PSI - Issue 57

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

252

3

• Achievable number of residual load-cycles under constant and variable load amplitudes for various initial crack depths, initial crack geometries and deep rolling forces.

Nomenclature a

Crack depth

Initial crack depth

a 0 a th

Threshold crack depth at which a crack is capable to propagate Maximum considered crack depth (in this investigation set to 8 mm) Major semi axis of semi-elliptical surface cracks Initial major semi axis of semi-elliptical surface cracks

a max

c

c 0 D

Outer diameter of the railway axle Outer radius of the railway axle

R

R -ratio Load stress ratio R i Radius of the hollow bore of the railway axle ∆K Range of the stress intensity factor ∆ ℎ Range of the threshold stress intensity factor 2. Methodology

2.1. Realistic boundary conditions

For this study, realistic boundary conditions are attempted to be used. Therefore, a railway axle made of high strength steel 34CrNiMo6 is chosen. This material is a frequently used material (Regazzi 2014) in addition to the materials EA1N and EA4T specified for railway applications in the European standard (EN 13261: 2020). The most highly loaded area of the railway axle are the transitions to press-fits for the assembly of add-on parts. These sections are designed as basket arches and are deep rolled. The investigated axle exhibits a full-scale railway axle diameter D in the most highly-stressed cross section, where the crack propagation investigations are carried out. A validated finite element deep rolling simulation model is used to determine the residual stress in-depth profiles introduced by deep rolling. The simulation model is based on the pre-described simulation model presented in (Pertoll et al. 2023a) and used with the adaptation to railway axle geometry shown in (Pertoll et al. 2023b). For the sake of completeness, the model will be described in this study very briefly. The simulation model is set-up in MSC Marc 2020 (MSC Software 2020) and consists of a representative meshed section of a railway axle with the outer diameter D and deep rolling tools modelled as rigid bodies, as shown in Figure 1 (a) in the starting position. The diameter of the disc tool is 100 mm and the contact radius equals a value of 9 mm. To simulate residual stresses a cyclic-plastic Chaboche material model, parameterised based on uniaxial low-cycle fatigue tests, is considered in the simulation model. Its stress-strain response for various exemplary applied strains is shown in Figure 1 (b). The deep rolling process is represented by the sequential rolling of the tools one after the other across the surface with an offset by the used feed rate of 0.5 mm. The sequence of figures in Figure 1 (c) shows the simulation process and thus the steps from the initial condition up to the deep rolled simulation result with an introduced uniform residual stress state. This simulation results are shown in detail in Figure 1 (d) using the von Mises stresses. 2.2. Deep rolling simulation model and introduced near surface residual stresses