PSI - Issue 75

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

295

7

feature, and though the results in Table 4 remain non-conservative in average, the extent of this issue is more acceptable. The simple message of this comparison is obvious. There are not that many engineering structures loaded solely in push-pull and likely some bending is usually involved. To establish the critical distance length, the use of fatigue tests in bending is advisable, as it generates less scattered results if used on other load cases, and it decreases the risk of non-conservativeness to some extent. If the results of using TCD are compared with RSG results, it is obvious that quality of TCD solutions is significantly worse than estimation quality delivered by RSG. Above all, the decision to use of the critical distance obtained from push-pull mode brings along a devastating effect. This stems obviously from the decision to use a single critical distance for any of evaluated configurations, though some of the specimens feature a very sharp notch, while another notch is quite blunt. This is illustrated in the best way in the comparison of U5.0 and OS0.2 configurations, which refer to the circumferential U-notch with 5.0 mm notch root radius and a circumferential fillet with a sharp radius of 0.2 mm in the transition. If U5.0 is chosen to generate the critical distance, it is comparatively big and thus the effective stress in other configurations is obtained too far from the notch root. This inevitably leads to very non-conservative prediction. OS0.2 works the other way and thus produces too conservative results in average. The use of the bending load mode to generate the critical distance alleviates these issues, but still the quality of fatigue estimation is not on par with results, which evaluated RSG methods deliver. Table 3. Statistics of ERRσ relative errors of chosen TCD solutions using the von Mises stress (100,000-500,000 cycles) if the push-pull load mode is chosen as the relevant one to establish L CD . Push-pull load mode (a notched and the unnotched configurations in push-pull compared) U1.5 V1.3 OS0.7 U5.0 OS0.2 U1.5 V1.3 OS0.7 U5.0 OS0.2 L CD defined from:

Point method

Line method

TCD version

-19.2% 36.4%

-13.7% 36.2%

3.5%

-82.3% 15.2%

47.4% 56.5%

-11.8% 35.8%

-7.2% 35.6%

5.7%

-63.0% 45.5% 15.4% 55.7%

Average

38.4%

37.3%

Maximum Minimum

-172.7% -151.7% -98.7% -310.6% 32.6%

-122.5% -107.0% -75.4% -232.0% 30.2%

209.1% 187.9% 137.1% 325.8%

23.9%

158.3% 45.0%

142.6% 112.7% 247.3% 25.5%

Range

54.5%

44.3%

89.8%

6.3%

41.8%

35.9%

66.2%

7.0%

Standard deviation 58.9%

Table 4. Statistics of ERRσ relative errors of chosen TCD solutions using the von Mises stress (100,000-500,000 cycles) if the bending load mode is chosen as the relevant one to establish L CD . Bending load mode (a notched and the unnotched configurations in push-pull compared) U1.5 V1.3 OS0.7 U5.0 OS0.2 U1.5 V1.3 OS0.7 U5.0 OS0.2

L CD defined from:

Point method

Line method

TCD version

3.2%

2.3%

12.6% 38.6%

-15.7% 17.8%

44.8% 56.9% 29.2% 27.7%

2.9%

5.0%

14.1% -10.8% 43.4%

Average

31.8%

30.9%

31.6%

30.7% 38.2%

17.8% 56.4%

Maximum Minimum

-100.5% -98.7%

-68.0% -134.0%

-72.0% -70.6% -50.5% -97.2% 26.7% 103.6% 101.3% 88.8% 115.0% 29.8%

132.3% 129.6% 106.6% 151.9%

Range

30.7%

31.7%

27.5%

38.7%

6.2%

28.6%

25.8% 23.2%

29.4%

6.7%

Standard deviation

One could argue that TCD should not simply use the critical distances derived from the blunt notches. However, even the best performing solution still provides results which suffer in comparison to quality brought by RSG. Compared to it, additionally, TCD is less standardized, and thus asks for an additional fatigue curve, from which the critical distance could be derived (or for a threshold stress intensity factor, if the theory of the critical distance being a material parameter is accepted).