Avalanches in 2D dislocation systems without applied stresses

Abstract

We study avalanches in two-dimensional ensembles of discrete dislocations subject to zero or small finite constant external stresses. These systems respond to local perturbations by exhibiting bursts of collective dislocation activity characterised by power-law distributions of various measures of sizes and durations of the avalanches. The cut-offs of these distributions diverge with the system size even for zero applied stresses. The avalanches are found to display slow, glass-like relaxation dynamics following the initial excitation, with the average avalanche shape depending on the avalanche duration.

Excitation Spectra in Crystal Plasticity

“…Dislocation systems exhibit slow, glasslike dynamics, argued to originate from the frustrated dislocation interactions [16]. Together with recent results of extended criticality [13,14,24] this suggests the possibility of interesting, nontrivial excitation spectra.…”

“…The likely cause is the anisotropic, nonpositive definite interactions between dislocations, in analogy to the quadrupolar Eshelby-type stress fields argued to be responsible for the similar behavior found recently for amorphous plasticity [17,18]. This then persists upon coarse graining, and manifests itself in the presence of critical-like fluctuations or plastic avalanches even at negligible external stresses [13,14,24]. The presence of a frozen impurity field, on the other hand, leads to a finite minimum for the excitation stress σ ex , in agreement with the idea of the presence of a true critical point or yield stress [11] instead of the extended criticality scenario of pure dislocation systems.…”

“…The 2D case is studied in more depth as the 3D one is intrinsically hard numerically. The starting point in both cases is a relaxed, zero-stress state, which we expect to be in the extended criticality regime of the pure dislocation systems [13,14,24]. The 2D DDD model represents a cross section (xy plane) of a single crystal, with a single slip geometry, and straight parallel edge dislocations along the z axis.…”

Glassy features of crystal plasticity

“…To address such questions in an appropriate fashion, high quality numerical studies of realistic discrete dislocation dynamics (DDD) models, capturing the avalanchelike deformation process, are essential [7,[17][18][19]. The majority of DDD studies of dislocation avalanches have so far been performed using relatively simple and computationally efficient 2D systems, describing point-like crosssections of ensembles of straight, parallel edge dislocations [17][18][19]. Real three-dimensional plastically deforming crystals are not described in all their aspects by the 2D DDD models [20].…”

Relation Between Yield Stress and Peierls Stress

“…It is also well known that plastic deformation is characterized by intermittent strain bursts which are also known as dislocation avalanches . When plastic deformation is occurring in micron‐scale crystals, internal dislocation avalanches lead to power‐law like distributions of strain bursts, while macroscopically yielding may appear as a smooth process due to the large number of randomly oriented crystals involved.…”