[SY-O1] Symposium O-1

[SY-O1] Two simple models for pull-off decay of self-affine rough surfaces

^○Antonio Papangelo^1,2, Michele Ciavarella^1,2 (1.Politecnico di Bari, Italy, 2.Hamburg University of Technology, Germany)

Predicting the adhesive behaviour of randomly rough multiscale surfaces nowadays remains a tough task. The classical asperity model of Fuller and Tabor (1975) reduces the rough surface to a set of independent asperities, which behave accordingly to the JKR model for adhesion of spheres (Jonshon et al. 1971). Fuller and Tabor showed that the pull-off force is strongly affected by the height root mean square (rms), so that a tiny variation in height rms leads to order of magnitudes reduction in surface stickiness. Nevertheless, the present understanding of rough contact as “fractals” poses serious questions about the validity of asperity models. Recent large numerical calculations by Pastewka and Robbins show that “slopes and curvatures” may play an important role, which is in contrast with asperity model predictions. We propose and discuss here two simple models for pull-off decay, namely the Bearing Area Model (BAM, Ciavarella, 2017) belonging to a DMT class of models, and Generalized Johnson Parameter (GJP, Ciavarella & Papangelo, 2018) model. BAM starts from the observation that the entire DMT solution for “hard” spheres (Tabor parameter tending to zero) assuming the Maugis law of attraction, is very easily obtained using the Hertzian load-indentation law and estimating the area of attraction as the increase of the bearing area geometrical intersection when the indentation is increased by the Maugis range of attraction. GJP instead postulates that stickiness of randomly rough multiscale surfaces depends on a generalization of the classical Johnson parameter valid for the single sinusoid. The GJP is obtained as the ratio between the adhesive energy and the elastic energy needed to flatten the surface. We make extensive comparisons of GJP and BAM predictions with respect to Pastewka and Robbins (2014) and Persson and Scaraggi (2014) numerical calculations showing reasonable agreement. We show that for low fractal dimensions, BAM and GJP are insensitive to rms slopes and curvatures, so being independent on “small-scale features”, which are difficult to define for fractal surfaces.