Maugis-Tabor parameter dependence of pull-off in viscoelastic line Hertzian contacts

ABSTRACT

We derive an extension of the Maugis-Dugdale-Johnson-Greenwood model for 2D adhesive Hertzian contact to viscoelastic materials. This results in extremely simple approximate results for the maximum amplification of the pull-off due to viscoelastic effects, for arbitrary form of the viscoelastic linear properties. In particular, we assume that the initial loading state is fully relaxed, and unloading occurs at very large pulling speeds. We show that the maximum amplification (of the order of ${\left(E_I/E_R\right)}^{2/3}$, the ratio between instantaneous and relaxed modulus to the 2/3 power) is only reached for large and soft cylinders, namely, large enough (relaxed) Tabor-Maugis parameters $\lambda$ of the order of the order of $E_I/E_R$, and therefore typically much larger than the Tabor-Maugis parameters to have a “short-range” JKR adhesion regime in quasi-static conditions, which is $\lambda \sim 1$. The results agree well with recent numerical ones by Muser-Persson, but there is an shift factor in the Tabor-Maugis parameter which requires further study and may depend on initial contact area.

KEYWORDS:

• Viscoelasticity
• adhesion
• cohesive models
• JKR models

Acknowledgements

MC acknowledges support from the Italian Ministry of Education, University and Research (MIUR) under the program “Departments of Excellence” (L.232/2016). Also, Prof. H.Gao from Singapore University for having inspired this model with fruitful discussions. Last but not least, Prof. Muser or Saarland University for providing with some additional data and info about his recent paper with B.Persson. QL acknowledges the support from the National Natural Science Foundation of China (12025203).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ If we assume that the elastic modulus is the same in the bulk and at the crack tip, essentially we return to the elastic Maugis-Dugdale result, which means for 3D contact that the pull-off is not enhanced, whereas in the present line 2D contact, that pull-off load is proportional to the elastic modulus to the power 1/3, so that the dimensionless load $\hat{P}$ is not enhanced.

² Private communication with Prof. Muser.