Creep and aging of hard-sphere glasses under constant stress

Probing cage dynamics in concentrated hard-sphere suspensions and glasses with high frequency rheometry

The cage concept, a central microscopic mechanism for glassy dynamics, has been utilized in concentrated colloidal suspensions to describe a number of phenomena. Here, we probe the evolution of cage formation and shear elasticity with increasing volume fraction in hard sphere suspensions, with emphasis on the short-time dynamics. To this end, we utilize linear viscoelastic (LVE) measurements, by means of conventional rotational rheometers and a home-made HF piezo-rheometer, to probe the dynamic response over a broad range of volume fractions up to the very dense glassy regime in proximity to random close packing. We focus on the LVE spectra and times shorter than those corresponding to the dynamic shear modulus G' plateau, where the system approaches transient localization and cage confinement. At these short times (higher frequencies), a dynamic cage has not yet fully developed and particles are not (strictly) transiently localized. This corresponds to an effective solid-to-liquid transition in the LVE spectrum (dynamic moduli) marked by a high frequency (HF) crossover. On the other hand, as the volume fraction increases caging becomes tighter, particles become more localized, and the onset of the localization time scale becomes shorter. This onset of transient localization to shorter times shifts the HF crossover to higher values. Therefore, the study of the dependence of the HF crossover properties (frequency and moduli) on volume fractions provides direct insights concerning the onset of particle in-cage motion and allows direct comparison with current theoretical models. We compare the experimental data with predictions of a microscopic statistical mechanical theory where qualitative and quantitative agreements are found. Findings include the discovery of microscopic mechanisms for the crossover between the two exponential dependences of the onset of the localization time scale and the elastic shear modulus at high volume fractions as a consequence of emergent many body structural correlations and their consequences on dynamic constraints. Moreover, an analytic derivation of the relationship between the high frequency localized short-time scale and the elastic shear modulus is provided which offers new physical insights and explains why these two variables are experimentally observed to exhibit nearly-identical behaviors.

Power law creep and delayed failure of gels and fibrous materials under stress

Motivated by recent experiments studying the creep and breakup of a protein gel under stress, we introduce a simple mesoscopic model for the irreversible failure of gels and fibrous materials, and demonstrate it to capture much of the phenomenology seen experimentally. This includes a primary creep regime in which the shear rate decreases as a power law over several decades of time, a secondary crossover regime in which the shear rate attains a minimum, and a tertiary regime in which the shear rate increases dramatically up to a finite time singularity, signifying irreversible material failure. The model also captures a linear Monkman-Grant scaling of the failure time with the earlier time at which the shear rate attained its minimum, and a Basquin-like power law scaling of the failure time with imposed stress, as seen experimentally. The model furthermore predicts a slow accumulation of low levels of material damage during primary creep, followed by the growth of fractures leading to sudden material failure, as seen experimentally.

Delayed elastic contributions to the viscoelastic response of foams

We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function. The associated power-law spectrum is consistent with soft glassy rheology of systems with mechanical noise temperatures just above the glass transition [Fielding et al., J. Rheol. 44, 323 (2000)] and originates from a combination of superdiffusive bubble dynamics and stress diffusion, as recently evidenced in simulations of coarsening foam [Hwang et al., Nat. Mater. 15, 1031 (2016)].

Yielding and resolidification of colloidal gels under constant stress

We examine the macroscopic deformation of a colloidal depletion gel subjected to a step shear stress. Three regimes are identified depending on the magnitude of the applied stress: (i) for stresses below yield stress, the gel undergoes a weak creep in which the bulk deformation grows sublinearly with time similar to crystalline and amorphous solids. For stresses above yield stress, when the bulk deformation exceeds approximately the attraction range, the sublinear increase of deformation turns into a superlinear growth which signals the onset of non-linear rearrangements and yielding of the gel. However, the long-time creep after such superlinear growth shows two distinct behaviors: (ii) under strong stresses, a viscous flow is reached in which the strain increases linearly with time. This indicates a complete yielding and flow of the gel. In stark contrast, (iii) for weak stresses, the gel after yielding starts to resolidify. More homogenous gels that are produced through enhancement of either interparticle attraction strength or strain amplitude of the oscillatory preshear, resolidify gradually. In contrast, in gels that are more heterogeneous resolidification occurs abruptly. We also find that heterogenous gels produced by oscillatory preshear at intermediate strain amplitude yield in a two-step process. Finally, the characteristic time for the onset of delayed yielding is found to follow a two-step decrease with increasing stress. This is comprised of an exponential decrease at low stresses, during which bond reformation is decisive and resolidification is detected, and a power law decrease at higher stresses where bond breaking and particle rearrangements dominate.

Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear

We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.

i-Rheo: determining the linear viscoelastic moduli of colloidal dispersions from step-stress measurements

We report on the application of a Fourier transform-based method, 'i-Rheo', to evaluate the linear viscoelastic moduli of hard-sphere colloidal dispersions, both in the fluid and glass states, from a direct analysis of raw step-stress (creep) experimental data. We corroborate the efficacy of i-Rheo by comparing the outputs of creep tests performed on homogenous complex fluids to conventional dynamic frequency sweeps. A similar approach is adopted for a number of colloidal suspensions over a broad range of volume fractions. For these systems, we test the limits of the method by varying the applied stress across the materials' linear and non-linear viscoelastic regimes, and we show that the best results are achieved for stress values close to the upper limit of the materials' linear viscoelastic regime, where the signal-to-noise ratio is at its highest and the non-linear phenomena have not appeared yet. We record that, the range of accessible frequencies is controlled at the higher end by the relative weight between the inertia of the instrument and the elasticity of the complex material under investigation; whereas, the lowest accessible frequency is dictated by the extent of the materials' linear viscoelastic regime. Nonetheless, despite these constrains, we confirm the effectiveness of i-Rheo for gaining valuable information on the materials' linear viscoelastic properties even from 'creep ringing' data, confirming its potency and general validity as an accurate method for determining the material's rheological behaviour for a variety of complex systems.

Precursors of fluidisation in the creep response of a soft glass

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

Creep dynamics of athermal amorphous materials: a mesoscopic approach

Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesoscale elasto-plastic descriptions to analyze such transient dynamics in athermal systems. Both our mean-field and space-dependent approaches consistently reproduce the typical experimental strain rate responses to different applied steps in stress. Moreover, they allow us to understand basic processes involved in the strain rate slowing down (creep) and the strain rate acceleration (fluidization) phases. The fluidization time increases in a power-law fashion as the applied external stress approaches a static yield stress. This stress value is related to the stress over-shoot in shear start-up experiments, and it is known to depend on sample preparation and age. By calculating correlations of the accumulated plasticity in the spatially resolved model, we reveal different modes of cooperative motion during the creep dynamics.

Mean-Field Scenario for the Athermal Creep Dynamics of Yield-Stress Fluids

We develop a theoretical description based on an existent mean-field model for the transient dynamics prior to the steady flow of yielding materials. The mean-field model not only reproduces the experimentally observed nonlinear time dependence of the shear-rate response to an external stress, but also allows for the determination of the different physical processes involved in the onset of the reacceleration phase after the initial slowing down and a distinct fluidization phase. The fluidization time displays a power-law dependence on the distance of the applied stress to an age-dependent yield stress, which is not universal but strongly dependent on initial conditions.