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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introduced residual stresses for the non-deep rolled condition and calculations considering the residual stress in depth profiles, presented in Section 2.2, are executed and compared. In addition to the residual stresses introduced by deep rolling, the longitudinal tensile stresses caused by the press fit of the adjacent parts, presented in Section 2.3, are considered and superimposed. Two separate examinations are carried out with different loadings: 2.6.1. Constant load amplitude The first investigation is performed with the maximum load amplitude of the block load sequence. This allows to determine whether and from which depth a certain crack is able to cyclically propagate. The initial a 0 / c 0 ratios of 1.0, 0.8, 0.6 and 0.4 are considered and respectively investigated with the surface conditions not deep rolled and deep rolled with 5, 10, 15 and 20 kN. In addition to the crack depth a th from which the initial cracks are capable of propagation, the tolerable number of load-cycles up to the defined maximum crack depth a max of 8 mm is determined. 2.6.2. Load spectrum The second investigation aims to determine the remaining service life or the tolerable number of load-cycles in the presence of a crack respectively. In this case, the calculations are carried out for a a 0 / c 0 ratio of 1.0. The initial depths of cracks are selected on the basis of the results of the first examination. The resulting starting crack depth a th for the different surface conditions resulting from deep rolling with the different forces are defined as starting crack depth. Thus, the four initial crack depths 3.0, 4.5, 5.5 and 6.5 mm are obtained. The component with present initial cracks is cyclically loaded with the load spectrum presented in Section 2.5 and the tolerable number of load-cycles are determined up to the maximum crack depth a max of 8 mm.

3. Results and Discussion

In the following subsections, the results of the analytical crack propagation calculation studies are presented.

3.1. Constant load amplitude

Within the scope of the first investigation, it is examined whether existing cracks with different starting crack geometries and different deep rolling post-treatment conditions are capable to propagate in railway axles. Therefore, the respective condition is set-up in INARA and the depth of the initial crack is changed with a constant a 0 / c 0 ratio for each case study. As already mentioned, the maximum load amplitude occurring in the load spectrum is applied as a constant load. In addition to the information on whether a crack is propagating or not, the number of tolerable load-cycles up to a crack depth of of 8 mm is determined in case of crack growth. The first part of the investigation results is shown in Figure 5. The colours of the curves represent the considered surface conditions, not deep rolled and deep rolled with a deep rolling force of 5 kN, 10 kN, 15 kN and 20 kN. If a curve does not appear in the diagrams, the crack is not capable to propagate up to a depth of 7.5 mm under the given boundary conditions. The curves show a very similar appearance. As the initial crack depth increases, the tolerable number of load-cycles quickly decreases and then flattens out. The propagation capacity and the depth from which cracks are capable of propagation are strongly dependent on the surface condition, but also, even to a lesser extent, on the starting crack geometry. The smallest starting crack depth occurs in a not-surface-treated condition, equalling a few tenths of a millimetre. With a deep rolling force of 5 kN, this crack depth increases to over 2.5 mm and with increasing deep rolling force at 20 kN to over 6.5 mm.