A Damage Mechanics Approach to Simulate Butterfly Wing Formation Around Nonmetallic Inclusions

Abstract

Nonmetallic inclusions such as sulfides and oxides are byproducts of the steel manufacturing process. For more than half a century, researchers have observed microstructural alterations around the inclusions commonly referred to as “butterfly wings.” This paper proposes a model to describe butterfly wing formation around nonmetallic inclusions. A 2D finite element model is developed to obtain the stress distribution in a domain subject to Hertzian loading with an embedded nonmetallic inclusion. It was found that mean stress due to surface traction has a significant effect on butterfly formation. Continuum damage mechanics (CDM) was used to investigate fatigue damage and replicate the observed butterfly wing formations. It is postulated that cyclic damage accumulation can be the reason for the microstructural changes in butterflies. A new damage evolution equation, which accounts for the effect of mean stresses, was introduced to capture the microstructural changes in the material. The proposed damage evolution law matches experimentally observed butterfly orientation, shape, and size successfully. The model is used to obtain S-N results for butterfly formation at different Hertzian load levels. The results corroborate well with the experimental data available in the open literature. The model is used to predict debonding at the inclusion/matrix interface and the most vulnerable regions for crack initiation on butterfly sides. The proposed model is capable of predicting the regions of interest in corroboration with experimental observations.

White etching area damage induced by shear localization in rolling contact fatigue of bearing steel

“…41 These studies focused on modeling stress distribution, fatigue life, and fatigue indicator parameter. For example, Moghaddam et al 40,49 studied the WEA damage through 2D and 3D finite element model based on continuum damage mechanics. It was reported that the reciprocating shear stress is the main driving force of butterfly formation compared to the mean shear stress.…”

Numerical study on butterfly wings around inclusion based on damage evolution and semi-analytical method

“…The effect of the mean stress cannot be neglected because the stress disturbance around the inclusion is asymmetrical. To incorporate the effects of both the mean stress and the stress amplitude during the rolling contact process, the equivalent stress is represented by [32]:…”

“…Cerullo and Tvergaard [31] obtained the stress field surrounding the inclusion and evaluated the contact fatigue using the DangVan multiaxial criterion. Moghaddam et al [32,33] investigated the formation of butterflies based on a FEM model and continuum damage mechanics (CDM). Guan et al [34] studied the crack nucleation and propagation induced by metallic carbides using the Voronoi finite element model.…”

The state-of-art of microstructural evolution of bearing materials under Rolling Contact Fatigue

“…Inclusions in steel play a significant role in crack initiation, and the appearance of WECs is affected by inclusion types [22,24,25,39,40,48,49,70,71,73,74,[88][89][90]. Among all kinds of inclusions, MnS is more probable to induce WECs [35,49,71].…”