Journal of Materials Science

, Volume 43, Issue 14, pp 4768–4779 | Cite as

Size effects in polyurethane bonds: experiments, modelling and parameter identification

  • Michael Johlitz
  • Stefan Diebels
  • Jan Batal
  • Holger SteebEmail author
  • Wulff Possart


In this study we examine polyurethane bonds of varying thickness between anodised aluminium substrates. The performed shear tests showed an intriguing size effect of the kind “thinner equals softer”. This size effect occurs not only in the basic elasticity (relaxed state), but also in the viscoelastic behaviour of the tested material. The cause of such size effects is supposed to be found in the existence of so-called interphases or boundary layers, which may differ considerably from the bulk in terms of mechanical behaviour, thus having an enormous impact on thin bonds. In thick bonds, however, these interphases or boundary layers have a minor effect on the overall mechanical behaviour. To account for these experimental results in bond modelling, an extended phenomenological continuum mechanics-based model, which explicitly includes such size effects in its calculation, is developed and presented. For this purpose, an abstract structure parameter with its corresponding balance equation is established describing the formation of the interphases by means of a phase transition. This makes it possible to define the bond stiffness at a macroscopic level, without entering into the microstructure. The extended model brings up a set of model parameters, which are determined efficiently by an ES (evolution strategy). The study concludes with a summary and an outlook on our further research work.


Shear Rate Basic Elasticity Maxwell Element Shear Sample Bond Thickness 



The authors are grateful to the DFG (Deutsche Forschungsgemeinschaft—German Research Foundation) for financial support under grant numbers Di 430/5-1 to 5-3 and Po 577/15-1.


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Michael Johlitz
    • 1
  • Stefan Diebels
    • 1
  • Jan Batal
    • 1
  • Holger Steeb
    • 1
    Email author
  • Wulff Possart
    • 1
  1. 1.Saarland UniversitySaarbruckenGermany

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