Dynamical heterogeneity in periodically deformed polymer glasses

Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids

When subject to cyclic forcing, amorphous solids can reach periodic, repetitive states, where the system behaves plastically, but the particles return to their initial positions after one or more forcing cycles, where the latter response is called multi-periodic. It is known that plasticity in amorphous materials is mediated by local rearrangements called ``soft spots' or ``shear transformation zones'.Experiments and simulations indicate that soft spots can be modeled as hysteretic two-state entities interacting via quadrupolar displacement fields generated when they switch states and that these interactions can give rise to multi-periodic behavior. However, how interactions facilitate multi-periodicity is unknown. Here we show, using a model of random interacting two-state systems and molecular dynamics simulations, that multi-periodicity arises from oscillations in the magnitudes of the switching field of soft spots which cause soft spots to be active during some forcing cycles and idle during others. We demonstrate that these oscillations result from cooperative effects facilitated by the frustrated interactions between the soft spots. The presence of such mechanisms has implications for manipulating memory in frustrated hysteretic systems.

Confinement effects on the mechanical heterogeneity of polymer fiber glasses

Both polymer fiber glasses and bulk polymer glasses exhibit nonlinear mechanical responses under uniaxial deformation. In polymer fibers, however, polymer chains are confined strongly and the surface area is relatively large compared to their volume. The confinement and the surface may lead to the spatially heterogeneous relaxation of chains in polymer fibers. In this work we perform molecular dynamics simulations and investigate the relation between the heterogeneous dynamics and the nonlinear mechanical responses at a molecular level. Our molecular simulations capture successfully not only the nonlinear mechanical response but also the dependence of mechanical properties on the strain rate of typical polymer glasses as in experiments. We find that the local elastic modulus and the nonaffine displacement are spatially heterogeneous in the pre-yield regime, which results in a lower elastic modulus for polymer fibers than bulk polymer glasses. In the post-yield regime, those mechanical properties become relatively homogeneous. Monomers with large nonaffine displacement are localized mainly at the interfacial region in the pre-yield regime while highly nonaffine monomers are distributed throughout the fibers in the post-yield regime. We show that the nonaffine displacement during deformation relates closely to the mechanical response of the polymer fibers. We also find that in the strain-hardening regime there is a significant difference in the energetic contribution to the stress between polymer fibers and bulk polymers, for which the modulus of the strain-hardening regime of the polymer fibers is smaller than that of bulk polymers.

Shear Band Formation in Amorphous Materials under Oscillatory Shear Deformation

The effect of periodic shear on strain localization in disordered solids is investigated using molecular dynamics simulations. We consider a binary mixture of one million atoms annealed to a low temperature with different cooling rates and then subjected to oscillatory shear deformation with a strain amplitude slightly above the critical value. It is found that the yielding transition occurs during one cycle but the accumulation of irreversible displacements and initiation of the shear band proceed over larger number of cycles for more slowly annealed glasses. The spatial distribution and correlation function of nonaffine displacements reveal that their collective dynamics changes from homogeneously distributed small clusters to a system-spanning shear band. The analysis of spatially averaged profiles of nonaffine displacements indicates that the location of a shear band in periodically loaded glasses can be identified at least several cycles before yielding. These insights are important for the development of novel processing methods and prediction of the fatigue lifetime of metallic glasses.

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.

Nonaffine rearrangements of atoms in deformed and quiescent binary glasses

The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements become increasingly long-ranged, although they remain present even in a quiescent system due to thermal fluctuations.

Reversible plastic events during oscillatory deformation of amorphous solids

The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; namely, they tend to aggregate into relatively compact clusters that become comparable with the system size near the yield strain. Along with reversible displacements there exist a number of irreversible ones. With increasing strain amplitude, the probability of irreversible displacements during one cycle increases, which leads to permanent structural relaxation of the material.

Reversibility and criticality in amorphous solids

The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

The effect of a reversible shear transformation on plastic deformation of an amorphous solid

Langevin dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkably, we also found that, for a given strain amplitude, the peak value of the density profiles is a function of the ratio of the damping coefficient and the time scale of the shear transformation.

Plastic deformation of a model glass induced by a local shear transformation

The effect of a local shear transformation on plastic deformation of a three-dimensional amorphous solid is studied using molecular dynamics simulations. We consider a spherical inclusion, which is gradually transformed into an ellipsoid of the same volume and then converted back into the sphere. It is shown that at sufficiently large strain amplitudes, the deformation of the material involves localized plastic events that are identified based on the relative displacement of atoms before and after the shear transformation. We find that the density profiles of cage jumps decay away from the inclusion, which correlates well with the radial dependence of the local deformation of the material. At the same strain amplitude, the plastic deformation becomes more pronounced in the cases of weakly damped dynamics or large time scales of the shear transformation. We show that the density profiles can be characterized by the universal function of the radial distance multiplied by a dimensionless factor that depends on the friction coefficient and the time scale of the shear event.

Variable-amplitude oscillatory shear response of amorphous materials

Variable-amplitude oscillatory shear tests are emerging as powerful tools to investigate and quantify the nonlinear rheology of amorphous solids, complex fluids, and biological materials. Quite a few recent experimental and atomistic simulation studies demonstrated that at low shear amplitudes, an amorphous solid settles into an amplitude- and initial-conditions-dependent dissipative limit cycle, in which back-and-forth localized particle rearrangements periodically bring the system to the same state. At sufficiently large shear amplitudes, the amorphous system loses memory of the initial conditions, exhibits chaotic particle motions accompanied by diffusive behavior, and settles into a stochastic steady state. The two regimes are separated by a transition amplitude, possibly characterized by some critical-like features. Here we argue that these observations support some of the physical assumptions embodied in the nonequilibrium thermodynamic, internal-variables based, shear-transformation-zone model of amorphous viscoplasticity; most notably that "flow defects" in amorphous solids are characterized by internal states between which they can make transitions, and that structural evolution is driven by dissipation associated with plastic deformation. We present a rather extensive theoretical analysis of the thermodynamic shear-transformation-zone model for a variable-amplitude oscillatory shear protocol, highlighting its success in accounting for various experimental and simulational observations, as well as its limitations. Our results offer a continuum-level theoretical framework for interpreting the variable-amplitude oscillatory shear response of amorphous solids and may promote additional developments.