Point defects in real crystals at finite temperatures are inevitable. Their dynamics severely influence the mechanical properties of crystals under shear giving rise to nonlinear effects such as ductility. Therefore, it is crucial to explore the interplay of the equilibrium point-defect diffusion timescales and shear-induced timescales to understand the plastic deformation of crystals. Using extensive nonequilibrium molecular dynamics simulations, we present a study on the yielding behavior of cluster crystals (CC), an archetypal model for defect-rich crystals where the crystalline structure is characterized by multiple occupancies (cluster) of particles at a lattice site. In equilibrium, particles diffuse via site-to-site hopping keeping the crystalline structure intact. We consider the CCs at a fixed density and different temperatures where it remains in the FCC structure, and the diffusion timescales of particles vary depending on the temperature. We choose the range of shear rates, which covers timescales higher and much lower than the equilibrium diffusion timescales at high temperatures. For the considered range of shear rates and temperatures, both the macro and microscopic responses of CCs to the shear suggest that the yielding scenario remains independent of the diffusion of particles. It involves the plastic deformation of the underlying crystalline structure. The averaged local bond order parameters and local angle measurements demonstrate the structural changes and cooperative movement of the center of masses of the clusters close to the yield point. A comparison with the soft-sphere (SS) FCC crystal reveals the similarities in the yielding behavior of both systems. Nonetheless, diffusion of particles influences certain features, such as a less prominent increase in the local bond order parameters and local angles close to the yield point.
Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress leve…
We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous sh…
Shear Unfreezing Explains Yielding, Plasticity and Neck Initiation of Glassy Polymers
School of Physics, Beihang University（北京航空航天大学物理学院）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭恒武科教协同中心）
We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behaviour of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve towards the threshold energy as the strain amplitude is increased towards the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behaviour, with…
Self-organization, and transitions from reversible to irreversible behaviour, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behaviour is related to yielding of amorphous solids, jamming, and memory formation, \emph{etc.} How these phenomena are related to each other has not, however, been much studied. In order to obtain a uni…
Yielding behavior in amorphous solids has been investigated in computer simulations employing uniform and cyclic shear deformation. Recent results characterise yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively…
We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, using a method that fully accounts for the fluid mechanics of the solvent between the particles, and between the particles and the walls, as well as for the solid mechanics of changes in the particle shapes. We thus capture the widely observed phenomenon of elastohydrodynamic wall slip, in which the soft particles become deformed in shear and lift away from the wall slightly, leaving behind a thin lubricating solvent layer of high shear. For imposed stresses below the materia…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
We study the yielding behaviour of a model glass under cyclic athermal quastistatic deformation computationally, and show that yielding is characterised by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localised. Strain localisation is accompanied by a corresponding change in the energies, and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band whereas the energies correspond to the highest possible energy minima at the given density within the s…
We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behaviour of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a non-trivial, non-monotonic approach to the yielded state. The timescale diverges as one approach…
Colloidal gels are formed through the aggregation of attractive particles, whose size ranges from 10~nm to a few micrometers, suspended in a liquid. Such gels are ubiquitous in everyday life applications, from food products to paints or construction materials, in particular thanks to their ability to easily "yield", i.e., to turn from a solid to a liquid under the application of a weak external load. Understanding and controlling the mechanical response of colloidal gels is therefore of prime importance. Depending on the details of the system, however, the resulting gel networks present differ…
We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a thr…
Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over $10^5$ particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for $Pe>1$, the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering …
Amorphous solids display a ductile to brittle transition as the kinetic stability of the quiescent glass is increased, which leads to a material failure controlled by the sudden emergence of a macroscopic shear band in quasi-static protocols. We numerically study how finite deformation rates influence ductile and brittle yielding behaviors using model glasses in two and three spatial dimensions. We find that a finite shear rate systematically enhances the stress overshoot of poorly-annealed systems, without necessarily producing shear bands. For well-annealed systems, the non-equilibrium disco…
The influence of alternating shear orientation and strain amplitude of cyclic loading on yielding in amorphous solids is investigated using molecular dynamics simulations. The model glass is represented via a binary mixture that was rapidly cooled well below the glass transition temperature and then subjected to oscillatory shear deformation. It was shown that periodic loading at strain amplitudes above the critical value first induces structural relaxation via irreversible displacements of clusters of atoms during a number of transient cycles, followed by an increase in potential energy due t…
Yielding behavior is well known in attractive colloidal suspensions. Adhesive non-Brownian suspensions, in which the interparticle bonds are due to finite-size contacts, also show yielding behavior. We use a combination of steady-state, oscillatory and shear-reversal rheology to probe the physical origins of yielding in the latter class of materials, and find that yielding is not simply a matter of breaking adhesive bonds, but involves unjamming from a shear-jammed state in which the micro-structure has adapted to the direction of the applied load. Comparison with a recent constraint-based rhe…
We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft m…
The time evolution and spatial correlations of nonaffine displacements in deformed amorphous solids are investigated using molecular dynamics simulations. The three-dimensional model glass is represented via the binary mixture, which is slowly annealed well below the glass transition temperature and then sheared at a constant strain rate. It is shown that with increasing strain, the typical size of clusters of atoms with large nonaffine displacements increases, and these clusters remain spatially homogeneously distributed, until the yielding point when mobile atoms become localized within a sy…
We consider the yielding under simple shear of a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glassformer as an effective system of icosahedra [Pinney et al. J. Chem. Phys. 143 244507 (2015)]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localisation behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localisation starts immediately upon shea…
The yielding transition of amorphous materials is studied with a two-dimensional Hamiltonian model that allows both shear and volume deformations. The model is investigated as a function of the relative value of the bulk modulus $B$ with respect to the shear modulus $μ$. When the ratio $B/μ$ is small enough, the yielding transition becomes discontinuous, yet reversible. If the system is driven at constant strain rate in the coexistence region, a spatially localized shear band is observed while the rest of the system remains blocked. The crucial role of volume fluctuations in the origin of this…
Predicting the time-dependent yielding of colloidal gels under constant stress enables control of their mechanical stability and transport. Using rotational rheometry, we show that the shear rate of colloidal gels during an early stage of deformation known as primary creep can forecast an eventual yielding. Irrespective of whether the gel strain-softens or strain-hardens, the shear rate before failure exhibits a characteristic power-law decrease as a function of time, distinct from the linear viscoelastic response. We model this early-stage behavior as a series of uncorrelated local plastic ev…
Amorphous solids are critical in the design and production of nanoscale devices, but under strong confinement these materials exhibit changes in their mechanical properties which are not well understood. Phenomenological models explain these properties by postulating an underlying defect structure in these materials but do not detail the microscopic properties of these defects. Using machine learning methods, we identify mesoscale defects that lead to shear banding in polymer nanopillars well below the glass transition temperature as a function of pillar diameter. Our results show that the pri…
We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low inertial number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress $Σ$ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied $Σ$, isotropically prepared states with size $L$ must undergo a total strain $γ_{\rm ms}(Σ,L)$. The number density of MS packings ($\propto γ_{\rm ms}^{-1}$) vanishes for $Σ> Σ_c \approx 0.…
Granular packings of non-convex or elongated particles can form free-standing structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for non-interlocking particles remains unclear. We report on experiments and numerical simulations of sheared columns of "hexapods," particles consisting of three mutually orthogonal sphero-cylinders whose centers coincide. We vary the length-to-diameter aspect ratio, $α$, of the sphero-cylinders and subject the packings to quasistatic direct shear. For s…
Non-equilibrium molecular dynamics simulations are performed to investigate the dynamic behavior of three-dimensional binary glasses prepared via an instantaneous quench across the glass transition. We found that with increasing strain amplitude up to a critical value, the potential energy approaches lower minima in steady state, whereas the amplitude of shear stress oscillations becomes larger. Below the yielding transition, the storage modulus dominates the mechanical response, and the gradual decay of the potential energy over consecutive cycles is accompanied by reduction in size of transi…
Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly and gradually (ductile behaviour) or fail abruptly and catastrophically (brittle behaviour); the roles of sample annealing, disorder and shear band formation in the onset of yielding and failure; and, most importantly from a practical viewpoint, whether any impending catastrophic failure can be anticipated before it happens. We address these questions by stu…
Using non-equilibrium molecular dynamics simulations we study the yielding behaviour of a model cluster crystal formed by ultrasoft particles under shear. We investigate the evolution of stress as a function of strain for different shear rates, $\dotγ$, and temperatures. The stress-strain relation displays a pronounced maximum at the yielding point; the height of this maximum, $σ_\text{p}$, increases via a power law with an increasing shear range and tends to saturate to a finite value if the limit shear rate goes to zero (at least within the considered temperature range). Interestingly, this …
Molecular-motor generated active stresses drive the cytoskeleton away from equilibrium, endowing it with tunable mechanical properties that are essential for diverse functions such as cell division and motility[1-5]. Designing analogous biomimetic systems is a key prerequisite for creating active matter that can emulate cellular functions[6-7]. These long-term goals requires understanding of how motor-generated stresses tune the mechanics of filamentous networks[8-11]. In microtubule-based active matter, kinesin motors generate extensile motion that leads to persistent breaking and reforming o…
