Quenched pinning and collective dislocation dynamics

Predicting elastic and plastic properties of small iron polycrystals by machine learning

Deformation of crystalline materials is an interesting example of complex system behaviour. Small samples typically exhibit a stochastic-like, irregular response to externally applied stresses, manifested as significant sample-to-sample variation in their mechanical properties. In this work we study the predictability of the sample-dependent shear moduli and yield stresses of a large set of small cube-shaped iron polycrystals generated by Voronoi tessellation, by combining molecular dynamics simulations and machine learning. Training a convolutional neural network to infer the mapping between the initial polycrystalline structure of the samples and features of the ensuing stress-strain curves reveals that the shear modulus can be predicted better than the yield stress. We discuss our results in the context of the sensitivity of the system's response to small perturbations of its initial state.

Nonsteady dynamics at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equation but agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.

Mild-to-wild plastic transition is governed by athermal screw dislocation slip in bcc Nb

Plastic deformation in crystals is mediated by the motion of line defects known as dislocations. For decades, dislocation activity has been treated as a homogeneous, smooth continuous process. However, it is now recognized that plasticity can be determined by long-range correlated and intermittent collective dislocation processes, known as avalanches. Here we demonstrate in body-centered cubic Nb how the long-range and scale-free dynamics at room temperature are progressively quenched out with decreasing temperature, eventually revealing intermittency with a characteristic length scale that approaches the Burgers vector itself. Plasticity is shown to be bimodal across the studied temperature regime, with conventional thermally-activated smooth plastic flow (‘mild’) coexisting with sporadic bursts (‘wild’) controlled by athermal screw dislocation activity, thereby violating the classical notion of temperature-dependent screw dislocation motion at low temperatures. An abrupt increase of the athermal avalanche component is identified at the critical temperature of the material. Our results indicate that plasticity at any scale can be understood in terms of the coexistence of these mild and wild modes of deformation, which could help design better alloys by suppressing one of the two modes in desired temperature windows.

Recent studies have recognized that plasticity in metals can be controlled by dislocation avalanches. Here the authors examine temperature-dependent microplasticity in bcc Nb and reveal the dominance of athermal screw dislocation activity during intermittent slip.

Dislocation avalanches from strain-controlled loading: A discrete dislocation dynamics study

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 durations of the dislocation avalanches are power law distributed up to a cutoff scale, and exhibit temporally asymmetric average shapes. We discuss the dependence of the results on the driving parameters and compare our results to those from previous simulations where quasistatic stress-controlled loading was used.

Variety of scaling behaviors in nanocrystalline plasticity

We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, submicron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.

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.

Superior plasticity stability and excellent strength in Ti-55531 alloy micropillars via harmony slip in nanoscale α/β phases

Excellent stability of plasticity and high strength are acquired in Ti55531 alloy micropillars via introducing a high density of deformable nanoscale α phase into a β matrix. The yield strength of the pillars is as high as 2.26 GPa irrespective of pillar sizes ranging from 6 to 0.3 μm, which is high enough to activate dislocation slip both in ductile α precipitates and the β matrix. The harmony slip model was proposed to interpret slip transmission between the nanoscale α phase and the divided β matrix, and both α and β accommodate their individual plasticity during compression. This results in an excellent combination of high strength and stable plasticity in Ti55531 alloy micron-to submicron pillars. The results highlight the novel strengthening and toughening mechanisms of nanostructured alloys and a specific type of microstructure that exhibits stable plasticity for nano/microdevices.

Machine learning plastic deformation of crystals

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 the stress-strain curves. The predictability vs strain relation is non-monotonic and exhibits a system size effect: larger systems are more predictable. Stochastic deformation avalanches give rise to fundamental limits of deformation predictability for intermediate strains. However, the large-strain deformation dynamics of the samples can be predicted surprisingly well.

Excitation Spectra in Crystal Plasticity

Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the marginal stability of ensembles of dislocations and compute their excitation spectrum in two and three dimensions. Our results show the presence of a singularity in the distribution of excitation stresses, i.e., the stress needed to make a localized region unstable, that is remarkably similar to the one measured in amorphous plasticity and spin glasses. These results allow us to understand recent observations of extended criticality in bursty crystal plasticity and explain how they originate from the presence of a pseudogap in the excitation spectrum.

Scaling laws in earthquake occurrence: Disorder, viscosity, and finite size effects in Olami-Feder-Christensen models

The relation between seismic moment and fractured area is crucial to earthquake hazard analysis. Experimental catalogs show multiple scaling behaviors, with some controversy concerning the exponent value in the large earthquake regime. Here, we show that the original Olami, Feder, and Christensen model does not capture experimental findings. Taking into account heterogeneous friction, the viscoelastic nature of faults, together with finite size effects, we are able to reproduce the different scaling regimes of field observations. We provide an explanation for the origin of the two crossovers between scaling regimes, which are shown to be controlled both by the geometry and the bulk dynamics.

Multiscale modeling of dislocation-precipitate interactions in Fe: From molecular dynamics to discrete dislocations

The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various pointlike defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a 1/2〈111〉{110} edge dislocation in BCC iron. We have implemented immobile spherical precipitates into the ParaDis discrete dislocation dynamics code, with the dislocations interacting with the precipitates via a Gaussian potential, generating a normal force acting on the dislocation segments. The parameters used in the discrete dislocation dynamics simulations for the precipitate potential, the dislocation mobility, shear modulus, and dislocation core energy are obtained from molecular dynamics simulations. We compare the critical stresses needed to unpin the dislocation from the precipitate in molecular dynamics and discrete dislocation dynamics simulations in order to fit the two methods together and discuss the variety of the relevant pinning and depinning mechanisms.