Session H24: Focus Session: Friction, Fracture, and Deformation II

The Complementary Roles of Noise and Energy in Deformation

It is generally recognized that noise--the internal stress fluctuations on a typical mobile dislocation-- is important in determining the final partially ordered state in a deformed sample. Current theories view the deformed state as a noise induced transition. But energy must play an equally important role in the determination of that ordered state, and we will present ideas to the effect that noise and energy actually play opposing roles. That is, just as in a thermodynamic phase transition, the final state is determined by a balance between the countervailing tendencies of energy minimization and the noise fluctuations. We will show that a function can be defined for this highly nonequilibrium case that has similarities to thermodynamic free energy, and that this psuedo free energy is minimized in the final state.   

Direct Visualization of Dislocation Dynamics in Grain Boundary Scars

We describe the structural features and the equilibrium dynamics of micron-scale spherical crystals formed by polystyrene particles adsorbed on the surface of a spherical water droplet. The ground state of sufficiently large crystals possesses finite-length grain boundaries (scars). The elastic response of the crystal is measured by single-particle diffusion and the fluctuations of individual dislocations about their equilibrium positions within a scar followed. We observed rapid dislocation glide with fluctuations over the barriers separating one local Peierls minimum from the next and rather weak binding of dislocations to their associated scars. The long-distance (renormalized) dislocation diffusion glide constant is extracted directly from the experimental data and is found to be moderately faster than single particle diffusion. We also determined the parameters of the Peierls potential induced by the underlying crystalline lattice.   

Atomistic simulation studies of dislocation patterning in plastic deformation

We present the first (to our knowledge) atomistic simulation study of dislocation pattern formation in a crystalline solid. The plastic response of a ductile single crystal under an applied bend depends on the nucleation, motion, and patterning of dislocations. The coalescence of dislocations to form microstructure is difficult to predict using mesoscale models because of the need to select arbitrary rules for defect nucleation, motion, and reactions. In the context of an atomistic simulation, no such approximations are needed. We simulate a Lennard-Jones crystal in two dimensions under an applied bend; the increasing strain gradient requires a growing density of geometrically necessary edge dislocations. When the dislocation density exceeds a threshold value, they coalesce to form tilt boundaries which subdivide the original single crystal into grains. We explore the relationship between rate and size effects in single crystal plasticity at the nanoscale where deformation is dislocation-source limited.   

Dislocation patterning in the deformed Ni- bicrystal from polychromatic microdiffraction

After plastic deformation geometrically necessary (polar) dislocations as well as geometrically necessary boundaries form in a crystal. The polar dislocations density is related to the incompatibility of the plastic deformation and to the local lattice curvature. Polar dislocations spread the conditions for x-ray (or neutron) diffraction transverse to the reciprocal space vector of each reflection. Polychromatic X-ray microdiffraction (PXM) is sensitive to the density and organization of the dislocations, which occurs at several structural levels. Diffracted intensity depends on the Nye dislocation tensor. Laue patterns are sensitive to the ratio between geometrically necessary and statistically stored dislocations density. Different slip systems of polar dislocations population cause distinctly different streaking in Laue patterns. The co-evolution of the statistically stored (dipolar) and geometrically necessary dislocations (polar) may be analyzed, and the ratio between the two densities may be obtained from the analysis of the Laue spots intensity distribution. The microbeam technique is applied to analyze a dislocation structure in a Ni bicrystal under in-situ uniaxial pulling. Formation of polar and dipolar dislocations arrangements together with lattice rotations were observed during in situ uniaxial pulling of a Ni bicrystal. Lattice rotations and dislocation density depends on the distance from the boundary and on the orientation of the grain relative to the tensile axis.   

Dynamics of Dislocations in Anisotropic Pattern

We report on experimental measurements of dislocation motion in an anisotropic pattern forming system, electroconvection. For electroconvection, nematic liquid crystals are placed between two glass plates. An ac voltage is applied perpendicular to the plates. When the applied voltage greater than a critical value of the voltage is applied suddenly, a striped pattern of convection rolls form. However, a high density of topological defects/dislocations is present immediately after the sudden change in voltage. These dislocations annihilate with each other over the course of time. Topological defects play a major role in the coarsening process, and they are known to exhibit complex dynamics in striped systems. In this report, we focus on the dynamics of dislocations during the coarsening under the influence of different wavevectors in the striped system.   

Geometric Frustration in 2d crystals

Two dimensional crystals on a curved manifold favor the appearance of defects, namely, dislocations and disclinations. These defects screen out the strains that arise as a consequence of the gaussian curvature. The optimal location of these defects and the actual resulting lattice structure becomes a difficult problem. In this talk we present a detailed general framework that combining elasticity theory, novel object oriented design tools and visualization techniques allow to essentially solve the problem under different situations such as different geometries (sphere, plane, torus..), lattices (triangular, square, etc..), boundary conditions, type of order (crystalline, hexatic), etc..   

Deformation and Contact Between Self-Affine Surfaces

Molecular interactions at contacts between surfaces determine the strength of adhesion and friction forces. The total area of contact and the spatial distribution of forces are determined by a complex interplay between surface topography and elastic and plastic deformation far below the surface. The situation is further complicated by the fact that many real surfaces have roughness on a wide range of lengths that can be described by self-affine scaling. The talk will provide a detailed analysis of contact between such self-affine surfaces. First continuum mechanics results for elastic and plastic solids will be contrasted. In both cases the contact area increases linearly with the applied normal load, implying that the mean pressure in the contacts $<$p$>$ is constant. For elastic surfaces $<$p$>$ increases linearly with the root mean squared slope of the surface, $\Delta$. For plastic surfaces, $<$p$>$ is bounded by about six times the yield stress $\sigma_y$, but over the typical range of $\sigma_y$, $<$p$>$ rises roughly as $\sigma_y^{2/3}$. The morphology of the contacts is complex. Individual contacts have fractal area and perimeters, and plastic deformation increases the fractal dimension. There is a power law probability distribution $P(a)$ of cluster areas $a$: $P(a)\sim a^{-\tau}$. The value of $\tau$ is larger than 2 for elastic surfaces, and $\tau \approx 2$ for plastic surfaces. The above continuum results are next tested against MD simulations of 2D and 3D solids with self-affine surfaces. We find that the contact area is still linearly related to the load, but the slope can differ from continuum predictions. For elastic surfaces this arises from the failure of the continuum assumption that surfaces are smooth and differentiable at small scales. For plastic surfaces the discrepancies reflect unusual modes of plastic deformation at the interface. These changes are correlated to frictional forces in the simulations.   

Molecular Dynamics study of Tribological Phenomena at High Sliding Velocities

Molecular dynamics (MD) simulations have been performed to obtain qualitative information on the response of crystalline and amorphous materials to sliding interactions, particularly at high speeds. The results help to explain the formation of tribomaterial that is mechanically mixed and may be nanocrystalline or amorphous, depending on the system chosen. When the sliding speed is sufficiently high, the strain rate allows vorticity to develop. It is suggested that the resulting eddies are largely responsible for frictional energy dissipation and mechanical mixing. Similarities of flow behavior with that of fluids are noted. It is observed that the friction force is sensitive to velocity. This may be due to changes in the flow properties of the material due to localized heating resulting from sliding.   

A Study Of High Speed Friction Behavior Under Elastic Loading Conditions

The role of interfacial dynamics under high strain-rate conditions is an important constitutive relationship in modern modeling and simulation studies of dynamic events ($<$100 $\mu$s in length). The frictional behavior occurring at the interface between two metal surfaces under high elastic loading and sliding speed conditions is studied using the Rotating Barrel Gas Gun (RBGG) facility. The RBGG utilizes a low-pressure gas gun to propel a rotating annular projectile towards an annular target rod. Upon striking the target, the projectile imparts both an axial and a torsional impulse into the target. Resulting elastic waves are measured using strain gauges attached to the target rod. The kinetic coefficient of friction is obtained through an analysis of the resulting strain wave data. Experiments performed using Cu/Cu, Cu/Stainless steel and Cu/Al interfaces provide some insight into the kinetic coefficient of friction behavior at varying sliding speeds and impact loads.   

Simulations of the Monolayer Lubricants on Solid Surfaces

Lifetimes of moving interfaces in MEMS devices can often be extended by using a thin lubricant coating. These lubricants, however, can have reasonably narrow conditions of temperature and pressure over which they provide effective protection against friction and wear. To gain new insights into the nanoscale properties of monolayer lubricants, we have been carrying out atomic and continuum simulations of several classes of molecular overlayers on metal and semiconductor surfaces under sliding conditions. This talk will focus on recent continuum simulations of benzene on copper and molecular modeling studies of novel bound+mobile lubricant systems (e.g. octadecyltrichlorosilane and tricresylphosphate), where we have characterized heating rates, frictional forces, and the potential for self-healing of these systems over a wide range of temperature and sliding conditions. This work is supported by a MURI grant from the Air Force Office of Scientific Research.   

Molecular Mechanisms of Anti-Wear Pad Formation and Function

Wear limits the lifespan of many mechanical devices with moving parts. To reduce wear, lubricants are frequently enriched with additives that form protective pads on rubbing surfaces. With first-principles molecular dynamics simulations of pads derived from commercial additives, namely zinc-phosphates, we unravel the molecular origin of how anti-wear pads can form and function. These effects originate from pressure-induced changes in the coordination number of atoms acting as cross- linking agents, in this case zinc, to form chemically connected networks. The proposed mechanism explains a diverse body of experiments and promises to prove useful in the rational design of anti-wear additives that operate on a wider range of surface materials with reduced environmental side-effects.   

Dissipation and quantum chemical processes: A case study of anti-wear pad forming zinc polyphophates

It is well established that the typically observed weak dependence of solid friction on sliding velocity must be due to instabilities and molecular hysteresis, as shown in the Prandtl-Tomlinson model. The relevant arguments, however, are by no means limited to plastic or viscoelastic deformations of solids or boundary lubricants, but also apply to chemical hysteresis. Using ab-initio molecular dynamics, we investigate the chemical changes in pure and zinc polyphosphates (ZPs) as a function of their thermomechanical history. ZPs are incorporated in most commercial lubricant mixtures, because they form anti-wear pads on top of rubbing asperities. Under the expected extreme variations of pressure, we find that pure and ZPs undergo changes in atomic coordination number. While the atoms typically move less than 0.1 Angstrom in these processes, large hysteresis effects occur in binding energies and elastic moduli. This implies dissipation due to (hysteresis in) the rearrangment of (local) chemical bonds.   

Statistical Analysis of Surface Roughness and Dynamic Friction Profiles During Metalforming

Laser confocal microscopy is used to image the surface roughness features of sheet metal before and after forming. This technique combines a statistically robust sampling protocol with fine-grained spatial resolution (approximately 100 nm) so that higher moments of the dynamic friction profiles and surface roughness profiles can be compared. These higher moments, including skew and kurtosis, are of interest because they characterize the extremes of the roughness distributions, which are thought to have a significant correlation with the overall friction behavior. Ultimately we seek an improved understanding of the relationship between surface roughness profiles, dynamic friction profiles, and metallurgical conditions in order to reliably predict the detailed friction behavior during actual metalforming operations.   

Dynamic Fracture in Drying Nanoparticle Suspensions

Minute concentrations of suspended particles can dramatically alter the behavior of a drying fluid. Most strikingly, drying suspensions can crack and buckle like elastic solids. We study the fracture of drying nanoparticle suspensions. Evenly-spaced cracks invade from the drying edge of thin films through intriguing intermittent jumps. We resolve individual jumps using high-speed video. While crack jumps within a single sample show a tremendous diversity of lengths and speeds, their scaled trajectories follow a single universal curve when scaled by the length and duration of the jump. The shape of the master curve is given by the coupling of the elastic deformation of the particle network to the flow of interstitial fluid. Scaling parameters are determined by the capillary forces driving fracture, the permeability of the colloidal medium and the geometry of the crack tip.   

High Density, High Velocity Sliding for Ta, Al Interfaces

The high density, high velocity behavior of ductile metal sliding has been investigated for Ta/Al, Al/Al, and Ta/Ta interfaces for pressures of order 10-20 GPa for a range of sliding velocities from 0.01-1.0 km/s. We discuss the plastic deformation and microstructural evolution manifested in large-scale ($\approx 10^6$ atoms) NEMD simulations using an optimized set of Ta, Al, and Ta-Al EAM potentials, and in particular the velocity weakening observed at high velocities of sliding.