Session R28: Interfaces

Creep and stress relaxation induced by interface diffusion in metal matrix composites

An analytical solution is developed to predict the creep rate induced by interface diffusion in unidirectional fiber-reinforced and particle reinforced composites. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The closed-form solution is an explicit function of the applied stress, volume fraction and radius of the fiber, as well as the modulus ratio between the fiber and the matrix. It is interesting that the solution is formally similar to that of Coble creep in polycrystalline materials. For the application of the present solution in the realistic composites, the scale effect is taken into account by finite element analysis based on a unit cell. Based on the solution, a closed-form solution is also given as a description of stress relaxation induced by interfacial diffusion under constant strain. In addition, the analytical solution for the interface stress presented in this study gives some insight into the relationship between the interface diffusion and interface slip.   

De-lamination and Pro-lamination of adhesive films on curved topographies

Attaching a solid film onto a sphere (or other curved shape) generates elastic stresses in the film. If the spherical substrate is totally rigid, the film will delaminate when its area exceeds a small fraction of the curved substrate. In contrast, if the substrate is very soft (such as a liquid drop), it will deform beneath the film, suppressing stresses and avoiding delamination of the film. Our theoretical analysis predicts that for very thin films, another scenario emerges - the film remains attached, developing tiny wrinkles that allow relaxation of stress without macro-scale deformation of the spherical shape of the substrate. Furthermore - as the film gets thinner, this predicted ``pro-lamination'' effect prevails parameter space, and should be observed for substrates with practically arbitrary stiffness.   

Elastomer-glass detachment front observation

When you peel an elastomeric band from a glass plate, the force needed changes with respect to the peeling angle and it is proportional to the width of the band [1]. As you approach to a zero angle, the process changes abruptly. Here we present the experimental study of a lap-test made on PVS elastomer and glass. We propose a simple imaging technique to observe the detachment front propagation.\\[4pt] [1] K. Kendall, ``Thin-film peeling - the elastic term'' Journal of Physics D : Applied Physics, vol. 8, p. 1449, Sep 1975.   

Stick-slip during the peeling of adhesive tape

Using a high-speed camera, we study the instable peeling dynamics of an adhesive tape pulled at an imposed controlled velocity - focusing on the stick-slip regime of the peeling. Thanks to high-resolution fast camera, we can observe directly the peeling point motion and thus quantify the details of the stick and slip phases. To study properly the influence of peeling angle on stick-slip dynamics, we have developed an original experimental set-up where we are able to control the peeling angle while peeling the adhesive from a plane substrate. In this geometry, we extracted the stick and slip periods and studied their evolution with the peeling speed V, the length between the detachment zone and the peeling motor L, and the peeling angle $\theta$. We observe that the stick and slip periods increase non-linearly with L. We report various regimes depending on V, with periods of Stick and Slip either independent or proportional to V. These experiments confirmed that the physics of adhesive peeling is strongly dependent on $\theta$, especially in the Stick-Slip regime. This general feature questions the correct fracture criterion to consider at the peeling point in order to model the Stick-Slip adhesive peeling.   

Crack propagation on curved surfaces

We investigate the propagation of cracks on curved surfaces. Using a stretched elastic sheet situated at a fluid interface, we generate a surface with spatially varying curvature and observe the trajectory and dynamics of an induced crack. We interpret the results from our experiments using a combination of numerical simulation and analytical considerations.   

Static and dynamic friction in sliding colloidal monolayers

In a recent experimental breakthrough, the controlled sliding of 2D colloidal crystals over perfectly regular, laser generated periodic or quasi-periodic `corrugation` potentials has been realized in Bechinger's group [1]. Based on realistic MD simulations which reproduce the main experimentally observed features, we explore the potential impact of colloid monolayer sliding in nanotribology [2]. The free motion of edge-spawned kinks and antikinks in smooth incommensurate sliding is contrasted with the kink-antikink pair nucleation at the large static friction threshold in the commensurate case. The Aubry pinning/depinning transition is also demonstrated, e.g., as a function of the corrugation amplitude. Simulated sliding data allow the extraction of frictional work directly from particles coordinates and velocities as a function of classic friction parameters, primarily speed, and corrugation strength. Analogies with sliding charge-density waves, driven Josephson systems, sliding of rare gas islands, and other novel features suggest further experiments and insights, which promote colloid sliding to a novel friction study instrument [3]. [1]T. Bohlein et al, Nature Mat. 11, 126 (2012) [2]A. Vanossi et al, PNAS 109, 16429 (2012) [3]A. Vanossi, E. Tosatti, Nature Mat. 11, 97 (2012)   

Contact mechanics of rough spheres

We use large scale numerical calculations to study the contact mechanics of rough spheres on flat elastic solids. Such geometries are encountered in systems that range from ball bearings to atomic force microscope tips, but the influence of roughness is seldom considered explicitly. Our calculations show that the contact area $A$ grows linearly with load $N$ at small loads and crosses over to Hertzian behavior $A \propto N^{2/3}$ at large loads. The total contact stiffness is defined as $K = dN/dz$ where $z$ is the normal displacement of the sphere. It shows power-law $K \propto N^{\alpha}$ behavior at all loads with an exponent $\alpha $ that is close to the value of $1/3$ expected from Hertzian contact mechanics. The results are discussed in the context of recent theories for flat rough contacts [1] and Greenwood-Williams theory as modified for spherical contacts [2]. \\[4pt] [1] B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001); S. Hyun, L. Pei, J.-F. Molinari, M.O. Robbins, Phys. Rev. E 70, 026117 (2004); S. Akarapu, T. Sharp, M.O. Robbins, Phys. Rev. Lett. 106, 204301 (2011) \\[0pt] [2] K.L. Johnson, Contact Mechanics, Cambridge University Press, 1987   

Effects of atomic-scale geometry in contact of rough surfaces

There has been great recent progress in continuum models of the effect of roughness on the area, friction, and stiffness of contacts between two solids. This talk will use molecular dynamics simulations to study how atomic scale features on surfaces can affect contact properties. Beginning from the established case of continuum linear elasticity that gives a linear relationship between real contact area and load, we systematically introduce atomic-scale physics to determine the affects on contact. Replacing an ideal linear isotropic elastic medium with a harmonic atomic lattice produces only small changes in the mechanical response. For more realistic interactions, anharmonicity and plasticity typically increase the contact area. The atomic steps present on rough crystal lattices lead to increased plasticity and change the small scale structure of contacts. Depending on the tendency for the material to yield, the presence of steps can increase or decrease the area of very high pressure, but steps always decrease the area of very low pressures. The large scale structure of the contact is the same for all cases. Application of continuum contact theories to surfaces with atomic-scale features will be discussed.   

Brittle Fracture In Disordered Media: A Unified Theory

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature, as well as several experiments on materials ranging from granite to bones. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit. We present a numerical validation of our theoretical results.   

Molecular dynamics simulation investigations of atomic-scale wear

Frictional running-in and material transfer in wear take place at the micro- and nano-scale but the fundamental physics remain poorly understood. Here we intend to investigate wear and running-in phenomena in silicon based materials, which are widely utilized in micro/nano electromechanical systems(MEMS/NEMS). We use an atomic force microscopy (AFM) model composed of a crystalline silicon tip and substrate coated with native oxide layers. Molecular dynamics simulation has been performed over a range of temperatures, external loads and slip rates. Results show that adhesive wear takes place across the interface in an atom-by-atom fashion which remodels the tip leading to a final steady state. We quantify the rate of material transfer as a function of the coverage of non-bridging oxygen (NBO) atoms, which has a pronounced change of the system's tribological and wear behaviors. A constitutive rate and state model is proposed to predict the evolution of frictional strength and wear. This work is supported by the National Science Foundation under Award No. 0926111.   

Elastic instabilities in perfect crystals: from planar dislocation-like modes to diffuse buckling-like modes

We perform atomistic computer simulations of a model two dimensional perfect hexagonal crystal subjected to nano-indentation loading. For most crystallographic orientations, we find agreement with previous results for the case where the nearest-neighbor direction was perpendicular to the loading axis (cond-mat/1205.1700). In these orientations, the unstable mode takes the form of a sharply localized pair of atomic planes that slide relative to each other and form what is essentially a dipole of edge dislocations. The pair separation scales with the thickness of the film, $L$, and radius of the nanoindenter, $R$, in a non-trivial way that is independent of crystallographic orientation. For some crystallographic orientations with high surface energy, such as when the nearest-neighbor direction is co-incident with the loading axis, we find a new failure mode that emerges for very flat indenters and competes with the dislocation-like mode. The new diffuse failure mode is reminiscent of a buckling instability with a predominantly transverse character but exhibits both a nontrivial spatial extent and dominant wavelength that both depend on $L$ and $R$.   

Defect mechanics in crystalline packings of spherical caps

Topological defects are ubiquitous in 2D curved crystals. We study the structural features and underlying principals of dislocation mechanics in a crystalline spherical cap. Using nonlinear elasticity, we show that frustration arising from the curvature drives the stability of finite length radial grain boundaries in the ground-state packing. For sufficiently large caps at intermediate Gaussian curvature, linear arrays of dislocations relieve the geometric stresses. The number and length of grain boundaries grows with both the curvature and the size of crystalline patch. We also determine the elastic response of the system subject to radial tension. The interplay between the geometrically induced stresses and the tension leads to inhomogeneous stresses that determines the stability of the grain boundaries. The imposed tension stretching the curved crystal radially destabilizes the curvature-induced compressive zone and decrease the length of the grain boundaries. We characterize the transition from a polycrystalline structure to the perfect packing where all dislocations will be expelled at a critical tension that depends on the system size and the curvature. We find scaling laws for the number and length of minimal configurations of grain boundaries.   

Stick-slip nanofriction in cold-ion traps

Trapped cold ions are known to form linear or planar zigzag chains, helices or clusters depending on trapping conditions. They may be forced to slide over a laser induced corrugated potential, a mimick of sliding friction [1,2]. We present MD simulations of an incommensurate 101 ions chain sliding subject to an external electric field. As expected with increasing corrugation, we observe the transition from a smooth-sliding, highly lubric regime to a strongly dissipative stick-slip regime. Owing to inhomogeneity the dynamics shows features reminiscent of macroscopic frictional behaviors [3]. While the chain extremities are pinned, the incommensurate central part is initially free to slide. The onset of global sliding is preceded by precursor events consisting of partial slips of chain portions further from the center. We also look for frictional anomalies expected for the chain sliding across the linear-zigzag structural phase transition. Although the chain is too short for a proper critical behavior, the sliding friction displays a frank rise near the transition, due to opening of a new dissipative channel via excitations of transverse modes.\\[4pt] [1] A. Benassi et al, Nature Comm. 2, 236;\\[0pt] [2] T. Pruttivarasin et al, New Jour. of Phys. 13, 075012;\\[0pt] [3] S.M. Rubinstein et al, Nature 4, 1005.   

Electronic friction at the atomic scale: Conduction, electrostatic and magnetic effects

We have performed a magnetic probe microscopy study of levitation and atomic-scale friction for Fe on YBCO (Tc $=$ 92.5K) in the temperature range 65 - 293 K, to explore electronic contributions to friction at the atomic scale. The samples were prepared with oxygen-depleted surfaces, with thin semiconducting surface layers present atop the bulk. Below Tc, the friction coefficient was observed to be constant at 0.19 and exhibited no correlation with the strength of superconducting levitation forces observed below Tc. The friction coefficient exhibited a change in slope within experimental error of Tc that increased progressively above Tc and reached 0.33 by room temperature. The results were analyzed within the context of underlying atomic-scale electronic and phononic mechanisms that give rise to friction we conclude that contact electrification and static electricity play a significant role above Tc.\\[4pt] [1] I. Altfeder and J. Krim, J. Appl. Phys. (2012) \textbf{111 }(9), art{\#}094916 (2012)   

A hydrodynamic study of corner flow with leakage to orient dilute suspensions of ellipsoids

The macroscopic characteristics of thin films are related to the microscale arrangement of the underlying particles. Directing the assembly of anisotropic colloids through the use of external fields, such as flow fields, can lead to materials with novel catalytic, transport, and optical properties. Such fields are used to bias particle orientation in solution before deposition onto a solid substrate. Corner flow with leakage, akin to the doctor blade used in the pulp and paper industry, is a solution-based, processing technique that has been used to create nanostructured materials. We present an analysis that describes how dilute suspensions of ellipsoids couple to this field. A Lagrangian and Eulerian perspective is necessary to identify regions with not only a high straining component but also a sufficient time scale for alignment. Trajectories that lie completely within these ``hot spots'' result in a distribution in which greater than 80\% of the particles have an angle less than 20$^{\circ}$ with respect to the flow direction. Our results can be used to describe previously reported trends of particle orientation in literature. Overall, our work gives a broader understanding of some of the difficulties associated with using flow fields to fully align ellipsoids in dilute suspensions