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Register a new userThe role of annealing in determining the yielding behavior of glasses under cyclic shear deformation
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Yielding behavior in amorphous solids has been investigated in computer simulations employing uniform and cyclic shear deformation. Recent results characterise yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively modest but clear discontinuous change at yielding. To understand better the role of annealing on yielding characteristics, we perform athermal quasistaic cyclic shear simulations of glasses prepared with a wide range of annealing in two qualitatively different systems -- a model of silica (a network glass), and an atomic binary mixture glass. Two strikingly different regimes of behavior emerge: Energies of poorly annealed samples evolve towards a unique threshold energy as the strain amplitude increases, before yielding takes place. Well annealed samples, in contrast, show no significant energy change with strain amplitude till they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems correspond to dynamical crossover temperatures associated with changes in the character of the energy landscape sampled by glass forming liquids. Uniform shear simulations support the recently discussed scenario of a random critical point separating ductile and brittle yielding, which our results now associate with dynamical crossover temperatures in the corresponding liquids.
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We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behaviour of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve towards the threshold energy as the strain amplitude is increased towards the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behaviour, with negligible change in energy with increasing strain amplitude, till they yield. Discontinuities in energy and stress at yielding increase with the degree of annealing, consistently with recent results found in three dimensions. We observe significant structural change with strain amplitude that closely mirrors the changes in energy and stresses. We investigate groups of particles that are involved in plastic rearrangements. We analyse the distributions of avalanche sizes, of clusters of connected rearranging particles, and related quantities, employing finite size scaling analysis. We verify previously investigated relations between exponents characterising these distributions, and a newly proposed relation between exponents describing avalanche and cluster size distributions.
We report on experiments that probe the stability of a two-dimensional jammed granular system formed by imposing a quasistatic simple shear strain $gamma_{rm I}$ on an initially stress free packing. We subject the shear jammed system to quasistatic cyclic shear with strain amplitude $deltagamma$. We observe two distinct outcomes after thousands of shear cycles. For small $gamma_{rm I}$ or large $deltagamma$, the system reaches a stress-free, yielding state exhibiting diffusive strobed particle displacements with a diffusion coefficient proportional to $deltagamma$. For large $gamma_{rm I}$ and small $deltagamma$, the system evolves to a stable state in which both particle positions and contact forces are unchanged after each cycle and the response to small strain reversals is highly elastic. Compared to the original shear jammed state, a stable state reached after many cycles has a smaller stress anisotropy, a much higher shear stiffness, and less tendency to dilate when sheared. Remarkably, we find that stable states show a power-law relation between shear modulus and pressure with an exponent $betaapprox 0.5$, independent of $deltagamma$. Based on our measurements, we construct a phase diagram in the $(gamma_{rm I},deltagamma)$ plane showing where our shear-jammed granular materials either stabilize or yield in the long-time limit.
The question of how a disordered materials microstructure translates into macroscopic mechanical response is central to understanding and designing materials like pastes, foams and metallic glasses. Here, we examine a 2D soft jammed material under cyclic shear, imaging the structure of ~50,000 particles. Below a certain strain amplitude, the structure becomes conserved at long times, while above, it continually rearranges. We identify the boundary between these regimes as a yield strain, defined without rheological measurement. Its value is consistent with a simultaneous but independent measurement of yielding by stress-controlled bulk rheometry. While there are virtually no irreversible rearrangements in the steady state below yielding, we find a largely stable population of plastic rearrangements that are reversed with each cycle. These results point to a microscopic view of mechanical properties under cyclic deformation.
Atomic correlations in a simple liquid in steady-state flow under shear stress were studied by molecular dynamics simulation. The local atomic level strain was determined through the anisotropic pair-density function (PDF). The atomic level strain has a limited spatial extension whose range is dependent on the strain rate and extrapolates to zero at the critical strain rate. A failure event is identified with altering the local topology of atomic connectivity by exchanging bonds among neighboring atoms.
Considering a recently proposed model for the yielding of amorphous solids under cyclic shear deformation, we show that it can be analyzed by mapping it, in the simplest case, to a random walk in a confining potential with an absorbing boundary. The dynamics is governed by the first passage time into the absorbing state, which captures the essential features of the original model, thereby providing insight into the observed robustness of earlier results. Including the possibility of activated escape from absorbing states leads to a unique determination of a threshold energy and yield strain, and further, suggests an appealing approach to understanding fatigue failure.
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