PSI - Issue 54

Sjoerd T. Hengeveld et al. / Procedia Structural Integrity 54 (2024) 34–43 S.T. Hengeveld et al. / Structural Integrity Procedia 00 (2023) 000–000

41

8

Figure 8e shows the predicted crack paths after approximately 1 mm crack growth with a fixed load step of ∆ a = 0 . 1 mm. Depending on the traction coe ffi cients the crack does or does not to deviate from the initial direction. For µ r − w = − 0 . 4 the crack starts to grow upward due to the high negative K II value. In practice, spalling of part of the rail head is sometimes seen. This could indicate upwards crack growth, however, such a a sharp deviation upwards is probably not realistic. It is foreseen that adding additional loads, such as bending and thermal loads, will alter these crack paths.

10

40

7 c =0 : 10 7 c =0 : 50

7 r ! w =0 : 4 7 r ! w =0 : 2 7 r ! w =0 : 0 7 r ! w = ! 0 : 2 7 r ! w = ! 0 : 4

8

20

6

0 : 5 ]

0 : 5 ]

4

0

-20 K II [MPam

2 K I [MPam

0

-2

-40

-6

-4

-2

0

2

4

6

-6

-4

-2

0

2

4

6

x c =b

x c =b

(a)

(b)

10

60

K max K min " K

8

40

6

0 : 5 ]

0 : 5 ]

20

4

0

K II [MPam

2 K I [MPam

-20

7 c =0 : 10 7 c =0 : 50

Current Literature

0

-2

-40

-0.4

-0.2

0

0.2

0.4

-0.4

-0.2

0

0.2

0.4

0.6

7 r ! w

7 r ! w

(c)

(d)

-1

-1.5

7 r ! w = ! 0 : 4 7 r ! w = ! 0 : 2 7 r ! w =0 : 0 7 r ! w =0 : 4

y [mm]

-2

3.5 4 4.5 5 5.5 6 6.5 x [mm]

(e) 234.0pt

Fig. 8: SIFs for di ff erent traction coe ffi cients (a) mode I, (b) mode II, (c-d) min. and max. K I and K II (d) Predicted crack paths for µ c = 0 . 1