PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

63

7

Mode II crack propagation originates from material defects or welding features and occurs due to transversal loading motion along the loading direction. Fig. 5 b) shows virtual SIF maximum and minimum values for the leading crack tip of a 50 mm length fatigue crack. While Table 3 shows that SIF K II (±7.0 MPam 1/2 , for a 20-ton transversal load and -20ºC temperature difference) dominates crack propagation. This results in ±1.8º crack propagation angle, according to MSS criterion, leading to an almost horizontal or coplanar (in-plane shear-mode) crack growth. Fig 5 c) also shows that as train weight moves along the loading direction, the total K’ II range will be equal to 14 MPam 1/2 , considerably higher than Δ K’ I . This type of crack propagation has been experimentally verified by Desimone and Beretta (2006), and explained by the higher mode II component. These authors also verified that as crack length increases, crack opening mode will eventually change to mode I, and crack might even branch in symmetrical directions, as K’ I maximum and minimum values are very similar (Fig. 5 b) or c)).

Transversal loading

Loading direction

Longitudinal loading

Sleepers

Sleepers

(a)

(c)

(b)

Fig. 5. (a) Rail track section between four sleepers, with central 50mm length crack; (b) maximum and minimum loading virtual SIF K’ I and K’ II ; and (c) virtual SIF K’ I and K’ II range on leading crack tip.

Table 3. Railway track crack SIF K I and K II , SIF K II /(K I +K II ) ratio and MTS and MSS criteria crack propagation direction prediction.

2a (mm) K I (MPam

1/2 ) K

II (MPam

1/2 ) K

II /(K I +K II ) MTS (degree) MSS (degree)

50

0.5

±7.0

±0.93

±68.4

±1.8

4. Conclusions FCG simulations using an automatic algorithm were performed on two different specimens. Both the MTS and MSS criteria were used and the obtained initial crack propagation angles compared. MTS criterion predicted crack paths along the direction where K II /(K I +K II ) ratio is minimized. Therefore, mode II influence is only visible in the initial plane crack kinking, while tensile mode dominated the crack growth process. MSS criterion might be applied to the CTS specimen, when α>60º with good agreement with experimental results. Several authors experimental work indicate that MTS should be applied to FPB specimen fatigue predictions, even for pure mode II FCG. This methodology was applied to a rail track section, where a mode II crack was analyzed. Virtual SIF analysis shows that MSS accurately predicts crack propagation, until an eventual crack branching and change to mode I propagation, with a crack deflection of ±68.4º. Future work should include the full FCG simulation of mode II rail track crack propagation, and experimental testing in order to understand crack mode transition behavior. Acknowledgements This work was supported by FCT, through IDMEC, under LAETA, project UIDB/50022/2020. References

Ayatollahi, M. R., Razavi, S. M. J. and Yahya, M. Y. (2015) ‘Mixed mode fatigue crack initiation and growth in a CT specimen repaired by stop hole technique’, Engineering Fracture Mechanics . Elsevier Ltd, 145, pp. 115 – 127.