Collective Dislocation Dynamics Research Articles

Serrated plastic flow in deforming complex concentrated alloys: universal signatures of dislocation avalanches

Under plastic flow, multi-element high/medium-entropy alloys (HEAs/MEAs) commonly exhibit complex intermittent and collective dislocation dynamics owing to inherent lattice distortion and atomic-level chemical complexities. Using atomistic simulations, we report on an avalanche study of model face-centered cubic (fcc) NiCoCrFeMn and NiCoCr chemically complex alloys aiming for microstructural/topological characterization of associated dislocation avalanches. The results of our avalanche simulations reveal a close correspondence between the observed serration features in the stress response of the deforming HEA/MEA and the incurred slip patterns within the bulk crystal. We show that such correlations become quite pronounced within the rate-independent (quasi-static) regime exhibiting scale-free statistics and critical scaling features as universal signatures of dislocation avalanches.

Machine learning reveals strain-rate-dependent predictability of discrete dislocation plasticity

Predicting the behavior of complex systems is one of the main goals of science. An important example is plastic deformation of micron-scale crystals, a process mediated by collective dynamics of dislocations, manifested as broadly distributed strain bursts and significant sample-to-sample variations in the response to applied loading. Here, by combining large-scale discrete dislocation dynamics simulations and machine learning, we study the problem of predicting the fluctuating stress-strain curves of individual small single crystals subject to strain-controlled loading using features of the initial dislocation configurations as input. Our results reveal an intriguing rate dependence of deformation predictability: For small strains predictability improves with increasing strain rate, while for larger strains the predictability vs strain rate relation becomes nonmonotonic. We show that for small strains the rate dependence of deformation predictability can be captured by considering the fraction of dislocations moving against the direction imposed by the external stress, serving as a measure of strain-rate-dependent complexity of the dislocation dynamics. The nonmonotonic predictability vs strain rate relation for large strains is argued to be related to a transition from fluctuating to smooth plastic flow when strain rate is increased.

Fluctuations in crystalline plasticity

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, and disorder content. A particular emphasis is placed on the associated emergent behaviors, including the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the "smaller is wilder" size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We show that the implied transition between different rheological behaviors is regulated by the ratio of length scales $R=L/l$, where $L$ is the system size and $l$ is the internal length. We link this new size effect with other related phenomena like size dependence of strength ("smaller is stronger") and the size induced switch between different hardening mechanisms. One of the technological challenges in nanoscience is to tame the intermittency of plastic flow. We show that this task can be accomplished by generating tailored quenched disorder which allows one to control micro- and nano-scale forming and opens new perspectives in micro-metallurgy and structural engineering of ultra-small load-carrying elements. These results could not be achieved by conventional methods that do not explicitly consider the stochastic nature of collective dislocation dynamics.

Plastic yielding and deformation bursts in the presence of disorder from coherent precipitates

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 $\rho_p = 10^{21}\,\text{m}^{-3}$ and at various dislocation-precipitate interaction strengths. When the dislocation-precipitate interactions do not play a major role the yielding is qualitatively as for pure crystals, i.e., dominated by "dislocation jamming", resulting in glassy dislocation dynamics exhibiting critical features at any stress value. We demonstrate that increasing the precipitate density and/or the dislocation-precipitate interaction strength creates a true yield or dislocation assembly depinning transition, with a critical yield stress. This is clearly visible in the statistics of dislocation avalanches observed when quasistatically ramping up the external stress, and is also manifested in the response of the system to constant applied stresses. The scaling of the yielding with precipitates is discussed in terms of the Bacon-Kocks-Scattergood relation.

Dislocation dynamics during cyclic loading in copper single crystal

Crystalline plasticity can take place through numerous, small, uncorrelated dislocation motions (mild plasticity) or through collaborative events: dislocation avalanches (wild plasticity). Here, we study the correlation between dislocation patterning under cyclic loading and the nature of collective dislocation dynamics. The dislocation motion of a [110] oriented pure copper single crystal was dynamically followed using Acoustic Emission (AE) for different imposed stress amplitudes. The dislocation structure between each cyclic stress step was investigated using Electron BackScattered Diffraction (EBSD) and Rotational-Electron Channeling Contrast Imaging (R-ECCI) in a Scanning Electron Microscope (SEM). At low imposed stress, when the structure consists of dislocation cells, few dislocation avalanches are observed, while for a wall structure, at higher imposed stress, the contribution of avalanches is increased during the first cycles. For a given stress amplitude, the evolution of mild plasticity is synchronous with the plastic strain-rate, and rapidly vanishes after few cycles due to work hardening. The mean free path of the dislocations in this mild plasticity regime corresponds to the characteristic size of the dislocation structure (cell size, distance between walls). From one stress level to another, brutal rearrangements of the dislocation structure occur within a few numbers of cycles. Those rearrangements take place, at least partly, through dislocation avalanches. Upon reloading at a larger stress amplitude, dislocation avalanches can travel over distances much larger than the former dislocation mean free path. As the dislocation avalanches spread within the crystal, the memory of the previous dislocation structure is lost and a new dislocation structure emerges.

Ice: the paradigm of wild plasticity.

Ice plasticity has been thoroughly studied, owing to its importance in glaciers and ice sheets dynamics. In particular, its anisotropy (easy basal slip) has been suspected for a long time, then fully characterized 40 years ago. More recently emerged the interest of ice as a model material to study some fundamental aspects of crystalline plasticity. An example is the nature of plastic fluctuations and collective dislocation dynamics. Twenty years ago, acoustic emission measurements performed during the deformation of ice single crystals revealed that plastic 'flow' proceeds through intermittent dislocation avalanches, power law distributed in size and energy. This means that most of ice plasticity takes place through few, very large avalanches, thus qualifying associated plastic fluctuations as 'wild'. This launched an intense research activity on plastic intermittency in the Material Science community. The interest of ice in this debate is reviewed, from a comparison with other crystalline materials. In this context, ice appears as an extreme case of plastic intermittency, characterized by scale-free fluctuations, complex space and time correlations as well as avalanche triggering. In other words, ice can be considered as the paradigm of wild plasticity. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Plastic intermittency during cyclic loading: From dislocation patterning to microcrack initiation

In metallic materials subjected to cyclic loading, strain hardening as well as fatigue crack initiation have been linked for a long time with the evolution of dislocation patterns and structures. In particular, the development of low-energy dislocation configurations such as persistent slip bands (PSBs) is considered as a precursor to crack initiation. However, the associated scenarios have been elaborated mainly from postmortem observations capturing only static pictures of dislocation patterns, while the dynamics of the problem has been somewhat overlooked. Here we analyze collective dislocation dynamics during cycling loading of aluminum using acoustic emission (AE). A strong link is revealed between dislocation patterning, cyclic hardening/softening, and the intermittency of plasticity: Plastic intermittency and dislocation avalanches rapidly decay during the initial hardening stage, in conjunction with the reduction of an internal length scale characterizing the dislocation structure. However, in nonannealed samples, a transient softening stage ensues, associated with a brutal reorganization of this structure. These initial stages of cyclic deformation illustrate the competition between two phenomena: collective dislocation dynamics, governed by long-ranged elastic interactions among dislocations, and the emergence of a self-organizing network controlled by short-range interactions and progressively inhibiting collective effects. Later on, the emergence of PSBs is accompanied by a reincrease of the AE intermittent activity. We propose that the associated AE bursts may be the signature of collective and coordinated dislocation motions along PSBs leading to the formation of incipient microcracks.

Complexity and Anisotropy of Plastic Flow of α-Ti Probed by Acoustic Emission and Local Extensometry.

Current progress in the prediction of mechanical behavior of solids requires understanding of spatiotemporal complexity of plastic flow caused by self-organization of crystal defects. It may be particularly important in hexagonal materials because of their strong anisotropy and combination of different mechanisms of plasticity, such as dislocation glide and twinning. These materials often display complex behavior even on the macroscopic scale of deformation curves, e.g., a peculiar three-stage elastoplastic transition, the origin of which is a matter of debates. The present work is devoted to a multiscale study of plastic flow in α-Ti, based on simultaneous recording of deformation curves, 1D local strain field, and acoustic emission (AE). It is found that the average AE activity also reveals three-stage behavior, but in a qualitatively different way depending on the crystallographic orientation of the sample axis. On the finer scale, the statistical analysis of AE events and local strain rates testifies to an avalanche-like character of dislocation processes, reflected in power-law probability distribution functions. The results are discussed from the viewpoint of collective dislocation dynamics and are confronted to predictions of a recent micromechanical model of Ti strain hardening.

Correlation versus randomization of jerky flow in an AlMgScZr alloy using acoustic emission.

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 precipitates and/or submicron grains. In the present work, jerky flow of an AlMgScZr alloy is studied using statistical analysis of stress serrations and the accompanying acoustic emission. As in the case of coarse-grained binary AlMg alloys, the amplitude distributions of acoustic events obey a power-law scaling which is usually considered as evidence of avalanchelike dynamics. However, the scaling exponents display specific dependences on the strain and strain rate for the investigated materials. The observed effects bear evidence to a competition between the phenomena of synchronization and randomization of dislocation avalanches, which may shed light on the mechanisms leading to a high variety of jerky flow patterns observed in applied alloys.

Peculiar Spatiotemporal Behavior of Unstable Plastic Flow in an AlMgMnScZr Alloy with Coarse and Ultrafine Grains

The work addresses the effects of nanosize particles and grain refinement on the patterns of stress serrations and kinematics of deformation bands associated with the Portevin–Le Chatelier instability of plastic flow. Ultra-fine-grained microstructure was obtained using equal-channel angular pressing of the initial coarse-grained alloy. Tensile tests were carried out on flat specimens at strain rates in the range from 3 × 10−5 to 1.4 × 10−2 s−1. Using local extensometry techniques, it was found that the presence of nanoscale precipitates promotes quasi-continuous propagation of deformation bands in the entire strain-rate range. The grain refinement leads to a transition to relay-race propagation at high strain rates and static strain localization at low rates. The results are discussed from the viewpoint of competition between various dynamical modes of plastic deformation associated with collective dynamics of dislocations.

Influence of loading control on strain bursts and dislocation avalanches at the nanometer and micrometer scale

Through three-dimensional discrete dislocation dynamics simulations, we show that by tuning the mode of external loading, the collective dynamics of dislocations undergo a transition from driven avalanches under stress control to quasiperiodic oscillations under strain control. We directly correlate measured intermittent plastic events with internal dislocation activities and collective dynamics. Under different loading modes, the roles of the weakest dislocation source and the defect population trend are significantly different. This finding raises new possibilities of controlling correlated dislocation activities and obtaining a low defect density in nanostructured devices by tuning external constraints. In addition, the effect of machine stiffness comes to light. The statistical analysis of the burst magnitude is revisited and carefully discussed. Self-organized criticality and scale-free statistics of strain bursts are obeyed under stress control. However, this behavior is shown to break down under strain control. Rapid stress drops under pure strain control force truncation of dislocation avalanches, leading to a dynamical transition to quasiperiodic oscillations.

Controlling Strain Bursts and Avalanches at the Nano- to Micrometer Scale.

We demonstrate, through three-dimensional discrete dislocation dynamics simulations, that the complex dynamical response of nano- and microcrystals 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 quasiperiodic oscillations, similar to stick-slip earthquakes. External load mode control is shown to enable a qualitative transition in the complex collective dynamics of dislocations from self-organized criticality to quasiperiodic oscillations.

Collective dynamics of dislocations interacting with mobile solute atoms

We study the effect of diffusing solute atoms on the collective dynamics of dislocations in plastically deforming crystals, by simulating a two-dimensional discrete dislocation dynamics model with solute atoms included. We employ various protocols to apply the external stress, including constant, oscillatory and quasistatically increasing stress, and study the resulting dynamics for various values of the solute mobility, temperature, and interaction strength with the dislocations. The values of these parameters dictate if Cottrell clouds are formed around the dislocations, and whether the dislocations are able to drag them along as they move. The relevant solute-induced processes include a temporally increasing average Cottrell cloud size due to cloud merging during the evolution of the dislocation structures subject to constant stresses, and a crossover between a solute-free ‘phase’ and a regime where solute drag is important for cyclic stresses, controlled by the solute mobility and temperature. Statistics of deformation bursts under quasistatic loading exhibit atypical scaling where the average burst size is directly proportional to its duration, and are also affected by solute-induced strain hardening in the high-stress regime.

Free energy of dislocations in a multi-slip geometry

The collective dynamics of dislocations is the underlying mechanism of plastic deformation in metallic crystals. Dislocation motion in metals generally occurs on multiple slip systems. The simultaneous activation of different slip systems plays a crucial role in crystal plasticity models. In this contribution, we study the energetic interactions between dislocations on different slip systems by deriving the free energy in a multi-slip geometry. In this, we restrict ourselves to straight and parallel edge dislocations. The obtained free energy has a long-range mean-field contribution, a statistical contribution and a many-body contribution. The many-body contribution is a local function of the total dislocation density on each slip system, and can therefore not be written in terms of the net dislocation density only. Moreover, this function is a strongly non-linear and non-convex function of the density on different slip systems, and hence the coupling between slip systems is of great importance.

Quenched pinning and collective dislocation dynamics.

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.

Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model.

Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density 1/f2 at high frequencies f. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternates at irregular times with high populations of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.

Dynamic Hysteresis in Cyclic Deformation of Crystalline Solids

The hysteresis or internal friction in the deformation of crystalline solids stressed cyclically is studied from the viewpoint of collective dislocation dynamics. Stress-controlled simulations of a dislocation dynamics model at various loading frequencies and amplitudes are performed to study the stress-strain rate hysteresis. The hysteresis loop areas exhibit a maximum at a characteristic frequency and a power law frequency dependence in the low frequency limit, with the power law exponent exhibiting two regimes, corresponding to the jammed and the yielding or moving phases of the system, respectively. The first of these phases of the system exhibits nontrivial critical-like viscoelastic dynamics, crossing over to intermittent viscoplastic deformation for higher stress amplitudes.

Multiscale study of acoustic emission during smooth and jerky flow in an AlMg alloy

The acoustic emission (AE) accompanying jerky flow in dilute alloys, the so-called Portevin–Le Chatelier effect, is usually considered to be composed of discrete bursts associated with the motion of large dislocation ensembles giving rise to stress serrations, which are superimposed on continuous AE generated during macroscopically smooth plastic flow. The data streaming technique which allows continuous AE recording is used to investigate the jerky flow of an AlMg alloy on different timescales. The apparent behavior, discrete or continuous, of AE is found to depend on the period of observation and the characteristic surveyed. However, it is proved that AE has a burst-like character during both stress serration and smooth flow. This behavior, revealed on timescales proper to the given strain rate, reflects the inherently intermittent, avalanche-like nature of collective dislocation dynamics, and unifies the concept generally applied to jerky flow with the similar approach to macroscopically uniform deformation flow, based on recent studies of AE during plastic deformation of pure materials.

Multiscale Modeling Approach to Acoustic Emission during Plastic Deformation

We address the long-standing problem of the origin of acoustic emission commonly observed during plastic deformation. We propose a framework to deal with the widely separated time scales of collective dislocation dynamics and elastic degrees of freedom to explain the nature of acoustic emission observed during the Portevin-Le Chatelier effect. The Ananthakrishna model is used as it explains most generic features of the phenomenon. Our results show that while acoustic emission bursts correlated with stress drops are well separated for the type C serrations, these bursts merge to form nearly continuous acoustic signals with overriding bursts for the propagating type A bands.

Effect of deformation geometry on the intermittent plastic flow associated with the Portevin–Le Chatelier effect

The unstable plastic flow caused by the Portevin–Le Chatelier effect is studied experimentally. Non-local effects due to strain heterogeneity are addressed by comparing the statistical and multifractal properties of tension and compression deformation curves of an AlMg alloy. Power-law statistical distributions and multifractal scaling are found in certain experimental conditions, and provide a quantitative characterization of the plastic-flow intermittency. The analysis reveals distinct temporal patterns associated with stress serrations in tension and compression, reflecting distinct modes of the collective dislocation dynamics. In contrast, the onset of instability follows similar relationships in both loading conditions. This similarity justifies the conventional approach to modeling the loss of stability of a uniform plastic flow as a local property, governed by the homogenized behavior of the dislocation ensemble.