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Contact Mechanics

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Tribology for Scientists and Engineers

Abstract

Contact mechanics is a fundamental field of tribology and generally refers to the interaction of solid surfaces. This interaction or contact can occur on many different scales, ranging from nanoscale asperities up to tires on roads and even contact between tectonic plates. This chapter reviews the basic technical information available in predicting the contact area, pressure, stresses, and forces that occur when surfaces interact. The chapter considers different geometries such as spheres and wavy surfaces and also outlines how to consider elastic and plastic deformation. The phenomena of creep and adhesion that are important for many tribological applications, and especially biological contacts, are also discussed. Finally, the chapter concludes by covering methods used to model the complicated situation of contact between rough surfaces that contain many different geometrical features.

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Notes

  1. 1.

    In this notation, the colon (:) marks a reduction of the full tensor grade by 2; i.e., a multiplication of a tensor of the fourth grade with a tensor of the second grade yields a tensor of second grade.

Abbreviations

a :

Radius of circular contact area

A :

Area of contact

An :

Nominal or apparent area of contact

b :

Cylindrical contact half width

B :

Aspect ratio

C :

Critical yield stress coefficient

Cn :

Creep material constant

d :

Distance between the mean of the surface peaks and a material and geometry dependent exponent

e :

Coefficient of restitution during impact

e y :

Plastic strain (ratio of yield strength to effective elastic modulus)

E :

Elastic modulus

E′:

Reduced or effective elastic modulus

f :

Spatial frequency (reciprocal of wavelength)

F :

Contact force

h :

Height of sinusoidal surface from base and distance between the mean of the surface heights

i :

Scale or frequency number

I :

Statistical contact integral

H :

Hardness or normalized layer thickness

L :

Length of cylindrical contact

m :

Mass of impact sphere

m n :

nth spectral moment of the surface

N :

Number of asperities or data points on surfaces

p :

Average pressure over entire sinusoidal surface in contact

p*:

Average pressure for complete contact (elastic)

p * ep :

Average pressure for complete contact (elastoplastic)

p ave :

Average pressure over entire asperity

P :

Spherical contact force

Q max :

Tangential load required cause sliding

R :

Radius of cylinder or sphere or asperity tip

S y :

Yield strength

t :

Time or layer thickness

T :

Temperature

V :

Velocity

W nm :

Work of adhesion between surfaces n and m

x :

Lateral surface coordinate

y s :

Distance between the mean of the surface peaks and mean of the surface heights

z :

Surface height at location x

α :

Layer model parameter and statistical contact parameter

β :

Exponential creep material constant and surface roughness parameter

γ n :

Surface energy of surface n

γ nm :

Interfacial energy between surfaces n and m

Δ:

Amplitude of the sinusoidal surface

δ:

Deflection of cylindrical or sinusoidal asperity surface

ε :

Strain

θa :

Adhesion parameter

κ :

Layer model parameter

λ:

Asperity wavelength or layer model parameter

μ :

Effective static friction coefficient

η :

Areal asperity density

φ :

Asperity height distribution

σ:

Normal stress and RMS surface roughness

σ s :

The RMS roughness of the asperity peak heights

v :

Poisson’s ratio

ω :

Deflection or interference of spherical contact

ψ:

Plasticity index

o :

Initial or at t = 0

1, 2 :

Property for material 1, 2, etc.

c :

Critical value at onset of plastic deformation

cr :

Creep dependent parameter

a :

Elastic area

ep :

Elastic-plastic

max :

Maximum

n :

Normal direction and nominal or apparent area of contact

p :

Elastic-plastic or elastic pressure integral

r :

Real area of contact

t :

Tangential

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Authors and Affiliations

  1. Department of Mechanical Engineering, Auburn University, Auburn, AL, USA

    Robert L. Jackson, Hamed Ghaednia, Hyeon Lee, Amir Rostami & Xianzhang Wang

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  1. Robert L. Jackson
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  2. Hamed Ghaednia
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  3. Hyeon Lee
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  4. Amir Rostami
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  5. Xianzhang Wang
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Corresponding author

Correspondence to Robert L. Jackson .

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Editors and Affiliations

  1. Department of Industrial Engineering, University of Wisconsin, Milwaukee, Wisconsin, USA

    Pradeep L. Menezes

  2. Department of Mechanical Engineering, University of Wisconsin, Milwaukee, Wisconsin, USA

    Michael Nosonovsky

  3. Department of Marine Engineering, Texas A&M University, Galveston, Texas, USA

    Sudeep P. Ingole

  4. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India

    Satish V. Kailas

  5. Department of Industrial Engineering, University of Wisconsin, Milwaukee, Wisconsin, USA

    Michael R. Lovell

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Jackson, R.L., Ghaednia, H., Lee, H., Rostami, A., Wang, X. (2013). Contact Mechanics. In: Menezes, P., Nosonovsky, M., Ingole, S., Kailas, S., Lovell, M. (eds) Tribology for Scientists and Engineers. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1945-7_3

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