PSI - Issue 75

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

294

6

Table 2. Statistics of ERRσ relative errors of chosen RSG solutions using the von Mises stress (100,000-500,000 cycles).

Average value

Method

Maximum Minimum

Range

St.dev.

Tension

Torsion

Bending

All

Stieler

48.3% 46.7% 50.4% 46.1% 62.2%

6.3% 4.6% 1.9%

42.0% 42.2% 48.5% 66.2% 66.3%

13.5% 13.2% 15.6% 22.1% 21.1%

26.9% 24.4% 17.0%

14.3% 13.5% 17.9% -0.7% 16.4%

13.2% 11.7% 16.5%

18.1% 16.5% 17.2%

FKMv6

new

Stieler

Hück

-20.1%

0.6%

0.1%

0.0%

Femfat

Eichlseder

-4.0%

20.8%

20.7%

19.3%

Remaining three methods provide relatively similar statistics of results – they tend to provide inherently safe results (minimum value of the error slightly above zero) and thus the biggest difference lies in the maximum value and the scatter monitored via the standard deviation. In this comparison, the use of the new FKMv6 solution results in slightly better results than the other two competitors. It must be noted that the RSG approaches are developed to the state, when no further experimental data except of the fatigue curve of the unnotched specimen is necessary. 4.2. Application of the theory of critical distances (TCD) The number of variants of the TCD solution evaluated in this paper is very large. First, it was checked how the solution performs for the critical distances derived from individual notched configurations in push-pull loading. Secondly, it was evaluated which of the stress metrics could provide us better results in the evaluation, whether the von Mises stress or the first principal stress. Thirdly, it was analysed whether the point or line variants of TCD could be superior to the other one. Further other details (way of interpolating the stress profile along the cross-section to derive critical distances and stress values or deriving the critical distances also for other load modes), but these outputs will not be commented on here. In the scheme in Fig. 1, the stress value at a given distance from the notch root defined by the critical distance is compared with the material fatigue curve. To get the evaluation closer to the meaning of the RSG solution, and to get comparable results of estimation quality, use of slightly different modification of the evaluation was pursued, see also the explication in [2]: 1. The critical distance is obtained for a chosen push-pull notched configuration, and it is applied on other configurations to read the effective stress at the given depth. 2. The nominal S-N curve was derived from the material curve by dividing the fatigue strengths of the material S-N curve by the K t factor and by the k  factor derived at the critical distance from the stress profile of the evaluated notch configuration normalized by the maximum stress at the notch. 3. The nominal fatigue strengths obtained from the Kohout- Věchet regression analysis of the experimental data at chosen lifetimes are compared to this predicted nominal S-N curve. If they are lower, this marks non conservative estimation accompanied by negative values of the relative error. Only excerpts of all analysed configurations are shown in Table 3 and Table 4 due to the lack of space. The difference between using von Mises stress and first principal stress in overall estimation quality is not that significant compared to the question whether to use the point or line variant of TCD. A very important point in the evaluation is, however, whether to use the critical distances L CD derived from the bending load mode or from push pull. Though the trends in the comparison between results could be expected (the push-pull mode leading to longer critical distances, and thus to results more non-conservative if used for bending load cases), it is astonishing to observe how big is this impact on overall quality of fatigue estimation. The most marked case is the U5.0, i.e., the case of a rather blunt notch, which induces long critical distance if analysed in push-pull, and thus significantly non conservative results for cases with sharp notches. Using the bending mode as the input decreases the impact of this