PSI - Issue 57

Tobias Pertoll et al. / Procedia Structural Integrity 57 (2024) 250–261 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Figure 5. Number of load-cycles for maximum constant amplitude up to a crack depth of 8 mm for not deep rolled and with different forces deep rolled surface conditions for a 0 / c 0 ratio (a) 1.0, (b) 0.8, (c) 0.6 and (d) 0.4 The threshold crack depth a th , is calculated for all curves to determine the crack depth above which a starting crack is capable to propagate. Therefore, all curves shown in Figure 5 are fitted with exponential functions and for each curve by means of limit value formation a th is determined. The results are shown in Figure 6, further in (a) as a 2D diagram and to better visualise the correlations with the a 0 / c 0 ratio in (b) as a 3D diagram. The correlations at a constant a 0 / c 0 ratio are described again with the help of exponential equations for the different deep rolling parameters used. The parameters of the equations can be found in Figure 6 (a). It can be seen that a th increases with increasing deep rolling force. The correlations towards higher deep rolling forces show decreasing tendencies, which aim to a certain maximum. For the present case, the investigation is limited to 20 kN. In the not deep-rolled state, the highest allowed threshold crack depth results from the largest considered a 0 / c 0 ratio of 1.0, and thus the shortest surface crack length compared to the crack depth. As soon as the railway axle is deep rolled, the a 0 / c 0 ratio shows the opposite behaviour on a th . This means that the lowest a 0 / c 0 ratio of 0.4 results in the largest threshold crack depth. The behaviour is consistent and the difference between the considered a 0 / c 0 ratios increases with increasing deep rolling force. For a 0 / c 0 ratios 0.4 and 0.6, cracks with an initial depth of 7.5 mm are not propagable. The results shown are applicable in practice, e.g. if a crack-like defect is detected on a railway axle, the crack geometry is determined and the deep rolling treatment properties are known, the presented trends in Figure 6 can be used to assess whether there is a risk of cyclic crack propagation or not.