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

Plastic Avalanches in Metal-Organic Framework Crystals Due to the Dynamic Phase Mixing

The compressive properties of metal-organic framework (MOF) crystals are not only crucial for their densification process but also key in determining their performance in many applications. We herein investigated the mechanical responses of a classic crystalline MOF, HKUST-1, using in situ compression tests. A serrated flow accompanied by the unique strain avalanches was found in individual and contacting crystals before their final flattening or fracture with splitting cracks. The plastic flow with serrations is ascribed to the dynamic phase mixing due to the progressive and irreversible local phase transition in HKUST-1 crystals, as revealed by molecular dynamics and finite element simulations. Such pressure-induced phase coexistence in HKUST-1 crystals also induces a significant loading-history dependence of their Young's modulus. The observation of plastic avalanches in HKUST-1 crystals here not only expands our current understanding of the plasticity of MOF crystals but also unveils a novel mechanism for the avalanches and plastic flow in crystal plasticity.

Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves

We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal an unexpected mechanism for temporal quasiperiodicity that results from a coupling between two distinct instabilities on the route to chaos.

Statistics of dislocation avalanches in FCC and BCC metals: dislocation mechanisms and mean swept distances across microsample sizes and temperatures

Plastic deformation in crystalline materials consists of an ensemble of collective dislocation glide processes, which lead to strain burst emissions in micro-scale samples. To unravel the combined role of crystalline structure, sample size and temperature on these processes, we performed a comprehensive set of strict displacement-controlled micropillar compression experiments in conjunction with large-scale molecular dynamics and physics-based discrete dislocation dynamics simulations. The results indicate that plastic strain bursts consist of numerous individual dislocation glide events, which span over minuscule time intervals. The size distributions of these events exhibit a gradual transition from an incipient power-law slip regime (spanning \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 2.5 decades of slip sizes) to a large avalanche domain (spanning \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 4 decades of emission probability) at a cut-off slip magnitude \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s}_{\mathrm{c}}$$\end{document}sc. This cut-off slip provides a statistical measure to the characteristic mean dislocation swept distance, which allows for the scaling of the avalanche distributions vis-à-vis the archetypal dislocation mechanisms in face-centered cubic (FCC) and body-centered cubic (BCC) metals. Our statistical findings provide a new pathway to characterizing metal plasticity and towards comprehension of the sample size effects that limit the mechanical reliability in small-scale structures.

Sliding Avalanches Between Nacreous Tablets

Nacre, also known as mother of pearl, possesses extraordinary mechanical properties resulting from its intriguing hierarchical brick-and-mortar microstructures. Despite prior studies, interactions between nanoasperities during sliding still need to be elucidated. In this study, we measure slip events between nanograins of microlayers at high temporal resolution during torsion-induced sliding. We model the slips as avalanches caused by interactions of atoms on nanograin surfaces, from which power laws and scaling functions describing statistics and dynamics of slip events are studied. The largest avalanche occurs when nanograins leave each other after the maximum contact. The agreement between measurements and predictions shows that avalanches act essentially in the inhomogeneous sliding of nacreous tablets. Further insights into nanofriction provided in this work may lead to the development of nanoscale tribological systems.

Applied-force oscillations in avalanche dynamics

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or "slip avalanches." In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force control. The studies show very good agreement between simulations and experiments. We find that an oscillatory external driving force changes the average avalanche shapes only for avalanches with durations close to the period of oscillation of the external force. This effect on the avalanche shapes can be addressed in experiments by choosing suitable specimen dimensions so that the mechanical resonance does not interact with the avalanche dynamics. These results are important for the interpretation of avalanche experiments with built-in oscillators, and for the prediction and analysis of avalanche dynamics in systems with resonant vibrations.

Simulating the mechanisms of serrated flow in interstitial alloys with atomic resolution over diffusive timescales

The Portevin-Le Chatelier (PLC) effect is a phenomenon by which plastic slip in metallic materials becomes unstable, resulting in jerky flow and the onset of inhomogeneous deformation. The PLC effect is thought to be fundamentally caused by the dynamic interplay between dislocations and solute atoms. However, this interplay is almost always inaccessible experimentally due to the extremely fine length and time scales over which it occurs. In this paper, simulations of jerky flow in W-O interstitial solid solutions reveal three dynamic regimes emerging from the simulated strain rate-temperature space: one resembling standard solid solution strengthening, another one mimicking solute cloud formation, and a third one where dislocation/solute coevolution leads to jerky flow as a precursor of dynamic strain aging. The simulations are carried out in a stochastic framework that naturally captures rare events in a rigorous manner, providing atomistic resolution over diffusive time scales using no adjustable parameters.

Understanding the plastic deformation mechanism within specific ranges of temperature and strain in metal alloys is of great technological importance. Here the authors report on dynamic simulations of dislocation–solute coevolution in tungsten crystals containing a few atomic parts per million of interstitial oxygen and their relation to unstable plastic flow.

Universality Class of Nanocrystal Plasticity: Localization and Self-Organization in Discrete Dislocation Dynamics

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 plasticity at large rates (>10^{3}/s) fundamentally controls the system's statistical character as it competes with dislocation nucleation: At large rates, the behavior is statistically dominated by long-range correlations of "dragged" mobile dislocations. At small rates, plasticity localization dominates in small volumes and a spatial integration of avalanche behavior takes place.

Rotatable precipitates change the scale-free to scale dependent statistics in compressed Ti nano-pillars

Compressed nano-pillars crackle from moving dislocations, which reduces plastic stability. Crackling noise is characterized by stress drops or strain bursts, which scale over a large region of sizes leading to power law statistics. Here we report that this “classic” behaviour is not valid in Ti-based nanopillars for a counterintuitive reason: we tailor precipitates inside the nano-pillar, which “regulate” the flux of dislocations. It is not because the nano-pillars become too small to sustain large dislocation movements, the effect is hence independent of size. Our precipitates act as “rotors”: local stress initiates the rotation of inclusions, which reduces the stress amplitudes dramatically. The size distribution of stress drops simultaneously changes from power law to exponential. Rotors act like revolving doors limiting the number of passing dislocations. Hence each collapse becomes weak. We present experimental evidence for Ti-based nano-pillars (diameters between 300 nm and 2 μm) with power law distributions of crackling noise P(s) ∼ s^−τ with τ ∼ 2 in the defect free or non-rotatable precipitate states. Rotors change the size distribution to P(s) ∼ exp(−s/s₀). Rotors are inclusions of ω-phase that aligns under stress along slip planes and limit dislocation glide to small distances with high nucleation rates. This opens new ways to make nano-pillars more stable.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

Size-Tuned Plastic Flow Localization in Irradiated Materials at the Submicron Scale

Three-dimensional discrete dislocation dynamics (3D-DDD) simulations reveal that, with reduction of sample size in the submicron regime, the mechanism of plastic flow localization in irradiated materials transitions from irradiation-controlled to an intrinsic dislocation source controlled. Furthermore, the spatial correlation of plastic deformation decreases due to weaker dislocation interactions and less frequent cross slip as the system size decreases, thus manifesting itself in thinner dislocation channels. A simple model of discrete dislocation source activation coupled with cross slip channel widening is developed to reproduce and physically explain this transition. In order to quantify the phenomenon of plastic flow localization, we introduce a "deformation localization index," with implications to the design of radiation-resistant materials.

Discrete shear band plasticity through dislocation activities in body-centered cubic tungsten nanowires

Shear band in metallic crystals is localized deformation with high dislocation density, which is often observed in nanopillar deformation experiments. The shear band dynamics coupled with dislocation activities, however, remains unclear. Here, we investigate the dynamic processes of dislocation and shear band in body-centered cubic (BCC) tungsten nanowires via an integrated approach of in situ nanomechanical testing and atomistic simulation. We find a strong effect of surface orientation on dislocation nucleation in tungsten nanowires, in which {111} surfaces act as favorite sites under high strain. While dislocation activities in a localized region give rise to an initially thin shear band, self-catalyzed stress concentration and dislocation nucleation at shear band interfaces cause a discrete thickening of shear band. Our findings not only advance the current understanding of defect activities and deformation morphology of BCC nanowires, but also shed light on the deformation dynamics in other microscopic crystals where jerky motion of deformation band is observed.

Probing Microplasticity in Small-Scale FCC Crystals via Dynamic Mechanical Analysis

In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a steplike 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 preyield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply alternate current load perturbations via dynamic mechanical analysis during quasistatic uniaxial compression experiments on single crystalline Cu nanopillars with diameters of 500 nm and compute dynamic moduli at frequencies 0.1, 0.3, 1, and 10 Hz under progressively higher static loads until yielding. By tracking the collective aspects of the oscillatory stress-strain-time series in multiple samples, we observe an evolving dissipative component of the dislocation network response that signifies the transition from elastic behavior to dislocation avalanches in the globally preyield regime. We postulate that microplasticity, which is associated with the combination of dislocation avalanches and slow viscoplastic relaxations, is the cause of the dependency of dynamic modulus on the driving rate and the quasistatic stress. We construct a continuum mesoscopic dislocation dynamics model to compute the frequency response of stress over strain and obtain a consistent agreement with experimental observations. The results of our experiments and simulations present a pathway to discern and quantify correlated dislocation activity in the preyield regime of deforming crystals.