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

40

7

10

50

7 c =0 : 50 7 c =0 : 30 7 c =0 : 10 7 c =0 : 00

8

40

6

30

0 : 5 ]

0 : 5 ]

4

20

10 K II [MPam

2 K I [MPam

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

0

0

-2

-10

-6

-4

-2

0

2

4

6

-6

-4

-2

0

2

4

6

x c =b

x c =b

(a)

(b)

10 20 30 40 50 K II [MPam 0 : 5 ]

K max II K min II Current Literature

-2.2 -2 -1.8 -1.6 -1.4 -1.2

7 c =0 : 50 7 c =0 : 30 7 c =0 : 10 7 c =0 : 10 (MTS)

-20 -10 0

y [mm]

7 r ! w =0 : 2

7 r ! w =0 : 4

4

4.5

5

5.5

6

0

0.1

0.2

0.3

0.4

0.5

x [mm]

7 c

(c)

(d)

Fig. 7: SIFs for di ff erent friction coe ffi cients (a) mode I, (b) mode II, (c) min. K II andmax. K II (d) Predicted crack paths for µ w − r = 0 . 4

with for example bending and thermal loads. The dashed yellow line is the predicted crack path when using the MTS criterium. This criterium is originally developed for proportional loading and is therefore not applicable to the case of an inclined crack, as shown.

3.3. Influence of traction coe ffi cient

In this section the influence of the traction coe ffi cient is studied and the results are shown in Figure 8. Distinction is made between two friction coe ffi cients µ c = 0 . 1 and µ c = 0 . 5. Figure 8a shows the evolution of K I as a function of the load position. The di ff erent colors represent di ff erent traction coe ffi cients. The dashed curves are the results for µ c = 0 . 1 and the solid curves are the results for µ c = 0 . 5. Figure 8c shows the minimum and maximum of K I of the entire load path as a function of the traction coe ffi cient. The crack is open at K max I , hence there is a limited influence of the crack face friction (corresponding to the results of Figure 7a). As expected, K max I is minimum when there is no traction force applied because the traction load opens the inclined crack when passing over the rail. A braking traction force µ r − w > 0 leads to a higher maximum K I component than an accelerating traction load, with the same absolute traction coe ffi cient. In a similar way Figure 8b shows the results for K II . Figure 8d shows the minimum (crosses) K II , maximum K II (circles) and maximum ∆ K II range (diamonds). From both figures a significant di ff erence in SIF is seen between the low and the high friction coe ffi cient: The latter gives a lower K max II , which is due to the increased load fraction transferred by friction, thereby shielding the crack tip. The minimum values are obtained when the traction coe ffi cient is zero. In mode II both a positive as well as negative traction coe ffi cient results in a significant increase in SIF range.