The 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 non-unique, 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.Comment: 4 pages, 4 figures, first of a two-paper series (experiments); no change in content, minor textual revision

Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a direct evidence for a diverging length scale at the glass transition (ii) an identification of the glass transition with the disappearance of fluid-like regions and (iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively.Comment: 5 pages, 5 figs.; 2 figs. omitted, new fig., quasi-crystal discussion omitted, new material on relaxation time

Non-universality in Micro-branching Instabilities in Rapid Fracture: the Role of Material Properties

In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced by 3-dimensional dynamics. In both cases the present ab-initio theoretical models are still too far from reality, disregarding some fundamental physics of the phenomena.Comment: 4 pages, 6 figures, PRL submitte

Nonequilibrium Thermodynamics of 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.Comment: 8 pages. Third of a three-part serie