Research Papers: Contact Mechanics

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

[+] Author and Article Information
Sina Mobasher Moghaddam

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: smobashe@purdue.edu

Farshid Sadeghi

Cummins Distinguished Professor of Mechanical Engineering,
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: sadeghi@ecn.purdue.edu

Nick Weinzapfel

Schaeffler Group USA, Inc.,
Troy, MI 48083
e-mail: Nick.Weinzapfel@schaeffler.com

Alexander Liebel

Advanced Bearing Analysis,
Schaeffler Technologies GmbH & Co. KG,
Herzogenaurach DE-91074, Germany
e-mail: liebeaex@schaeffler.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 20, 2014; final manuscript received September 17, 2014; published online November 6, 2014. Assoc. Editor: Robert Wood.

J. Tribol 137(1), 011404 (Nov 06, 2014) (13 pages) Paper No: TRIB-14-1092; doi: 10.1115/1.4028628 History: Received April 20, 2014; Revised September 17, 2014

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.

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Fig. 1

Normalized stress history experienced by a point located at 0.5b under a bearing surface

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Fig. 2

Schematic of a typical pair of butterfly wings: note the ORD.

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Fig. 3

Schematic of the domain with relative dimensions (inclusion location and diameter vary in different cases)

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Fig. 4

Centerline stresses for two domains with (jagged) and without (smooth) an inclusion for a 16 μm diameter inclusion located at 0.5b. Dashed lines mark the inclusion/matrix interface.

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Fig. 5

Shear stress variations around the inclusion as the Hertzian load passes over the surface. x/b indicates the relative location of the center of the Hertzian pressure distribution.

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Fig. 6

Effect of surface traction on amplitude and mean value of shear stress

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Fig. 7

Shear stress amplitude, mean, and their summation during one load pass over pristine domain

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Fig. 8

(a) Chronological order in butterfly evolution: (1) beginning of the microstructural change, (2) microstructural alteration near the inclusion/matrix interface, (3) formation of the actual body of the wings, and (4) fully formed butterfly wings. (b) Grayscale spectrum showing the butterfly evolution versus number of cycles (Pmax = 2.0 GPa).

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Fig. 9

Butterfly wings formed around an inclusion (a) as observed by Grabulov et al. [14] (b) as predicted by the model (figure on left is flipped as opposed to the original to set the ORD consistent with the simulation).

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Fig. 10

Effect of inclusion depth on butterfly wing development: (a) as observed by Evans [16] (b) as predicted by the model (some of the figures on left are flipped as opposed to the original to set the ORD consistent with the simulation).

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Fig. 11

Butterfly wings formed around (a) 2 μ and (b) 16 μ inclusions. Note that the relative wingspan to inclusion size is larger for the smaller inclusion.

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Fig. 12

Wingspan to inclusion diameter ratio versus the inclusion size variation according to experimental observations [27] and current model

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Fig. 13

Color spectrums illustrating butterfly formation growth versus number of cycles at different load levels

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Fig. 14

S-N curve for butterfly formation. Experimental data are extracted from Ref. [2].

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Fig. 15

Schematic showing the stresses resolved along the inclusion matrix interface. Maximum shear along the interface dominates the debonding regions.

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Fig. 16

Comparison of the debonding and deformation regions at inclusion/matrix interface (a) as observed by Grabulov et al. [31] and (b) Simulation results.

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Fig. 17

Maximum tensile stress acting on butterfly/matrix interface. Bold dashed lines show where the model predicts the cracks to grow.




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