Effect of non-metallic inclusions on butterfly wing initiation, crack formation, and spall geometry in bearing steels Sina Mobasher Moghaddam a , Farshid Sadeghi a,⇑ , Kristin Paulson b , Nick Weinzapfel c , Martin Correns d , Vasilios Bakolas d , Markus Dinkel e a Purdue University, School of Mechanical Engineering, West Lafayette, IN 47907, United States b Purdue University, School of Material Science Engineering, West Lafayette, IN 47907, United States c Schaeffler Group USA, Inc., Troy, MI 48083, United States d Schaeffler Technologies GmbH & Co. KG, Industriestraße 1-3, 91074 Herzogenaurach, Germany e Schaeffler Technologies GmbH & Co. KG, Georg-Schäfer-Straße 30, 97421 Schweinfurt, Germany article info Article history: Received 12 January 2015 Received in revised form 1 May 2015 Accepted 17 May 2015 Available online 8 June 2015 Keywords: Rolling contact fatigue Bearing steel Non-metallic inclusions Butterfly wings Damage mechanics abstract Non-metallic inclusions such as sulfides and oxides are byproducts of the bearing steel manufacturing process. Stress concentrations due to such inclusions can originate cracks that lead to final failure. This paper proposes a model to simulate subsurface crack formation in bearing steel from butterfly-wing origination around non-metallic inclusions until final failure. A 2D finite element model was developed to obtain the stress distribution in a domain subjected to Hertzian loading with an embedded non-metallic inclusion. Continuum Damage Mechanics (CDM) was used to introduce a new variable called Butterfly Formation Index (BFI) that manifests the dependence of wing formation on depth. The value of critical damage inside the butterfly wings was obtained experimentally and was used to simulate damage evolution. Voronoi tessellation was used to develop the FEM domains to capture the effect of microstructural randomness on butterfly wing formation, crack initiation and crack propagation. Then, the effects of different inclusion characteristics such as size, depth, and stiffness on RCF life are studied. The results show that stiffness of an inclusion and its location have a significant effect on the RCF life: stiffer inclusions and inclusions located at the depth of maximum shear stress reversal are more detrimental to the RCF life. Stress concentrations are not significantly affected by inclusion size for the cases investigated; however, a stereology study showed that larger inclusions have a higher chance to be located at the critical depth and cause failure. Crack maps were recorded and compared to spall geometries observed experimentally. The results show that crack initiation locations and final spall shapes are similar to what has been observed in failed bearings. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Ball and rolling element bearings are crucial parts of all machinery which have rotary and relative motion. Because of their geometry, these elements usually function under large stresses. Bearings can fail because of environmental debris, improper lubri- cation systems, excessive loading, or bad installation. If a bearing is properly installed and maintained, the main mode of failure will be due to material fatigue. It has been observed that a loaded rotating element has a limited life because of the probability of the surface or subsurface initiated fatigue damage. Failure due to this phe- nomenon is commonly referred to as rolling contact fatigue (RCF). In general, rolling contact fatigue happens due to two different phenomena: surface originated pitting and subsurface originated spalling [1]. Fig. 1 shows two typical cracks due to surface and sub- surface failure. As can be seen, the depths at which the cracks ini- tiate are different. Hence, these two phenomena commonly can act separately; however, they might interfere in the Propagation stage and cooperate to fail the material. While surface initiated fatigue can be hindered by employing better lubricants and more efficient lubrication techniques, there are not actually many ways to stop subsurface initiated fatigue after the bearing is manufactured and installed. So, it is important to understand the mechanisms leading to this type of failure in order to improve the bearing design and manufacturing process. http://dx.doi.org/10.1016/j.ijfatigue.2015.05.010 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: smobashe@purdue.edu (S. Mobasher Moghaddam), sadeghi@ ecn.purdue.edu (F. Sadeghi), kpaulson@purdue.edu (K. Paulson), Nick.Weinzapfel@ schaeffler.com (N. Weinzapfel), corremrt@schaeffler.com (M. Correns), vasilios. bakolas@schaeffler.com (V. Bakolas), markus.dinkel@schaeffler.com (M. Dinkel). International Journal of Fatigue 80 (2015) 203–215 Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue