Eran Bouchbinder

The Near-Tip Fields of Fast Cracks

Slightly Cracked While there are detailed theories to explain the propagation of a crack in the bulk of a material, our understanding of cracking breaks down near the tip of the crack. Experimentally, it is very hard to observe the propagation of a crack at the tip region because it tends to move very quickly. Livne et al. (p. 1359) approached this problem by working with a polyacrylamide gel in which cracks progress slowly enough to monitor them. A hierarchy of linear and nonlinear regions was observed through which energy is transported before being dissipated by the growing crack. How stresses are distributed during cracking will determine whether the resulting failure will be brittle or ductile. The linear and nonlinear elastic responses near a growing crack tip can reveal how materials fail. In a stressed body, crack propagation is the main vehicle for material failure. Cracks create large stress amplification at their tips, leading to large material deformation. The material response within this highly deformed region will determine its mode of failure. Despite its great importance, we have only a limited knowledge of the structure of this region, because it is generally experimentally intractable. By using a brittle neo-Hookean material, we overcame this barrier and performed direct and precise measurements of the near-tip structure of rapid cracks. These experiments reveal a hierarchy of linear and nonlinear elastic zones through which energy is transported before being dissipated at a crack’s tip. This result provides a comprehensive picture of how remotely applied forces drive material failure in the most fundamental of fracture states: straight, rapidly moving cracks.

Nonequilibrium thermodynamics of driven amorphous materials. II. Effective-temperature theory.

We develop a theory of the effective disorder temperature in glass-forming materials driven away from thermodynamic equilibrium by external forces. Our basic premise is that the slow configurational degrees of freedom of such materials are weakly coupled to the fast kinetic-vibrational degrees of freedom and therefore that these two subsystems can be described by different temperatures during deformation. We use results from the preceding paper on the nonequilibrium thermodynamics of systems with internal degrees of freedom to derive an equation of motion for the effective temperature and to learn how this temperature couples to the dynamics of the system as a whole.

Breakdown of linear elastic fracture mechanics near the tip of a rapid crack.

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities (0.2-0.8c(s)), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be nonunique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the r(-1/2) divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.

Cell reorientation under cyclic stretching

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations – cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell’s passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells, measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.

Fracture toughness of metallic glasses: annealing-induced embrittlement.

Quantitative understanding of the fracture toughness of metallic glasses, including the associated ductile-to-brittle (embrittlement) transitions, is not yet available. Here, we use a simple model of plastic deformation in glasses, coupled to an advanced Eulerian level set formulation for solving complex free-boundary problems, to calculate the fracture toughness of metallic glasses as a function of the degree of structural relaxation corresponding to different annealing times near the glass temperature. Our main result indicates the existence of an elastoplastic crack tip instability for sufficiently relaxed glasses, resulting in a marked drop in the toughness, which we interpret as annealing-induced embrittlement transition similar to experimental observations.

Dynamics of Simple Cracks

Cracks are the major vehicle for material failure and often exhibit rather complex dynamics. The laws that govern their motion have remained an object of constant study for nearly a century. The simplest kind of dynamic crack is a single crack that moves along a straight line. We first briefly review the current understanding of this “simple” object. We then critically examine the assumptions of the classic, scale-free theory of dynamic fracture and note when it works and how it may fail if certain assumptions are relaxed. Several examples are provided in which the introduction of physical scales into this scale-free theory profoundly affects both a crack’s structure and the resulting dynamics.

Nonequilibrium thermodynamics of driven amorphous materials. III. Shear-transformation-zone plasticity.

We use the internal-variable, effective-temperature thermodynamics developed in two preceding papers to reformulate the shear-transformation-zone (STZ) theory of amorphous plasticity. As required by the preceding analysis, we make explicit approximations for the energy and entropy of the STZ internal degrees of freedom. We then show that the second law of thermodynamics constrains the STZ transition rates to have an Eyring form as a function of the effective temperature. Finally, we derive an equation of motion for the effective temperature for the case of STZ dynamics.

On the velocity‐strengthening behavior of dry friction

The onset of frictional instabilities, e.g., earthquakes nucleation, is intimately related to velocity-weakening friction, in which the frictional resistance of interfaces decreases with increasing slip velocity. While this frictional response has been studied extensively, less attention has been given to steady state velocity-strengthening friction, in spite of its potential importance for various aspects of frictional phenomena such as the propagation speed of interfacial rupture fronts and the amount of stored energy released by them. In this note we suggest that a crossover from steady state velocity-weakening friction at small slip velocities to steady state velocity-strengthening friction at higher velocities might be a generic feature of dry friction. We further argue that while thermally activated rheology naturally gives rise to logarithmic steady state velocity-strengthening friction, a crossover to stronger-than-logarithmic strengthening might take place at higher slip velocities, possibly accompanied by a change in the dominant dissipation mechanism. We sketch a few physical mechanisms that may account for the crossover to stronger-than-logarithmic steady state velocity strengthening and compile a rather extensive set of experimental data available in the literature, lending support to these ideas.

Thermodynamic theory of dislocation-mediated 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.

Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation

This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we study a solid whose internal degrees of freedom are vacancies that govern irreversible volume changes. Using this model, we compare a thermodynamic theory based on the Clausius-Duhem inequality to a statistical analysis based directly on the law of increase of entropy. The statistical theory is used first to derive the Clausius-Duhem inequality. We then use the theory to go beyond those results and obtain detailed equations of motion, including a rate factor that is enhanced by deformation-induced noisy fluctuations. The statistical analysis points to the need for understanding how both energy and entropy are shared by the vacancies and their environments.