17,892 research outputs found
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.Comment: 7 pages, 5 figure
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.Comment: 8 pages, 5 figure
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.Comment: 8 pages, 4 figure
Shear-transformation-zone theory of plastic deformation near the glass transition
The shear-transformation-zone (STZ) theory of plastic deformation in
glass-forming materials is reformulated in light of recent progress in
understanding the roles played the effective disorder temperature and entropy
flow in nonequilibrium situations. A distinction between fast and slow internal
state variables reduces the theory to just two coupled equations of motion, one
describing the plastic response to applied stresses, and the other the dynamics
of the effective temperature. The analysis leading to these equations contains,
as a byproduct, a fundamental reinterpretation of the dynamic yield stress in
amorphous materials. In order to put all these concepts together in a realistic
context, the paper concludes with a reexamination of the experimentally
observed rheological behavior of a bulk metallic glass. That reexamination
serves as a test of the STZ dynamics, confirming that system parameters
obtained from steady-state properties such as the viscosity can be used to
predict transient behaviors.Comment: 15 pages, four figure
Local Geometric Invariants of Integrable Evolution Equations
The integrable hierarchy of commuting vector fields for the localized
induction equation of 3D hydrodynamics, and its associated recursion operator,
are used to generate families of integrable evolution equations which preserve
local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics
Unified derivation of phase-field models for alloy solidification from a grand-potential functional
In the literature, two quite different phase-field formulations for the
problem of alloy solidification can be found. In the first, the material in the
diffuse interfaces is assumed to be in an intermediate state between solid and
liquid, with a unique local composition. In the second, the interface is seen
as a mixture of two phases that each retain their macroscopic properties, and a
separate concentration field for each phase is introduced. It is shown here
that both types of models can be obtained by the standard variational procedure
if a grand-potential functional is used as a starting point instead of a
free-energy functional. The dynamical variable is then the chemical potential
instead of the composition. In this framework, a complete analogy with
phase-field models for the solidification of a pure substance can be
established. This analogy is then exploited to formulate quantitative
phase-field models for alloys with arbitrary phase diagrams. The precision of
the method is illustrated by numerical simulations with varying interface
thickness.Comment: 36 pages, 1 figur
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