Experimental Mechanics

, Volume 56, Issue 3, pp 359–368 | Cite as

The Role of Surface Structure in Normal Contact Stiffness

  • C. ZhaiEmail author
  • Y. Gan
  • D. Hanaor
  • G. Proust
  • D. Retraint


The effects of roughness and fractality on the normal contact stiffness of rough surfaces were investigated by considering samples of isotropically roughened aluminium. Surface features of samples were altered by polishing and by five surface mechanical treatments using different sized particles. Surface topology was characterised by interferometry-based profilometry and electron microscopy. Subsequently, the normal contact stiffness was evaluated through flat-tipped diamond nanoindentation tests employing the partial unloading method to isolate elastic deformation. Three indenter tips of various sizes were utilised in order to gain results across a wide range of stress levels. We focus on establishing relationships between interfacial stiffness and roughness descriptors, combined with the effects of the fractal dimension of surfaces over various length scales. The experimental results show that the observed contact stiffness is a power-law function of the normal force with the exponent of this relationship closely correlated to surfaces’ values of fractal dimension, yielding corresponding correlation coefficients above 90 %. A relatively weak correlation coefficient of 60 % was found between the exponent and surfaces’ RMS roughness values. The RMS roughness mainly contributes to the magnitude of the contact stiffness, when surfaces have similar fractal structures at a given loading, with a correlation coefficient of −95 %. These findings from this work can be served as the experimental basis for modelling contact stiffness on various rough surfaces.


Contact mechanics Contact stiffness Rough surfaces Fractal dimension Nanoindentation 



Financial support for this research from the Australian Research Council through grants DE130101639 and Civil Engineering Research Development Scheme (CERDS) in School of Civil Engineering at The University of Sydney is greatly appreciated. The authors acknowledge the facilities and the scientific and technical assistance of the Australian Microscopy & Microanalysis Research Facility at the Australian Centre for Microscopy & Microanalysis at the University of Sydney where the SEM images were taken.


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Copyright information

© Society for Experimental Mechanics 2015

Authors and Affiliations

  1. 1.School of Civil EngineeringThe University of SydneySydneyAustralia
  2. 2.ICD-Lasmis, Université de Technologie de Troyes (UTT), CNRS UMR 6279TroyesFrance

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