Ductile and Brittle Yielding in Thermal and Athermal Amorphous Materials

Barlow, Hugh J.; Cochran, James O.; Fielding, Suzanne M.

doi:10.1103/physrevlett.125.168003

Cited by 65 publications

(64 citation statements)

References 42 publications

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“…Just after the overshoot, the abrupt decrease in the stress corresponds to a sharp transition to a fluidized state. Such a behavior is characteristic of a "brittle" yielding transition and qualitatively close to the one discussed recently in [86][87][88].…”

Section: Influence Of Boundary Conditions In the Presence Of Avalanchessupporting

confidence: 85%

“…Finally, with respect to previous experimental and numerical work on the ductile-to-brittle transition in soft materials [88,[94][95][96][97][98][99], a feature highlighted by our study is that boundary conditions may control such a transition in soft glassy materials. We have used the simplest boundary conditions that allow or suppress phase nucleation at the moving wall.…”

Section: Discussionsupporting

confidence: 53%

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Continuum modeling of shear startup in soft glassy materials

et al. 2021

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Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ y such that YSFs are solid for stresses σ imposed below σ y , whereas they flow like liquids for σ > σ y . Under an applied shear rate γ , the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ M and strain γ M as a function of γ , which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ M ( γ ) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling σ M ( γ ). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

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Section: Influence Of Boundary Conditions In the Presence Of Avalanchessupporting

confidence: 85%

Section: Discussionsupporting

confidence: 53%

Continuum modeling of shear startup in soft glassy materials

et al. 2021

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“…20. Indeed, even for uniform shear, a recent theoretical investigation (40) suggests that in the athermal case, stress jumps always remain finite, whereas ref. 21 predicts a very slowly decaying N dependence.…”

Section: D Inset)mentioning

confidence: 98%

The role of annealing in determining the yielding behavior of glasses under cyclic shear deformation

Bhaumik

Foffi

Sastry

2021

Proc. Natl. Acad. Sci. U.S.A.

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Yielding behavior in amorphous solids has been investigated in computer simulations using uniform and cyclic shear deformation. Recent results characterize 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 quasistatic 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 toward 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 until they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems corresponds to dynamical cross-over temperatures associated with changes in the character of the energy landscape sampled by glass-forming liquids.

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“…A proper description should account for the anisotropic, quadrupolarlike character of the Eshelby kernel 4,43 . This is known to induce marginal stability in the sheared amorphous solids 25 but the degree to which it influences the yielding transition is an unsettled question 19,20,[26][27][28]44 . To the least, one expects that the mapping of the yielding transition to a random-field Ising model should involve a modified model with Eshelby-like interactions 45 .…”

Section: Discussionmentioning

confidence: 99%

“…Nonetheless, this shortcoming is not central for describing the yielding transition at the mean-field level since the improved model in which sites receive small random kicks of both signs from plastic events taking place in the whole sample yields the same qualitative description of the yielding transition as a function of the material's initial degree of stability 21 . What may be more troublesome for applications to finite-dimensional systems is the fact that the mean-field EPMs are predicted to encounter a linear instability leading to a discontinuous stress drop whenever an overshoot (i.e., a local maximum) appears in the average stress-strain curve 26,27 . However, the outcome of this instability in real materials is still debated 28 as it is not clear whether or not this instability can be pinned (and the average stress still be a continuous function of the strain) by the disorder associated with the nonuniform structure of amorphous solids.…”

Section: Relevance Of the Mean-field Epm For The Yielding Of Amorphou...mentioning

confidence: 99%

Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model

Rossi,

Tarjus

2022

Preprint

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We study the mean-field limit of an elasto-plastic model introduced to describe the yielding transition of athermally and quasi-statically sheared amorphous solids. We focus on the sample-tosample fluctuations, which we characterize analytically, and investigate in detail the analogy with the athermally driven random-field Ising model. We stress that the random field at the yielding transition is an emerging disorder and we investigate the various factors that determine its strength.

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Ductile and Brittle Yielding in Thermal and Athermal Amorphous Materials

Cited by 65 publications

References 42 publications

Continuum modeling of shear startup in soft glassy materials

Continuum modeling of shear startup in soft glassy materials

The role of annealing in determining the yielding behavior of glasses under cyclic shear deformation

Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model

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