Quenched pinning and collective dislocation dynamics

Abstract

Several experiments show that crystalline solids deform in a bursty and intermittent fashion. Power-law distributed strain bursts in compression experiments of micron-sized samples, and acoustic emission energies from larger-scale specimens, are the key signatures of the underlying critical-like collective dislocation dynamics - a phenomenon that has also been seen in discrete dislocation dynamics (DDD) simulations. Here we show, by performing large-scale two-dimensional DDD simulations, that the character of the dislocation avalanche dynamics changes upon addition of sufficiently strong randomly distributed quenched pinning centres, present e.g. in many alloys as immobile solute atoms. For intermediate pinning strength, our results adhere to the scaling picture of depinning transitions, in contrast to pure systems where dislocation jamming dominates the avalanche dynamics. Still stronger disorder quenches the critical behaviour entirely.

Learning local, quenched disorder in plasticity and other crackling noise phenomena

“…2 The evidence for quenched disorder in initial defect microstructures has been accumulated through observations of abrupt plastic events or material-crackling noise in a large variety of materials, such as FCC and BCC crystals, [3][4][5][6] amorphous solids 7 and also earthquake geological faults. 8,9 This crackling noise 10 has been commonly explained by random field models 11,12 or interface depinning ones, [13][14][15][16][17][18] where the major component is homogeneous solid elasticity, but also a spatially inhomogeneous and random distribution of local, quenched disorder (typically entering local flow stress information) 4,17,[19][20][21] and the allowed microstates are characterized by its stress and strain and minimize the elastic energy functional. The evidence of crackling noise has led to an extensive study of the local, statistical properties of abrupt events and their properties, such as their sizes, durations, average shapes, and their critical exponents.…”

Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity

“…As the underlying lower-scale model we use conventional 2D discrete dislocation dynamics (DDD) models that have been studied extensively in the literature [23][24][25][26][27]. We consider load-controlled quasistatic plastic deformation where individual avalanches can be readily identified [28].…”

Excitation Spectra in Crystal Plasticity

“…3(a) the Pðσ ex Þ's for a system with a quenched pinning field generated by randomly distributed pinning centers of "intermediate" strength, with A ¼ 0.1 and N s =L 2 ¼ 0.8b −2 chosen to transform the glasslike jamming scenario of pure dislocation systems into a depinninglike problem, but the disorder is not so strong that it would eliminate the scale-free nature of the avalanches (see Ref. [11] for details); we consider the same three stress rates as above to apply the local perturbation. One may make two main observations: (i) the exponent θ assumes lower stress-rate-dependent values as compared to the pure dislocation system and (ii) the power laws exhibited by the Pðσ ex Þ's appear to have low-σ ex cutoffs; hence, we fit the data with the function Pðσ ex Þ ∝ σ θ ex exp½−ðσ 0 =σ ex Þ α , where σ 0 is the cutoff stress scale.…”

“…The key phenomena include power-law distributed strain bursts [4][5][6][7] and intermittent acoustic emission signals [8][9][10], originating from avalanches of dislocation activity. The theoretical description of such crackling noise response in plasticity has been debated, and ideas from depinning transitions [11,12], jamming [13][14][15], and glassy dynamics [16] of the dislocation assembly have been brought up.…”

“…In addition, to test the effect of quenched disorder on the excitation spectrum, we perform a set of simulations including also N s randomly positioned immobile pinning centers ("solute atoms") interacting with the dislocations via short-range interactions, employing a regularized interaction energy U ¼ As n sin θ=rf1− exp½−ðk 2 =a 2 Þr 2 g, with k ¼ 1.65, a the atomic distance, s n the sign of the Burgers vector of the dislocation, and A ¼ ð1 þ νÞμbΔV=3πð1 − νÞ an interaction strength parameter, with ΔV the misfit area [25]. These pinning centers generate a short-range correlated random pinning field [with a correlation length ξ ≈ ðN s =L 2 Þ −1=2 and strength proportional to A] interfering with the dislocation motion [11]. Dislocation dynamics is taken to be overdamped, such that the dislocation velocity is proportional to the Peach-Koehler force due to the total stress (with contributions from dislocation interactions, the random pinning field, as well as from the external stress σ ext when present) acting on it.…”