Research Papers: Contact Mechanics

Spherical Elastic–Plastic Contact Model for Power-Law Hardening Materials Under Combined Normal and Tangential Loads

[+] Author and Article Information
Bin Zhao

Key Laboratory of High Efficiency
and Clean Mechanical Manufacture
(Ministry of Education),
School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China

Song Zhang

Key Laboratory of High Efficiency and Clean
Mechanical Manufacture (Ministry of Education),
School of Mechanical Engineering,
Shandong University,
Jinan, Shandong 250061, China
e-mail: zhangsong@sdu.edu.cn

Leon M. Keer

Fellow ASME
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: l-keer@northwestern.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received November 4, 2015; final manuscript received May 11, 2016; published online August 11, 2016. Assoc. Editor: James R. Barber.

J. Tribol 139(2), 021401 (Aug 11, 2016) (8 pages) Paper No: TRIB-15-1395; doi: 10.1115/1.4033647 History: Received November 04, 2015; Revised May 11, 2016

The contact between a power-law hardening elastic–plastic sphere and a rigid flat under combined normal and tangential loads in full stick is studied in this work. The displacement-driven loading is used since the frictional contact problems under the displacement-driven loading are widespread in the fields of metal forming and orthogonal cutting. The loading process is as follows: First, a normal displacement-driven loading is imposed on the rigid flat and kept constant; then, an additional tangential displacement-driven loading is applied to the rigid flat. The elastic–plastic contact behavior in presliding is investigated with a proposed finite element (FE) model, including the tangential force, the von Mises stress, the normal force, the contact pressure, and the contact area. The effect of the strain-hardening exponent on contact behavior is considered. It is seen that the tangential force increases nonlinearly with the increase of the tangential displacement, exhibiting gradual stiffness reduction which implies that the junction becomes more plastic. The von Mises stresses moves along the direction of the tangential load, while the maximum stress moves to the contact surface from the below. The normal force diminishes as the tangential load increases, and more obviously for the lower hardening exponent cases. The contact pressure also decreases more significantly for the lower hardening exponent cases. In addition, smaller exponents result in a greater increase of the contact area. The empirical expressions of the tangential force and the contact area in the tangential loading process are also proposed by fitting to the FE results.

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Fig. 1

Stress–strain diagram for the power-law hardening materials

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Fig. 2

Schematic diagram of the contact model under the combined normal and tangential loads

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Fig. 4

The relation between the dimensionless tangential force Q* and the dimensionless tangential displacement ux* under different normal displacement preloads w0*: (a) w0* = 3, (b) w0* = 10, (c) w0* = 25, and (d) w0* = 70

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Fig. 5

The relation between the static friction coefficient μs and the dimensionless normal load P* during the tangential loading process for the elastic-perfectly plastic material. The experimental results [17], the numerical results given by Brizmer et al. [14], and the proposed results in this work are compared.

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Fig. 6

The von Mises stress only under moderate normal preload w0* = 10 (shown in (a)–(c)) and under the additional tangential displacement ux*= 10 (shown in (d)–(f)) for some selected cases n = 0.1, 0.5, and 0.9

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Fig. 7

The dimensionless relations between the normal load P/P0 and the tangential displacement ux* under typical normal preloads w0*: (a) w0* = 10 and (b) w0* = 70

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Fig. 8

The distribution of the dimensionless contact pressure, p/Y0, along the contact radius under the initial normal preload w0* = 10 and the subsequent tangential loading process

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Fig. 9

The relation between the dimensionless contact area, A/A0, and the dimensionless tangential load, Q*, under two initial normal preloads w0*: (a) w0* = 3 and (b) w0* = 10



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