Research Papers

Asperity Interaction and Substrate Deformation in Statistical Summation Models of Contact Between Rough Surfaces

[+] Author and Article Information
Antonis I. Vakis

Faculty of Mathematics and Natural Sciences,
University of Groningen,
Nijenborgh 4,
Groningen 9747 AG,Netherlands
e-mail: a.vakis@rug.nl

Manuscript received June 25, 2013; final manuscript received September 6, 2013; accepted manuscript posted September 12, 2013; published online October 16, 2013. Assoc. Editor: Anand Jagota.

J. Appl. Mech 81(4), 041012 (Oct 16, 2013) (10 pages) Paper No: JAM-13-1259; doi: 10.1115/1.4025413 History: Received June 25, 2013; Revised September 06, 2013; Accepted September 12, 2013

A method is proposed to account for asperity interaction and bulk substrate deformation in models that utilize statistical summation of asperity forces to characterize contact between rough surfaces. Interaction deformations of noncontacting asperities are calculated based on the probability that they have taller neighbors in their vicinity, whose deformation upon contact, in turn, induces local substrate deformations. The effect of the order of interaction on the total contact force is explored and a limit is proposed based on asperity density. The updated contact force accounting for asperity interaction is found to tend to a constant fraction of the nominal contact force at the mathematical limit of asperity contact independent of the order of interaction, roughness, or material properties. For contact in the vicinity of zero mean plane separation, rough surfaces are found to exhibit greater asperity interaction resulting in reduced contact forces. A simplified curve-fitted expression is introduced that can be used to account for asperity interaction by adjusting the nominal contact force predicted by other models.

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Fig. 1

Evolution of GW-type, rough surface contact (highly skewed aspect ratio): asperities with taller neighbors will experience interaction through substrate deformation, resulting in modified distributions of asperity heights

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Fig. 2

Schematic representation of the interaction between three neighboring asperities through substrate deformation (highly skewed aspect ratio)

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Fig. 3

Dimensionless contact force versus mean plane separation for up to first, eleventh, and fiftieth order interactions (σ = 10 nm, R = 0.5 μm, η = 100 μm−2, E* = 70 GPa, H = 9.6 GPa)

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Fig. 4

Closeup of the dimensionless contact force versus mean plane separation for up to first, eleventh, and fiftieth order interactions, including the prediction of Ciavarella et al.'s model

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Fig. 5

Normalized contact force versus interference comparison with Chandrasekar et al.'s analytical model and FE results

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Fig. 6

Comparison of cumulative interaction deformation for up to first, eleventh, and fiftieth order of interaction with normal (nominal) asperity height distribution. The maximum dimensionless first order interaction deformation (black cross marks) is 7.6 × 10−4 at d* ≈ −0.8.

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Fig. 7

Ratio of new to nominal contact force versus mean plane separation for up to fiftieth order interactions. Arrow indicates direction of increasing order of interaction.

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Fig. 8

Ratio of new to nominal contact force at zero mean plane separation as a function of the order of interaction

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Fig. 9

Results of variable roughness 32 full factorial study (E* = 70 GPa, H = 9.6 GPa). The roughness parameter β = σRη increases in the direction of the arrow.

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Fig. 10

Results of variable material properties 32 full factorial study (σ = 10 nm, R = 0.5 μm, and η = 100 μm−2)

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Fig. 11

Curve fits to full model results for minimum and maximum roughness parameter β

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Fig. 12

Snapshot of 500th test counting the number of noncontacting asperities for d* = 1 that lie within r < r2 (σ = 10 nm, R = 0.5 μm, and η = 100 μm−2)

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Fig. 13

Asperities found to lie within second order cut-off circle over 500 tests for zref* = 1

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Fig. 14

Comparison of the number of asperities shorter than the reference and lying within the second interaction order cut-off circle predicted analytically and found from numerical experiments as a function of dimensionless mean plane separation (d* = zref*)





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