89 research outputs found
Fluctuation phenomena in crystal plasticity - a continuum model
On microscopic and mesoscopic scales, plastic flow of crystals is
characterized by large intrinsic fluctuations. Deformation by crystallographic
slip occurs in a sequence of intermittent bursts ('slip avalanches') with
power-law size distribution. In the spatial domain, these avalanches produce
characteristic deformation patterns in the form of slip lines and slip bands
which exhibit long-range spatial correlations. We propose a generic continuum
model which accounts for randomness in the local stress-strain relationships as
well as for long-range internal stresses that arise from the ensuing plastic
strain heterogeneities. The model parameters are related to the local dynamics
and interactions of lattice dislocations. The model explains experimental
observations on slip avalanches as well as the associated slip and surface
pattern morphologies
Some Limitations of Dislocation Walls as Models for Plastic Boundary Layers
It has recently become popular to analyze the behavior of excess dislocations
in plastic deformation under the assumption that such dislocations are arranged
into walls with periodic dislocation spacing along the wall direction. This
assumption is made plausible by the fact that periodic walls represent minimum
energy arrangements for dislocations of the same sign, and it allows to use the
analytically known short-ranged stress fields of such walls for analyzing the
structure of plastic boundary layers. Here we show that unfortunately both the
idea that dislocation walls are low-energy configurations and the properties of
their interactions depend critically on the assumption of a periodic
arrangement of dislocations within the walls. Once this assumption is replaced
by a random arrangement, the properties of dislocation walls change completely.Comment: To appear in: Proceedings of the International conference on
numerical analysis and applied mathematics (ICNAAM) 2011, 4 pages, to appear
in APS proceeding
Depinning of a dislocation: the influence of long-range interactions
The theory of the depinning transition of elastic manifolds in random media
provides a framework for the statistical dynamics of dislocation systems at
yield. We consider the case of a single flexible dislocation gliding through a
random stress field generated by a distribution of immobile dislocations
threading through its glide plane. The immobile dislocations are arranged in a
"restrictedly random" manner and provide an effective stress field whose
statistical properties can be calculated explicitly. We write an equation of
motion for the dislocation and compute the associated depinning force, which
may be identified with the yield stress. Numerical simulations of a discretized
version of the equation confirm these results and allow us to investigate the
critical dynamics of the pinning-depinning transition.Comment: 8 pages, 4 figures. To appear in the proceedings of the
Dislocations2000 meeting (published by Materials Science and Engeneering A
Determining Cosserat constants of 2D cellular solids from beam models
We present results of a two-scale model of disordered cellular materials
where we describe the microstructure in an idealized manner using a beam
network model and then make a transition to a Cosserat-type continuum model
describing the same material on the macroscopic scale. In such scale
transitions, normally either bottom-up homogenization approaches or top-down
reverse modelling strategies are used in order to match the macro-scale
Cosserat continuum to the micro-scale beam network. Here we use a different
approach that is based on an energetically consistent continuization scheme
that uses data from the beam network model in order to determine continuous
stress and strain variables in a set of control volumes defined on the scale of
the individual microstructure elements (cells) in such a manner that they form
a continuous tessellation of the material domain. Stresses and strains are
determined independently in all control volumes, and constitutive parameters
are obtained from the ensemble of control volume data using a least-square
error criterion. We show that this approach yields material parameters that are
for regular honeycomb structures in close agreement with analytical results.
For strongly disordered cellular structures, the thus parametrized Cosserat
continuum produces results that reproduce the behavior of the micro-scale beam
models both in view of the observed strain patterns and in view of the
macroscopic response, including its size dependence
Slip avalanches in crystal plasticity: scaling of the avalanche cutoff
Plastic deformation of crystals proceeds through a sequence of intermittent
slip avalanches with scale-free (power-law) size distribution. On macroscopic
scales, however, plastic flow is known to be smooth and homogeneous. In the
present letter we use a recently proposed continuum model of slip avalanches to
systematically investigate the nature of the cut-off which truncates scale-free
behavior at large avalanche sizes. The dependence of the cut-off on system
size, geometry, and driving mode, but also on intrinsic parameters such as the
strain hardening rate is established. Implications for the observability of
avalanche behavior in microscopic and macroscopic samples are discussed.Comment: 12 pages, 4 figure
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