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 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.Comment: Supporting Videos available at http://dx.plos.org/10.1371/journal.pone.002041

Champs élastiques et forces configurationnelles dans des tri-cristaux anisotropes: application aux empilements de dislocations aux joints de grains

International audienceProgress in the modeling of the mechanical behavior of metallic polycrystals depends on a better consideration of the interactions between dislocations and crystalline interfaces like grain boundaries. Dislocation pile up mechanisms at grain boundaries are often not well taken into account in crystal plasticity-based micromechanical models due to the discreteness of such mechanisms. The role of crystalline elastic anisotropy on this mechanism is not frequently studied. Here, from the Leknitskii-Eshelby-Stroh (LES) formalism for two-dimensional elastic anisotropy, elastic fields of straight dislocations in bi-materials (bi-crystals) are theoretically calculated using the solution in a homogeneous medium and a "perturbation" for which the solution is derived from the standard analytic continuation method. Besides, in the case of tri-materials (or tri-crystals) where the grain boundary can be considered as an interphase with a certain thickness and stiffness, an alternating technique using the bi-material solution is applied leading to a formal solution in the form of series. The method allows to compute the configurational forces due to the grain boundary on the dislocations ("image forces") as functions of the inter-granular misorientation and the grain boundary elastic stiffness. Furthermore, their effects on discrete dislocation pileup lengths and stress concentrations in the adjacent grain of pileup are discussed.Les progrès dans la modélisation du comportement mécanique des polycristaux métalliques se jouent actuellement par une meilleure prise en compte des interactions entre les dislocations et les interfaces cristallines comme les joints de grains. Les mécanismes d'empilements de dislocations aux joints de grains ne sont pas encore bien pris en compte dans les modèles micromécaniques en plasticité cristalline du fait du caractère discret de ces mécanismes. Le rôle de l'anisotropie élastique cristalline sur ces mécanismes est très peu étudié. Ici, à partir du formalisme de Leknitskii-Eshelby-Stroh (LES) pour l'élasticité anisotrope bi-dimensionnelle, les champs élastiques de dislocations rectilignes dans les bi-matériaux (ou bi-cristaux) sont calculés théoriquement en utilisant la solution du problème homogène et une "perturbation" dont la solution provient d'une méthode standard de continuation analytique. De plus, dans le cas des tri-matériaux (ou matériaux tri-cristallins) où le joint de grains peut être considéré comme une interphase d'une certaine épaisseur et d'une certaine rigidité, une technique appropriée utilisant alternativement la solution du bi-matériau est utilisée conduisant à une solution formelle sous forme de série. La méthode permet en élasticité anisotrope de calculer les forces configurationnelles exercées par le joint de grains sur les dislocations (ou "forces images") en fonction de la désorientation inter-granulaire et de la rigidité du joint de grains. De plus, leurs effets sur les longueurs d'empilements discrets de dislocations et les concentrations de contraintes (cissions résolues) dans le grain adjacent sont discutés

Cast aluminium single crystals cross the threshold from bulk to size-dependent stochastic plasticity

Metals are known to exhibit mechanical behaviour at the nanoscale different to bulk samples. This transition typically initiates at the micrometre scale, yet existing techniques to produce micrometre-sized samples often introduce artefacts that can influence deformation mechanisms. Here, we demonstrate the casting of micrometre-scale aluminium single-crystal wires by infiltration of a salt mould. Samples have millimetre lengths, smooth surfaces, a range of crystallographic orientations, and a diameter D as small as 6 μm. The wires deform in bursts, at a stress that increases with decreasing D. Bursts greater than 200 nm account for roughly 50% of wire deformation and have exponentially distributed intensities. Dislocation dynamics simulations show that single-arm sources that produce large displacement bursts halted by stochastic cross-slip and lock formation explain microcast wire behaviour. This microcasting technique may be extended to several other metals or alloys and offers the possibility of exploring mechanical behaviour spanning the micrometre scale

Energy dissipation via acoustic emission in ductile crack initiation

The final publication is available at Springer via http://dx.doi.org/10.1007/s10704-016-0096-8.This article presents a modeling approach to estimate the energy release due to ductile crack initiation in conjunction to the energy dissipation associated with the formation and propagation of transient stress waves typically referred to as acoustic emission. To achieve this goal, a ductile fracture problem is investigated computationally using the finite element method based on a compact tension geometry under Mode I loading conditions. To quantify the energy dissipation associated with acoustic emission, a crack increment is produced given a pre-determined notch size in a 3D cohesive-based extended finite element model. The computational modeling methodology consists of defining a damage initiation state from static simulations and linking such state to a dynamic formulation used to evaluate wave propagation and related energy redistribution effects. The model relies on a custom traction separation law constructed using full field deformation measurements obtained experimentally using the digital image correlation method. The amount of energy release due to the investigated first crack increment is evaluated through three different approaches both for verification purposes and to produce an estimate of the portion of the energy that radiates away from the crack source in the form of transient waves. The results presented herein propose an upper bound for the energy dissipation associated to acoustic emission, which could assist the interpretation and implementation of relevant nondestructive evaluation methods and the further enrichment of the understanding of effects associated with fracture

Incompatibility stresses at grain boundaries in Ni bicrystalline micropillars analyzed by an anisotropic model and slip activity

International audienceIncompatibility stresses can develop in bicrystals due to material elastic and plastic anisotropies owing to different crystal orientations separated by grain boundaries. Here, these stresses are investigated by combining experimental and theoretical studies on 10 gm diameter Ni bicrystalline micropillars. Throughout stepwise compression tests, slip traces are analyzed by scanning electron microscopy to identify the active slip planes and directions in both crystals. An analytical model is presented accounting for the effects of heterogeneous elasticity coupled to heterogeneous plasticity on the internal mechanical fields. This model provides explicit expressions of stresses in both crystals considering experimentally observed non-equal crystal volume fractions and inclined grain boundaries. It is used to predict the resolved shear stresses on the possible slip systems in each crystal. The predictions of the onset of plasticity as given by the present model in pure elasticity are compared with those given by the classical Schmid's law. In contrast with Schmid's law, the predictions of the analytical model are in full agreement with the experimental observations regarding the most highly stressed crystal and active slip systems. The effects of plastic incompatibilities are also considered in addition to the elastic ones throughout the model. The analysis shows that elastic/plastic coupling incompatibilities together with different crystal volume fractions have significant effects on the slip system activation process

From Mild to Wild Fluctuations in Crystal Plasticity

International audienceMacroscopic crystal plasticity is classically viewed as an outcome of uncorrelated dislocation motions producing Gaussian fluctuations. An apparently conflicting picture emerged in recent years emphasizing highly correlated dislocation dynamics characterized by power-law distributed fluctuations. We use acoustic emission measurements in crystals with different symmetries to show that intermittent and continuous visions of plastic flow are not incompatible. We demonstrate the existence of crossover regimes where strongly intermittent events coexist with a Gaussian quasiequilibrium background and propose a simple theoretical framework compatible with these observations