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

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

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

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

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

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

Estimating single-crystal elastic constants of polycrystalline β metastable titanium alloy: A Bayesian inference analysis based on high energy X-ray diffraction and micromechanical modeling

The authors also thank the Laboratoire Léon Brillouin (France) for beamtime allocation and Sebastien GAUTROT (LLB, France) for his help during the experiments. Vincent Jacquemain, Dr. Jean-Baptiste Marijon, and Dr. Stefan Michalik are acknowledged for their help during the synchrotron campaign at Diamond.A two-phase near- beta titanium alloy (Ti–10V–2Fe–3Al, or Ti-1023) in its as-forged state is employed to illustrate the feasibility of a Bayesian framework to identify single-crystal elastic constants (SEC). High Energy X-ray diffraction (HE-XRD) obtained at the Diamond synchrotron source are used to character- ize the evolution of lattice strains for various grain orientations during in situ specimen loading in the elastic regime. On the other hand, specimen behavior and grain deformation are estimated using the elastic self-consistent (ELSC) homogenization scheme. The XRD data and micromechanical modelling are revisited with a Bayesian framework. The effect of different material parameters (crystallographic and morphological textures, phase volume fraction) of the micromechanical model and the biases intro- duced by the XRD data on the identification of the SEC of the βphase are systematically investigated. In this respect, all the three cubic elastic constants of the βphase ( C11(beta) , C12(beta) , C44(beta) ) in the Ti-1023 alloy have been derived with their uncertainties. The grain aspect ratio in the ELSC model, which is often not considered in the literature, is found to be an important parameter in affecting the identified SEC. The Bayesian inference suggests a high probability for non-spherical grains (aspect ratio of ∼3 . 8+/-0 . 8 ) : C11(beta) = 92 . 6+/-19 . 1 GPa , C12(beta) = 82 . 5+/-16 . 3 GPa , C44(beta) = 43 . 5+/-7 . 1 GPa . The uncertainty obtained by Bayesian approach lies in the range of ~1-3 GPa for the shear modulus mu’ = (C11(beta) −C12(beta) )/2 , and ~7 GPa for the shear modulus mu’’ = C44(beta) , while it is significantly larger in the case of the bulk modulus (C11(beta) +2C12(beta))/3 (~17-24 GPa).This research is supported by the “Région Grand Est” and by the French State through two programs operated by the National Research Agency (ANR), (1) “Investment in the future” referenced by ANR-11-LABX-0 0 08-01 (Laboratory of Excellence “DAMAS”: De- sign of Alloy Metals for low-mAss Structures) and (2) “Plan d’Investissement d’Avenir” (PIA) in the frame of a research pro- gram managed by "Institut de Recherche Technologique Matériaux, Métallurgie, Procédés" (IRT M2P). We acknowledge DIAMOND for provision of synchrotron radiation beamtime at beamline I12-JEEP

Incompatibility Stresses and Lattice Rotations Due to Grain Boundary Sliding in Heterogeneous Anisotropic Elasticity

Non-uniform grain boundary sliding can induce strain and rotation incompatibilities at perfectly planar interfaces. Explicit analytic expressions of stress and lattice rotation jumps are thus derived at a planar interface in the general framework of heterogeneous anisotropic thermo-elasticity with plasticity and grain boundary sliding. Both elastic fields are directly dependent on in-plane gradients of grain boundary sliding. It is also shown that grain boundary sliding is a mechanism that may relax incompatibility stresses of elastic, plastic and thermal origin although the latter are not resolved on the grain boundary plane. This relaxation may be a driving force for grain boundary sliding in addition to the traditionally considered local shears on the grain boundary plane. Moreover, the obtained analytic expressions are checked by different kinds of bicrystal shearing finite element simulations allowing grain boundary sliding and where a pinned line in the interface plane aims at representing the effect of a triple junction. A very good agreement is found between the analytic solutions and the finite element results. The performed simulations particularly emphasize the role of grain boundary sliding as a possible strong stress generator around the grain boundary close to the triple line because of the presence of pronounced gradients of sliding