arXiv subjects

J. S. Langer

Publications and source records attributed to J. S. Langer.

At least 19 recordsLinked to original sources

arXiv2022

Statistical Thermodynamics of Dislocations in Solids

This review is a simplified summary of the thermodynamic dislocation theory, with special emphasis on the role of an effective temperature. Materials scientists, for decades, have asserted that statistical thermodynamics is not applicable to dislocations. By use of simple, first-principles analyses and comparisons with experimental data, I argue that these scientists have been wrong, and that this venerable field urgently needs to be revitalized because of its wide-ranging fundamental and technological importance. In addition to describing recent progress in understanding strain hardening, yielding, shear banding, and the like, I argue that the thermodynamic dislocation theory can lead to a much needed, first-principles understanding of brittle and ductile fracture in crystalline solids.

cond-mat.mtrl-sci↗

arXiv2021

Fracture Toughness of Crystalline Solids

This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a sharpening instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The theory includes a mathematical conjecture regarding tip dynamics at small dislocation densities. Nevertheless, its predictions agree quantitatively with the experimental data, including both brittle and ductile fracture, over a wide range of temperatures, loading rates, and initial conditions.

cond-mat.mtrl-sci↗

arXiv2020

Scaling Confirmation of the Thermodynamic Dislocation Theory

We show that the thermodynamic dislocation theory (TDT) predicts a scaling relation between stresses, strain rates, and temperatures for steady-state deformations of crystalline solids, and that this relation is accurately obeyed by a wide range of experimental data for both aluminum and copper. Unlike conventional phenomenological dislocation theories, the TDT is based on the second law of thermodynamics. Its success implies that descriptions of solid deformation that are not based on the statistical mechanics of nonequilibrium processes cannot be relied upon to be predictive. Thus there is an urgent need -- and a new opportunity -- to revitalize this central part of materials physics.

cond-mat.mtrl-sci↗

arXiv2020

Brittle-Ductile Transitions in a Metallic Glass

Recent computational and laboratory experiments have shown that the brittle-ductile transitions in metallic glasses such as Vitreloy1 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 slightly rounded notch as predicted by the shear-transformation-zone (STZ) 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 breaks down suddenly producing a discontinuous transition between brittle and ductile failure, in agreement with the numerical and experimental observations.

cond-mat.mtrl-sci↗

arXiv2018

Statistical Thermodynamics of Crystal Plasticity

This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline solids. This topic is especially appropriate for the Journal of Statistical Physics because materials scientists, for decades, have asserted that statistical thermodynamics is inapplicable to dislocations. By use of simple, first-principles analyses and comparisons with experimental data, I argue that these materials scientists have been wrong, and that this field should now be revisited because of its broad-ranging intellectual and technological importance.

cond-mat.mtrl-sci↗

arXiv2018

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 campared 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 flow and of a transient stress peak 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.

cond-mat.mtrl-sci↗

arXiv2017

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.

cond-mat.mtrl-sci↗

arXiv2017

Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperatures and smallest strain rates.

cond-mat.mtrl-sci↗

arXiv2017

Yielding Transitions and Grain-Size Effects in Dislocation Theory

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of Meyers et al. for polycrystalline copper under strain-hardening conditions. The main assertion is that the well known Hall-Petch effects are caused by enhanced strengths of dislocation sources at the edges of grains instead of the commonly assumed resistance to dislocation flow across grain boundaries. The theory describes rapid transitions between elastic and plastic deformation at yield points; thus it can be used to predict grain-size dependence of both yield stresses and flow stresses

cond-mat.mtrl-sci↗

arXiv2016

Thermal Effects in Dislocation Theory II: Shear Banding and Yielding Transitions

The thermodynamic dislocation theory presented in preceding 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 deformation rate determined by thermally activated depinning of entangled dislocations. An important feature of this paper is an interpretation of yielding transitions in polycrystalline solids.

cond-mat.mtrl-sci↗

arXiv2016

Thermal Effects in Dislocation Theory

The mechanical behaviors of polycrystalline solids are determined by the interplay between phenomena governed by two different thermodynamic temperatures: the configurational effective temperature that controls the density of dislocations, and the ordinary kinetic-vibrational temperature that controls activated depinning mechanisms and thus deformation rates. This paper contains a review of the effective-temperature theory and its relation to conventional dislocation theories. It includes a simple illustration of how these two thermal effects can combine to produce a predictive theory of spatial heterogeneities such as shear-banding instabilities. Its main message is a plea that conventional dislocation theories be reformulated in a thermodynamically consistent way so that the vast array of observed behaviors can be understood systematically.

cond-mat.mtrl-sci↗

arXiv2015

Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations

We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.

cond-mat.soft↗

arXiv2015

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. 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.

cond-mat.mtrl-sci↗

arXiv2015

Shear-Transformation-Zone Theory of Yielding in Athermal Amorphous Materials

Yielding transitions in athermal amorphous materials resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. In particular, there is a correlation length that grows rapidly, but ultimately saturates near the yield point.

cond-mat.mtrl-sci↗

arXiv2014

Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume

Naturally-occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation of shear band volume with shear rate in angular particles -- recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone (STZ) theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration, and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions, and propose additional experiments that provide stringent tests on the new theoretical elements.

cond-mat.stat-mech↗

arXiv2013

Theories of Glass Formation and the Glass Transition

This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the most intriguing features of glassy behavior, but are too unrealistic to provide bases for predictive theories. As illustrations of what I mean, the first part of this article is devoted to brief summaries of imaginative, sensible, but disparate and often contradictory ideas for solving glass problems. Almost all of these ideas remain alive today, with their own enthusiastic advocates. I then describe numerical simulations, mostly by H. Tanaka and coworkers, in which it appears that very simple, polydisperse systems of hard disks and spheres develop long range, Ising-like, bond-orientational order as they approach glass transitions. Finally, I summarize my recent proposal that topologically ordered clusters of particles, in disordered environments, tend to become aligned with each other as if they were two-state systems, and thus produce the observed Ising-like behavior. Neither Tanaka's results nor my proposed interpretation of them fit comfortably within any of the currently popular glass theories.

cond-mat.stat-mech↗

arXiv2013

Ising Model of a Glass Transition

Numerical simulations by Tanaka and coworkers indicate that glass forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.

cond-mat.stat-mech↗

arXiv2013

Nonequilibrium thermodynamics and glassy rheology

Mechanically driven glassy systems and complex fluids exhibit a wealth of rheological behaviors that call for theoretical understanding and predictive modeling. A distinct feature of these nonequilibrium systems is their dynamically evolving state of structural disorder, which determines their rheological responses. Here we highlight a recently developed nonequilibrium thermodynamic framework in which the structural state is characterized by an evolving effective disorder temperature that may differ from the ordinary thermal temperature. The specific properties of each physical system of interest are described by a small set of coarse-grained internal state variables and their associated energies and entropies. The dynamics of the internal variables, together with the flow of energy and entropy between the different parts of the driven system, determine continuum-level rheological constitutive laws. We conclude with brief descriptions of several successful applications of this framework.

cond-mat.soft↗