Session Y30: Jamming & Shearing

Plastic Deformation of Semicrystalline Polyethylene under Extension, Compression, and Shear using Molecular Dynamics Simulation

Molecular dynamics simulation has been performed to investigate the plastic deformation of semicrystalline polyethylene under various modes of deformation, such as extension, compression and shear. Many mechanical and structural properties of semicrystalline polyethylene are examined and compared with previous study [Lee and Rutledge, Macrmol. 44, 3096 (2011)]. Under tensile deformation, we observed crystallographic slip at low strains (e$_{3}$ \textless\ 0.08) regardless of deformation rate. However, two different yield mechanisms were monitored as a function of deformation rate at intermediate strains (e$_{3}$ \textless\ 0.25). At high strains (e$_{3}$ \textgreater\ 0.25), melting and recrystallization were observed for slow deformation (5$\times$10$^{6}$s$^{-1})$ whereas cavitations were monitored for fast deformation (5$\times$10$^{7}$s$^{-1})$. Under compressive deformation, stress-strain curve shows very similar behavior to tensile deformation at low strain, and crystallographic slip plays an important role for mechanical response of semicrystalline polyethylene. Under shear deformation, the chains tend to stretch and align into the shear direction. We also calculated stiffness constants for shear deformation and compared these to results of previous study [In't Veld et al. Macromol. 39, 439 (2006)]. Interestingly, semicyrstalline polyethylene shows typical transient behavior of Newtonian fluids under shear deformation, which we compare to various constitutive models, such as the Upper-Convected Maxwell (UCM) and Giesekus models.   

Size Segregation in Sheared Jammed Colloids

It is well known that granular materials can spontaneously size segregate when continuously driven. However, in jammed colloidal suspensions, this phenomenon is not well understood. Colloidal dispersions provide a unique system to study the structure and dynamics of jammed matter. In this talk, we present results of size segregation of a continuously sheared binary colloidal suspension well above point J. Our colloidal system is comprised of indexed-matched bi-disperse silica particles with diameters $a = \{2.3\mu m$ and $3.2\mu m\}$ and at $\phi\approx 61\%$, well above the colloidal glass transition. We apply a highly controlled shear at a constant shear rate through the use of a rheometer. By coupling our rheometer with a high-speed laser scanning confocal microscope, we directly image the structure and flow profiles of the suspension as it un-jams. We observe migration of the small and large species; large particles move to the top while the small particles move toward the bottom conserving the total volume fraction in all regions. Moreover, we find that an associating feature of segregation is a sustained shear band. Our results are consistent with a recently proposed void filling and squeeze expulsion mechanism.   

Reversible and irreversible deformation in hard-sphere colloidal glasses

Colloidal glass provides a unique experimental system with which to study the structure, defects, and dynamics of amorphous materials. We report experiments on 1.55-$\mu$m-diameter, hard-sphere silica colloidal glasses under conditions of uniform shear. We deform the samples to maximum strains ranging from 0.5\% to 10\% at various strain rates, and then reverse the deformation so that the net bulk strain is zero at the end of the experiment. We use confocal microscopy to follow the 3D, real-time trajectories of roughly 50,000 particles over the course of an experiment. In this way, we probe the elastic, anelastic, and plastic response of the system, with particular emphasis on the specific, local mechanisms of deformation. We directly observe yield as the onset of local, irreversible deformation. In both sheared and unsheared (quiescent) samples, we observe thermally-activated clusters of particles that behave as Eshelby inclusions, undergoing highly localized plastic strain that couples elastically to the surrounding material. We identify and characterize these regions as they develop in the glass, with particular focus on density-related properties including the Voronoi volume and free volume.   

Shearbanding in Amorphous Solids and Interacting Eshelby Singularities

We will describe recent work in which it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists of a highly correlated line of Eshelby quadrupoles all having the same orientation and some density $\rho$. We describe how the energy $E(\rho,\gamma)$ associated with such highly correlated structures as a function of the density $\rho$ and the external strain $\gamma$ can be calculated. We then show that when the strain $\gamma$ is smaller than some characteristic yield stress $\gamma_y$ the minimum energy solution is attained for $\rho=0$ (i.e. isolated localized plastic events). While for $\gamma \ge \gamma_y$ there is a bifurcation allowing a finite density of quadrupoles. We finally suggest how the universal Johnson-Samwer $T^{2/3}$ temperature reduction of the yield stress in metallic glasses can be accounted for by such ideas.   

Compression of granular pillars with constant width at top and bottom

Granular media display both elastic and plastic behavior, including the formation of shear bands under extreme loading. In this study, we performed two-dimensional granular pillar compression experiments and tracked of grain- and macro- scale flows via video imaging and force measurement. Especially we focus on the condition that the top and bottom widths of the granular pillars are constrained to avoid free expansion along the contact edge. This causes more energy to be stored elastically deep inside of the pillars, which gives rise to a different kind of shear banding than for free top/bottom widths. Furthermore we tried several series of experiments with different elastic/frictional particles and also ordered/disordered systems. We demonstrate how the micro properties and packing structure contribute to the formation of shear band to discuss the mechanical failure in disordered packing.   

The Chaotic Dynamics of Jamming

Despite the appearance of simplicity, much of the behavior of granular materials remains mysterious. One intriguing puzzle is the dynamical mechanism underlying the ``jamming'' transition, in which disordered grains become rigid at high density. By applying nonlinear dynamical techniques to simulated 2D shear cells, we reveal the mechanisms of jamming and find they conflict with the prevailing picture of growing cooperative regions. Additionally, at the density corresponding to random close packing, we find a dynamical transition from chaotic to non-chaotic states accompanied by diverging dynamical length and time scales. Furthermore, we find that the dominant cooperative dynamical modes are strongly correlated with particle rearrangements and become increasingly unstable before stress jumps, providing a way to predict the times and locations of these earthquake-like stress-release events.   

Shear Transformation Zone theory parameters from molecular dynamics and experiment

Shear Transformation Zone (STZ) theory provides a continuum framework to describe the deformation of amorphous systems. However, as a phenomenological theory it relies upon parameters which must be determined for a specific material system. We present current progress towards a set of theoretical and computational methodologies for determining the parameters of STZ theory. We investigate two distinct systems, a copper-zirconium lamellar nanocomposite, and a simple yield stress fluid (YSF), where both systems are loaded in simple shear. We show that the molecular dynamics simulations of the nanocomposite system and experimental measurements of the YSF can be used to provide the initial conditions of the dynamical fields as well as the essential STZ parameters.   

Heterogeneous relaxation dynamics in amorphous materials under cyclic loading

Molecular dynamics simulations are performed to investigate heterogeneous dynamics in amorphous glassy materials under oscillatory shear strain. We consider three-dimensional binary Lennard-Jones mixture well below the glass transition temperature. The structural relaxation and dynamic heterogeneity are quantified by means of the self-overlap order parameter and the four-point correlation function. We found that at small strain amplitudes, the mean square displacement develops an extended sub-diffusive plateau followed by the diffusive regime; whereas at larger amplitudes only the diffusive regime is present. At intermediate time and length scales, the dynamic susceptibility exhibits a pronounced peak, whose magnitude increases at larger strain amplitudes, indicating progressively larger size of dynamically correlated regions. The analysis of particle hopping dynamics reveals that the periodic deformation generates a heterogeneous temporal response characterized by intermittent bursts of large particle displacements. The role of dynamical facilitation in the formation of clusters of mobile particles is discussed.   

Shear deformation of naocrystal-metallic glass composites: A computational analysis

Due to the shear strain localization, the limited ductility becomes the major drawback for the application of metallic glass materials, and the introducing of crystalline phase has been regarded as the effective method for improving the ductility of these materials. Here, we systematically investigate the nanocrystal-metallic glass composites by using Molecular Dynamic (MD) simulations. The three--dimension (3D) atomic configurations with different crystalline grain sizes and factions are constructed based on the ZrCu EAM potential. The phase diagram based on the crystalline grain size-fraction is established between single nanocrystal phase and amorphous phase. The mechanical responses of these materials are investigated by applying the shear deformation, and the relationships between the mechanical properties and atomic structure information (crystalline fraction, grain size ?) are established.   

Criticality of non-colloidal suspensions under periodic shear

Suspensions of non-colloidal particles under slow periodic strain undergo a dynamical phase transition: they can either relax to an absorbing configuration in which particles are not displaced after every cycle or can reach a stationary fluctuating state. We correlate microscopic particle motion with macroscopic rheology and explain the existence of the critical transition experimentally by comparing particles of different surface roughness and by varying the volume fraction towards jamming. Particle roughness is implicated in the transition to reversibility, as smoother particles push the critical strain to higher values. Theoretically, we attempt to construct quasi-particles that encompass the strain-induced particle interactions and discover that geometry is not sufficient to understand suspension irreversibility under strain.   

Temperature-equivalent of strain rate for the yield stress of amorphous solids

We couple the recently developed self-learning metabasin escape (SLME) algorithm with continuous shear deformations to probe the yield stress as a function of temperature for a binary Lennard-Jones amorphous solid. At room temperature and laboratory strain rates, the activation volume associated with yield is less than 10 atoms, while the yield stress is found to be as sensitive to a 1.5{\%}Tg increase in temperature as it is to a one order of magnitude decrease in strain rate. Our SLME results suggest a transition in yield mechanism for temperatures lower than about 0.54Tg that is not captured by extrapolating high strain rate molecular dynamics simulations to laboratory strain rates.   

Identifying Defects in Disordered and Ordered Solids

Characterizing defects in solids is an important step to developing continuum equations for failure in materials. Defects in crystalline solids (i.e. dislocations) are easy to characterize, but in disordered solids the lack of crystalline order makes it difficult to identify where particle rearrangements are likely to occur. Here we describe simulations of quasi-statically sheared athermal jammed packings of bidisperse discs in 2D. We perform energy minimization at each step using a combination of conjugate gradient and line search algorithms. By analyzing localized excitations in low-frequency vibrational modes, one can identify flow defects in disordered solids. We have developed tools to carefully match these flow defects to corresponding plastic events, and we analyze how the properties of defects change across packings ranging from disordered to completely ordered. This will allow us to understand the fundamental connections between dislocations and flow defect dynamics in solids.   

Atomic-scale flow defect population in Cu-Zr metallic glass

We adapt the method developed by Manninget al.[PRL 107, 108302 (2011)] to characterize the flow defects population of a Cu-Zr metallic glass modeled using embedded atom method potentials. We investigate how the statistics of Shear Transformation Zones (STZs) change as a function of system size and quench rate during glass formation. We also consider the evolution of the STZ population during mechanical loading. On the basis of this analysis, we relate our results with predictions of the STZ theory of amorphous plasticity to consider the history dependence implicit in the strain-stress response of the metallic glass.   

Viscous rheology of soft particles near jamming

We investigate the effect of changing the exact nature of the viscous interaction in simulations of sheared soft, viscous, repulsive disks, which are considered to be a good model for foams and emulsions. We determine the way in which the power-law exponent of the rheological curve, in other words the shear-thinning or shear-thickening part, depends on the microscopic viscous interaction around the jamming density. We attempt to find a model that describes and predicts this dependence.