Session Y37: Fracture, Friction, and Deformation

Tearing Fracture of Polymer Foam Sheet

We study crack propagation in a sheet of polymer foam. The sheet was stretched, and an initial crack was introduced to induce the crack propagation. When the sheet width is shorter than the crack length, the energy release rate (ERR) $G$ of the system is independent of the crack length and constant during the propagation. Under the constant ERR condition, we find that the crack propagates at a constant speed. We observed the crack propagation for various values of ERR by changing the width of the sheet and the applied strain. Depending on values $G$ of ERR, the measured velocity of the crack propagation was in the range from 0.01 mm/s to 10000 mm/s. We also found power laws between the velocity of the crack $V$ and $G$. While in the literature the power law with the exponent close to three ($V\sim G^3$) has been reported, we found that polymer foam sheets have different exponents depending on physical characteristics of polymer foam. In this presentation, we report the experimental result and its analysis.   

Effect of system compliance on crack nucleation in soft materials

Puncture mechanics in soft materials is critical for the development of new surgical instruments, robot assisted-surgery as well as new materials used in personal protective equipment. However, analytical techniques to study this important deformation process are limited. We have previously described a simple experimental method to study the resistive forces and failure of a soft gel being indented with a small tip needle. We showed that puncture stresses can reach two orders of magnitude greater than the material modulus and that the force response is insensitive to the geometry of the indenter at large indentation depths. Currently, we are examining the influence of system compliance on crack nucleation (e.g. puncture) in soft gels. It is well known that system compliance influences the peak force in adhesion and traditional fracture experiments; however, its influence on crack nucleation is unresolved. We find that as the system becomes more compliant, lower peak forces required to puncture a gel of certain stiffness with the same indenter were measured. \quad We are developing scaling relationships to relate the peak puncture force and system compliance. Our findings introduce new questions with regard to the possibility of intrinsic materials properties related to the critical stress and energy for crack nucleation in soft materials.   

Crack proparagation in attractive colloidal systems

Despite its importance, the fracture of materials, especially the regime of slow, plastic fracture, remains poorly understood. This is especially true in amorphous materials, where local inhomogeneities and structural disorder are crucial to determine the mode of failure, yet they cannot be modeled with classical homogenization methods. We use new attractive colloidal systems to study fracture at time and length scales much longer than in molecular systems. In this specific project, we focus on gels made of fluorescent pNipam microgel particles aggregated via critical Casimir interactions, to analyze, at the microscopic level, nonlinear and dissipative processes in the material ahead of the propagating crack tip.   

Localized Plastic Deformation in Colloidal Micropillars

When driven beyond yield, many amorphous solids exhibit concentrated regions of large plastic strain referred to as shear bands. Shear bands are the result of localized, cooperative rearrangements of particles known as shear transformations (STs). STs are dilatory: their operation results in an increase of free volume and local softening that leads to spatially concentrated plasticity. However, the evolution of STs into a macroscopic shear band remains poorly understood. To study the process, we perform compression experiments on amorphous colloidal micropillars. The micropillars, which are composed of fluorescent 3 \({\mu}\text{m}\) PMMA particles, are made freestanding so that shear banding instabilities are not suppressed by confining boundaries. During compression, we observe strong localization of strain in a band of the pillar. As deformation proceeds, the sheared region continues to dilate until it reaches the colloidal glass transition, at which point dilation terminates. We quantify a length scale by measuring the extent of spatial correlations in strain. This length scale decreases gradually with increasing dilation and becomes static beyond the glass transition. Our results reinforce the idea of yield as a stress-induced glass transition in amorphous solids.   

Theory of rate dependent fracture size effects

The idea that the solid failure can be described by means of the Kramer theory, where the intrinsic energy barrier is reduced proportionally to the applied field, first appeared in material science to treat the kinetic fracture of solids under applied stresses and dates back to '40s. Most previous works focused on the thermal dependence of the average strength or the failure time in creep experiments and did not address the survival distribution and its size dependence. To this end, we start from recent theories developed for single-molecule pulling, where the molecule rate coefficient for rupture (or unbinding) is modified by the presence of an external time-dependent force, and we adjust it to a macroscopic elastic object. We generalize the extreme value theory to account for failures of materials with an explicit dependence on temperature, strain rate and size of the object. We show that in the limit of macroscopic objects, large strain rate and low temperature, thermal fluctuations are negligible and the usual extreme value theory is recovered. We provide the critical interpretation of several experiments in terms of our theory, furnishing a clearcut criterion for thermal effects to become relevant. [Phys. Rev. Applied , 024011]   

Major and minor slip-events in frictional stick-slip

Several universal phenomena characterize friction that are independent of the materials involved such as the logarithmic aging of the static friction coefficient and the logarithmic velocity weakening of the dynamic friction coefficient. We study dry friction between rough surfaces with programmed statistical profiles. By measuring the displacement field at the frictional interface we observe stick-slip behavior which reveals two kinds of slip: major events that tend to grow large and unbounded and minor events that usually stay small and bounded.   

Tribological Properties of Nanodiamonds in Aqueous Suspensions: Effect of the Surface Charge.

The presence of granular nanoparticulates, be they wear particles created naturally by frictional rubbing at a geological fault line or products introduced as lubricant additives, can dramatically alter friction at solid-liquid interfaces. Given the complexity of such systems, understanding system properties at a fundamental level is particularly challenging. The Quartz Crystal Microbalance (QCM) is an ideal tool for studies of material-liquid-nanoparticulate interfaces. We have employed it here to study the uptake and nanotribological properties of positively and negatively charged 5-15 nm diameter nanodiamonds dispersed in water[1] in the both the presence and absence of a macroscopic contact with the QCM electrode. The nanodiamonds were found to impact tribological performance at both nanometer and macroscopic scales. The tribological effects were highly sensitive to the sign of the charge: negatively (positively) charged particles were more weakly (strongly) bound and reduced (increased) frictional drag at the solid-liquid interface. For the macroscopic contacts, negatively charged nanodiamonds appeared to be displaced from the contact, while the positively charged ones were not. Overall, the negatively charged nanodiamonds were more stable in an aqueous dispersion for extended time periods.   

Transition from superlubrically sliding islands to pinned monolayer, demonstrated in Xe/Cu(111) (*)

A molecular dynamics simulation case study of Xe on Cu(111) reveals unexpected information on the exceptionally smooth sliding state associated with incommensurate superlubricity which is argued to emerge in the large size limit of naturally incommensurate Xe islands. As coverage approaches a full monolayer, theory predicts an abrupt adhesion-driven two-dimensional density compression on the order of several per cent, implying a hysteretic jump from superlubric free islands to a pressurized sqrt()x sqrt()commensurate (and pinned, and therefore immobile) monolayer. These results match with recent quartz crystal microbalance data which show remarkably large slip times with increasing submonolayer coverage, signalling superlubricity, followed by a dramatic drop to zero for the dense commensurate monolayer [1]. Careful analysis of this variety of island sliding phenomena should be essential in future applications of friction at crystal/adsorbate interfaces. (*) Matching experimental work by M. Pierno, L. Bruschi, G. Mistura, G. Paolicelli, A. di Bona, S. Valeri. [1] M. Pierno, L. Bruschi, G. Mistura, G. Paolicelli, A. di Bona, S.Valeri, R. Guerra, A. Vanossi, E.Tosatti, Nature Nanotechnology 10, 714 (2015).   

Elastic deformations disrupt structural superlubricity in large contacts

Force microscopy experiments observe ultra-low friction between solids with incommensurate lattice structures. This phenomenon is referred to as superlubricity and is due to a cancellation of lateral forces because surfaces sample all relative local configurations with equal probability. We use simulations to show that elasticity disrupts superlubricity in sufficiently large circular contacts. The simulations include atomic-scale geometry and reach micron-scales. For rigid solids, cancellation is complete except at the contact boundary. The static friction force per contact area, $\tau$, falls as a power of contact radius, $\tau \sim a^{-3/2}$. Elastic deformations limit this cancellation when the contact radius $a$ is larger than a characteristic length scale set by the core width of interfacial dislocations, $b_{core}$. For $a>b_{core}$ sliding of moderately incommensurate contacts is dominated by dislocation motion and, at large $a$, $\tau$ approaches a constant value near the Peierls stress needed to move edge dislocations. Surprisingly, the stress in commensurate contacts drops to nearly the same value at large $a$. We conclude that true structural lubricity does not occur in large contacts, although the constant shear stress drops rapidly with $b_{core}$.   

Subharmonic Shapiro steps in sliding colloidal monolayers

We examine the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential modulation is applied to two mutually sliding incommensurate 2D lattices. Specifically we present realistic MD simulations of a monolayer of charged colloids that are dragged by an external force over an optically generated periodic potential, where the colloid sliding is enacted through the motion of soliton or antisoliton lines between locally commensurate domains. Clear integer Shapiro steps, with the synchronous rigid advancement of the whole monolayer, known from previous studies [1], are found. The jump between one step and the next during each AC cycle corresponding to particles jumping from one patch to the next, across the soliton boundary. We find additional smaller ``subharmonic'' steps. Here, the overall colloid advancement takes several AC cycles. At each cycle, different subsets of particles negotiate the soliton line between commensurate domains [2]. The wide parameter tunability of colloid monolayers makes these predictions potentially easy to access in an experimentally rich 2D geometry. [1] A. Libal et al., Phys. Rev. Lett. 96, 188301 (2006). [2] S. Paronuzzi et al., J. Phys. Cond. Matt., in press (2015)   

Superlubric-pinned Aubry transition of two dimensional monolayers in optical lattices.

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice ``corrugation'' potential emulate friction between ideal crystal surfaces. Static friction is always present when the monolayer and the optical lattices are commensurate, but when they are incommensurate the presence or absence of static friction depends upon the system parameters. In 1D, at the Aubry dynamical phase transition the static friction goes continuously from zero (superlubricity) to finite as the periodic corrugation strength is increased. We look for the Aubry-like transition in the more realistic 2D case of a monolayer in an incommensurate periodic potential using molecular dynamics simulations. Results confirm a clear and sharp 2D superlubric-pinned transition upon increasing corrugation strength. Unlike the 1D Aubry transition which is continuous, the 2D transition is first-order, with a jump of static friction. At the 2D Aubry transition there is no change of symmetry, a sudden rise of the colloid-colloid interaction energy, and a compensating drop of the colloid-corrugation energy. The observability of the superlubric-pinned colloid transition is proposed and discussed [1]. [1] D. Mandelli, et al., Phys. Rev. B, to be published (2015).   

Superlubricity in a nutshell.

Cold ion chains in optical lattices emulate the Frenkel-Kontorova model, whose frictional behavior depends on commensurability or incommensurability between the two lattices. In the latter and more interesting case, there are two different regimes: one with pinning and static friction, and one without pinning, called superlubric. Only in an infinite chain the two regimes exist, separated by a dynamical Aubry transition. A cold ion chain is necessarily finite and short, we nevertheless proposed that a clear remnant of that transition should persist in trapped ion chains[1]. Recent experiments showed how in fact a small number of ions suffices to demonstrate incommensuration effects, with a change of friction by orders of magnitude from matched to mismatched geometries[2]. Here we present simulation results suggesting for increasing optical lattice amplitude a clear vestigial Aubry transition for very few ions, with a weak dependence upon the ion number and a stronger one upon the relative mismatch. A properly chosen amplitude should therefore show the vestigial transition from pinning at small mismatch to superlubricity at large mismatch. Alternatively, a chain which at T$=$0 is pinned at all mismatches could develop an Aubry transition at finite temperature to a state of "thermally induced superlubricity", due to the thermal smearing of the optical lattice amplitude. [1] A. Benassi et al., Nat. Comm. 2, 236 (2011). [2] A. Bylinskii et al, Science 348, 1115-1118 (2015).   

An Artificial Ising System with Phononic Excitations

Many intractable systems and problems can be reduced to a system of interacting spins. Here, we report mapping collective phononic excitations from different sources of crystal vibrations to spin systems. The phononic excitations in our experiments are due to micro and nano cracking (yielding crackling noises due to lattice distortion). We develop real time mapping of the multi-array senores to a network-space and then mapping the excitation- networks to spin-like systems. We show that new mapped system satisfies the quench (impulsive) characteristics of the Ising model in 2D classical spin systems. In particular, we show that our artificial Ising system transits between two ground states and approaching the critical point accompanies with a very short time frozen regime, inducing formation of domains separated by kinks. For a cubic-test under a true triaxial test (3D case), we map the system to a 6-spin ring under a transversal-driving field where using functional multiplex networks, the vector components of the spin are inferred (i.e., XY model). By visualization of spin patterns of the ring per each event, we demonstrate that ``kinks'' (as defects) proliferate when system approach from above to its critical point. We support our observations with employing recorded acoustic excitations during distortion of crystal lattices in nano-indentation tests on different crystals (silicon and graphite), triaxial loading test on rock (poly-crystal) samples and a true 3D triaxial test.   

Gluing Soft Interfaces by Nanoparticles

Using a combination of the molecular dynamics simulations and scaling analysis we studied reinforcement of interface between two soft gel-like materials by spherical nanoparticles. Analysis of the simulations shows that the depth of penetration of a nanoparticle into a gel is determined by a balance of the elastic energy of the gel and nanoparticle deformations and the surface energy of nanoparticle/gel interface. In order to evaluate work of adhesion of the reinforced interface, the potential of mean force for separation of two gels was calculated. These simulations showed that the gel separation proceeds through formation of necks connecting nanoparticle with two gels. The shapes of the necks are controlled by a fine interplay between nanoparticle/gel surface energies and elastic energy of the neck deformation. Our simulations showed that by introducing nanoparticles at soft interfaces, the work required for separation of two gels could be 10-100 times larger than the work of adhesion between two gels without nanoparticle reinforcement. These results provide insight in understanding the mechanism of gluing soft gels and biological tissues by nano- and micro-sized particles.