PSI - Issue 57

Yuri Kadin et al. / Procedia Structural Integrity 57 (2024) 236–249 Kadin et. al / Structural Integrity Procedia 00 (2023) 000 – 000

240

5

Concerning the surface length, b (see Fig. 3), the inspection result are presented in Fig. 4 in dimensionless form. It was found, that the length of horizonal cracks, is somewhat higher compared to the cracks of vertical and inclined orientation, which is most probably linked to the roller manufacturing. According to the statistical data in Fig. 4, the crack length b is scattered in rather wide range; additionally, there are few outliers, which length can considerably deviate from the mean value.

Crack depth at specific cross-section, [  m]

b

d

Position on the crack surface, [  m]

Fig. 6. Results of serial cross-sectioning (see Fig. 5) identifying the 3D shape and the depth of cracks. The example demonstrates how the crack shape is reconstructed by few subsequent cross-sectioning, which eventually enables to link (statistically) the crack length to its depth.

Using the serial cross-sectioning the 3D shape of cracks can be identified. For this procedure the chamfer containing imperfection is sliced (cross-sectioned few times) as is shown in Fig. 5. At each cross-section the crack depth is measured (see again Fig. 5), and by having few depth values the shape is reconstructed (see Fig. 6). The serial cross sectioning was performed for few rollers in attempt to determine statistically the relation between the crack length, b , and its depth, d . 3. Solution strategy It is not unusual to utilize fracture mechanics for the RCF analysis: numerous theoretical studies based on this approach are applied to bearings (see e.g. Mahdavi et. al (2022), Zolotarevskiy et. al (2020), Nazir et. al (2018), Lai and Kadin (2018)). The analysis is realized by the evaluation of SIF range and comparing this parameter to the fatigue threshold. By having sufficient computer power and advanced FE softwares, the computational fracture mechanics is widely used to treat 3D cracks, which geometry sometimes can become rather complex. In the case of RCF, the crack modelling is combined with contact analysis, which for rollers becomes computationally expensive. Thus, the contact problem and the imperfection modelling are split from each other, according to the methodology presented by Kadin et. al (2022). The contact pressure is evaluated semi-analytically, and is applied as the stress boundary conditions to the FE domain, which mimics the roller fragment containing an edge imperfection. To simulate over- rolling, the contact pressure evaluated as static load, is “animated”. This is done by varying the contact zone position relatively to the domain origin in the FE pre-processor. It is important to note, that this approach is based on the two main assumptions: i) The detailed geometry description of contacting bodies (radii of curvature, roller profile) and their mutual interaction (loading level, misalignment) is included only in the contact analysis, while the roller raceway in the FE model (containing an edge crack) is assumed as flat.