Journal of Materials Science

, Volume 41, Issue 19, pp 6441–6452 | Cite as

Analysis of the apparent friction of polymeric surfaces

  • S. Lafaye
  • C. GauthierEmail author
  • R. Schirrer


The apparent friction coefficient is the ratio between the tangential force and the normal load applied to moving body in contact with the surface of a material. This coefficient includes a so-called “true local friction” at the interface and a “geometrical friction” which is the ploughing effect. The material underneath a moving tip may display various types of behaviour: elastic, elastic–plastic where elastic and plastic strain are present in the contact area, or fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model of a scratching tip which links the apparent friction to the local friction and contact geometry was recently proposed. An inverse analysis is used in the present work to estimate the local friction from the measured apparent friction and a knowledge of the contact area and tip shape. The polymer true friction coefficient displays temperature and sliding speed dependency, which may be attributed to the surface thermodynamics. It is shown that the local friction depends on the level of strain in the polymer at the contact interface.


PMMA Contact Pressure Real Contact Area Glass Temperature Plastic Contact 



Apparent friction coefficient


True friction


Adhesive friction coefficient


Ploughing friction coefficient


Viscoelastic friction coefficient


Plastic friction coefficient


Tangential force


Adhesive force


Normal load


Apparent interfacial shear stress

τ(or τtrue)

Shear stress at the moving contact area


Ploughing shear stress


Contact pressure


Yield stress


Local pressure at the contact


Normalised contact pressure


Real normal contact area


Tangential contact area


Contact surface element


A constant




Loss factor


Half apex angle of the conical tip


Rear contact angle


Elementary action integrals of the local pressure and shear

dɛ/dt (or \(\mathop\varepsilon\limits^\bullet\))

Mean effective strain rate


Sliding speed


Scratch contact width


Contact radius


Radius of the tip




Axes moving with the tip


Axis of the indentation direction


Axis of the scratching direction


Elementary normal load vector


Elementary tangential load vector


Normal unit vector


Unit vector tangential to the flow lines


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Institut Charles Sadron, CNRS-UPR 22StrasbourgFrance

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