Review Articles

Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies

[+] Author and Article Information
Izhak Etsion

Department of Mechanical Engineering, Technion, Haifa 32000, Israeletsion@technion.ac.il

J. Tribol 132(2), 020801 (Apr 26, 2010) (9 pages) doi:10.1115/1.4001238 History: Received July 13, 2009; Revised February 03, 2010; Published April 26, 2010; Online April 26, 2010

The Cattaneo–Mindlin concept of interfacial slip in tangentially loaded compliant bodies is revisited and its basic simplifying assumptions are critically examined. It is shown that these assumptions, which, in the absence of modern numerical techniques, were essential in 1949 to enable an elegant quantitative solution of the basic problem of presliding between contacting bodies, may be nonphysical. An alternative approach to the same problem that is based on treating sliding inception as a failure mode involving material plastic yield is discussed. This alternative approach was suggested even before 1949 but for the same lack of modern numerical techniques could only be promoted qualitatively. Some recent theoretical models, which are based on this earlier alternative approach, and in which the simplifying assumptions of the Cattaneo–Mindlin concept were completely relaxed, are described along with their experimental verification. It is shown that the presliding problem between contacting bodies can be accurately solved by these models using realistic physical assumptions and failure criterion.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Shear stress distribution showing the case of no slip in comparison with that when a slip is assumed over an annulus where τ=μp

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Figure 2

The contact of a deformable sphere and a rigid flat

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Figure 3

Typical junction growth formation obtained with a 3 mm copper sphere loaded against a sapphire flat (10) (the direction of the tangential load is shown by the dashed arrow). A superposition of two in situ contact area images where the inner darker image was captured at normal preload alone and the larger brighter image was captured at sliding inception is shown in part (a), and the non-in situ images of the contact area imprint due to the normal preload alone, and after sliding inception are shown in parts (b) and (c), respectively.

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Figure 5

Spherical contact under combined normal and tangential loading (25)

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Figure 6

The dimensionless tangential load Q/P versus the dimensionless tangential displacement ux/ω0 for different normal preloads P∗(25).

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Figure 10

Spherical specimens and a detailed close up of the friction force measurement module

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Figure 11

A comparison of the experimental results (27) and the prediction of the theoretical model in Ref. 25 for the static friction coefficient of various copper (Cu) and steel (St) spheres versus the dimensionless normal preload P∗

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Figure 12

A comparison of the experimental results (10,28) and the prediction of the theoretical model in Ref. 29 for the junction growth of various copper (Cu) and steel (St) spheres versus the dimensionless normal preload P∗

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Figure 14

The evolution of plastic region in the symmetry plane, for P∗=1 at the completion of normal preload (represented by the single point at x/ac=0), and at sliding inception (the solid line) (25). This case corresponds to that shown in Fig. 8.

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Figure 13

SEM images of damaged colloidal probes that were obtained under various fretting loading conditions: (a) displacement amplitude 25 nm, normal load 20.4 μN, 1015 fretting cycles; and (b) displacement amplitude 6 nm, normal load 19.6 μN, 3315 fretting cycles (38)

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Figure 9

Schematic representation of the experimental setup with four modules: (I) actuation module consisting of a parallelogram frame (1), mechanical lever (2), piezoelectric actuator (3), and proximity probe (4); (II) friction force measurement module (5); (III) normal force module (6); and (IV) optical module (7)

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Figure 8

The dimensionless contact pressure p/Y0, shear stress τxz/Y0, and friction coefficient τxz/p distributions over the contact diameter in the symmetry plane, at sliding inception for P∗=1 (a), 10 (b), and 100 (c) (25)

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Figure 7

The dimensionless contact pressure distribution over the contact diameter in the symmetry plane, after normal preload (dashed line), at Q=0.5Qmax, and at sliding inception (solid lines), for P∗=10(25). The flat slides from right to left.

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Figure 4

The mechanism of junction growth demonstrated with a 5 mm copper sphere loaded against a sapphire flat (10): non-in situ spherical surface image prior to loading showing micro indentation markers (a). In situ contact area images at tangential loads: Q=0 (b), 0.5Qmax (c), 0.75Qmax (d), and Qmax (e), showing the increasing number of indentations inside the contact area without a change in the distance between them. Post-test non-in situ surface area imprint (f), with the dashed circle corresponding to the image in (b).




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