The yielding transition in amorphous solids under oscillatory shear deformation

Premkumar, Leishangthem; Parmar, Anshul D. S.; Sastry, Srikanth

doi:10.1038/ncomms14653

Cited by 192 publications

(283 citation statements)

References 39 publications

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“…We also comment that the transition from reversible dynamics at γ 0 = 0.07 to the plastic regime at γ 0 = 0.08 occurs at higher strain amplitudes than the critical value γ 0 = 0.06 reported in the previous MD study [10], where simulations were performed at the higher oscillation frequency ωτ = 0.02 and higher temperature T LJ = 0.1 ε/k B . At the same time, our results are in agreement with the critical strain amplitude γ 0 = 0.07, which marks the onset of energy dissipation and particle diffusion in a binary glass under oscillatory athermal quasistatic shear deformation [11,17].…”

Section: Resultssupporting

confidence: 79%

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Priezjev

2017

Phys. Rev. E

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Using molecular dynamics simulations, we study the transient response of a binary LennardJones glass subjected to periodic shear deformation. The amorphous solid is modelled as the three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.

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Section: Resultssupporting

confidence: 79%

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Priezjev

2017

Phys. Rev. E

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“…According to our picture, this kind of critical behavior should also be found at the yielding transition, conditional that one is able to derive the expression of the right correlator to measure. This suggestion seems even more reasonable in light of a recent study (21), wherein the similarity of shear bands with dynamical heterogeneities has been pointed out; also, some oscillatory shear simulations seem to indicate that a slowdown of the dynamics on approaching yielding may indeed be present (22,23). It is important to stress here that the reason that a spinodal point can be exposed and measured is that the glassy timescales and the athermal conditions stabilize the metastable system until the spinodal point is crossed and the system becomes unstable against constrained ergodization.…”

mentioning

confidence: 93%

Shear bands as manifestation of a criticality in yielding amorphous solids

Parisi

Procaccia

Rainone

et al. 2017

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

109

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Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.shear bands | yielding | glass | spinodal | criticality A solid, be it crystalline or amorphous, is operatively defined as any material capable to respond elastically to an externally applied shear deformation (1). However, any solid material, when subject to a large-enough shear strain, finally undergoes a mechanical yield. Here, we focus on the mechanical yield of amorphous materials, such as molecular and colloidal glasses, foams, and granular matter. The phenomenology exhibited by the yielding point within this vast class of materials, as reported in countless strain-controlled simulations (2-8) and experiments (9-11), shows a remarkable degree of universality, despite the highly varied nature of the model systems involved. Among these universal features is the presence, at the onset of flow at yielding, of system-spanning excitations referred to as shear bands (12, 13), wherein the shear strongly localizes, leaving the rest of the material unperturbed. This phenomenon is of capital importance for engineering applications, because it is responsible for the brittleness typical of glassy materials, in particular metallic glasses (14), whose potential for practical use is stymied by their tendency to shear band and fracture (13,15,16).In athermal amorphous solids, the phenomenon has universal features. For strains γ smaller than some critical value denoted as γY , the stress in the material grows on the average when the strain is increased. After yield, the stress cannot grow on the average, no matter how much the strain is increased. The universality of the basic phenomenology of yielding begs a picture of its characteristics in terms of a universal theory, in the sense that such a theory should rely on a statistical-mechanical framework and be independent of details, such as chemical composition and production process of the material. This need was addressed in a recent work (17), wherein building up from ideas first advanced in ref. 18, there emerged a picture of mechanical yielding as a first-order phenomenon [i.e., as a discontinuous ph...

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“…The mechanical response of glasses to applied stress is complex, including strain hardening [11], plastic yielding [12][13][14][15][16][17], and brittle failure [18][19][20], and the particular response that is observed for a given glass sample depends on the protocol used to prepare and characterize it (e.g. its thermal history) [21].…”

Section: Introductionmentioning

confidence: 99%

Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses

et al. 2017

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Amorphous materials such as metallic, polymeric, and colloidal glasses, exhibit complex preparation-dependent mechanical response to applied shear. In particular, glassy solids yield, with a mechanical response that transitions from elastic to plastic, with increasing shear strain. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate R used to prepare them. The ensemble-averaged stress versus strain curve σ(γ) resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak in stress at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve σ(γ) consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. To explain the nonlinearity of σ(γ) , we quantify the shape of the small stress-strain segments and the frequency and size of the stress drops in each glass configuration. We decompose the stress loss (i.e., the deviation in the slope of σ(γ) from that at σ(0) ) into the loss from particle rearrangements and the loss from softening (i.e., the reduction of the slopes of the linear segments in σ(γ)), and then compare the two contributions as a function of R and γ. For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different R, and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as an order parameter for the yielding transition, which sharpens for slow cooling rates and in the large system-size limit.

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The yielding transition in amorphous solids under oscillatory shear deformation

Cited by 192 publications

References 39 publications

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear

Shear bands as manifestation of a criticality in yielding amorphous solids

Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses

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