PSI - Issue 66

Ramdane Boukellif et al. / Procedia Structural Integrity 66 (2024) 55–70 Ramdane Boukellif et al. / Structural Integrity Procedia 00 (2025) 000 – 000

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1. Introduction Engineering structures are typically exposed to cyclic or stochastic mechanical loading. Exhibition of incipient cracks, particularly in bearings and gears suffering from rolling contact fatigue (RCF), limits the life cycle of the structure and supplies the risk of a fatal failure. In an investigation of the propagation of surface initiated rolling fatigue cracks in bearing steel by Rycerz et al. (2017), it was found that the crack growth occurs in two stages. In the first stage, cracks grow slowly, consuming most of the total life. In the second stage, the crack reaches a critical crack length of around 100 µm, at which the speed of propagation increases rapidly. The speed of propagation is controlled by the contact pressure and the size of the crack. In contrast to the sub-surface-initiated spall, surface-initiated fatigue cracks have typical features such as the entry angle. In Tallian (1992) usually, this angle is smaller than 30°. In Otsuka et al. (2004), tests were performed with a newly developed testing apparatus for describing mode II fatigue crack growth. This is based on the assumption that flaking occurs in rolling contact fatigue due to mode II loading. Here, the mode I component is suppressed due to the compressive stress. When the applied ∆ is larger than a certain critical value, mode I occurs at the plane of maximum tensile stress. The application of the finite element method (FEM) to describe the growth of short cracks in the event of RCF was proposed by Ringsberg et al. (2003). It was found that the application of the elastic-plastic analysis is necessary to describe cracks of lengths between 0.1- 0.2 mm. Various numerical methods based on linear-elastic fracture mechanics (LEFM) were used to describe crack propagation under rolling contact fatigue. In Datsyshyn et al. (2020), solutions of the singular integral equations were used to calculate the SIFs. Criterion of maximum circumferential stress was used to predict the crack path by Erdogan et al. (1963). The crack path prediction by the asperity point load mechanism was implemented using FEM by Hannes et al. (2011). In this case, it is assumed that the crack will propagate perpendicular to the largest principal stress direction in the uncracked material position. Using X-FEM, the crack propagation under rolling contact fatigue was investigated by Trollé et al. (2013), Hannes et al. (2014) and Meray et al. (2022). Using experimental and numerical methods, mode II fatigue crack propagation under reversed shear and static biaxial compression was investigated in two bearing steels (Zaid et al. (2022). Based on Hertzian theory and applying Continuum Damage Mechanics, numerical models were developed to simulate fatigue behaviour under rolling contact (Sukumar et al. (2003)). In addition, FEM was used by Sukumar et al. (2003) to simulate the mechanical behaviour of a planetary gear system, which is subject to the RCF phenomenon. Here, bearing gear steels such as AISI 52100 and SAE 4340 were used as a reference for simulations. In a planetary gear containing an integrated bearing, microcracks were observed starting from the bearing race surface and leading to spalling. This type of damage is regarded as typical for these components. In some cases, however, these cracks bifurcate into the core. In Depouhon et al. (2017), the contact pressure, rim ovalization and residual stresses due to a thermochemical treatment were possible drivers of crack propagation. Small defects or cracks due to fatigue crack growth that initially appear harmless can reach a critical length. In order to assess the safety of a structure, it is important to predict the crack path. If the load, component geometry, and material properties are known, the fracture mechanical stress analysis can be carried out using the finite element method (FEM). This work deals with the 2D simulation of the crack path of surface initiated rolling contact fatigue. This is to understand the damage process and predict the crack path in the structure. Due to the large number of interacting influencing parameters, such as contact geometry, load, lubricating film, rolling velocity, coefficient of friction, material properties, inclusions, microstructure, surface treatment, and impurities, rolling contact fatigue is a complex problem (Hannes (2014)). In this study the following important parameters are considered: contact geometry, loading, friction at cylinder/half-plane and at crack faces. The crack growth simulation is carried out using stress intensity factor approach, using the program system ADAPCRACK3D developed by Schöllmann et al. (2003). The calculation of SIFs in this work is performed using the MVCCI-method from Rybicki et al. (1977). Using the 1 ′ - criterion by Schöllmann et al. (2002), the cyclic equivalent SIF ∆ as well as the kink angles are determined. The