Advertisement

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
Article

Abstract

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.

Keywords

Contact stiffness Digital image correlation Ultrasound Titanium alloy 

Abbreviations

DIC

Digital image correlation

FE

Finite element

FFT

Fast Fourier transform

RMS

Root mean square

UPR

Ultrasound pulser-receiver

Nomenclature

c

Wave speed

E1,2

Young’s modulus of bodies 1 and 2

E*

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

f

Coefficient of friction

fu

Ultrasound frequency

H

Hardness

P

Total normal force

pm

Mean normal pressure

Q

Total tangential force

R

Reflection coefficient

Sq

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

x, y, z

Cartesian coordinates, (z is normal to a surface)

Z

Acoustic impedance

Z1,Z2

Acoustic impedance in bodies 1 and 2

κ

Contact stiffness per unit nominal area

κn

Normal (longitudinal) contact stiffness per unit nominal area

κt

Tangential (shear) contact stiffness per unit nominal area

κDIC

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

κFE

Contact stiffness derived from a finite element model

κInterface

Contact stiffness of an interface isolated from other contributions

ν1,2

Poisson’s ratio of bodies 1 and 2

ρ

Density

σm

rms surface slope

Ψ

Plasticity index

ω

Angular frequency

Notes

Acknowledgments

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.

References

  1. 1.
    Eriten M, Polycarpou A, Bergman L (2011) Development of a lap joint fretting apparatus. Exp Mech 51(8):1405–1419CrossRefGoogle Scholar
  2. 2.
    Berthoud P, Baumberger T (1998) Shear stiffness of a solid-solid multicontact interface. Proc Math Phys Eng Sci 454(1974):1615–1634MathSciNetCrossRefGoogle Scholar
  3. 3.
    Schwingshackl CW, Petrov EP, Ewins DJ (2012) Measured and estimated friction interface parameters in a nonlinear dynamic analysis. Mech Syst Signal Process 28:574–584CrossRefGoogle Scholar
  4. 4.
    de Crevoisier J, Swiergiel N, Champaney L, Hild F (2012) Identification of in situ frictional properties of bolted assemblies with digital image correlation. Exp Mech 52(6):561–572CrossRefGoogle Scholar
  5. 5.
    Segalman DJ, Bergman LA, Ewins DJ (2007) “Report of the SNL/NSF International Workshop on Joint Mechanics”, Arlington, Virginia, 16–18 October 2006, Sandia Report 2007–7761. Sandia National Labs, AlbuquerqueGoogle Scholar
  6. 6.
    Mulvihill DM, Kartal ME, Olver AV, Nowell D, Hills DA (2011) Investigation of non-Coulomb friction behaviour in reciprocating sliding. Wear 271(5–6):802–816CrossRefGoogle Scholar
  7. 7.
    Mulvihill DM, Kartal ME, Nowell D, Hills DA (2011) An elastic-plastic asperity interaction model for sliding friction. Tribol Int 44(12):1679–1694CrossRefGoogle Scholar
  8. 8.
    Kartal ME, Mulvihill DM, Nowell D, Hills DA (2011) Determination of the frictional properties of titanium and nickel alloys using the digital image correlation method. Exp Mech 51(3):359–371CrossRefGoogle Scholar
  9. 9.
    Kartal ME, Mulvihill DM, Nowell D, Hills DA (2011) Measurements of pressure and area dependent tangential contact stiffness between rough surfaces using digital image correlation. Tribol Int 44(10):1188–1198CrossRefGoogle Scholar
  10. 10.
    Kendall K, Tabor D (1971) An ultrasonic study of the area of contact between stationary and sliding surfaces. Proc Roy Soc Lond Math Phys Sci 323(1554):321–340CrossRefGoogle Scholar
  11. 11.
    Królikowski J, Szczepek J, Witczak Z (1986) “High pressure in ultrasonic study of contact of solids,” Physica B + C, 139–140, pp 803–805Google Scholar
  12. 12.
    Królikowski J, Szczepek J, Witczak Z (1989) Ultrasonic investigation of contact between solids under high hydrostatic pressure. Ultrasonics 27(1):45–49CrossRefGoogle Scholar
  13. 13.
    Królikowski J, Szczepek J (1991) Prediction of contact parameters using ultrasonic method. Wear 148(1):181–195CrossRefGoogle Scholar
  14. 14.
    Królikowski J, Szczepek J (1993) Assessment of tangential and normal stiffness of contact between rough surfaces using ultrasonic method. Wear 160(2):253–258CrossRefGoogle Scholar
  15. 15.
    Drinkwater BW, Dwyer-Joyce RS, Cawley P (1996) A study of the interaction between ultrasound and a partially contacting solid-solid Interface. Proc Math Phys Eng Sci 452(1955):2613–2628CrossRefGoogle Scholar
  16. 16.
    Dwyer-Joyce RS, Drinkwater BW, Quinn AM (2001) The use of ultrasound in the investigation of rough surface interfaces. J Tribol 123(1):8–16CrossRefGoogle Scholar
  17. 17.
    Baltazar A, Rokhlin SI, Pecorari C (2002) On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces. J Mech Phys Solid 50(7):1397–1416zbMATHCrossRefGoogle Scholar
  18. 18.
    Kim J-Y, Baltazar A, Rokhlin SI (2004) Ultrasonic assessment of rough surface contact between solids from elastoplastic loading-unloading hysteresis cycle. J Mech Phys Solid 52(8):1911–1934CrossRefGoogle Scholar
  19. 19.
    Dwyer-Joyce RS, Gonzalez-Valadez M (2004) “Ultrasonic determination of normal and shear interface stiffness and the effect of Poisson’s ratio”. In: Dalmaz G, Lubrecht AA, Dawson D, Priest M (eds). Transient processes in tribology: Proceedings of the 30th Leeds-Lyon Symposium, Lyon, France, Sept 2nd–5thGoogle Scholar
  20. 20.
    Gonzalez-Valadez M, Baltazar A, Dwyer-Joyce RS (2010) Study of interfacial stiffness ratio of a rough surface in contact using a spring model. Wear 268(3–4):373–379CrossRefGoogle Scholar
  21. 21.
    Malik HK, Singh AK (2010) Engineering physics. Tata McGraw Hill, New DelhiGoogle Scholar
  22. 22.
    Tattersall HG (1973) The ultrasonic pulse-echo technique as applied to adhesion testing. J Appl Phys D Appl Phys 6(7):819–832CrossRefGoogle Scholar
  23. 23.
    Baik JM, Thompson RB (1984) Ultrasonic scattering from imperfect interfaces: a quasi-static model. J Nondestruct Eval 4(3):177–196CrossRefGoogle Scholar
  24. 24.
    Rose JH (1989) “Ultrasonic reflectivity of diffusion bonds”. In: Thompson DO, Chimenti DE (eds). Review of progess in quantitative NDE, vol 8B, pp 1925–1931Google Scholar
  25. 25.
    Sheu S, Hector LG Jr, Richmond O (1998) Tool surface morphologies for friction and wear control in metalworking processes. ASME J Tribol 120:517–527CrossRefGoogle Scholar
  26. 26.
    Tong W, Tao H, Jiang X, Zhang N, Marya MP, Hector LG Jr, Gayden XQ (2005) Deformation and fracture of minature tensile bars with resistance-spot-weld microstructures. Metall Mater Trans A 36(10):2651–2669CrossRefGoogle Scholar
  27. 27.
    Savic V, Hector L (2007) “Tensile deformation and fracture of press hardened boron steel using digital image correlation,” SAE Technical Paper, No. 2007-01-0790Google Scholar
  28. 28.
    Zavattieri PD, Savic V, Hector LG Jr, Fekete JR, Tong W, Xuan Y (2009) Spatio-temporal characteristics of the Portevin-Le Châtelier effect in austenitic steel with twinning induced plasticity. Int J Plast 25(12):2298–2330CrossRefGoogle Scholar
  29. 29.
    Abu-Farha F, Hector LG Jr, Khraisheh M (2009) Cruciform-shaped specimens for elevated temperature biaxial testing of lightweight materials. JOM 61(8):48–56CrossRefGoogle Scholar
  30. 30.
    Savic V, Hector LG Jr, Fekete JR (2010) Digital image correlation study of plastic deformation and fracture in fully martensitic steels. Exp Mech 50(1):99–110CrossRefGoogle Scholar
  31. 31.
    TiMetal 6–4 datasheet (2000) Titanium Metals Corporation (TIMET), Hartford, CT, USAGoogle Scholar
  32. 32.
    PixeLINK PL-B741U monochrome camera data sheet (2009) PixeLINK, Ottawa, CanadaGoogle Scholar
  33. 33.
    Questar QM1 Long Distance Microscope Datasheet, Questar Corporation, New Hope, PA, USAGoogle Scholar
  34. 34.
    Video Gauge User Guide (2009) Imetrum Limited, Bristol, UKGoogle Scholar
  35. 35.
    Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39(11):2915–2921CrossRefGoogle Scholar
  36. 36.
    Knauss WG, Chasiotis I, Huang Y (2003) Mechanical measurements at the micron and nanometer scales. Mech Mater 35(3–6):217–231CrossRefGoogle Scholar
  37. 37.
    Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurment: a review. Meas Sci Technol 20(6):1–17CrossRefGoogle Scholar
  38. 38.
    Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties—a review. Strain 42(2):69–80CrossRefGoogle Scholar
  39. 39.
    McFarlane JS, Tabor D (1950) Relation between friction and adhesion. Proc Roy Soc Lond Math Phys Sci 202(1069):244–253CrossRefGoogle Scholar
  40. 40.
    DaVis StrainMaster 2D Software Product Manual (2010) LaVision GmbH, Goettingen, GermanyGoogle Scholar
  41. 41.
    Medina S, Nowell D, Dini D (2013) Analytical and numerical models for tangential stiffness of rough elastic contacts. Tribol Lett 49(1):103–115CrossRefGoogle Scholar
  42. 42.
    Mindlin RD (1949) Compliance of elastic bodies in contact. J Appl Mech 16:259MathSciNetzbMATHGoogle Scholar
  43. 43.
    Greenwood JA, Williamson JBP (1966) Contact of nominally flat surfaces. Proc Roy Soc Lond Math Phys Sci 295(1442):300–319CrossRefGoogle Scholar
  44. 44.
    Johnson KL (1955) Surface interaction between elastically loaded bodies under tangential forces. Proc Roy Soc Lond Math Phys Sci 230(1183):531–548CrossRefGoogle Scholar
  45. 45.
    O'Connor JJ, Johnson KL (1963) The role of surface asperities in transmitting tangential forces between metals. Wear 6(2):118–139CrossRefGoogle Scholar
  46. 46.
    Shi X, Polycarpou AA (2005) Measurement and modeling of normal contact stiffness and contact damping at the meso scale. J Vib Acoust 127(1):52–60CrossRefGoogle Scholar
  47. 47.
    Campañá C, Persson BNJ, Müser MH (2011) Transverse and normal interfacial stiffness of solids with randomly rough surfaces. J Phys Condens Matter 23(8):1–9CrossRefGoogle Scholar
  48. 48.
    Sevostianov I, Kachanov M (2008) Contact of rough surfaces: a simple model for elasticity, conductivity and cross-property connections. J Mech Phys Solid 56(4):1380–1400MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Mikić BB (1974) Thermal contact conductance; theoretical considerations. Int J Heat Mass Transf 17(2):205–214CrossRefGoogle Scholar
  50. 50.
    Proprentner D (2012) PhD thesis, Imperial College LondonGoogle Scholar

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

Personalised recommendations