517 research outputs found
Statistical Physics of the Yielding Transition in Amorphous Solids
The art of making structural, polymeric and metallic glasses is rapidly
developing with many applications. A limitation to their use is their
mechanical stability: under increasing external strain all amorphous solids
respond elastically to small strains but have a finite yield stress which
cannot be exceeded without effecting a plastic response which typically leads
to mechanical failure. Understanding this is crucial for assessing the risk of
failure of glassy materials under mechanical loads. Here we show that the
statistics of the energy barriers \Delta E that need to be surmounted changes
from a probability distribution function (pdf) that goes smoothly to zero to a
pdf which is finite at \Delta E=0. This fundamental change implies a dramatic
transition in the mechanical stability properties with respect to external
strain. We derive exact results for the scaling exponents that characterize the
magnitudes of average energy and stress drops in plastic events as a function
of system size.Comment: 4 pages, 5 figure
A microscopic view of the yielding transition in concentrated emulsions
We use a custom shear cell coupled to an optical microscope to investigate at
the particle level the yielding transition in concentrated emulsions subjected
to an oscillatory shear deformation. By performing experiments lasting
thousands of cycles on samples at several volume fractions and for a variety of
applied strain amplitudes, we obtain a comprehensive, microscopic picture of
the yielding transition. We find that irreversible particle motion sharply
increases beyond a volume-fraction dependent critical strain, which is found to
be in close agreement with the strain beyond which the stress-strain relation
probed in rheology experiments significantly departs from linearity. The
shear-induced dynamics are very heterogenous: quiescent particles coexist with
two distinct populations of mobile and `supermobile' particles. Dynamic
activity exhibits spatial and temporal correlations, with rearrangements events
organized in bursts of motion affecting localized regions of the sample.
Analogies with other sheared soft materials and with recent work on the
transition to irreversibility in sheared complex fluids are briefly discussed.Comment: 11 pages, 10 figures. Submitted to Soft Matte
Driving rate dependence of avalanche statistics and shapes at the yielding transition
We study stress time series caused by plastic avalanches in athermally
sheared disordered materials. Using particle-based simulations and a mesoscopic
elasto-plastic model, we analyze size and shear-rate dependence of the
stress-drop durations and size distributions together with their average
temporal shape. We find critical exponents different from mean-field
predictions, and a clear asymmetry for individual avalanches. We probe scaling
relations for the rate dependency of the dynamics and we report a crossover
towards mean-field results for strong driving.Comment: 5 pages, 3 figures, 1 table, supplementary material to be found at
http://www-liphy.ujf-grenoble.fr/pagesperso/martens/documents/liu2015-sm.pd
Scaling description of the yielding transition in soft amorphous solids at zero temperature
Yield stress materials flow if a sufficiently large shear stress is ap-
plied. Although such materials are ubiquitous and relevant for indus- try,
there is no accepted microscopic description of how they yield, even in the
simplest situations where temperature is negligible and where flow
inhomogeneities such as shear bands or fractures are ab- sent. Here we propose
a scaling description of the yielding transition in amorphous solids made of
soft particles at zero temperature. Our description makes a connection between
the Herschel-Bulkley expo- nent characterizing the singularity of the flow
curve near the yield stress {\Sigma}c, the extension and duration of the
avalanches of plasticity observed at threshold, and the density P(x) of soft
spots, or shear transformation zones, as a function of the stress increment x
be- yond which they yield. We argue that the critical exponents of the yielding
transition can be expressed in terms of three independent exponents {\theta},
df and z, characterizing respectively the density of soft spots, the fractal
dimension of the avalanches, and their duration. Our description shares some
similarity with the depinning transition that occurs when an elastic manifold
is driven through a random potential, but also presents some striking
differences. We test our arguments in an elasto-plastic model, an automaton
model similar to those used in depinning, but with a different interaction
kernel, and find satisfying agreement with our predictions both in two and
three dimensions.Comment: 6 pages + 2 pages supplementary informatio
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