Shear-transformation-zone theory of yielding in athermal amorphous materials

Effective temperatures in nonequilibrium statistical physics

This paper summarizes two related effective-temperature analyses of nonequilibrium phenomena: first, dislocations in deforming crystals and, second, chaotic behaviors of defects in thermally driven Rayleigh-Bénard hydrodynamic systems. The results are encouraging for broader applications of this statistical concept.

Power fluctuations in sheared amorphous materials: A minimal model

The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical microrheological experiments.

Bond-space operator disentangles quasilocalized and phononic modes in structural glasses

The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low-energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a linear operator defined on the space of particle interactions (bonds) in a disordered material. We find that this bond-force-response operator offers a different interpretation of QLMs in glasses and cleanly recovers some of their important statistical and structural features. The analysis presented here reveals the dependence of the number density (per frequency) and spatial extent of QLMs on material preparation protocol (annealing). Finally, we discuss future research directions and possible extensions of this work.

Brittle-ductile transitions in a metallic glass

Recent computational and laboratory experiments have shown that brittle-ductile transitions in the notch toughnesses of metallic glasses such as Vitreloy 1 are strongly sensitive to the initial effective disorder (or "fictive") temperature. Glasses with lower effective temperatures are weak and brittle; those with higher effective temperatures are strong and ductile. The analysis of this phenomenon presented here examines the onset of fracture at the tip of a notch as predicted by the shear-transformation-zone theory of spatially varying plastic deformation. The central ingredient of this analysis is an approximation for the dynamics of the plastic zone formed by stress concentration at the notch tip. This zone first shields the tip but then, with increasing stress, expands suddenly, producing a discontinuous transition between brittle and ductile failure in satisfactory agreement with the numerical and experimental observations.

Thermodynamic analysis of the Livermore molecular-dynamics simulations of dislocation-mediated plasticity

Results of recent large-scale molecular dynamics simulations of dislocation-mediated solid plasticity are compared with predictions of the statistical thermodynamic theory of these phenomena. These computational and theoretical analyses are in substantial agreement with each other in both their descriptions of strain-rate-dependent steady plastic flows and of transient stress peaks associated with initially small densities of dislocations. The comparisons between the numerical simulations and basic theory reveal inconsistencies in some conventional phenomenological descriptions of solid plasticity.

On the universality of the flow properties of soft-particle glasses

We identify the minimal interparticle interactions necessary for a particle dynamics simulation to predict the structure and flow behaviour of soft particle glasses (SPGs). Generally, two kinds of forces between the particles must be accounted for in simulations of SPGs: viscous or frictional drag forces and elastic contact forces. Far field drag forces are required to dissipate energy in the simulations and capture the effect of the rheology of the suspending fluid. Elastic forces are found to be dominant compared to near-field drag or other forms of friction forces and are the most important component to compute the rheology. The shear stress, the first and second normal stress differences for different interparticle force laws collapse onto universal master curves of the Herschel-Bulkley form by non-dimensionalizing the stress with the yield stress and the shear rate with the viscosity of the suspending fluid divided by the low-frequency shear modulus. The Herschel-Bulkley exponents are close to 0.5 with a slight dependence on the repulsive pairwise elastic forces.

Understanding the mechanisms of amorphous creep through molecular simulation

Molecular processes of creep in metallic glass thin films are simulated at experimental timescales using a metadynamics-based atomistic method. Space-time evolutions of the atomic strains and nonaffine atom displacements are analyzed to reveal details of the atomic-level deformation and flow processes of amorphous creep in response to stress and thermal activations. From the simulation results, resolved spatially on the nanoscale and temporally over time increments of fractions of a second, we derive a mechanistic explanation of the well-known variation of creep rate with stress. We also construct a deformation map delineating the predominant regimes of diffusional creep at low stress and high temperature and deformational creep at high stress. Our findings validate the relevance of two original models of the mechanisms of amorphous plasticity: one focusing on atomic diffusion via free volume and the other focusing on stress-induced shear deformation. These processes are found to be nonlinearly coupled through dynamically heterogeneous fluctuations that characterize the slow dynamics of systems out of equilibrium.

Thermodynamic theory of dislocation-enabled plasticity

The thermodynamic theory of dislocation-enabled plasticity is based on two unconventional hypotheses. The first of these is that a system of dislocations, driven by external forces and irreversibly exchanging heat with its environment, must be characterized by a thermodynamically defined effective temperature that is not the same as the ordinary temperature. The second hypothesis is that the overwhelmingly dominant mechanism controlling plastic deformation is thermally activated depinning of entangled pairs of dislocations. This paper consists of a systematic reformulation of this theory followed by examples of its use in analyses of experimentally observed phenomena including strain hardening, grain-size (Hall-Petch) effects, yielding transitions, and adiabatic shear banding.

Non-trivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins of non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

Modeling energy storage and structural evolution during finite viscoplastic deformation of glassy polymers

The enthalpic response of amorphous polymers depends strongly on their thermal and deformation history. Annealing just below the glass transition temperature (T_{g}) causes a large endothermic overshoot of the isobaric heat capacity at T_{g} as measured by differential scanning calorimetry, while plastic deformation (cold work) can erase this overshoot and create an exothermic undershoot. This indicates that a strong coupling exists between the polymer structure, thermal response, and mechanical deformation. In this work, we apply a recently developed thermomechanical model for glassy polymers that couples structural evolution and viscoplastic deformation to investigate the effect of annealing and plastic deformation on the accumulation of stored energy during cold work and calorimetry measurements of heat flow. The thermomechanical model introduces the effective temperature as an additional state variable in a nonequilibrium thermodynamics setting to describe the structural evolution of the material. The results show that the model accurately describes the stress and enthalpy response of quenched and annealed polymers with different plastic predeformations. The model also shows that at 30% strain in uniaxial compression, 45% of the applied work is converted into stored energy, which is consistent with experimental data from literature.

Thermal effects in dislocation theory. II. Shear banding

The thermodynamic dislocation theory presented in previous papers is used here to describe shear-banding instabilities. Central ingredients of the theory are a thermodynamically defined effective configurational temperature and a formula for the plastic strain rate determined by thermally activated depinning of entangled dislocations. This plastic strain rate is extremely sensitive to variations of the stress and the ordinary temperature. As a result of this sensitivity, the system undergoes rapid shear banding instabilities when ordinary thermal relaxation is slow. It also undergoes rapid changes from elastic to plastic behaviors at yielding transitions.

Edwards Thermodynamics for a Driven Athermal System with Dry Friction

We obtain, using semianalytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear divergence of the correlation length as a function of energy density observed in direct numerical simulations of the model under tapping dynamics. We further characterize analytically this divergence using a Gaussian approximation for the distribution of mechanically stable configurations, and show that it is related to the existence of a peculiar infinite temperature critical point.

Statistical thermodynamics of strain hardening in polycrystalline solids

This paper starts with a systematic rederivation of the statistical thermodynamic equations of motion for dislocation-mediated plasticity proposed in 2010 by Langer, Bouchbinder, and Lookman [Acta Mat. 58, 3718 (2010)ACMAFD1359-645410.1016/j.actamat.2010.03.009]. It then uses that theory to explain the anomalous rate-hardening behavior reported in 1988 by Follansbee and Kocks and to explore the relation between hardening rate and grain size reported in 1995 by Meyers et al. A central theme is the need for physics-based, nonequilibrium analyses in developing predictive theories of the strength of polycrystalline materials.