The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other non-equilibrium systems under external loading: dilute colloidal suspensions, plastically-deformed amorphous solids, granular materials, and dislocation-based simulations of crystals. These other systems exhibit transitions with clear analogies to work hardening and yield stress, with many typically undergoing purely elastic behavior only after 'training' through repeated cyclic loading; studies in these other systems show a power law scaling of the hysteresis loop extent and of the training time as the peak load approaches a so-called reversible-irreversible transition (RIT). We discover here that deformation of small crystals shares these key characteristics: yielding and hysteresis in uniaxial compression experiments of single-crystalline Cu nano- and micro-pillars decay under repeated cyclic loading. The amplitude and decay time of the yield precursor avalanches diverge as the peak stress approaches failure stress for each pillar, with a power law scaling virtually equivalent to RITs in other nonequilibrium systems.
We study the properties of strain bursts (dislocation avalanches) occurring in two-dimensional discrete dislocation dynamics models under quasistatic stress-controlled loading. Contrary to previous suggestions, the avalanche statistics differs fundamentally from predictions obtained for the depinning of elastic manifolds in quenched random media. Instead, we find an exponent τ=1 of the power-law distribution of slip or released energy, with a cut-off that increases exponentially with the applied stress and diverges with system size at all stresses. These observations demonstrate that the avala…
Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this letter, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is…
Recently, mechanical tests on ice as well as dislocation dynamics simulations have revealed that plastic flow displays a scale-free intermittent dynamics characterized by dislocation avalanches with a power law distribution of amplitudes. To further explore the complexity of dislocation dynamics during plastic flow, we present a statistical analysis of dislocation avalanche correlations and avalanche triggering. It is shown that the rate of avalanche triggering immediately after any avalanche is larger than the background activity due to uncorrelated events. This self-induced triggering increa…
The existence of a well defined yield stress, where a macroscopic piece of crystal begins to plastically flow, has been one of the basic observations of materials science. In contrast to macroscopic samples, in micro- and nanocrystals the strain accumulates in distinct, unpredictable bursts, which makes controlled plastic forming rather difficult. Here we study by simulation, in two and three dimensions, plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still spec…
We capture the spatiotemporal velocity dynamics of dislocation avalanches in face-centered cubic (FCC) gold and body-centered cubic (BCC) niobium crystals by compression testing of cylindrical microcrystals. In niobium, avalanche peak-velocities are over one order of magnitude lower, have distinctly rougher avalanche shapes, and relax more slowly to zero velocity than in gold. The avalanche dynamics (including averaged avalanche shapes) can be described reasonably well by mean-field predictions for avalanches near the depinning transition in the case of gold, but not for niobium. A detailed an…
The sequence of deformation bursts during plastic deformation exhibits scale-free features. In addition to the burst or avalanche sizes and the rate of avalanches the process is characterized by correlations in the series which become manifest in the resulting shape of the stress-strain curve. We analyze such features of plastic deformation with 2D and 3D simulations of discrete dislocation dynamics models and we show, that only with severe plastic deformation the ensuing memory effects become negligible. The role of past deformation history and dislocation pinning by disorder are studied. In …
The propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first atomic-scale evidence that the paradigm of second order phase transitions applies to the depinning of elastic interfaces in random media.
We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^α$. The noise exponent is far away from a Lorentzian, with $α\approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.
We propose a numerical model to study the viscoplastic deformation of ice single crystals. We consider long-range elastic interactions among dislocations, the possibility of mutual annihilation, and a multiplication mechanism representing the activation of Frank-Read sources due to dislocation pinning. The overdamped equations of motion for a collection of dislocations are integrated numerically using different externally applied stresses. Using this approach we analyze the avalanche-like rearrangements of dislocations during the dynamic evolution. We observe a power law distribution of avalan…
Three-dimensional discrete dislocation dynamics simulations are used to study strain-controlled plastic deformation of face-centered cubic aluminium single crystals. After describing the rate and size dependence of the average stress-strain curves, we study the power-law distributed strain bursts and the average avalanche shapes, and find a universal power-law exponent $τ\approx 1.0$ for all imposed strain rates and system sizes, characterizing both the event sizes and their durations. We discuss the dependence of our results on loading rate and compare these with previous studies of strain-co…
We study strain-controlled plastic deformation of crystalline solids via two-dimensional discrete dislocation dynamics simulations. To this end, we characterize the average stress-strain curves as well as the statistical properties of strain bursts and the related stress drops as a function of the imposed strain rate and the stiffness of the specimen-machine system. The dislocation system exhibits strain rate sensitivity such that a larger imposed strain rate results in a higher average stress at a given strain. In the limit of small strain rate and driving spring stiffness, the sizes and dura…
Compression experiments on micron-scale specimens and acoustic emission (AE) measurements on bulk samples revealed that the dislocation motion resembles a stick-slip process - a series of unpredictable local strain bursts with a scale-free size distribution. Here we present a unique experimental set-up, which detects weak AE waves of dislocation slip during the compression of Zn micropillars. Profound correlation is observed between the energies of deformation events and the emitted AE signals that, as we conclude, are induced by the collective dissipative motion of dislocations. The AE data a…
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 rando…
Crystal plasticity is mediated through dislocations, which form knotted configurations in a complex energy landscape. Once they disentangle and move, they may also be impeded by permanent obstacles with finite energy barriers or frustrating long-range interactions. The outcome of such complexity is the emergence of dislocation avalanches as the basic mechanism of plastic flow in solids at the nanoscale. While the deformation behavior of bulk materials appears smooth, a predictive model should clearly be based upon the character of these dislocation avalanches and their associated strain bursts…
Until now, most of our knowledge about the universality class of crystal plasticity has come from simulations using discrete dislocation dynamics. These are force-controlled, typically at zero temperature, and deal with the creation and annihilation of dislocations phenomenologically. In this work, we go beyond these limitations by using phase field crystal simulations in two dimensions at finite temperature to extract the avalanche statistics of a simulated crystal under constant shear velocity. In addition to the avalanche size and energy distributions we extract the avalanche duration distr…
In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a step-like plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active pre-yield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply Alternate Current (AC) load perturbations via Dynamic Mechanical Analysis (DMA) during quasi-static uniaxial compression expe…
Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars
School of Mechanics & Engineering Science, Shanghai University（上海大学力学与工程科学学院）；Department of Mechanical & Aerospace Engineering, University of Miami（迈阿密大学机械与航空航天工程系）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Department of Mechanical & Aerospace Engineering, University of California Los Angeles（加州大学洛杉矶分校机械与航空航天工程系）
The dynamics of dislocation assemblies in deforming crystals indicate the emergence of collective phenomena, intermittent fluctuations and strain avalanches. In polycrystalline materials, the understanding of plastic deformation mechanisms depends on grasping the role of grain boundaries on dislocation motion. Here the interaction of dislocations and elastic, low angle grain boundaries is studied in the framework of a discrete dislocation representation. We allow grain boundaries to deform under the effect of dislocation stress fields and compare the effect of such a perturbation to the case o…
Crystal plasticity occurs by deformation bursts due to the avalanche-like motion of dislocations. Here we perform extensive numerical simulations of a three-dimensional dislocation dynamics model under quasistatic stress-controlled loading. Our results show that avalanches are power-law distributed, and display peculiar stress and sample size dependence: The average avalanche size grows exponentially with the applied stress, and the amount of slip increases with the system size. These results suggest that intermittent deformation processes in crystalline materials exhibit an extended critical-…
We demonstrate, through 3-dimensional discrete dislocation dynamics simulations, that the com- plex dynamical response of nano and micro crystals to external constraints can be tuned. Under load rate control, strain bursts are shown to exhibit scale-free avalanche statistics, similar to critical phenomena in many physical systems. For the other extreme of displacement rate control, strain burst response transitions to quasi-periodic oscillations, similar to stick-slip earthquakes. External load mode control is shown to enable a qualitative transition in the complex collective dynamics of dislo…
The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal (PFC) model. In the model, dislocations are naturally created, without any \textit{ad hoc} creation rules, by applying a shearing force to the perfectly periodic ground state. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. By data collapsing the event energy probability density function for different shearing rates, a connection to interface depinning dynamics is confirmed. The relevant critical exponents agree with mean field theory predictio…
The universality class of the avalanche behavior in plastically deforming crystalline and amorphous systems has been commonly discussed, despite the fact that the microscopic defect character in each of these systems is different. In contrast to amorphous systems, crystalline flow stress increases dramatically at high strains and/or loading rates. We perform simulations of a two-dimensional discrete dislocation dynamics model that minimally captures the phenomenology of nanocrystalline deformation. In the context of this model, we demonstrate that a classic rate-dependence of dislocation plast…
Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value $σ=σ_c$. Nevertheless the nature of this transition has not been ascertained. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to $σ_c$, by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first passage time distribution exhibits scaling, and a related peak {\it dynamical} susceptibility $χ_4^*$ diverges as $χ_4^* \sim (σ-σ_c)^{-α}$, with $α\app…
We propose a model to study the plasticity of ice single crystals by numerical simulations. The model includes the long-range character of the interaction among dislocations, as well as the possibility of mutual annihilation of these line defects characterized by its Burgers vector. A multiplication mechanism representing the activation of Frank-Read sources due to dislocation pinning is also introduced in the model. With our approach we are able to probe the dislocation patterns, which result from the dislocation dynamics. Furthermore, our results exhibit features characteristic of driven dyn…
Size-dependence of plastic flow is studied by discrete dislocation dynamical simulation of systems with various numbers of interacting linear edge dislocations while the stress is slowly increased. Regions between avalanches in the individual stress curves as functions of the plastic strain were found nearly linear and reversible, where the plastic deformation obeys an effective equation of motion with a nearly linear force. For small plastic deformation, the means of the stress-strain curves are power law over two decades. Here and for somewhat larger plastic deformations, the mean stress-str…
The plastic deformation of metal alloys localizes in the Portevin--Le Chatelier effect in bands of different types, including propagating, or type 'A' bands, usually characterised by their width and a typical propagation velocity. This plastic instability arises from collective dynamics of dislocations interacting with mobile solute atoms but the resulting sensitivity to the strain-rate lacks fundamental understanding. Here we show, by employing high-resolution imaging in tensile deformation experiments of an aluminum alloy, that the band velocities exhibit large fluctuations. Each band produc…
Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material fails. We use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast to granular materials, which only…
Mechanical deformation of nanopillars displays features that are distinctly different from the bulk behavior of single crystals: Yield strength increases with decreasing size and plastic deformation comes together with strain bursts or/and stress drops (depending on loading conditions) with a very strong sensitivity of the stochasticity character on material preparation and conditions. The character of the phenomenon is standing as a paradox: While these bursts resemble the universal, widely independent of material conditions, noise heard in bulk crystals using acoustic emission (AE) technique…
Plastic deformations in crystals often produce textures in the form of randomly oriented patches of the unstressed lattice. We use a novel mesoscopic Landau-type model of crystal plasticity to show that in such textures large crystallographic lattice rotations can originate from a highly coordinated inelastic slip at the microscale. Our numerical experiments show that dislocation avalanches, which lead to the formation of such rotations, involve pseudo-turbulent motions with power-law distributed spatial correlations.
Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-…
Crystal plasticity of sub-micron finite volumes is characterized by the flow of emergent dislocation defects, giving rise to size effects in mechanical properties and avalanche phenomena. In this chapter, we present a minimal model for discrete edge dislocations in a finite volume, that has been benchmarked against experimental data and displays known phenomenological trends. We discuss how this model can explain seemingly disconnected effects of rate, size and prior deformation on microcrystal plasticity. We demonstrate the statistical features of dislocation ensembles for both stress and dis…
Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in determining the nature of collective dislocation dynamics remains to be understood. Here, three-dimensional discrete dislocation dynamics simulations of FCC single crystals are performed with fully coherent spherical precipitates from zero precipitate density upto $ρ_p = 10^{21}\,\text{m}^{-3}$ and at various dislocation-precipitate interaction strengths. When the d…
Plastic deformation of micron-scale crystalline materials differ considerably from bulk ones, because it is characterized by random strain bursts. To obtain a detailed picture about this stochastic phenomenon, micron sized pillars have been fabricated and compressed in the chamber of a SEM. An improved FIB fabrication method is proposed to get non-tapered micro-pillars with a maximum control over their shape. The in-situ compression device developed allows high accuracy sample positioning and force/displacement measurements with high data sampling rate. The collective avalanche-like motion of …
Deciphering Acoustic Emission with Machine Learning
ELTE Eötvös Loránd University（厄特沃什·罗兰大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Hochschule Karlsruhe - University of Applied Sciences (HKA)（卡尔斯鲁厄应用技术大学）
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, …
We study a one-dimensional model of a dislocation pileup driven by an external stress and interacting with random quenched disorder, focusing on predictability of the plastic deformation process. Upon quasistatically ramping up the externally applied stress from zero the system responds by exhibiting an irregular stress--strain curve consisting of a sequence of strain bursts, i.e., critical-like dislocation avalanches. The strain bursts are power-law distributed up to a cutoff scale which increases with the stress level up to a critical flow stress value. There, the system undergoes a depinnin…
Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material resistance to irreversible deformation depends on sample morphology. Here we study the mechanisms of yield and plastic flow in inherently small crystals under uniaxial compression. Discrete structural rearrangements emerge as series of abrupt discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry …
Although scaling phenomena have long been documented in crystalline plasticity, the universality class has been difficult to identify due to the rarity of avalanche events, which require large system sizes and long times in order to accurately measure scaling exponents and functions. Here we present comprehensive simulations of two-dimensional dislocation dynamics under shear, using finite-size scaling to extract scaling exponents and the avalanche profile scaling function from time-resolved measurements of slip-avalanches. Our results provide compelling evidence that both the static and dynam…
Previous acoustic emission (AE) experiments on ice single crystals, as well as numerical simulations, called for the possible occurrence of self-organized criticality (SOC) in collective dislocation dynamics during plastic deformation. Here, we report AE experiments on hcp metallic single crystals. Dislocation avalanches in relation with slip and twinning are identified with the only sources of AE. Both types of processes exhibit a strong intermittent character. The AE waveforms of slip and twinning events seem to be different, but from the point of view of the AE event energy distributions, n…
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to avalanche, strain bursts, intermittent energy spikes, and nonlocal interactions producing anomalous features across different time- and length-scales, directly affecting plasticity, void and crack nucleation. Discrete Dislocation Dynamics (DDD) simulations are often used at the meso-level, but the cost and complexity increase dramatically with simulation time.…
On microscopic and mesoscopic scales, plastic flow of crystals is characterized by large intrinsic fluctuations. Deformation by crystallographic slip occurs in a sequence of intermittent bursts ('slip avalanches') with power-law size distribution. In the spatial domain, these avalanches produce characteristic deformation patterns in the form of slip lines and slip bands which exhibit long-range spatial correlations. We propose a generic continuum model which accounts for randomness in the local stress-strain relationships as well as for long-range internal stresses that arise from the ensuing …
Plastic deformation of microsamples is characterised by large intermittent strain bursts caused by dislocation avalanches. Here we investigate how ion irradiation affects this phenomenon during single slip single crystal plasticity. To this end, in situ compression of Zn micropillars oriented for basal slip was carried out in a SEM. The unique experimental setup also allowed the concurrent recording of the acoustic emission (AE) signals emitted from the sample during deformation. It was shown that irradiation introduced a homogeneous distribution of basal dislocation loops that lead to hardeni…
We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by t…
We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain tensors while operating with an infinite number of equivalent energy wells. The advantage of this approach is that it eliminates arbitrariness in dealing with topological transitions involved, for instance, in nucleation and annihilation of dislocations. We use discontinuous yielding of pristine micro-crystals as a benchmark problem for the new theory and sh…
Most of crystalline materials exhibit a hysteresis on their deformation curve when mechanically loaded in alternating directions. This Bauschinger effect is the signature of mechanisms existing at the atomic scale and controlling the materials damage and ultimately their failure. Here, three-dimensional simulations of dislocation dynamics and statistical analyses of the microstructure evolution reveal two original elementary mechanisms. An asymmetry in the dislocation network junctions arising from the stress driven curvatures and the partial reversibility of plastic avalanches give an explana…
Jerky flow in solids results from collective dynamics of dislocations which gives rise to serrated deformation curves and a complex evolution of the strain heterogeneity. A rich example of this phenomenon is the Portevin-Le Chatelier effect in alloys. The corresponding spatiotemporal patterns showed some universal features which provided a basis for a well-known phenomenological classification. Recent studies revealed peculiar features in both the stress serration sequences and the kinematics of deformation bands in Al-based alloys containing fine microstructure elements, such as nanosize prec…
Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Even more recently, the intermittent plastic response was found to be generic for micro- and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size…
Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show, by employing machine learning techniques such as regression neural networks and support vector machines that deformation predictability evolves with strain and crystal size. Using data from discrete dislocations dynamics simulations, the machine learning models are trained to infer the mapping from features of the pre-existing dislocation configuration to th…
Plastic deformation of micron and sub-micron scale specimens is characterized by intermittent sequences of large strain bursts (dislocation avalanches) which are separated by regions of near-elastic loading. In the present investigation we perform a statistical characterization of strain bursts observed in stress-controlled compressive deformation of monocrystalline Molybdenum micropillars. We characterize the bursts in terms of the associated elongation increments and peak deformation rates, and demonstrate that these quantities follow power-law distributions that do not depend on specimen or…
