Session P26: Focus Session: Friction, Fracture and Deformation Across Length Scales - Friction and Geometric Effects

Effect of Atomic Scale Geometry on Contact and Friction Between Rough Solids

Microscopic roughness on real surfaces is known to have a profound influence on macroscopic contact mechanics. It has previously been reported that surfaces that differ only at the atomic level can show different relationships between load, stiffness, and friction. Here we use molecular dynamics simulations to study contact properties of self-affine rough surfaces that are identical at continuum scales, but differ at the atomic scale. We compare surfaces that have atomic positions displaced to a self affine surface to ``stepped'' surfaces that have been cut from a lattice. The stepped surfaces exhibit more plasticity, contributing to a larger contacting area at a given load. A unified framework captures the relation between roughness, system size, surface separation, stiffness, and contact area.   

Breakdown of Amontons' Law of Friction in Sheared-Elastomer with Local Amontons' Friction

It is well known that Amontons' law of friction i.e. the frictional force against the sliding motion of solid object is proportional to the loading force and not dependent on the contact area, holds well for various systems. Here we show, however, the breakdown of the Amontons' law for the elastic object which have local friction obeying Amontons' law and is under uniform pressure by FEM calculation The external shearing force applied to the trailing edge of the sample induces local slip. The range of the slip increases with the increasing external force adiabatically at first. When the range reaches the critical magnitude, the slips moves rapidly and reaches the leading edge of the sample then the whole system slides. These behaviors are consistent with the experiment by Rubinstein et.al. (Phys. Rev. Lett. 98, 226103). The static frictional coefficient, the ratio between the static frictional force for the whole system and the loading force, decreases with the increasing pressure. This means the breakdown of Amontons' law. The pressure dependence of the frictional coefficient is caused by the change of the critical length of the local slip. The behaviors of the local slip and the frictional coefficient are well explained by the 1 dimensional model analytically.   

Geometry and elasticity for detachment fronts in friction

Mesoscale friction bridges nanoscale contact mechanics to the macroscopic Amontons laws and is relevant for several mechanical problems including seismology. Recent experiments on polymeric blocks show that the onset of friction occurs by nucleation of detachment fronts and that frictional properties vary along the sample surface. The earthquake-like dynamics found at the millimeter scale is in contrast with the usual assumption of uniform detachment without a coherent pattern in the front formation. Simulating the quasi-equilibrium dynamics of an elastic sample sliding on a rough surface under a shear force, we show that the dynamics of detachment fronts depends on the sample geometry. In particular, we study the effect of the sample aspect ratio by computing the elastic Green function for a finite three-dimensional slider. Our model allows to study the onset of friction in different geometries, from the thin slabs used in the aforementioned experiments to more general samples shapes.   

Local friction at a rubber/glass multicontact interface

When rubber is squeezed against a hard, rough surface contact only occurs at localized spots between surface asperities. Friction thus involves the shearing of a myriad of micro-contacts which are distributed over length scales ranging from micrometers down to nanometers. In order to get more insights into this widely debated problem, spatially resolved measurements of frictional stresses are much needed. We recently proposed a method to measure local friction of rubbers by means of a contact imaging approach. Silicon rubber substrates marked on their surface are prepared in order to measure the displacement field induced by the steady state friction of a glass lens. Then, the deconvolution of this displacement field provides a spatially resolved measurement of the actual shear stress and contact pressure distributions within the contact interface. As a result, the local friction law, i.e. the relationship between the actual shear stress and normal pressure, is obtained. The effect of roughness are analyzed from experiments using statistically rough surfaces differing in their roughness power density spectrum. Experimental results are discussed in the light of theoretical contact models for the friction of multi-contact interfaces.   

Adhesive contact of randomly rough surfaces

The contact area, stiffness and adhesion between rigid, randomly rough surfaces and elastic substrates is studied using molecular statics and continuum simulations. The surfaces are self-affine with Hurst exponent 0.3 to 0.8 and different short $\lambda _{s}$ and long $\lambda _{L}$ wavelength cutoffs. The rms surface slope and the range and strength of the adhesive potential are also varied. For parameters typical of most solids, the effect of adhesion decreases as the ratio $\lambda _{L}$/$\lambda _{s}$ increases. In particular, the pull-off force decreases to zero and the area of contact A$_{c }$becomes linear in the applied load L. A simple scaling argument is developed that describes the increase in the ratio A$_{c}$/L with increasing adhesion and a corresponding increase in the contact stiffness [1]. The argument also predicts a crossover to finite contact area at zero load when surfaces are exceptionally smooth or the ratio of surface tension to bulk modulus is unusually large, as for elastomers. Results that test this prediction will be presented and related to the Maugis-Dugdale [2] theories for individual asperities and the more recent scaling theory of Persson [3]. [1] Akarapu, Sharp, Robbins, Phys. Rev. Lett. 106, 204301 (2011) [2] Maugis, J. Colloid Interface Sci. 150, 243 (1992) [3] Persson, Phys. Rev. Lett. 74, 75420 (2006)   

The Effect of Surface Topography on Interface Stresses During Peeling

Surface topography can have a large impact on the adhesive strength of soft interfaces. While previous experiments have revealed some of the underlying mechanisms, there has been no direct measurement of interface stresses during adhesive failure. We use traction force microscopy to measure the microscopic distribution of interface stresses during peeling. We focus on the relationship between local stresses and topography near the peeling front.   

Direction dependence of static friction for commensurate and moderately incommensurate surfaces

We present results from our calculations of quasi-static sliding of two atomically flat surfaces in dry, wearless contact using the Density Functional Theory package \emph{VASP}. The main focus of our work was to determine to which extent commensurability of the surfaces and the sliding direction effects the friction force. The examined systems include commensurable fcc (111) Aluminium slabs and moderately incommensurate surfaces like bcc (110) Titanium on hcp (001) Titanium. A model consistent with stick-slip friction was devised to calculate the friction forces along sliding paths of up to 1 $\mu$m on a quantum mechanical basis. To map all forces and energies for rigid and relaxed atomic positions the top slab was scanned over the bottom one on a properly fine grid, which covers the entire unit cell. In this manner, it is shown that the mean friction force depends on the sliding direction and that due to relaxations incommensurate paths may result, counter-intuitively, in higher friction then commensurate ones.   

Laser induced projectile impact test (LIPIT): A micron-scale ballistic test for high-strain rate mechanical study of nano-structures

We present a method to apply a highly localized deformation at a high-strain-rate for the study of mechanical characteristics of micro- and nano-structures. In the technique, Laser Induced Projectile Impact Test (LIPIT), micro-projectiles (solid silica spheres of 3.7$\mu $m diameter) are accelerated to a supersonic speed (up to 4 km/s) in air by a micro-explosion created by laser ablation of polystyrene and impact a sample target. The velocity information of the micro-projectiles is explicitly determined by two consecutive high-speed images during the flight of the projectiles. For demonstration, a glassy-rubbery nanocomposite consisting of a periodic self-assembled stack of 20 nm thick layers of polystyrene and polydimethylsiloxane blocks (PS-b-PDMS) is tested by LIPIT at the extremely high-strain rate of 10$^{8}$ s$^{-1}$. The polymer nanocomposite demonstrates new orientation dependent deformation and failure mechanisms including a surprising order to disorder transition fluidization, and the energy absorbing ability of a layered nanocomposite through plastic deformation leading to a melting of the layered structure.   

Probing the sliding interactions between bundled actin filaments

Assemblies of filamentous biopolymers are hierarchical materials in which the properties of the overall assemblage are determined by structure and interactions between constituent particles at all hierarchical levels. For example, the overall bending rigidity of a two bundled filaments greatly depends on the bending rigidity of, and the adhesion strength between individual filaments. However, another property of importance is the ability for the filaments to slide freely against one another. Everyday experience indicates that it is much easier to bend a stack of papers in which individual sheets freely slide past each other than the same stack of papers in which all the sheets are irreversibly glued together. Similarly, in filamentous structures the ability for local re-arrangement is of the utmost importance in determining the properties of the structures observed. We have developed a method to directly measure the frictional interactions between a pair of aligned filaments in a well-defined and controllable configuration. This enables us to systematically investigate the role of adhesion strength, filament orientation, length, and surface structure.   

Harnessing polymer gels to regulate friction between sliding surfaces

We examine the microscale tribological behavior of a pair of gel coated surfaces separated by a thin layer of lubricant. The soft, elastic gel is modeled using a bond-bending lattice spring model that captures the micromechanics of a random network of interconnected filaments. We couple this model with the dissipative particle dynamics that explicitly models the hydrodynamics of a viscous fluid. We probe how elasticity and internal structure of compliant gels affect the tribological behavior and examine how gel elasticity can be harnessed to regulate friction between sliding surfaces. We also study the effect of lubricant composition and the inclusion of nanoscopic particles of different shapes on the friction forces between wet compliant surfaces. Our findings could be useful for developing new methods for regulating friction and reducing wear of lubricated surfaces and also for understanding the micro-mechanics of friction in biological systems.   

On the Equilibrium of an Heavy Elastic Cylinder on Horizontal Nondeformable Plane

The plane static contact problem of the equilibrium of a homogeneous heavy elastic cylinder on fixed non-deformable horizontal plane is discussed. In the vicinity of the initial contact between these bodies, there is some contact area, which covers the central angle and which are unknown contact stresses. The elastic equilibrium of a cylinder under the influence of its gravity and some unknown contact stress is discussed. To determine the distribution of contact stress, the size of the contact area of the cylinder and immersion in the horizontal plane is required.   

Internal friction peak in silicon revealed by moderate temperature annealing

In order to maximize of the quality factor of a mechanical resonator, one must minimize energy loss mechanisms. We have identified a new internal friction (IF) peak that is present in as-fabricated ultra-high $Q$ silicon resonators known as Double Paddle Oscillators. The IF peak can be removed (and thus its presence revealed) by annealing at moderate ($300\,^{\circ}$C) temperatures in both inert (Argon) and reactive (H${}_2$) atmospheres, and does not re-appear after aging for $10^7\,$s. The success of a relatively low temperature operation in eliminating this mechanism indicates that the phenomenon is surface-, as opposed to bulk- related. We compare this loss mechanism to other known loss mechanisms in silicon.   

Investigation of stability for an electrostatically actuated flexible electrode

An argument for employing dimensional analysis to explore stability in an electrostatically actuated flexible electrode is presented theoretically and experimentally. The electrode is configured as a cantilever beam, as many applications in MEMs, medical devices, and sensing devices have been studied for years. This study investigates a macro scale beam (length = 100mm - 150mm), for applications in cooling fan and flapping micro air vehicle devices. The influence of scale is validated, voltage potential and frequency contributions are quantitatively measured, and a comparison of input signal (analog versus digital) is discussed using dynamical systems analysis. Based on experimental data and numerical models, characteristics of stability are presented that could influence design considerations for various micro- and macro-scale devices.