PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64

62 6

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

Considering the MSS criterion, Fig 4. d) shows the simulated crack propagation along the direction where K’ II is maximized (Fig. 4 h)). Table 2 shows a 70º difference between MSS and MTS crack propagation direction prediction. Decreasing L 2 value, introduces mixed mode crack propagation. In this case MSS simulations resulted in crack kinking, deflecting crack paths towards the left (or fixed) roller, Fig. 4 c). While MTS simulations also resulted in crack kinking, deflecting crack paths to the right (or movable) roller, Fig. 4 b) and a). As L 2 value decreases, F 2 increases up to 4.93 kN producing almost pure mode I propagation (Fig. 4 e)). These results are in line with Huang et al. (2019) work, where even for pure mode II loading, crack propagation always occurs along the direction where K’ I is maximized. Negative K’ I values have no physical meaning. A negative value would lead to crack face overlapping, due to compressive circumferential stresses. Therefore, crack propagation under negative K’ I values does not occur, and negative K’ I values were set to zero, Infante-García et al. (2019). This implies that even for high mixicity ratios (Fig. 3 g) and h) and Fig. 4 g) and h)), no crack branching might occur in the analyzed specimens.

(b)

(d)

(c)

(a)

(e)

(f)

(g)

(h)

Fig. 4. FPB specimen FCG according to (a) MTS criterion with L 2 =1mm; (b) MTS criterion with L 2 =5mm; (c) MSS criterion with L 2 =25mm; and (d) MSS criterion with L 2 =30mm; Virtual SIF K’ I and K’ II when (e) L 2 =1mm; (f) L 2 =5mm; (g) L 2 =25mm; and (h) L 2 =30mm.

Table 2. FPB specimen SIF K I and K II , SIF K II /(K I +K II ) ratio and MTS and MSS criteria crack propagation direction prediction.

L 2 (mm)

K I (MPam

1/2 )

II (MPam

1/2 )

MTS (degree) MSS (degree)

K

K

II /(K I +K II )

30 25 20 15 10

0.2 5.1

4.5 5.0 5.3 5.5 5.3 4.2 2.6

0.96 0.49 0.34 0.25 0.19 0.12 0.07

-69.7 -52.8 -40.6 -31.6 -23.7 -15.6

0.0

16.0 28.0 37.3 45.7 54.3 61.6

10.5 16.5 22.9 29.2 33.6

5 1

-8.7

A possible case study where both mode I and mode II crack propagation may occur, is FCG on railway track sections between sleepers, Fig. 5 a). Subjected to transversal (train weight) and longitudinal loads (resulting from differences between environment and rail neutral track installation temperatures), rail cracks propagate vertically (mode I), due to high transversal loads, or horizontally (mode II), due to low transversal loads. Baptista et al. (2018) have previously studied typical mode I crack propagation. In this case crack propagation occurs due to bending stresses, when the transversal load is applied at half distance between two sleepers.