PSI - Issue 2_B

K.-H. Lang et al. / Procedia Structural Integrity 2 (2016) 1133–1142

1140

8

K.-H. Lang et al. / Structural Integrity Procedia 00 (2016) 000–000

testing frequency dominates the fatigue limit or surface initiated fracture. The location of inclusions (surface or subsurface) could be taken into account with the geometry factors Y O = 0.9 (surface) and Y V = 0.7 (subsurface). The two parameters are approximated from the different calculations for the stress intensity factor according to (Murakami 1989). A linear relationship could be observed (Fig. 5 (left)). The fatigue limit areas describes the threshold stress for crack initiation as a function tempering temperature, inclusion size and inclusion position (f O = surface, f V = subsurface). Also the critical inclusion size for the first decrease of fatigue resistance is labeled in Fig. 3 (red line). As it is shown in Fig. 6 the predicted fatigue limit approach Δσ th = (S xz 0,25 /(4Y 2 r 0 fπ 0.5 )) · ΔK th,l has an accuracy less than 10 %. For a more conservative approach of the threshold stress the usage of √S ODA/E is necessary. As a result of the observed size effect the number of cycles to failure could be calculated by the approach of (Akiniwa 2006). The determined parameter m and C are listed for several heat treatment conditions in Tab. 3 and the influence of tempering temperature is illustrated in Fig. 3 (right).

Table 3. Parameters m and C for the predicted approach according to (Akiniwa 2006).

570 (16)

450 (14) 5.45

300 (11) 7.14

250 (10)

180

90 (7)

T t P t m C

(9)

- -

11.33

11.46 2E-19

12.41

6.92E-15

1.49E-16

4.25E-19

8.73E-20

1000

2 2,5 3

10 20

Tolerance range 10 %

2 Relative crack growth resistance [Fuj01] [Mur89] rSIF 450 14  S xz 14 V/O

Tolerance range 1dGO DoK 450 14 VoA 450 14  S xz

1 kHz

VoA 450 14 DoK 450 14

N f/0

+ 20%

1,5  K xz /  th/l

800

300 11 250 10 180 9 90 7

600 R xz (MPa)

10 15

300 11 250 10 180 9 90 7 rSIF 90 7

300 11 250 10 180 9 90 7 90 7  S ODA/E

 2

- 20%

2

 2

1

10 10

 S ODA/E 7 P t

 2 dGO

400

10 5

0,5

200

7 V/O

0 200 400 600 800 1000 0 ODA-formation

0,3

10 0

10 -4

10 -2

10 0

10 2

10 4

10 0

10 5

10 10 N f/E

10 15

10 20

 S xz /4Y 2

1 r 0

 /2 (MPa)

Fig. 6. Normalized crack growth resistance curve (left) and accuracy of the predicted predictions for threshold stress and lifetime (right)

4. Conclusion Based on the experimental results for the fatigue strength at 10 7 and 10 9 cycles of different heat-treatment conditions of the steel 42CrMo4, expressions of the fatigue strength and number of cycles to failure were proposed to predict the S-N diagram in the VHCF-regime for critical heat-treatment conditions (R m/c > 1400 MPa). The combination of the predictions accords well with the experimental results and there is a possibility to predict the life scatter in the VHCF-regime (see fig. 7). On the other hand the present results lead to a differentiated conception on the sensitivity for failure in the VHCF-regime. The occurrence of VHCF-failure depends on the loading situation which is induced in the surroundings of an inclusion. This loading situation is controlled by the arising local stress state and the yielding characteristics of the matrix nearby the inclusion. Maybe there is a relation between the ODA-size and plastic zone around the inclusions. As current work in the research project a VHCF-sensitivity model will be proposed which assesses the VHCF sensitivity of different microstructural conditions of steels. The model will base on the presented results and will give an explanation to the observation that the inclusion size is decreasing with increasing life time and for the ODA-formation as a function of tempering temperature.