Role of surface roughness in hysteresis during adhesive elastic contact

Abstract

In experiments that involve contact with adhesion between two surfaces, as found in atomic force microscopy or nanoindentation, two distinct contact force (P) versus indentation-depth (h) curves are often measured depending on whether the indenter moves towards or away from the sample. The origin of this hysteresis is not well understood and is often attributed to moisture, plasticity or viscoelasticity. Here we report experiments which show that hysteresis can exist in the absence of these effects, and that its magnitude depends on surface roughness. We develop a theoretical model in which the hysteresis appears as the result of a series of surface instabilities, in which the contact area grows or recedes by a finite amount. The model can be used to estimate material properties from contact experiments even when the measured P–h curves are not unique.

Keywords:

• atomic force microscopy
• nanoindentation
• surface roughness
• adhesion
• contact mechanics

Acknowledgements

This work is partly supported by the Center for Probing the Nanoscale (CPN), an NSF NSEC, NSF Grant No. PHY-0425897, by the NSF Career programs CMS-0547681, ECS-0449400 and CMMI-0747089, NIH R01-EB006745, and by the NSF award CNS-0619926 for computer resources. J.C. Doll is supported in part by NSF and NDSEG Graduate Research Fellowships. H. Kesari is supported by the Herbert Kunzel Stanford Graduate Fellowship and he thanks Dr. Bjorn Backes for helping perform the NI experiments.

Notes

Notes

1. In this work, we estimate glass-PDMS adhesion energy to be 26 mJ/m² (Section 3.4). Cao et al. 31 report the diamond-PDMS adhesion energy to be 227 mJ/m². However, from other sources the glass-PDMS adhesion energy is seen to lie in the range 12–150 mJ/m² 6,32, and the diamond-PDMS adhesion energy is seen to lie in the range 20–500 mJ/m² 33–35.

2. The derivation of Equations (1a) and (1b) requires considerable space to be properly explained, so it will be published separately. Briey, however, when λ/R ≪ 1 and A/λ ∼ O(1), the equilibrium P–h curve given by Equations (2), (3) in 14, which are parametric equations of the form P(a), h(a), reduces to a form which contains terms given by the JKR contact theory and additional oscillatory terms arising due to the sinusoidal topography. We derive the equation for the envelope by replacing the oscillatory terms with their respective maximum and minimum values.

3. Reduced adhesion under water has also been observed between mica surfaces 36.

4. The derivation of this expression will be published elsewhere.