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Review Articles

Dry and Wet Contact Modeling of Multilayered Rough Solid Surfaces

[+] Author and Article Information
Bharat Bhushan1

Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM), The Ohio State University, 201 West 19th Avenue, Columbus, OH 43210-1142bhushan.2@osu.edu

Shaobiao Cai

Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM), The Ohio State University, 201 West 19th Avenue, Columbus, OH 43210-1142

1

Corresponding author.

Appl. Mech. Rev 61(5), 050803 (Sep 08, 2008) (34 pages) doi:10.1115/1.2972161 History: Received January 31, 2008; Revised June 02, 2008; Published September 08, 2008

Adhesion, friction/stiction, and wear are among the main issues in various commercial applications, including magnetic storage devices, microelectromechanical systems, and nanoelectromechanical systems, having contact interfaces with normal or tangential motion. The contact analysis of multilayered structures under both dry and wet conditions with and without relative motion, which simulates the actual contact situations of the devices, is needed to obtain optimum design parameters, including materials with desired mechanical properties and layer thicknesses. The contact analyses have been used to predict the contact pressure profile on the interface and contact statistics, namely, fractional contact area, the [value of contact pressure, von Mises, principal tensile and shear stresses, and relative meniscus force. The early work does not consider surface roughness and this has been carried out in the later studies for single and multilayered solid surfaces. A numerical three-dimensional multilayered rough contact model is presented in detail to investigate the effects of roughness, stiffness, hardness, layer thicknesses, load, coefficient of friction, and meniscus contribution. Applications of the model to magnetic storage devices are presented.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 5

Schematics of (a) 3D profiles of two rough surfaces in contact with one or two layers, and (b) top view of contact regions

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Figure 6

(a) Definition of strain energy and complementary energy; (b) relationship between elastic strain energy and internal complementary energy for a linear elastic or a linear elastic–perfectly plastic material

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Figure 7

Schematics of surface discretization at the contact interface, 3D view (a) in space domain, (b) in space domain, and (c) in frequency domain

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Figure 8

(a) Geometrical interference area and real area of contact in the normal contact of two identical spheres, and (b) determination of the total prescribed z-direction surface displacement from geometrical interference

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Figure 9

Surface height maps of three computer generated rough surfaces (37)

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Figure 10

Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the maximum J2 plane, principal tensile stresses on the maximum σt plane, and shear stresses on the maximum σxz plane with H3∕E3=0.05, h1∕σ=h2∕σ=10, H1=H2=H3, E3=100GPa, and σ=1nm, β*=0.5μm; σ=10nm, β*=0.5μm; and σ=1nm, β*=0.05μm, pn∕E3=4×10−6. The vertical scale representing pn axis is magnified (37).

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Figure 19

At different values of E1∕E3, E2∕E3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=4×10−6, h1∕σ=h2∕σ=10, H1=H2=H3, E3=100GPa, variation of maximum stresses with coefficient of friction, (a) von Mises stress, (b) tensile stress, and (c) shear stress (39)

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Figure 26

Variation of relative meniscus force with normal pressure pn for H3∕E3=0.05 at different values of E1∕E3, E2∕E3 with H1=H2=H3, E3=100GPa and h1=h2=1nm for three roughness cases with σ=1nm and β*=0.5 and 0.05, and σ=10nm and β*=0.5μm

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Figure 27

Cross-sectional schematic of magnetic storage media: thin-film rigid disk

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Figure 28

Schematic showing normal and shear stresses acting on a volume element

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Figure 17

At different values of E1∕E3, E2∕E3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=4×10−6, h1∕σ=h2∕σ=1, H1=H2=H3, E3=100GPa, and μ=0.5, profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the maximum J2 plane, principal tensile stresses on the maximum σt plane, and shear stresses on the maximum σxz plane (39)

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Figure 1

Various methods classified into several categories: direct, weighted residual, and minimum total potential energy formulations in radial direction; analytical and numerical (FDM, FEM, or BEM) methods in circumferential direction. Among them, the analytical weighted residual formulation applies exclusively to single asperity contact, and the numerical direct formulation and minimum total potential energy formulation apply to both single asperity contact and multiple asperity contact (35).

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Figure 2

(a) Schematic of a sphere in contact with a layered half-space, and (b) profile of contact pressures beneath sphere at various E1∕E2(21,26)

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Figure 3

Contours of J2∕p0 at y=0 at various E1∕E2 and coefficient of friction μ(21)

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Figure 4

(a) Profiles of a rough sphere with R=0.0137mm, and corresponding contact pressures and z-direction surface displacements at the contact interface; and (b) contours of von Mises stresses (in GPa) on x-z plane through the center of the rough sphere in a homogenous half-space (top), and a layered half-space (bottom) (20)

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Figure 11

Variation of maximum pressure, and fractional real area of contact with normal pressure pn for different values of E1∕E3, E2∕E3, H3∕E3=0.05, h1∕σ=h2∕σ=10, H1=H2=H3, E3=100GPa, and (a) σ=1nm, β*=0.5μm, (b) σ=10nm, β*=0.5μm, and (c) σ=1nm, β*=0.05μm(37). The arrows indicate the transition from elastic to elastic–perfectly plastic deformation.

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Figure 12

Variation of maximum displacement with normal pressure pn for different values of E1∕E3, E2∕E3, σ=1nm, β*=0.5μm, H3∕E3=0.05, h1∕σ=h2∕σ=10, and H1=H2=H3, E3=100GPa(37). The arrow in the figure indicates the transition from elastic to elastic–perfectly plastic deformation.

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Figure 18

At different values of E1∕E3, E2∕E3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=4×10−6, h1∕σ=h2∕σ=1, H1=H2=H3, E3=100GPa, variation of maximum stresses with coefficient of friction, (a) von Mises stress, (b) tensile stress, and (c) shear stress (39)

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Figure 20

At different values of H1∕H3, H2∕H3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=1×10−5, h1∕σ=h2∕σ=1, E1=E2=E3=100GPa, μ=0.5, profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the maximum J2 plane, principal tensile stresses on the maximum σt plane, and shear stresses on the maximum σxz plane (39)

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Figure 21

At different values of H1∕H3, H2∕H3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=1×10−5, h1∕σ=h2∕σ=1, E1=E2=E3=100GPa, variation of maximum stresses with coefficient of friction, (a) von Mises stress, (b) tensile stress, and (c) shear stress (39)

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Figure 22

At different values of H1∕H3, H2∕H3, σ=1nm, β*=0.5μm, H3∕E3=0.05, pn∕E3=1×10−5, h1∕σ=h2∕σ=10, E1=E2=E3=100GPa, variation of maximum stresses with coefficient of friction, (a) von Mises stress, (b) tensile stress, and (c) shear stress (39)

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Figure 23

Schematic of a rough surface in contact with a smooth surface in the presence of a liquid film

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Figure 24

Variation of relative meniscus force with normal pressure pn for σ=1nm, β*=0.5μm, H3∕E3=0.05 at different values of E1∕E3, E2∕E3 for h1∕σ=h2∕σ=10 and h1∕σ=h2∕σ=1 with H1=H2=H3, E3=100GPa(38)

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Figure 25

Variation of relative meniscus force with normal pressure pn for σ=1nm, β*=0.5μm, H3∕E3=0.05 at different values of H1∕H3, H2∕H3 for three homogeneous cases and h1∕σ=h2∕σ=1 with E1=E2=E3=100GPa(38). The arrows in the figure indicate the transition from elastic to elastic-perfectly plastic deformation

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