M.-Carmen Miguel

Intermittent dislocation flow in viscoplastic deformation.

The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated ‘dislocation dynamics’ simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behaviour of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.

Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Complexity in dislocation dynamics: experiments

We present a statistical analysis of the acoustic emissions induced by dislocation motion during the creep of ice single crystals. The recorded acoustic waves provide an indirect measure of the inelastic energy dissipated during dislocation motion. Compression and torsion creep experiments indicate that viscoplastic deformation, even in the steady-state (secondary creep), is a complex and inhomogeneous process characterized by avalanches in the motion of dislocations. The distribution of avalanche sizes, identified with the acoustic wave amplitude (or the acoustic wave energy), is found to follow a power law with a cutoff at large amplitudes which depends on the creep stage (primary, secondary, tertiary). These results suggest that viscoplastic deformation in ice and possibly in other materials could be described in the framework of non-equilibrium critical phenomena.

Complexity in dislocation dynamics: model

Abstract 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 avalanche sizes which we compare with acoustic emission experiments in ice single crystals under creep deformation. We emphasize the connections of our model with nonequilibrium phase transitions and critical phenomena.

Tearing transition and plastic flow in superconducting thin films

A new class of artificial atoms, such as synthetic nanocrystals or vortices in superconductors, naturally self-assemble into ordered arrays. This property makes them applicable to the design of novel solids, and devices whose properties often depend on the response of such assemblies to the action of external forces. Here we study the transport properties of a vortex array in the Corbino disk geometry by numerical simulations. In response to an injected current in the superconductor, the global resistance associated to vortex motion exhibits sharp jumps at two threshold current values. The first corresponds to a tearing transition from rigid rotation to plastic flow, due to the reiterative nucleation around the disk centre of neutral dislocation pairs that unbind and glide across the entire disk. After the second jump, we observe a smoother plastic phase proceeding from the coherent glide of a larger number of dislocations arranged into radial grain boundaries.

Dynamical Correlations near Dislocation Jamming

Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value σ=σ{c}. 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 dynamical susceptibility χ{4}{*} diverges as χ{4}{*}∼(σ-σ{c}){-α}, with α≈1.1. We relate this scaling to an avalanche description of the dynamics. While the static structural correlations are found to be independent of the external stress, we identify a diverging dynamical correlation length ξ{y} in the direction perpendicular to the dislocation glide motion.

Deformation and failure of curved colloidal crystal shells

Significance Substantial experimental and theoretical work has been devoted to understand the equilibrium properties of curved crystals, but these crystals’ stability under mechanical forces remains largely unexplored and unknown. Understanding how curved crystals can adapt their shape and resist failure is of fundamental importance because these structures are at the forefront in the drive to fabricate new functionalized self-assembled materials. Here, we address these questions by numerical simulations of the deformation of colloidal crystalline shells. Our results highlight the fundamental role played by geometrically necessary crystal defects in controlling mechanical stability and plastic rearrangements of the shell. Designing and controlling particle self-assembly into robust and reliable high-performance smart materials often involves crystalline ordering in curved spaces. Examples include carbon allotropes like graphene, synthetic materials such as colloidosomes, or biological systems like lipid membranes, solid domains on vesicles, or viral capsids. Despite the relevance of these structures, the irreversible deformation and failure of curved crystals is still mostly unexplored. Here, we report simulation results of the mechanical deformation of colloidal crystalline shells that illustrate the subtle role played by geometrically necessary topological defects in controlling plastic yielding and failure. We observe plastic deformation attributable to the migration and reorientation of grain boundary scars, a collective process assisted by the intermittent proliferation of disclination pairs or abrupt structural failure induced by crack nucleating at defects. Our results provide general guiding principles to optimize the structural and mechanical stability of curved colloidal crystals.

Irreversible flow of vortex matter: Polycrystal and amorphous phases

We investigate the microscopic mechanisms giving rise to plastic depinning and irreversible flow in vortex matter. The topology of the vortex array crucially determines the flow response of this system. To illustrate this claim, two limiting cases are considered: weak and strong disorder forces. In the first case disorder is strong enough to introduce plastic effects in the vortex lattice. Diffraction patterns unveil polycrystalline lattice topology with dislocations and grain boundaries determining the electromagnetic response of the system. Filamentary flow is found to arise as a consequence of dislocation dynamics. We analyze the stability of vortex lattices against the formation of grain boundaries, as well as the steady-state dynamics for currents approaching the depinning critical current from above, when vortex motion is mainly localized at the grain boundaries. On the contrary, a dislocation description proves no longer adequate in the second limiting case examined. For strong disorder forces, the vortex array appears completely amorphous and no remnant of the Abrikosov lattice order is left. Here we obtain the critical current as a function of impurity density, its scaling properties, and characterize the steady-state dynamics above depinning. The plastic depinning observed in the amorphous phase is tightly connected with the emergence of channel-like flow. Our results suggest the possibility of establishing a clear distinction between two topologically disordered vortex phases: the vortex polycrystal and the amorphous vortex matter.

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.

Yielding and irreversible deformation below the microscale: surface effects and non-mean-field plastic avalanches

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 a series of abrupt discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry and elucidate the statistical properties of plastic deformation at such scales. Our results show that the absence of dislocation storage leads to crucial effects on the statistics of plastic events, ultimately affecting the universal scaling behavior observed at larger scales.