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Research Papers

Elastic-Plastic Analysis of Adhesive Sliding Contacts

[+] Author and Article Information
H. Xu

Research Assistant

K. Komvopoulos

Professor
Fellow ASME
e-mail: kyriakos@me.berkeley.edu
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720

1Corresponding author.

Manuscript received April 3, 2012; final manuscript received September 30, 2012; accepted manuscript posted October 8, 2012; published online May 16, 2013. Assoc. Editor: Krishna Garikapati.

J. Appl. Mech 80(4), 041010 (May 16, 2013) (11 pages) Paper No: JAM-12-1134; doi: 10.1115/1.4007788 History: Received April 03, 2012; Revised September 30, 2012; Accepted October 08, 2012

The effect of adhesion on the elastic-plastic deformation of sliding contacts was examined with the finite element method. The adhesive interaction of a rigid asperity moving over a homogeneous elastic-plastic half-space was modeled by nonlinear springs obeying a constitutive law derived from the Lennard–Jones potential. The effects of the work of adhesion, interaction distance (interfacial gap), Maugis parameter, and plasticity parameter (defined as the work of adhesion divided by the half-space yield strength and the intermolecular equilibrium distance) on the evolution of the normal and friction forces, subsurface stresses, and plastic deformation at steady-state sliding are interpreted in light of finite element results of displacement-control simulations of sliding contact. The normal and friction forces and the rate of energy dissipation due to plastic deformation at steady-state sliding sharply increase with the interaction distance. Although a higher work of adhesion produces a lower normal force, it also intensifies the friction force, enhances material pile-up ahead of the sliding asperity, and exacerbates the asymmetry of both the deformed surface profile and the normal stress field. The variation of the normal force with the plasticity parameter is explained by the dominant effect of subsurface plastic deformation above a critical plasticity parameter. Simulation results are shown to be in good agreement with those of previous experimental and numerical studies.

Copyright © 2012 by ASME
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Figures

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Fig. 1

(a) Schematic of a cylinder (asperity) moving over a half-space, and (b) finite element mesh of the half-space

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Fig. 2

Cross-sectional schematic of a cylindrical asperity in close proximity with a half-space. Adhesion forces are modeled by nonlinear springs attached to the asperity center and surface nodes of the half-space.

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Fig. 3

Illustration of the method used to obtain the interaction energy of macroscopic solid bodies from the interaction energy of atoms: (a) a single atom close to a line of atoms, (b) a single atom close to a cylindrical asperity, and (c) a column of atoms in a half-space close to a cylindrical asperity

Grahic Jump Location
Fig. 4

Solutions of the pull-off force Fpo/(E*RΔγ2)1/3 versus the Maugis parameter λ obtained from different 2D adhesion models of elastic line contact: (-·-·-) Bradley model, (----) DMT model, (....) JKR model, (——) Maugis model (Johnson and Greenwood [18]), (---) numerical solution (Wu [19]), and (○) this study

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Fig. 5

(a) Normal force L/RΔγ and (b) friction force F/RΔγ versus sliding distance xs/ɛ for δ/ɛ = −0.933, −0.466, 0, 0.466, and 0.933, λ = 0.306, and S = 1.46

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Fig. 6

Friction force F/RΔγ versus normal force L/RΔγ at steady-state sliding for λ = 0.306 and S = 1.46

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Fig. 7

(a) Normal force L/RΔγ due to sliding and indentation, (b) friction force F/RΔγ, and (c) rate of energy dissipation in the form of plastic deformation E·p/RΔγ versus interaction distance δ/ɛ for λ = 0.306 and S = 1.17, 1.30, and 1.46. Sliding results are for steady-state sliding.

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Fig. 8

Distributions of normal stress σyy/Y at steady-state sliding for δ/ɛ equal to (a) −0.466, (b) 0, (c) 0.466, and (d) 0.933, λ = 0.306, and S = 1.46. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 9

Distributions of equivalent plastic strain ɛeqp at steady-state sliding for δ/ɛ equal to (a) −0.466, (b) 0, (c) 0.466, and (d) 0.933, λ = 0.306, and S = 1.46. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 10

Deformed surface profiles at steady-state sliding for δ/ɛ = −0.933, −0.466, 0, 0.466, and 0.933, λ = 0.306, and S = 1.46. Note the significantly different scales on the x- and y-axis. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 11

(a) Normal force L/RΔγ due to sliding and indentation and (b) friction force F/RΔγ versus work of adhesion Δγ/E*R for δ/ɛ = 0 and E*/Y = 110. Sliding results are for steady-state sliding.

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Fig. 12

Distributions of normal stress σyy/Y at steady-state sliding for δ/ɛ = 0 and E*/Y = 110: (a) Δγ/E*R = 2.28 × 10−5 (λ = 0.193, S = 0.59), (b) Δγ/E*R = 4.57 × 10−5 (λ = 0.306, S = 1.17), (c) Δγ/E*R = 5.71 × 10−5 (λ = 0.355, S = 1.46), and (d) Δγ/E*R = 8.15 × 10−5 (λ = 0.450, S = 2.09). The center of the sliding asperity is at x/ɛ = 0.

Grahic Jump Location
Fig. 13

Distributions of equivalent plastic strain ɛeqp at steady-state sliding for δ/ɛ = 0 and E*/Y = 110: (a) Δγ/E*R = 2.28 × 10−5 (λ = 0.193, S = 0.59), (b) Δγ/E*R = 4.57 × 10−5 (λ = 0.306, S = 1.17), (c) Δγ/E*R = 5.71 × 10−5 (λ = 0.355, S = 1.46), and (d) Δγ/E*R = 8.15 × 10−5 (λ = 0.450, S = 2.09). The center of the sliding asperity is at x/ɛ = 0.

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Fig. 14

Deformed surface profiles at steady-state sliding for δ/ɛ = 0, E*/Y = 110, and Δγ/E*R = 2.28 × 10−5 (λ = 0.193, S = 0.59), 5.71 × 10−5 (λ = 0.355, S = 1.46), and 8.15 × 10−5 (λ = 0.450, S = 2.09). Note the significantly different scales on the x- and y-axis. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 15

(a) Normal force L/RΔγ due to sliding and indentation and (b) friction force F/RΔγ versus plasticity parameter S for δ/ɛ = –0.466, 0, and 0.466 and λ = 0.306. Sliding results are for steady-state sliding.

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Fig. 16

Distributions of equivalent plastic strain ɛeqp at steady-state sliding for δ/ɛ = 0, S = 1.46, and λ equal to (a) 0.105, (b) 0.193, (c) 0.306, and (d) 0.485. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 17

Distributions of equivalent plastic strain ɛeqp at steady-state sliding for δ/ɛ = 0, S = 1.17, and λ equal to (a) 0.105, (b) 0.193, and (c) 0.306. The center of the sliding asperity is at x/ɛ = 0.

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Fig. 18

(a) Normal force L/RΔγ due to sliding and indentation and (b) friction force F/RΔγ versus Maugis parameter λ for δ/ɛ = 0 and S = 1.46 and 1.17. Sliding results are for steady-state sliding.

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