A 3D numerical and experimental investigation of microstructural alterations around non-metallic inclusions in bearing steel
Introduction
Ball and roller bearings are among the most important components in all the machinery that have rotary motion. Bearings carry the load through Hertzian contacts between the rollers and the races. Due to geometric restrictions, non-conformal contacts are commonly associated with very large values of stresses. Factors such as improper design and lubrication, environmental debris, unexpected large loads, or bad installation can cause bearing failure. However, if a bearing is well lubricated and operates under the designated loads, the main mode of failure would be due to fatigue. Failure because of this phenomenon is referred to as rolling contact fatigue (RCF).
RCF failure can be divided into two main categories: (i) surface pitting and (ii) subsurface spalling. While surface pitting can be inhibited significantly by proper lubrication and adequate surface preparation, there are not many ways to stop subsurface initiated fatigue after the bearing is manufactured and installed. So, it is of great importance to better understand the mechanisms leading to this type of failure in order to improve the bearing design and manufacturing process.
There are a number of differences between RCF and other types of classical fatigue. As opposed to other types of fatigue such as bending or uniaxial fatigue, RCF occurs due to a complex state of stress in which there is no significant tensile component. Fig. 1 plots different stress components experienced by a point located at the subsurface of the material. As can be seen, shear stress is the only stress component which alternates between positive and negative values. That is why RCF is generally known as a shear driven phenomenon. It should be noted that in RCF, unlike other types of fatigue, the volume of the material subjected to large stresses is very small, about few hundred microns in depth for most cases. Consequently, fatigue phenomena occur in a scale comparable to grain size of the material. This makes the fatigue behavior of the material strongly microstructural sensitive.
It has been observed that when bearing steel is subjected to rolling contact loading certain microstructural alterations can occur in the matrix [1]. Such changes are commonly categorized as butterfly wings, white etching cracks (WECs), dark etching region (DER), and white etching bands (WEBs). Fig. 2 shows examples of each microstructural alteration type. Among these features, butterfly wings and WECs are more concerning since they appear before L10 life of bearing and can result in premature failure of the component. The current work investigates butterfly formation experimentally and numerically.
First observed in 1951 [5], butterfly wings have been known for more than sixty years. Butterflies are commonly addressed as regions of microstructurally altered material in the vicinity of the nonmetallic inclusions. Most of the butterflies are comprised of two wings that emanate from the inclusion at a 45 degree angle relative to over rolling direction (ORD). The grain size within the wings can be as small as 5 nanometers. The regions are most probably made of ultrafine ferrite grains. Butterflies can lead to failure since they are accompanied with many micro-cracks. Two major cracks are commonly observed on top of the upper wing and bottom of the lower wing which can propagate beyond the wings and cause the RCF failure [6].
Since the first observation of butterflies, many experimental attempts have been conducted to investigate their root cause analysis, morphology, and detrimental effects. Early attempts included optical microscopy of the butterflies to study their geometry, size, and location relative to ORD. In the recent years, newer techniques such as SEM, TEM, FIB, and EBSD [2], [7], [8], [9] have been implemented to obtain a more in depth knowledge of butterflies. Thanks to these new tools more information regarding the grain size, crystal orientation, etc. of butterflies is obtained. However, all these methods are destructive. This makes it difficult to accurately relate the butterfly formation life to crack initiation and propagation stages which lead to final fatigue. It should be noted that butterflies form at the subsurface of the material and only non-destructive techniques (NDT) would be able to track their initiation and propagation before the failure. Consequently, NDT methods have recently been used to study butterfly formation in bearing steels. Among different techniques ultrasonic inspection, acoustic emission, and X-ray tomography has been the most widely used because of their capability to look inside the matrix [10], [11], [12], [13], [14]. Among all these methods ultrasounds have obtained the most popularity due their high accuracy, ease of use, and practicality for in-situ application. Guy et al. [12] used high frequency ultrasound to spot inclusions and monitor butterfly progression from them in bearing steel. Their work was continued by Nelias et al. [15] to determine butterfly appearance dependence on inclusion depth. Post failure micrography proved the method to be a reliable tool to inspect inclusions as small as 30 μm in diameter. A similar procedure was followed by Umezawa et al. [13]. They investigated the size of the echo image from the inclusion as the number of cycles increased to assess the butterfly and crack progression from the inclusions. Auclair and Daguier [16] found a probability of detection of more than 95% for inclusion which are at least 30 μm in diameter as well. Other researchers have used similar approaches such as Rayleigh waves to detect C-cracks on the surface of the balls [17], fractal dimension analysis to detect WEBs [18], or acoustic emission all around the bearing race to quantify RCF damage [14].
Although butterflies have been known for more than half a century, due to many complications in their root cause analysis, it was only in 1992 when the first attempt was made to suggest a model for their formation. Salehizadeh and Saka [19] proposed residual stress evolution around an inclusion as a possible reason for crack formation in butterflies. In 1998, Melander et al. [20], [21], [22] analyzed the stress intensity factor variation at the crack tip for cracks that were inserted in an FE model at 45 degrees relative to ORD. Vincent et al. [23] suggested accumulation of dislocations due to stress concentrations can lead to butterfly formation and eventually crack generation, also in 1998. Hiraoka et al. [24] looked at the hydrostatic stress distribution around inhomogeneties for cases with and without cracks in 2005. Later on in 2010, Alley and Neu [25] investigated plastic strain accumulation near an inclusion during rolling contact loading to simulate the wings. In 2014, Cerullo [26] predicted crack growth by means of irreversible cohesive elements for different crack orientations from inclusion. Also in 2014, the current authors [6] used damage mechanics to predict butterfly wings shape, size, and orientation. Shortly after them, Cerullo and Tvergaard [27] suggested a model to predict wing formation based on Dang Van theorem. Both the current works found the mean shear stress due to surface traction to be important on butterfly wing formation, independently. Moghaddam et al. [28] expanded their model to simulate crack propagation from inclusion till final failure. It should be noted that all the previous efforts to model butterfly wing formation has been confined to 2D models and almost all the models have neglected the possible 3D aspects of the problem. (Alley and Neu [25] used a 3D FE model; however, they used cylindrical or rectangular inclusions that were extended into the page, which basically reduces the 3D problem to 2D.)
The current work implements an experimental as well as an analytical approach to investigate butterfly wing formation in 3D. A FE model is coupled with a postulated damage law to simulate microstructural alterations around inclusions. Butterfly-to-inclusion size ratio was observed at different cross sections and a closed form solution was suggested for the wing span to inclusion diameter ratio which is compared to experimental data from literature. High frequency ultrasonic inspection of inclusions was conducted to detect inclusions inside the bearing steel. Experimental serial sectioning of one of these inclusions was used as a reference to validate the simulation results. Comparison of the experimental and numerical serial sectioning suggested the lateral expansion of the butterflies in the plane transverse to ORD.
Section snippets
2D vs 3D models
As discussed in the previous section, almost all the previous efforts to simulate butterfly wing formation have been confined to 2D models. It should be noted that a 2D model assumes plane strain condition. This means that the depth of the features into the page is practically infinite. Following this approach, a circular inclusion is actually equivalent to an infinitely long cylindrical inclusion with its main axis into the page. This is an unrealistic case. In reality, most of the inclusions
Test rig description
RCF tests have been conducted on samples made of bearing steel to investigate butterfly wing formation experimentally. A 3-ball & rod RCF tester made by Federal-Mogul was used for this purpose. The test rig is shown in Fig. 8a. The schematic of the contact between the balls and the rod-shaped specimen is illustrated in Fig. 8b, and the dimensions of the specimen are mentioned in Fig. 8c. Three 12.7 mm diameter balls, made of M50 steel, are separated by a retainer and are radially loaded against
Analytical serial sectioning
The 3D model described earlier was exercised in a shell script and a C++ post processor code was used to update damage in each cycle. To make the phase transition smoother and to increase the accuracy of the model, the ΔD value in each cycle was set to 0.01. This way, after ten loading cycles, the first element was converted from martensite to ferrite. The simulation was run to model the wing propagation. The criterion to stop the simulation was the appearance of the second pair of wings
Summary and conclusion
The current work implements experimental and analytical techniques to tackle butterfly wing formation around nonmetallic inclusions in bearing steel. A 3D FE model is coupled with a postulated damage law to simulate microstructural alterations around inclusions. The model was exercised to simulate the wing formation. Analytical serial sectioning illustrated how the butterfly, as a 3D object, may appear in 2D planes under the microscope. High frequency ultrasonic inspection was used to detect
Acknowledgment
Authors would like to thank Schaeffler Technologies for their funding of this project and the very helpful comments.
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2023, WearCitation Excerpt :And in the last couple of decades, these aspects have been the focus of numerous research papers. In the field of WEAs/WECs and RCF, it has been observed that many researchers have focused only on non-metallic inclusions (NMIs) such as aluminum oxides (Al2O3) or manganese sulfides (MnS) and voids/pores [46–52]. The majority of them presume, that the stress state surrounding NMIs as the source of fatigue damage nucleation, which is correlated to the formation of WEAs (butterfly wings) i.e. hypothesis 1 [46–50,53,54].