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[en] The shear-transformation-zone (STZ) theory of plastic deformation predicts that sufficiently soft, noncrystalline solids are linearly unstable against forming periodic arrays of microstructural shear bands. A limited nonlinear analysis indicates that this instability may be the mechanism responsible for strain softening in both constant-stress and constant-strain-rate experiments. The analysis presented here pertains only to one-dimensional banding patterns in two-dimensional systems, and only to very low temperatures. It uses the rudimentary form of the STZ theory in which there is only a single kind of zone rather than a distribution of them with a range of transformation rates. Nevertheless, the results are in qualitative agreement with essential features of the available experimental data. The nonlinear theory also implies that harder materials, which do not undergo a microstructural instability, may form isolated shear bands in weak regions or, perhaps, at points of concentrated stress
[en] 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.
[en] I propose a model of fracture in which the curvature of the crack tip is a relevant dynamical variable and crack advance is governed solely by plastic deformation of the material near the tip. This model is based on a rate-and-state theory of plasticity introduced in earlier papers by Falk, Lobkovsky, and myself. In the approximate analysis developed here, fracture is brittle whenever the plastic yield stress is nonzero. The tip curvature finds a stable steady-state value at all loading strengths, and the tip stress remains at or near the plastic yield stress. The crack speed grows linearly with the square of the effective stress intensity factor above a threshold that depends on the surface tension. This result provides a possible answer to the fundamental question of how breaking stresses are transmitted through plastic zones near crack tips. (c) 2000 The American Physical Society
[en] The excitation-chain theory of the glass transition, proposed in an earlier publication, predicts diverging, super-Arrhenius relaxation times and, via a similarly diverging length scale, suggests a way of understanding the relations between dynamic and thermodynamic properties of glass-forming liquids. I argue here that critically large excitation chains play a role roughly analogous to that played by critical clusters in the droplet model of vapor condensation. Unlike a first-order condensation point in a vapor, the glass transition is not a conventional phase transformation, and may not be a thermodynamic transition at all
[en] 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. (key issues reviews)
[en] We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate. Those features include linear viscoelastic flow at small applied stresses, strain hardening at larger stresses, and a dynamic transition to viscoplasticity at a yield stress. In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters. The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics. (c) 1999 The American Physical Society
[en] 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. Here, 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.
[en] Exact expressions for the amplitudes for scattering of a particle by a complex nucleus are written down. It is then shown that, with a particular weight function, the scattering amplitude can be averaged over energy by going to a complex energy, i. e., [S (E)]AV = S(E + iI), where I is the interval averaged over. The average amplitude is then expressed in terms of a perturbation expansion. In perturbation theory of the first kind, expansion in powers of the nucleus is carried out. In the second kind of perturbation theory, all particles are treated symmetrically and all but the average effects of the interactions are treated as perturbations. This allows one to relate the parameters of the optical potential back to nucleon-nucleon forces. It is shown that these expansions are, in general, convergent, due to the fact that the excitation into which a given excitation decays has a longer life-time than the original one. Reprint of a paper published in 'Annals of physics', vol 6, N. 3, mar 1959, p. 209-229