117 research outputs found
General contact mechanics theory for randomly rough surfaces with application to rubber friction
We generalize the Persson contact mechanics and rubber friction theory to the
case where both surfaces have surface roughness. The solids can be rigid,
elastic or viscoelastic, and can be homogeneous or layered. We calculate the
contact area, the viscoelastic contribution to the friction force, and the
average interfacial separation as a function of the sliding speed and the
nominal contact pressure. We illustrate the theory with numerical results for a
rubber block sliding on a road surface. We find that with increasing sliding
speed, the influence of the roughness on the rubber block decreases, and for
typical sliding speeds involved in tire dynamics it can be neglected
Role of surface roughness in superlubricity
We study the sliding of elastic solids in adhesive contact with flat and
rough interfaces. We consider the dependence of the sliding friction on the
elastic modulus of the solids. For elastically hard solids with planar surfaces
with incommensurate surface structures we observe extremely low friction
(superlubricity), which very abruptly increases as the elastic modulus
decreases. We show that even a relatively small surface roughness may
completely kill the superlubricity state.Comment: 11 pages, 17 figures, format revte
On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness
It has recently been suggested that many contact mechanics problems between
solids can be accurately studied by mapping the problem on an effective one
dimensional (1D) elastic foundation model. Using this 1D mapping we calculate
the contact area and the average interfacial separation between elastic solids
with nominally flat but randomly rough surfaces. We show, by comparison to
exact numerical results, that the 1D mapping method fails even qualitatively.
We also calculate the normal interfacial stiffness and compare it with the
result of an analytical study. We attribute the failure of the elastic
foundation model to the neglect of the long-range elastic coupling between the
asperity contact regions.Comment: 5 pages, 4 figures, 29 reference
Squeezing Molecularly thin Lubricant Films between curved Corrugated Surfaces with long range Elasticity
Velocity Dependence of Friction of Confined Hydrocarbons
We present molecular dynamics friction calculations for confined hydrocarbon "polymer" solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: (a) polymer sliding against a hard substrate and (b) polymer sliding on polymer. We discuss the velocity dependence of the frictional shear stress for both cases. In our simulations, the polymer films are very thin (approximately 3 nm), and the solid walls are connected to a thermostat at a short distance from the polymer slab. Under these circumstances we find that frictional heating effects are not important, and the effective temperature in the polymer film is always close to the thermostat temperature. In the first setup (a), for hydrocarbons with molecular lengths from 60 to 1400 carbon atoms, the shear stresses are nearly independent of molecular length, but for the shortest hydrocarbon C(20)H(42) the frictional shear stress is lower. In all cases the frictional shear stress increases monotonically with the sliding velocity. For polymer sliding on polymer (case b) the friction is much larger, and the velocity dependence is more complex. For hydrocarbons with molecular lengths from 60 to 140 C atoms, the number of monolayers of lubricant increases (abruptly) with increasing sliding velocity (from 6 to 7 layers), leading to a decrease of the friction. Before and after the layering transition, the frictional shear stresses are nearly proportional to the logarithm of sliding velocity. For the longest hydrocarbon (1400 C atoms) the friction shows no dependence on the sliding velocity, and for the shortest hydrocarbon (20 C atoms) the frictional shear stress increases nearly linearly with the sliding velocity
Finite-size scaling in the interfacial stiffness of rough elastic contacts
The total elastic stiffness of two contacting bodies with a microscopically
rough interface has an interfacial contribution K that is entirely attributable
to surface roughness. A quantitative understanding of K is important because it
can dominate the total mechanical response and because it is proportional to
the interfacial contributions to electrical and thermal conductivity in
continuum theory. Numerical simulations of the dependence of K on the applied
squeezing pressure p are presented for nominally flat elastic solids with a
range of surface roughnesses. Over a wide range of p, K rises linearly with p.
Sublinear power-law scaling is observed at small p, but the simulations reveal
that this is a finite-size effect. We derive accurate, analytical expressions
for the exponents and prefactors of this low-pressure scaling of K by extending
the contact mechanics theory of Persson to systems of finite size. In agreement
with our simulations, these expressions show that the onset of the low-pressure
scaling regime moves to lower pressure as the system size increases.Comment: Supplementary material is available at arXiv:1210.4255, 5 pages, 3
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