77 (2026) 119–126 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

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Table 2 - Fatigue strengths  FS,a,N at different numbers of cycles for series A, G and H for load ratios R=0.1 and R=-1 based on the Kohout & Věchet regression. Note that * marks extrapolated values. Number of cycles N [-]  FS,a,N [MPa] R =0.1 R =-1 A-specimen G-specimen H-specimen A-specimen G-specimen H-specimen 10.000 141 132 126 198* 162 170 20.000 127 114 114 162 144 154 50.000 107 92 95 127 119 130 100.000 93 79 81 108 101 112 200.000 81 70 70 95 87 99 500.000 69 63 61 84 73 89 1.000.000 64* 60* 57 80 67* 84 Its depiction against the number of cycles in Fig. 3 indicates that the mean stress sensitivity is not only a material parameter, but it also depends on the geometry of the specimens (and the lifetime). The H-specimens with the machined outer surface and the as-built hole inside have the highest mean stress sensitivity for the whole high-cycle fatigue region. For the standard as-built hourglass specimens (geometry A), mean stress sensitivity first decreases and then increases again when it comes to a higher number of cycles. In that region, it reaches just about one half of the mean stress sensitivity related to the H-specimens. The specimens with the smallest diameter (Series G) seem to have the lowest mean stress sensitivity both at the LCF region and above 300,000 cycles. Analyzing the available data, it can be concluded, that mean stress sensitivity is not solely a material parameter, but also relates to the specific geometry, and substantially different values can be reached for different specimen designs.

Fig. 3. Mean stress sensitivity diagram for all series with a range from 1e4 to 1e6 cycles. It must be noted that the line segments between measurement points are shown linearly interpolated to show the trends, and they do not represent mean stress sensitivity directly

2.5. Mean stress model fit As briefly mentioned in the introduction, there are various models describing the effect of mean stresses. In this study selected models listed in Table 2 were examined. Their formulas predict the  a,eq stress amplitude at R =-1 load case, which, in damage caused, is equivalent to the stress cycle described by  a and  m stress parameters. The fatigue index error formula described by Papuga et al. using real test data is used to determine the accuracy of the models (see Table 3) for current use cases [12] , compared to  a, -1 experimental fatigue strength derived directly for R =-1 condition :