PSI - Issue 75

Jan Papuga et al. / Procedia Structural Integrity 75 (2025) 289–298 Author name / Structural Integrity Procedia (2025)

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The comparison of results obtained for critical distances from U5.0 and OS0.2 configurations shows the biggest deficiency of the TCD: Whichever is the way of deriving the critical distance, it is a single value that should fit all configurations. This forms the major issue the method cannot overcome. For short critical distances (OS0.2), the obtained results are seemingly of minimum scatter (standard deviation of ERR  below 8%), but this is due to the results being extremely shifted to the conservative average of about 40%. If a less sharp notch is chosen, the scatter gets too excessive compared to RSG, which is caused above all due to failure in complying with the OS0.2 variant, which drives the minimum value to extremely non-conservative prediction. In this parameter, transition to the first principal stress from von Mises stress slightly helps. The last comment relevant to TCD concerns the version to be used. The application of the line method in this case brings along better results both in the average value of the error and of its standard deviation. 1. For every configuration of a specimen and of a load mode, the critical volume is computed from the finite element model of the specimen as a volume at which the chosen equivalent stress measure exceeds the z multiple of the maximum stress at the notch root. 2. At chosen fatigue life, the characteristics of the critical volume vs experimental local fatigue strength at the notch root is analysed across all configurations, and a power law is fitted to it. 3. For the analysed configuration (notch and load mode), the obtained critical volume provides the estimate of the experimental fatigue strength. If this value is smaller than the one found experimentally, the estimation is classified as non-conservative. The initial expectation while preparing [8] was that both axial load modes (push-pull and plane bending) could result in a single curve CV vs. fatigue strength. An example from all configurations depicted in Fig. 3 left shows this is not true. It must be mentioned that the equivalent stress used to compute the local fatigue strength for this variant was von Mises stress. If the first principal stress had been used, the position of the torsion curve would be too low. It is obvious that three significantly different trends can be observed even for von Mises stress. In the case of the topmost lying torsion curve, it can be reasoned that even multiaxial criteria commonly show that the ratio between fatigue strength in push-pull and in torsion reaches the value of 1.73 relevant to von Mises stress only seldom, and the typical ratio for structural steels is 1.4-1.5 approximately (see also e.g. the MMP method in [9]). Such ratio would move the torsion curve downwards to overlap with the tension curve. However, the biggest nut to crack is how to explain the obviously separate trends for tension and bending load modes. They both refer to load modes, which induce axial normal stress. It is admitted that they do not get significantly closer for any value of z . The trends propose that only the single value of the critical volume is not enough to describe the notch and size effect. Further research to integrate also the trend in the critical volume change with z factor is ongoing. Despite reaching graphically unsatisfactory results, all three trends for different lifetimes and different z factors were interpolated by a single power law. The results of this operation can be observed in Fig. 3 right, where the coefficient of determination R 2 is depicted for each combination. It is worth noting several trends: 1. The trends are very flat and the variation within the region of z from 0.7 to 0.9 is relatively minor. For lower numbers of cycles, the optimum z factor moves to lower values (z=0.85), while with increasing numbers of cycles it increases as well ( z =0.95). 2. For two shortest lifetimes, the coefficient of determination is high. The use of von Mises stress is pushing the tension and torsion curves closer together, but the bending curve remains distinctly lower. It must be noted that for some S-N curves depicted in Fig. 1, the fatigue strengths used to define the curve had to be extrapolated to 50,000 cycles, and this is the reason why the comparison with other methods is focused on the domain of 100,000 - 500,000 cycles only. 4.3. Critical volume (CV) approach The concept and the applied solution are described in [8]. In short: