PSI - Issue 42

Martin Matušů et al. / Procedia Structural Integrity 42 (2022) 102 – 109 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

107

6

of Eq. (3) equal to zero, resulting in four unique roots:

i

  

  

  

  

ln 1 0.35  −

ln



a b 

a b 

(4)

;

r

r

=

=

1,2

3,4

b

b

With the assumption that the values of parameters a and b are real positive numbers, only the value of r 2 can be a real number, while all other roots are complex. This single root represents the minimal curvature radius for the exponential approximation of the evolution of R 0 and Rs . The  FL estimates from the S-N curves were compared to the points where the minimal curvature radius as a representation of the transition between the two distinct domains was found via Eq. (4), see Fig. 6.

Fig. 6 a) Exponential approximation of the R 0 and R s parameters displaying breakpoints estimated from the minimal curvature radius. b) Evolution of R 0 for A01-A04 with illustration of the minimal curvature radius with different colors corresponding to each series. The graph is limited to R 0 = 0.5 rad aiming for the area of interest, though further data points can be found above this limit.

Table 1. Comparison of  FL estimates from the S-N curve and from the minimal curvature radii analyses.

 FL [MPa] estimates

Relative difference [%] between R x and S-N estimates

Series

From S-N curve

From R 0

From R s

From R 0

From R s

A01 A02 A03 A04

500 470 490 480

660 575 634 565

656 571 615 541

32.0 31.3 22.3 21.5 29.4 25.6 17.6 12.7

The evolution of R 0 and R s for the A04 series is shown in Fig. 6a, where both trends are approximated with the exponential curve. The comparison shows that  FL estimated from the S-N curve is significantly lower than any of the values delivered by the analysis of the minimal curvature radius. To see a larger scale comparison on the A01-A04 series, Fig. 6b is provided to show the differences between each series regarding the exponential evolution and the minimal curvature radius for the R 0 parameter. The graphs show that the critical volume highly affects the temperature increase rate in the area above  FL , as the increase in temperatures for longer specimens is clearly steeper. The results are also analyzed in Table 1. It shows that this method leads to differences in the fatigue limit estimates compared to the S-N curve estimates ranging between 17.6-32.0% for the parameter R 0 and 12.7-31.3% for the parameter R s . The fact that the method efficiently finds the minimal curvature radius is not a sufficient output since the detected values are substantially higher than  FL . This outcome may be caused by using other temperature parameters and other exponential functions than Huang et al. (2017) originally proposed. The fact that the detected fatigue limits are above the traditionally detected values opposes even the possible assumption that instead of a conventional fatigue limit, some true fatigue limit was found that could be detected in the very high-cycle domain (see Pyttel et al. 2011).