Yield stresses and flow curves in metallic glass formers and granular systems

Active microrheology of a bulk metallic glass

The glass transition remains unclarified in condensed matter physics. Investigating the mechanical properties of glass is challenging because any global deformation that might result in shear rejuvenation would require a prohibitively long relaxation time. Moreover, glass is well known to be heterogeneous, and a global perturbation would prevent exploration of local mechanical/transport properties. However, investigation based on a local probe, i.e., microrheology, may overcome these problems. Here, we establish active microrheology of a bulk metallic glass, via a probe particle driven into host medium glass. This technique is amenable to experimental investigations via nanoindentation tests. We provide distinct evidence of a strong relationship between the microscopic dynamics of the probe particle and the macroscopic properties of the host medium glass. These findings establish active microrheology as a promising technique for investigating the local properties of bulk metallic glass.

Slow and long-ranged dynamical heterogeneities in dissipative fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

Multi-scale lattice Boltzmann and mode-coupling theory calculations of the flow of a glass-forming liquid

We present a hybrid-lattice Boltzmann (LB) algorithm for calculating the flow of glass-forming fluids that are governed by integral constitutive equations with pronounced nonlinear, non-Markovian dependence of the stresses on the flow history. The LB simulation for the macroscopic flow fields is combined with the mode-coupling theory (MCT) of the glass transition as a microscopic theory, in the framework of the integration-through transients formalism. Using the combined LB-MCT algorithm, pressure-driven planar channel flow is studied for a schematic MCT model neglecting spatial correlations in the microscopic dynamics. The cessation dynamics after removal of the driving pressure gradient shows strong signatures of oscillatory flow both in the macroscopic fields and the microscopic correlation functions.

Nonlinear rheology of glass-forming colloidal dispersions: transient stress-strain relations from anisotropic mode coupling theory and thermosensitive microgels

Transient stress-strain relations close to the colloidal glass transition are obtained within the integration through transients framework generalizing mode coupling theory to flow driven systems. Results from large-scale numerical calculations are quantitatively compared to experiments on thermosensitive microgels, which reveals that theory captures the magnitudes of stresses semi-quantitatively even in the nonlinear regime, but overestimates the characteristic strain where plastic events set in. The former conclusion can also be drawn from flow curves, while the latter conclusion is supported by a comparison to single particle motion measured by confocal microscopy. The qualitative picture, as previously obtained from simplifications of the theory in schematic models, is recovered by the quantitative solutions of the theory for Brownian hard spheres.

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Athermal jamming versus thermalized glassiness in sheared frictionless particles

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature T, packing fraction φ, and uniform applied shear strain rate γ[over ·]. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters φ and T/γ[over ·]. Here T/γ[over ·]→0 defines the athermal limit in which a shear-driven jamming transition occurs at a well defined φ(J) and T/γ[over ·]→∞ defines the thermalized limit where an equilibrium glass transition may take place at φ(G). This conclusion argues that athermal jamming and equilibrium glassy behavior are not controlled by the same critical point. Preliminary results suggest φ(G)<φ(J).

Unified study of glass and jamming rheology in soft particle systems

We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning, and yield stress regimes near the "colloidal" glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the "jamming" transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass-to-jamming crossover in the flow curves, and discuss the experimental implications of our results.

Glass dynamics at high strain rates

We present a shear-transformation-zone (STZ) theoretical analysis of molecular-dynamics simulations of a rapidly sheared metallic glass. These simulations are especially revealing because, although they are limited to high strain rates, they span temperatures ranging from well below to well above the glass transition. With one important discrepancy, the simplified STZ theory used here reproduces the simulation data, including the way in which those data can be made to collapse approximately onto simple curves by a scaling transformation. The STZ analysis implies that the system's behavior at high strain rates is controlled primarily by effective-temperature thermodynamics, as opposed to system-specific details of the molecular interactions. The discrepancy between theory and simulations occurs at the lower strain rates for temperatures near the glass transition. We argue that this discrepancy can be resolved by the same multispecies generalization of STZ theory that has been proposed recently for understanding frequency-dependent viscoelastic responses, Stokes-Einstein violations, and stretched-exponential relaxation in equilibrated glassy materials.

Creep in colloidal glasses

We investigate the nonlinear response to shear stress of a colloidal hard-sphere glass, identifying several regimes depending on time, sample age, and the magnitude of applied stress. This emphasizes a connection between stress-imposed deformation of soft and hard matter, in particular, colloidal and metallic systems. A generalized Maxwell model rationalizes logarithmic creep for long times and low stresses. We identify diverging time scales approaching a critical yield stress. At intermediate times, strong aging effects are seen, which we link to a stress overshoot seen in stress-strain curves.