102 research outputs found
Effect of shear-coupled grain boundary motion on coherent precipitation
We examine the interaction between precipitates and grain boundaries, which
undergo shear-coupled motion. The elastic problem, emerging from grain boundary
perturbations and an elastic mismatch strain induced by the precipitates, is
analysed. The resulting free elastic energy contains interaction terms, which
are derived numerically via the integration of the elastic energy density. The
interaction of the shear-coupled grain boundary and the coherent precipitates
leads to potential elastic energy reductions. Such a decrease of the elastic
energy has implications on the grain boundary shape and also on the solubility
limit near the grain boundary. By energy minimisation we are able to derive the
grain boundary shape change analytically. We apply the results to the Fe-C
system to predict the solubility limit change of cementite near an
-iron grain boundary.Comment: 8 page
Fast crack propagation by surface diffusion
We present a continuum theory which describes the fast growth of a crack by
surface diffusion. This mechanism overcomes the usual cusp singularity by a
self-consistent selection of the crack tip radius. It predicts the saturation
of the steady state crack velocity appreciably below the Rayleigh speed and tip
blunting. Furthermore, it includes the possibility of a tip splitting
instability for high applied tensions
Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts
The strength and stability of frictional interfaces, ranging from
tribological systems to earthquake faults, are intimately related to the
underlying spatially-extended dynamics. Here we provide a comprehensive
theoretical account, both analytic and numeric, of spatiotemporal interfacial
dynamics in a realistic rate-and-state friction model, featuring both
velocity-weakening and strengthening behaviors. Slowly extending, loading-rate
dependent, creep patches undergo a linear instability at a critical nucleation
size, which is nearly independent of interfacial history, initial stress
conditions and velocity-strengthening friction. Nonlinear propagating rupture
fronts -- the outcome of instability -- depend sensitively on the stress state
and velocity-strengthening friction. Rupture fronts span a wide range of
propagation velocities and are related to steady state fronts solutions.Comment: Typos and figures corrected. Supplementary information at:
http://www.weizmann.ac.il/chemphys/bouchbinder/frictional_instabilities.htm
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.Comment: Updated to published version: 2 Figures and a section adde
Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation
Frictional interfaces are abundant in natural and manmade systems and their
dynamics still pose challenges of fundamental and technological importance. A
recent extensive compilation of multiple-source experimental data has revealed
that velocity-strengthening friction, where the steady-state frictional
resistance increases with sliding velocity over some range, is a generic
feature of such interfaces. Moreover, velocity-strengthening friction has very
recently been linked to slow laboratory earthquakes and stick-slip motion. Here
we elucidate the importance of velocity-strengthening friction by theoretically
studying three variants of a realistic rate-and-state friction model. All
variants feature identical logarithmic velocity-weakening friction at small
sliding velocities, but differ in their higher velocity behaviors. By
quantifying energy partition (e.g. radiation and dissipation), the selection of
interfacial rupture fronts and rupture arrest, we show that the presence or
absence of velocity-strengthening friction can significantly affect the global
interfacial resistance and the total energy released during frictional
instabilities ("event magnitude"). Furthermore, we show that different forms of
velocity-strengthening friction (e.g. logarithmic vs. linear) may result in
events of similar magnitude, yet with dramatically different dissipation and
radiation rates. This happens because the events are mediated by interfacial
rupture fronts with vastly different propagation velocities, where stronger
velocity-strengthening friction promotes slower rupture. These theoretical
results may have significant implications on our understanding of frictional
dynamics.Comment: 9 pages, 6 figure
Modeling of grain boundary dynamics using amplitude equations
We discuss the modelling of grain boundary dynamics within an amplitude
equations description, which is derived from classical density functional
theory or the phase field crystal model. The relation between the conditions
for periodicity of the system and coincidence site lattices at grain boundaries
is investigated. Within the amplitude equations framework we recover
predictions of the geometrical model by Cahn and Taylor for coupled grain
boundary motion, and find both and
coupling. No spontaneous transition between these modes occurs due to
restrictions related to the rotational invariance of the amplitude equations.
Grain rotation due to coupled motion is also in agreement with theoretical
predictions. Whereas linear elasticity is correctly captured by the amplitude
equations model, open questions remain for the case of nonlinear deformations.Comment: 21 pages. We extended the discussion on the geometrical
nonlinearities in Section
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