Experimental Mechanics

, Volume 53, Issue 7, pp 1245–1263 | Cite as

A Comparison of Contact Stiffness Measurements Obtained by the Digital Image Correlation and Ultrasound Techniques

  • D. M. Mulvihill
  • H. Brunskill
  • M. E. Kartal
  • R. S. Dwyer-Joyce
  • D. Nowell


The digital image correlation (DIC) and ultrasound techniques have both previously been employed to measure the contact stiffness of real engineering interfaces, but a comprehensive comparison of these techniques has not previously been carried out. Such a comparison is addressed in the present paper. The principal novelty in this work is that DIC and ultrasound are used to simultaneously measure contact stiffness in the same tests and on the same contact interface. The results show that ultrasound measures somewhat higher contact stiffness magnitudes than DIC: at an average normal contact pressure of 70 MPa, ultrasound was around three times stiffer. Given that the techniques are vastly different in their measurement approach (DIC measures micron-scale relative displacements from external side-on images of the interface, while ultrasound uses the reflection of an Ångstrom scale ultrasonic perturbation from the interior of the interface itself), this level of agreement is thought to be encouraging. The difference in results can partly be explained by consideration of inherent physical differences between the techniques which have previously received little attention. Ultrasound measurement will always give the local elastic ‘unloading stiffness’ (even at a plastically deforming contact); whereas, a load-deflection technique like DIC, will give the ‘loading stiffness’. The reason for this difference is discussed in the paper and tests carried out under increasing tangential load in the pre-sliding regime illustrate this difference experimentally. Under normal loading, the increase in real contact area obscures the effect to some extent as both DIC and ultrasound stiffnesses increase with normal load. The results suggest that rough interfaces may be satisfactorily modelled as a variable stiffness spring whose stiffness increases with contact pressure as the smooth contact case is approached.


Contact stiffness Digital image correlation Ultrasound Titanium alloy 



Digital image correlation


Finite element


Fast Fourier transform


Root mean square


Ultrasound pulser-receiver



Wave speed


Young’s modulus of bodies 1 and 2


Material stiffness of the interface pair \( \left( {E^*={{{\left\{ {{{{\left( {1-{\nu_1}} \right)}}^2}/{E_1}+{{{\left( {1-{\nu_2}} \right)}}^2}/{E_2}} \right\}}}^{-1 }}} \right) \)


Coefficient of friction


Ultrasound frequency




Total normal force


Mean normal pressure


Total tangential force


Reflection coefficient


Areal root mean square roughness (standard deviation of surface heights)

x, y, z

Cartesian coordinates, (z is normal to a surface)


Acoustic impedance


Acoustic impedance in bodies 1 and 2


Contact stiffness per unit nominal area


Normal (longitudinal) contact stiffness per unit nominal area


Tangential (shear) contact stiffness per unit nominal area


Contact stiffness (per unit area) measured by digital image correlation


Contact stiffness derived from a finite element model


Contact stiffness of an interface isolated from other contributions


Poisson’s ratio of bodies 1 and 2




rms surface slope


Plasticity index


Angular frequency



The authors would like to acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC) under grant reference EP/E058337/1: “A Predictive Approach to Modelling Frictional Joint Performance (PAMFJP)”. Mr Richard Duffin and Mr Wolfgang Mix are also thanked for their work on machining the various test components. Thanks are due also to the British Society for Strain Measurement (BSSM) and Imetrum Ltd for providing the digital image correlation software as part of the 2011 Young Stress Analyst Competition first prize which was awarded to the first author.


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Copyright information

© Society for Experimental Mechanics 2013

Authors and Affiliations

  • D. M. Mulvihill
    • 1
  • H. Brunskill
    • 2
  • M. E. Kartal
    • 1
  • R. S. Dwyer-Joyce
    • 2
  • D. Nowell
    • 1
  1. 1.Department of Engineering ScienceUniversity of OxfordOxfordUK
  2. 2.Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK

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