https://doi.org/10.1007/s100510050374
Hysteresis and elastic interactions of microasperities in dry friction
1
Groupe de Physique des Solides,
Université Paris 6 et Paris 7 et CNRS,
Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
2
Institut Laue-Langevin et Collège de France,
BP 156, 38042 Grenoble Cedex 9, France
Corresponding author: a nozieres@ill.fr
Received:
3
February
1998
Accepted:
19
March
1998
Published online: 15 July 1998
Velocity independent dry friction of a slider upon a base is due to an hysteretic
response of relative displacement ρ to a tangential driving force F.
We show that the purely
elastic model for multistability considered in a previous publication is in no way essential:
multistability arises just as well from adhesion. We emphasize the physical consequences of
multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an
amount ρ the transition from the zero force static configuration to dynamic behaviour is
progressive, spreading on a range equal to
the width of the hysteresis cycle. When ρ is small,
an elastic restoring force ensues, in agreement
with observations. The competition of that
elastic pinning with bulk elasticity generates
a screening length which we believe is the natural
size of Burridge Knopoff blocks. We then study the effect of elastic interactions between
asperities: it is weak for dilute asperities, but its long range makes it important. In lowest
order the interaction mediated displacement of a given asperity has logarithmically divergent
fluctuations: they become comparable to the asperity radius when the slider size reaches
another characteristic "Larkin length" ,
which for dilute micronic asperities is exponentially
large. We give arguments suggesting
that individually monostable asperities display
collective
multistability on scales larger than
. For individually multistable sites we show that elastic
interactions give rise to cascade processes in which the spinodal jump of a given asperity
triggers the jump of others. We estimate the size of these cascades that should show up in the
noise spectrum.
PACS: 46.30.Pa – Friction, wear, adherence, hardness, mechanical contacts, and tribology / 81.40.Pq – Friction, lubrication, and wear
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998