Research Papers: Contact Mechanics

Semi-Analytical Viscoelastic Contact Modeling of Polymer-Based Materials

[+] Author and Article Information
W. Wayne Chen

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208

Q. Jane Wang1

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208qwang@northwestern.edu

Z. Huan, X. Luo

 United Technology Research Center, East Hartford, CT 06108


Corresponding author.

J. Tribol 133(4), 041404 (Oct 14, 2011) (10 pages) doi:10.1115/1.4004928 History: Received November 16, 2010; Revised June 07, 2011; Accepted June 20, 2011; Published October 14, 2011; Online October 14, 2011

Contact of viscoelastic materials with complicated properties and surface topography require numerical solution approaches. This paper presents a 3-D semianalytical contact model for viscoelastic materials. With the hereditary integral operator and elastic-viscoelastic correspondence principle, surface displacement is expressed in terms of viscoelastic creep compliance and contact pressure distribution history in the course of a contact process. Through discretizing the contact equations in both spatial and temporal dimensions, a numerical algorithm based on the robust Conjugate Gradient method and Fast Fourier transform has been developed to solve the normal approach, contact pressure, and real contact area simultaneously. The transient contact analysis in the time domain is computationally expensive. The fast Fourier transform algorithm can help reduce the computation cost significantly. The comparisons of the new numerical results with an analytical viscoelastic contact solution for Maxwell materials and with an indentation test measurement reported in the literature has validated and demonstrated the accuracy of the proposed model. Moreover, the present model has been used to simulate the contact between a polymethyl methacrylate (PMMA) substrate and a rigid sphere driven by step, ramped, and harmonic normal loads. The validated model and numerical method can successfully compute the viscoelastic contact responses of polymer-based materials with time-dependent properties and surface roughness subjected to complicated loading profiles.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematics of the generalized Weichert viscoelasticity model

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Figure 2

Normal contact of a rigid sphere with a viscoelastic half-space

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Figure 3

Comparison between the present model and Radok and Lee’s [2] solution: pressure distribution history beneath the spherical indenter (the substrate is a Maxwell viscoelastic material with the relaxation time of τ=η/g; a0 and p0 are Hertz radius and peak pressure based on the instantaneous modulus, ψr(0)=g)

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Figure 4

Measured relaxation modulus function of the PMMA material from a standard uniaxial compression test by Kumar and Narasimhan [20]

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Figure 5

Comparison between the numerical simulation result and experimental measurement by Kumar and Narasimhan [20]: load-displacement curves for a spherical indentation on a PMMA half-space (subjected to a triangular loading history with loading rate λ 10 N/sec)

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Figure 6

Contact pressure distributions of a spherical indentation with a triangular loading history: simulation results at the peak load (100 N) and at two moments in the loading and unloading stages when the indentation load equals 30 N

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Figure 7

Contact simulation results of a sphere on a viscoelastic half-space at different loading rates: (a) contact pressure distribution, and (b) indentation load versus depth curve

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Figure 8

Viscoelastic contact simulation with computer-generated rough surfaces: contact area evolution with time

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Figure 9

Contact area maps on surfaces with RMS roughness Rq  = 5 um (blue regions are in contact): (a) at the time t = 0 sec, and (b) at the time t = 300 sec

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Figure 10

Variations of contact approach response and indentation load excitation with time from the numerical simulation (the frequency of harmonic load is ω = 0.0092 sec−1 )

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Figure 11

Contact approach amplitude versus the excitation load frequency: comparison between the numerical results and the analytical solutions with the approach by Huang [19]

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Figure 12

Hysteresis curves of indentation load versus approach at two different excitation load frequencies of ω = 0.0092 and 0.3 sec−1 (area enclosed by the curve represents the hysteresis energy loss per loading cycle)

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Figure 13

Hysteresis energy loss per loading cycle versus the excitation load frequency: comparison between the numerical results and the analytical solutions in Eq. (25)




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