On the critical character of plasticity in metallic single crystals

Previous acoustic emission (AE) experiments on ice single crystals, as well as numerical simulations, called for the possible occurrence of self-organized criticality (SOC) in collective dislocation dynamics during plastic deformation. Here, we report AE experiments on hcp metallic single crystals. Dislocation avalanches in relation with slip and twinning are identified with the only sources of AE. Both types of processes exhibit a strong intermittent character. The AE waveforms of slip and twinning events seem to be different, but from the point of view of the AE event energy distributions, no distinction is possible. The distributions always follow a power law, even when multi-slip and forest hardening occur. The power law exponent is in perfect agreement with those previously found in ice single crystals. Along with observed time clustering and interactions between avalanches, these results are new and strong arguments in favour of a general, SOC-type, framework for crystalline plasticity.Comment: 12 pages, 10 figure

Elastic fields due to dislocations in anisotropic bi-and tri-materials: applications to discrete dislocation pile-ups at grain boundaries

International audienceElastic fields due to single dislocations and dislocation pileups are computed in heterogeneous media like bi-materials, half-spaces and tri-materials thanks to the Leknitskii-Eshelby-Stroh formalism for two-dimensional anisotropic elasticity. The tri-material configuration allows to consider grain boundary regions with finite thickness and specific stiffness. The effects of these parameters are first studied in the case of a single dislocation in a Ni bicrystal. Image forces may arise because of both dissimilar grain orientations and the presence of a finite grain boundary region. In particular, it is shown that the Peach-Koehler force projected along the dislocation glide direction can exhibit a change of sign with the dislocation position. Therefore, an equilibrium position in the absence of applied stress can be found by coupling an attractive compliant grain boundary region with a repulsive orientation of the adjacent crystal, or a repulsive stiff grain boundary region with an attractive orientation. Regarding dislocation pileups , it is shown that the resolved shear stress scales approximately with the inverse of the square root distance from the leading dislocation in the pileup. This scaling law remains valid in anisotropic elasticity for the chosen heterogeneous media. Both the grain boundary stiffness and grains misorientation influence pileup length and resolved shear stress, but the effect of misorientation is clearly seen to be predominant. In the case where the leading dislocation is unlocked, the resolved shear stress at a given position in the neighboring grain is reduced when the grain boundary stiffness is increased due to the pushing back of dislocations from the grain boundary.

Effect of anisotropic elasticity on dislocation pile-ups at grain boundaries

This study deals with in-situ micromechanical tests of micron-sized bi-crystals and observations coupling SEM, AFM and EBSD. Different FCC bi-crystals are obtained from FIB machining. A SEM in-situ compression test with a low strain is performed on a micron-sized bi-crystal in order to induce single slip deformation. Spatial variations in the surface step height due to dislocation activity in localized slip bands terminating at the grain boundary (GB) are measured by AFM. This allows the determination of the Burgers vector distribution and hence the dislocation positions in the pile-up as shown in Figure 1. Furthermore, local misorientation along slip bands is measured by high resolution EBSD in order to determine the deformation caused by the dislocation pile-ups. In parallel, an analytical approach based on the Leknitskii-Eshelby-Stroh (LES) formalism (1,2), which provides the elastic fields of straight dislocation pile-ups in anisotropic bi- and tri- materials (3) while considering (or not) free surface effects (4), are performed. The tri-material configuration allows considering a non-zero thickness in the nanometer range and a specific stiffness for the GB region. The configuration with two free surfaces could be used to study size effects. The effects of anisotropic elasticity, crystallographic orientation, GB stiffness and free surfaces are first studied in the case of a single dislocation in a Ni bi-crystal. Image forces may arise because of both dissimilar grain orientations, the presence of a finite grain boundary region and the presence of free surfaces. In particular, it is shown that the Peach-Koehler force projected along the dislocation glide direction can exhibit a change of sign with the dislocation position (5). The dislocation positions in a pile-up are calculated by an iterative relaxation scheme minimizing the Peach-Koehler force on each dislocation as shown in Figure 2. Both, GB stiffness and grains misorientation, influence pile-up length and the induced resolved shear stress in the neighboring grain, but the effect of misorientation is clearly predominant (5). Hence, the driving force for slip activation in the neighboring grain can be computed and compared to the observed GB resistance for slip transmission. Please click Additional Files below to see the full abstract

Atomic Force Microscopy Study of Discrete Dislocation Pile-ups at Grain Boundaries in Bi-Crystalline Micro-Pillars

Compression tests at low strains were performed to theoretically analyze the effects of anisotropic elasticity, misorientation, grain boundary (GB) stiffness, interfacial dislocations, free surfaces, and critical force on dislocation pile-ups in micro-sized Face-Centered Cubic (FCC) Nickel (Ni) and α -Brass bi-crystals. The spatial variations of slip heights due to localized slip bands terminating at GB were measured by Atomic Force Microscopy (AFM) to determine the Burgers vector distributions in the dislocation pile-ups. These distributions were then simulated by discrete pile-up micromechanical calculations in anisotropic bi-crystals consistent with the experimentally measured material parameters. The computations were based on the image decomposition method considering the effects of interphase GB and free surfaces in multilayered materials. For Ni and α -Brass, it was found that the best predicted step height spatial profiles were obtained considering anisotropic elasticity, free surface effects, a homogeneous external stress and a certain critical force in the material to equilibrate the dislocation pile-ups

Micromechanical modeling of the effect of elastic and plastic anisotropies on the mechanical behavior of β-Ti alloys

International audienceNear β-titanium alloys like Ti-5553 or Ti-1023 often exhibit bimodal phase constituents embedded in a retained β-phase matrix, which represents up to 40% of the volume. The highly elastic anisotropic β-phase may strongly influence the mechanical behavior of these alloys. The present work models the effect of the coupled role of β-phase elastic and plastic anisotropies on the local and overall responses of a fully β-phase polycrystalline aggregate like the Ti-17 alloy. The model is based on an advanced elasto-viscoplastic self-consistent (EVPSC) homogenization scheme solved by the "translated field" method together with an affine linearization of the viscoplastic flow rule. The effects of elastic anisotropy, crystallographic texture and grain morphology are theoretically studied during uniaxial tensile tests, tension-compression tests as well as multiaxial plastic yielding. First, it is shown that different sets of elastic constants taken from literature give rise to similar effective responses but to widely scattered incompatibility stresses. During uniaxial tensile loading, the highest local incompatibility stresses are achieved in oriented grains at the end of the elastic regime. Likewise, the effect of the β-grain morphology for realistic grain aspect ratios is seen to be weak on the overall behavior but strong on incompatibility stresses. In addition, the elastic anisotropy can have a significant influence on yield surfaces for β-forged textured polycrystals. Finally, the simulated Bauschinger stress monotonically increases with the elastic anisotropy coefficient for a random texture while it may be reduced in case of β-forged texture due to a competition between elastic and plastic sources of incompatibility stresses

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

Stress partitioning in a near-β Titanium alloy induced by elastic and plastic phase anisotropies: experimental and modeling

International audienceThe load transfer induced by the elas c and plas c phase anisotropies of a Ti-10V-2Fe-3Al tanium alloy is studied. The microstructure consists in α nodules embedded in elongated β grains. EBSD performed on the alloy shows no crystallographic texture neither for α nor β phase. Tensile tests along the elonga on direc on, at a strain rate of 2 x 10-3 s-1 give a yield stress of 830 MPa with 13% duc lity. Simula ons based on an advanced two-phase polycrystalline elasto-viscoplas c self-consistent (EVPSC) model predict that the β phase first plas fies with a sequen al onset of plas city star ng from oriented β grains, then and finally oriented β grains. This leads to a strong load transfer from the β grains to the α nodules whose average behavior remains elas c up to high stresses (~940 MPa). However, addi onal simula ons considering exclusively β grains of specific orienta on show that the behavior of α nodules is strongly dependent on the β texture in which they are embedded. Especially, in β grains, which plas fy the latest, the model predicts the onset of plas city in favorably orientated α nodules. Moreover, the orienta on spread within the β grains can modify the average plas c behavior of α phase. In future, these results will be compared to data obtained from in-situ High Energy XRD and SEM/EBSD experiments

Application of time–stress superposition to viscoelastic behavior of polyamide 6,6 fiber and its “true” elastic modulus

The viscoelastic behavior of semi-crystalline polyamide 6,6 fiber is exploited in viscoelastically prestressed polymeric matrix composites. To understand better the underlying prestress mechanisms, strain–time performance of the fiber material is investigated in this work, under high creep stress values (330–665 MPa). A latch-based Weibull model enables prediction of the “true” elastic modulus through instantaneous deformation from the creep-recovery data, giving 4.6 ± 0.4 GPa. The fiber shows approximate linear viscoelastic characteristics, so that the time–stress superposition principle (TSSP) can be implemented, with a linear relationship between the stress shift factor and applied stress. The resulting master creep curve enables creep behavior at 330 MPa to be predicted over a large timescale, thus creep at 590 MPa for 24 h would be equivalent to a 330 MPa creep stress for ∼5200 years. Similarly, the TSSP is applied to the resulting recovery data, to obtain a master recovery curve. This is equivalent to load removal in the master creep curve, in which the yarns would have been subjected to 330 MPa creep stress for ∼4.56 × 107 h. Since our work involves high stress values, the findings may be of interest to those involved with long-term load-bearing applications using polyamide materials

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

Étude de l'activité plastique dans des bi-cristaux métalliques: modélisation et expériences

Des contraintes d’incompatibilité et des rotations de réseau peuvent se développer dans les bi-cristaux en raison des anisotropies élastique et plastique qui existent en lien avec les différentes orientations cristallines présentes de part et d’autre du joint de grains. Récemment, un modèle a été développé qui tient compte pleinement des effets couplés entre élasticité et plasticité hétérogènes. Ce modèle fournit les expressions analytiques explicites des champs de contrainte et de désorientation du réseau dans un bi-cristal en supposant une interface plane infinie et une élasticité et une plasticité uniformes par morceaux. Ces expressions permettent de prédire les valeurs des cissions résolues sur tous les systèmes de glissement d’un bi-cristal. Dans cette étude, le cas général d'une fraction volumique de cristaux quelconque a également été pris en compte. Considérant un chargement uniaxial en élasticité pure, ce modèle permet de retomber sur deux autres théories classiques. Les cissions résolues par système calculées à partir du modèle de Hook-Hirth sont retrouvées en supposant une élasticité hétérogène isotrope et en négligeant l'effet de Poisson. En considérant une élasticité homogène dans le bi-cristal, les « facteur de Schmid » classiques sont retrouvés. A partir d’une cartographie EBSD de Ni pur, ce modèle a été appliqué à la prédiction des possibles systèmes de glissement actifs dans des bi-cristaux suite à des essais de compression parallèle aux joints de grains. L'étude s´est concentrée sur les bi-cristaux où la nouvelle approche conduit à des prédictions différentes concernant l’entrée en plasticité par rapport aux modèles de Schmid et Hook-Hirth. Expérimentalement, les essais de compression uniaxiale sont réalisés par nanoindentation sur des micropilliers fabriqués au FIB. Enfin, les propriétés élastiques effectives de tous les bi-cristaux sont calculées et comparées à celles obtenues à partir des approches de Voigt, Reuss et Hook-Hirth, ainsi qu’aux mesures expérimentales