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Research Papers

Plastic Ploughing of a Sinusoidal Asperity on a Rough Surface

[+] Author and Article Information
H. Song, E. Van der Giessen

Zernike Institute for Advanced Materials,
University of Groningen,
Groningen 9747 AG, The Netherlands

R. J. Dikken, L. Nicola

Department of Materials Science
and Engineering,
Delft University of Technology,
Delft 2628CD, The Netherlands

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 21, 2014; final manuscript received December 30, 2014; published online June 3, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(7), 071006 (Jul 01, 2015) (8 pages) Paper No: JAM-14-1533; doi: 10.1115/1.4030318 History: Received November 21, 2014; Revised December 30, 2014; Online June 03, 2015

Part of the friction between two rough surfaces is due to the interlocking between asperities on opposite surfaces. In order for the surfaces to slide relative to each other, these interlocking asperities have to deform plastically. Here, we study the unit process of plastic ploughing of a single micrometer-scale asperity by means of two-dimensional dislocation dynamics simulations. Plastic deformation is described through the generation, motion, and annihilation of edge dislocations inside the asperity as well as in the subsurface. We find that the force required to plough an asperity at different ploughing depths follows a Gaussian distribution. For self-similar asperities, the friction stress is found to increase with the inverse of size. Comparison of the friction stress is made with other two contact models to show that interlocking asperities that are larger than ∼2 μm are easier to shear off plastically than asperities with a flat contact.

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References

Bowden, F. P., and Tabor, D., 1950, The Friction and Lubrication of Solids, Part I, Clarendon, Oxford, UK, Chap. 5.
Greenwood, J. A., and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, 295(1442), pp. 300–319. [CrossRef]
Gao, Y. F., and Bower, A. F., 2006, “Elastic-Plastic Contact of a Rough Surface With Weierstrass Profile,” Proc. R. Soc. London, Ser. A, 462(2065), pp. 319–348. [CrossRef]
Pei, L., Hyun, S., Molinari, J. F., and Robbins, M. O., 2005, “Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces,” J. Mech. Phys. Solids, 53(11), pp. 2385–2409. [CrossRef]
Cha, P. R., Srolovitz, D. J., and Vanderlick, R. K., 2004, “Molecular Dynamics Simulations of Single Asperity Contact,” Acta Mater., 52(13), pp. 3983–3996. [CrossRef]
Widjaja, A., Van der Giessen, E., Deshpande, V. S., and Needleman, A., 2007, “Contact Area and Size Effects in Discrete Dislocation Modeling of Wedge Indentation,” J. Mater. Res., 22(03), pp. 655–663. [CrossRef]
Sun, F., van der Giessen, E., and Nicola, L., 2012, “Plastic Flattening of a Sinusoidal Metal Surface: A Discrete Dislocation Plasticity Study,” Wear, 296(1–2), pp. 672–680. [CrossRef]
Deshpande, V. S., Needleman, A., Van der Giessen, E., 2004, “Discrete Dislocation Plasticity Analysis of Static Friction,” Acta Mater., 52(10), pp. 3135–3149. [CrossRef]
Dikken, R. J., Van der Giessen, E., and Nicola, L., “Plastic Shear Response of a Single Asperity: A Discrete Dislocation Plasticity Analysis,” (submitted).
Van der Giessen, E., and Needleman, A., 1995, “Discrete Dislocation Plasticity: A Simple Planar Model,” Model. Simul. Mater. Sci. Eng., 3, pp. 689–735. [CrossRef]
Rice, J. R., 1987, “Tensile Crack Tip Fields in Elastic-Ideally Plastic Crystals,” Mech. Mater., 6(4), pp. 317–335. [CrossRef]
Widjaja, A., Needleman, A., and Van der Giessen, E., 2007, “The Effect of Indenter Shape on Sub-Micron Indentation According to Discrete Dislocation Plasticity,” Model. Simul. Mater. Sci. Eng., 15(1), pp. 121–131. [CrossRef]
Johnson, K. L., 1985, Contact Mechanics, Cambridge University, Cambridge, UK, Chap. 2.

Figures

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Fig. 2

Two-dimensional model of a single asperity ploughed by a rigid asperity. Both asperities are characterized by a single sinusoidal wave of amplitude A and wavelength w. Plastic deformation inside the bottom crystal takes by the motion of edge dislocations on three slip systems.

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Fig. 1

Two rough surfaces in contact

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Fig. 11

Comparison of the friction stress (at U = 0.04 μm) predicted by the three models

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Fig. 12

Comparison between the ploughing model and the asperity contact model

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Fig. 9

Fraction of the amount of slip inside the asperity compared to the total slip in the plastic zone during ploughing for different sizes and shapes of the asperity

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Fig. 10

(a) Asperity-free contact model [8], (b) asperity contact model [9], and (c) ploughing model

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Fig. 3

Ploughing response of an asperity with w = 4 μm and amplitude A = 0.4 μm at depth Δ = 0.4 μm. (a) Force response of each realization. The thick curve is the average of 10 realizations, while the error bars denote the standard deviation. (b) The distribution of the shear stress normalized by τ¯nuc in the elastic regime (shown here at the moment that the ploughing force is 0.14 × 10−4N/μm as indicated by the dot in figure (a)) (see color figure online).

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Fig. 4

Influence of the source strength distribution on ploughing force Fp. The positions of the sources and the obstacles in the ten realizations are the same as in Fig. 3 (see color figure online).

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Fig. 5

(a) Ploughing response of an asperity with w = 4 μm and amplitude A = 0.4 μm at different depths Δ. (b) Distribution of all the friction forces F (at U = 0.04 μm) for all depths. The smooth curve is a Gaussian fit to the histograms (see color figure online).

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Fig. 14

Comparison of force and dislocation density between the Flamant boundary condition and the simple boundary condition for the asperity size w = 4 μm and A = 0.2 μm (see color figure online)

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Fig. 6

(a) Ploughing response of an asperity with w = 4 μm and amplitude A = 0.2 μm at different depths Δ. (b) Distribution of the friction forces F at U = 0.04 μm for all depths. The smooth curve is a Gaussian fit to the histograms (see color figure online).

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Fig. 8

Plastic shear strain for different asperity sizes after ploughing to U = 0.04 μm. (a) w = 1 μm, A = 0.05 μm, (b) w = 2 μm, A = 0.1 μm, (c) w = 4 μm, A = 0.2 μm, (d) w = 8 μm, A = 0.4 μm, (e) w = 4 μm, and A = 0.4 μm (see color figure online).

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Fig. 7

(a) Size dependence of the friction stress F/w at constant shape A/w = 0.05, when ploughing depth Δ = A, and displacement U = 0.04 μm. (b) Shear stress distribution according to Flamant's theoretical solution of a point force on a half-space (see color figure online).

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Fig. 13

Iteration procedure in the implementation of the Flamant boundary condition

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