PSI - Issue 2_B

K.-H. Lang et al. / Procedia Structural Integrity 2 (2016) 1133–1142 K.-H. Lang et al. / Structural Integrity Procedia 00 (2016) 000–000

1138

6

strength reduction factor Z * and the absolute deviation between R

w/O and R w/1E9 are listed in Tab. 2 and labeled in

Fig. 3 (left).

Table 2. Absolute deviation Δ R50 (50 Hz), Δ R1 (1 kHz) between R w/1E6 and R w/1E9 and fatigue strength reduction factor Z 50 * (50 Hz), Z 50 * (1 kHz).

T t

570

450

300 123 0.21

250 160 0.26

180 176 0.28 119 0.21

90

Δ R50 Z 50* Δ R1 Z 1*

0 0 0 0

0 0 0 0

207 0.32 127 0.23

47

81

0.09

0.15

700

700

216

600

6

7

600

63

0

50

400 R w/O (MPa) 500

500 R w/N (MPa)

9

8

0

339

-123

-160 -176

-47

63 216

0

-207

-81

-119

-127

400

0

Fatigue Limit R w/O 50 Hz für P B = 50 %

300

Fatigue Resistance R w/O /surface für N = 10 6 /50Hz für N = 10 6 /1 kHz Fatigue Resistance R w/V

300

1 kHz 1 kHz Exponential-Approach 50 Hz Exponential-Approach 1 kHz Parabol-Approach

200

1

200

1

/subsurface für N = 10 9

100

100

6 Cycles in (log(N)) 0,05 Test frequency in (kHz) -123 Fatigue Resistance Drop in (MPa)

339 Testing Volume V 0 in (mm³)

0,05

0 500 1000 1500 2000 2500 3000 0

0 500 1000 1500 2000 2500 3000 0

R m (MPa)

R m (MPa)

Fig. 3. Relationship between tensile strength and fatigue strength at 10 6 and 10 9 cycles with black lines = 50 Hz and blue lines = 1 kHz (left) and prediction areas of threshold stress and number of cycles to failure (right).

The linear relations between fatigue limit and tensile strength for the high tempering conditions is related to surface fatigue crack initiation mechanisms, while for low tempering conditions, a fracture process given by an internal fatigue crack initiation defines the relationship between fatigue limit and material strength (Pang 2014). As a failure criterion for the failure in the VHCF regime the stress intensity factor (SIF) at inclusions was chosen. Thus we are able to calculate the SIF at the edge of interior inclusion and ODA (Fig. 4) with the following equation (Murakami 1989): K max = f ∙ Δσ /2 ∙ π 0,5 ∙ S xz 0,25 with Δσ/2 = nominal stress in the gauge section in MPa, S xz = inclusion area in µm and f = location parameter (f V = 0.5 for subsurface defects and f O = 0.65 for surface defects). The threshold value for crack initiation at inner and surface inclusions is also given by (Murakami 1989): Δ K th = i ∙ (HV+120) ∙ S xz 1/6 with i V = 2.77 ∙ 10 -3 for subsurface defects, i O = 3.3 ∙ 10 -3 for surface defects and S xz = inclusion area in m.

Fig. 4. Calculation of SIF for inclusion (550 MPa) and Inclusion + ODA (513 MPa).

Energy dispersive X-ray spectroscopy shows that the crack initiating particles in the investigated heat-treatment conditions of the low alloyed steel 42CrMo4 are nonmetallic inclusions of type AlCaO. The square root of the