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Research Papers

An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading

[+] Author and Article Information
Aizhong Wu

 School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

Xi Shi1

 School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China; State Key Laboratory of Mechanical System and Vibration,  Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

Andreas A. Polycarpou

 Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

1

Corresponding author.

J. Appl. Mech 79(5), 051001 (Jun 21, 2012) (9 pages) doi:10.1115/1.4006457 History: Received March 22, 2011; Revised October 08, 2011; Posted March 29, 2012; Published June 21, 2012; Online June 21, 2012

Spherical contact under combined normal and tangential loading has been investigated by many researchers, and some physically based criteria were proposed to capture the sliding inception, e.g., the local yielding criterion of the Kogut-Etsion (KE) model and the tangential stiffness criterion of the Brizmer-Kligerman-Etsion (BKE) model. In this work, by utilizing the maximum frictional shear stress criterion for the sliding inception, a finite element model for obliquely loaded spherical contact has been developed, which realized a friction transition from the KE model to the BKE model, with an increasing normal approach. The stress, strain, tangential force, normal force, and contact area during tangential loading are investigated using different models. It was found that with an elastic normal displacement preload, material failure is initiated on the surface, while with an elastic-plastic normal displacement preload the failure is initiated under the surface and then extends to the surface with the increasing tangential load. With an elastic-plastic normal displacement preload, there is an obvious normal force release during tangential loading. Different from the full stick model, both the Coulomb friction model and the proposed model are partial slip models in nature. However, the Coulomb friction is more empirically determined with some arbitrary friction coefficient, whereas the proposed model is based on physics parameters. Furthermore, both the Coulomb friction model and the proposed model predict a lower tangential force at the same tangential displacement, a slower growth of the contact area under elastic normal displacement preload, and a faster growth of the contact area under an elastic-plastic normal displacement preload compared to the full stick model.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

FEM model of an elastic-plastic sphere in contact with a rigid flat under combined normal and tangential loading

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Figure 2

Development of von Mises stresses during tangential loading (ω = 0.5ωc )

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Figure 3

Development of the plastic zone during tangential loading (ω = 0.5ωc )

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Figure 4

Development of von Mises stresses during tangential loading (ω = 3ωc )

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Figure 5

Development of the plastic zone during tangential loading (ω = 3ωc )

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Figure 6

Dimensionless maximum shear stress distributions along the symmetry line in the contact area: (a) ω = 0.5ωc , and (b) ω = 3ωc

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Figure 7

Dimensionless normal force versus dimensionless tangential displacement: (a) ω = 0.5ωc , and (b) ω = 3ωc

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Figure 8

Dimensionless tangential force versus dimensionless tangential displacement: (a) ω = 0.5ωc (b) ω = 3ωc , (c) ω = 12ωc , and (d) ω = 72ωc

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Figure 9

Friction coefficient dependence of the Coulomb friction model

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Figure 10

Friction transition from the KE model to the BKE model using the proposed model

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Figure 11

Predicted friction coefficient with load control

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Figure 12

Dimensionless contact area versus dimensionless tangential load: (a) ω = 0.5ωc , (b) ω = 3ωc , (c) ω = 12ωc , and (d) ω = 72ωc

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