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REVIEW ARTICLES

Contact mechanics of multilayered rough surfaces

[+] Author and Article Information
Bharat Bhushan, Wei Peng

Department of Mechanical Engineering, Nanotribology Laboratory for Information Storage and MEMS/NEMS, Ohio State University, Columbus OH 43210-1107; bhushan.2@osu.edu

Appl. Mech. Rev 55(5), 435-480 (Sep 11, 2002) (46 pages) doi:10.1115/1.1488931 History: Online September 11, 2002
Copyright © 2002 by ASME
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Figures

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Contours of J2/p0 at y=0 at various E1/E2 and coefficient of friction μ 59.
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Variation of the maximum contact pressure pmax and half contact width a with layer thickness h at various γ=E1/E223.
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3D finite element mesh of the layered half-space in the first octant indented by a rigid sphere centered along z-axis, the inset is the magnified finer meshed region at the contact interface 34.
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Variation of Cuz(0,0,0), the influence coefficient corresponding to z-direction surface displacement at the origin, with layer thickness h at various E1/E2, for a homogeneous 62 and a layered elastic half-space.
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Profiles of von Mises stresses (in pressure unit) on the surface and in the subsurface (x=0.3 unit in length, y=0) at various E1/E2 and coefficient of friction μ 22.
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Schematic of a smooth surface in contact with a composite rough surface in the presence of a liquid film.
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Flowchart of a 3D layered rough surfaces contact model based on a variational principle and FFT.
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Profiles of two computer generated rough surfaces. The lower surface (σ=2 nm, β* =1 μm) is magnified twice and cut off at the 20×20 μm2 margin to obtain the upper surface (σ=1 nm, β* =0.5 μm).
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Variation of Ar/An,pmax/E2, and Fm/W with pn/E2 at various E1/E258.
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Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max σt plane, and shear stresses on the max σxz plane at various E1/E2, with σ=1 nm, β* =0.5 μm, pn/E2=4×10−6,h=1 μm. All contours are plotted after taking natural log values of the calculated stresses (in kPa). Negative values of σt and σxz in the plot represent the compressive stress and shear stress along the negative x direction, respectively 22.
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Various methods classified into several categories: direct, weighted residual, and minimum total potential energy formulations in radial direction; analytical and numerical (Finite Difference Method or FDM, Finite Element Method or FEM, Boundary Element Method 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.
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Schematic of a smooth cylinder in contact with a layered half-space.
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Schematic of a smooth sphere in contact with a layered half-space.
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Profile of contact pressures beneath sphere at various E1/E21659.
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Stress components along z-axis at various E1/E2 and coefficient of friction μ (σxz is plotted along the line x/a0=0.5,y=0) 59.
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Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max σt plane, and shear stresses on the max σxz plane at various layer thickness h with a) E1/E2=2 and b) E1/E2=0.5. μ=0.5 22.
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Cross sectional schematic of a typical thin-film magnetic disk.
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Variation of σ with scan size for two glass ceramic substrates (GC1 and GC2) and corresponding finished magnetic disks (GC1f and GC2 f), Ni-P coated Al-Mg substrate (Ni-P), and glass substrate (G1) measured by atomic force microscope (AFM), stylus profiler (SP) and non-contact optical profiler (NOP) 84.
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Variation of Ar/An, δ, pmax/E2, and Fm/W with layer thickness h at various E1/E2 and a) σ=0.1 nm, b) σ=1 nm, and c) σ=10 nm, in the normal contact of a rigid head-slider on elastic-perfectly plastic disk in the presence of a liquid film 84.
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Schematics of a) two identical half circles in contact and b) a flat surface in contact with a composite half ellipse.
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Contours of von Mises stresses (in GPa) on x-z plane through the center of the rough sphere in a) a homogenous half-space and b) a layered half-space 48.
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Schematics of a) rough surface in contact with a layer rough surface and b) top view of contact regions.
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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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Schematics of surface discretization at the contact interface, a) 3D view in space domain, b) top view in space domain, and c) top view in frequency domain.
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a) Geometrical interference area and real contact area 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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Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max σt plane, and shear stresses on the max σxz plane at various E1/E2, with σ=0.1 nm, β* =0.5 μm, pn/E2=4×10−7,h=1 μm22.
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Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max σt plane, and shear stresses on the max σxz plane at various E1/E2, with σ=2 nm, β* =1 μm, pn/E2=4×10−6,h=2 μm22.
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Variation of Ar/An with pn/E2β*/σ and pmax/E2 with [pn/E2(σ/β*)2]1/3 at various E1/E2. These values are independent of β* and μ 22.
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Profiles of a) a composite layered rough surface and b) corresponding contact pressures at various h and E1/E2. These values are independent of μ.
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Variation of Ar/An,pmax/E2, and Fm/W with layer thickness h at various E1/E2. These values are independent of μ.
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Profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max σt plane, and shear stresses on the max σxz plane at various layer thickness h with a) E1/E2=2 and b) E1/E2=0. μ=0 59.
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Contours of εeqpxx and σyy in the quadrant (y>0,z>0) at sliding distance Δx equal to a) 2ay,b) 4ay,c) 8ay, and d) 12ay, with E1/E2=H1/H2=2,μ=0.1,W/WY=100.ay and WY represent the sliding distance and normal loading corresponding to the initial yield condition of the substrate, respectively 34.
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Profiles of a) the nominally flat rough surface being superposed on the smooth cylinder and b) corresponding contact pressures. The smooth curve is contact pressure profile of the smooth cylinder in Hertzian contact 45.
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Profiles of contact pressures at various layer thickness h and coefficients of friction μ with a) E1/E2=0.17 and b) E1/E2=3.245.
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Profiles of a rough sphere with R=0.0137 μm, and corresponding contact pressures and z-direction surface displacements at the contact interface 48.

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