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Research Papers: Contact Mechanics

Multiple Contacts of Similar Elastic Materials

[+] Author and Article Information
N. Sundaram1

School of Aeronautics and Astronautics, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907-2045nsundara@purdue.edu

T. N. Farris

School of Aeronautics and Astronautics, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907-2045farrist@purdue.edu

It is also possible to arrive at the same results based on considerations of normal displacement continuity at the surface.

This technique is pervasive in the computational contact literature.

Flat regions in the profile are a special case.

Again, these techniques rely on path independence and would fail otherwise (e.g., dissimilar material contacts in the presence of friction).

1

Corresponding author.

J. Tribol 131(2), 021405 (Mar 05, 2009) (11 pages) doi:10.1115/1.3078772 History: Received June 24, 2008; Revised January 08, 2009; Published March 05, 2009

The contact problem for an elastic body indenting a similar half-space resulting in multiple contacts is important for various applications. In this paper an exact fast numerical method based on singular integral equations is developed to solve the normal contact (including applied moments), partial slip, and shear-reversal problems for such contacts. The contact patches are considered to be fully interacting, with no simplifying assumptions. A contact algorithm to automatically generate trial values based on an analysis of the profile and to subsequently guide the solver toward convergence is detailed. Some applications are discussed, including regular rough cylinders and a regularly rough flat punch with rounded edges. The examples involve between 3 and 29 contacts. The partial slip problems include demonstration of cases with multiple stick zones in some contact patches and complete sliding in others.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Indentation of a half-space forming multiple contacts

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Figure 2

SIE normalized pressure tractions p(x)/p∗ for indentation of a half-space by a polynomial punch. The applied normal loads are P0/F∗=0.225 and 0.750, and the applied moments are M0/M∗=−0.06 and −0.20, respectively, at the two stages of loading.

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Figure 3

SIE (solid lines) normalized pressure tractions p(x)/pHzmax for indentation of a half-space by a regular rough cylinder with superimposed Hertzian tractions (dashed line). The pressures are normalized to the peak Hertzian pressure and the x-axis to the Hertzian contact half-length.

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Figure 4

SIE normalized postcontact gap function gap(x)/Δ for indentation of a half-space by a regular rough cylinder. The x-axis is normalized to the Hertzian contact half-length.

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Figure 5

Normalized subsurface stresses σxx/pHzmax for the rough cylinder (left) and smooth cylinder (right) for the same applied load, material properties, and cylinder radius

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Figure 6

Normalized pressure tractions (solid lines) obtained using the SIE solver when roughness is added to the flat with rounded indenter for applied loads of P0=1208 N/mm and zero moment. The roughness wavelength equals R/15 in all cases, and the amplitudes are (clockwise from the top left) λ/160, λ/640, λ/1600, and λ/800. The dashed line in each plot shows the pressure traction obtained when there is no roughness (Δ=0).

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Figure 7

Normalized pressure tractions (solid lines) obtained using the SIE solver when roughness is added to the c=R/2 flat with rounded indenter for applied loads of P0=1208 N/mm and M0=400 N-mm/mm. The amplitudes are the same in both cases (Δ=R/12,000), and the wavelengths are λ=600Δ (left) and λ=400Δ (right). The dashed line in each plot shows the pressure traction obtained when there is no roughness (Δ=0).

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Figure 8

SIE normalized shear tractions q(x)/μpHzmax for a regular rough cylinder in load step 2 with Q/μP0=0.45 and σ0/μpmax=−0.15 and load step 3 with both Q and σ0=0. The discontinuous lines indicate full sliding everywhere and are included to easily identify the slip zones.

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Figure 9

SIE normalized shear tractions q(x)/μpHzmax for a regular rough cylinder with Q/μP0=0.6 and σ0/μpmax=0.26 in load step 2 and Q and σ0 fully reversed in load step 3. The outer contacts are in full sliding, and the inner contact has five stick zones. The shear traction in the smooth case is also superimposed. The discontinuous lines indicate full sliding everywhere and are included to easily identify the slip zones.

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Figure 10

SIE normalized slip functions s(x)/Δ for a regular rough cylinder with Q/μP0=0.6 and σ0/μpmax=0.26 in load step 2 and Q and σ0 fully reversed in load step 3. The slip function in the smooth case is also superimposed (dashed line). The outer contacts are in full sliding, and the inner contact has five stick zones.

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Figure 11

SIE normalized shear traction q(x)/μpΔ=0max for a rough flat with a rounded punch in load step 2 with Q/μP0=0.7 and σ0/μpmax=0.40. The shear traction in the smooth case (Δ=0) is also superimposed. The eight leftmost contacts are in sliding, and the other 11 are in partial slip.

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