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

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

Comprendre les effets de tailles mécaniques dans les microfils métalliques : synergie entre expérience et simulation

Polycrystalline metallic microwires produced by cold-drawing exhibit significant mechanical strength that make them ideal candidates for reinforcement of composites. Previous studies on polycrystalline pure nickel wires have indicated a significant size dependence of their yield and tensile strength as well as their ductility. The aim of this study is to understand these size effects by in-situ X-ray diffraction (XRD) analysis and crystal plasticity finite element (CPFE) simulations. In-situ monotonous and cyclic tensile tests under synchrotron radiation were carried on microwires with diameters ranging from 100 to 40 µm. The commercially obtained 100µm as-drawn wires exhibit a core-shell architecture with fiber texture dominant in core and heterogeneous dual fiber texture and in the shell. Reduction of specimen size by electropolishing leads to wires having a homogeneous microstructure, whereas reduction of specimen size by further cold drawing leads to wires with a sharper texture while retaining the core-shell architecture.The yield and tensile strength of the electropolished wires increase with decreasing diameter, whereas the ductility decrease with decreasing diameter. In the case of cold-drawn wires, the yield and tensile strength, and also the ductility was observed to increase with decreasing diameter. The XRD analysis indicates successive yielding of grain families under iso-strain condition. The gradient in the texture of the microwire was seen to activate deformation mechanisms which are not seen for microwires with homogeneous texture. To understand the influence of different microstructural parameters, and notably the influence of crystallographic texture, 3D representative microstructure was generated and CPFE simulations were carried out. The simulated average behavior of different grain families (, ) agrees well with the experimental results. The CPFE simulations indicate heterogeneity in stress field across the microstructure in the presence of a gradient in crystallographic texture.We show that the microstructure engineering of micro-texture components (single- or dual-texture) and their spatial spread (homogenous or architectured) can be used as design guidelines for obtaining optimal microstructure in accordance with desired set of mechanical properties.Les microfils métalliques polycristallins produits par étirage à froid présentent une résistance mécanique significative en faisant des candidats idéaux pour les renforts de composites. Des études antérieures sur des fils de nickel polycristallin pur ont montré une dépendance importante par rapport à la taille de la limite d'élasticité et de la résistance à la traction, ainsi que de la ductilité.Le but de cette étude est de comprendre cet effet de la taille dans les microfils de nickel pur polycristallin par analyse de diffraction des rayons X in-situ (DRX) et simulations de la plasticité cristalline par éléments finis (CPFE). Des essais de traction monotone et cyclique in-situ sous rayonnement synchrotron ont été réalisés sur des microfils de diamètres allant de 100 à 40 μm. Les fils étirés à 100 micromètres obtenus dans le commerce présentent une architecture cœur-coquille avec une texture de fibre dominante dans le cœur et une texture à double fibre hétérogène et dans la coquille. La réduction de la taille de l'échantillon par polissage électrolytique conduit à des fils ayant une microstructure homogène, tandis que la réduction de la taille de l'échantillon par un étirage à froid supplémentaire conduit à des fils avec une texture plus intense tout en conservant l'architecture cœur-coquille.La limite d'élasticité et la résistance à la traction des fils électropolis augmentent avec la diminution du diamètre, tandis que la ductilité diminue avec la réduction du diamètre. Dans le cas des fils étirés à froid, on observe que la limite d'élasticité et la résistance à la traction, ainsi que la ductilité, augmentent avec la diminution du diamètre. L'analyse DRX indique une plasticité successive des familles de grains sous iso-déformation. Nous avons observé que le gradient de la texture du microfil active des mécanismes de déformation qui ne sont pas observés pour les microfils à texture homogène. Pour comprendre l'influence de différents paramètres microstructuraux, notamment l'influence de la texture cristallographique, une microstructure représentative 3D a été générée et des simulations CPFE ont été réalisées. Le comportement simulé moyen des différentes familles de grains (, ) concorde bien avec les résultats expérimentaux. La simulation CPFE indique une hétérogénéité du champ de contrainte à travers la microstructure en présence d'un gradient de texture cristallographique.Nous montrons que la micro-texture (texture simple ou double texture) et leur dispersion spatiale (homogène ou architecturée) peuvent être utilisées comme stratégie de conception pour obtenir une microstructure optimale en fonction de l’ensemble désiré de propriétés mécaniques

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

The load transfer induced by the elastic and plastic phase anisotropies of a Ti–10V–2Fe–3Al titanium 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 elongation direction, at a strain rate of 2 x 10-3 s-1 give a yield stress of 830 MPa with 13% ductility. Simulations based on an advanced two-phase polycrystalline elasto-viscoplastic self-consistent (EVPSC) model predict that the β phase first plastifies with a sequential onset of plasticity starting 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 elastic up to high stresses (~940 MPa). However, additional simulations considering exclusively β grains of specific orientation show that the behavior of α nodules is strongly dependent on the β texture in which they are embedded. Especially, in β grains, which plastify the latest, the model predicts the onset of plasticity in favorably orientated α nodules. Moreover, the orientation spread within the β grains can modify the average plastic behavior of α phase. In future, these results will be compared to data obtained from in-situ High Energy XRD and SEM/EBSD experiments

Phase transition and twinning in polycrystals probed by in situ high temperature 3D reciprocal space mapping

Polycrystalline materials exhibit physical properties that are driven by both the interatomic crystallographic structure as well as the nature and density of structural defects. Crystallographic evolutions driven by phase transitions and associated twinning process can be observed in situ in three-dimensional (3D) using monochromatic synchrotron radiation at very high temperatures (over 1000 C). This paper focuses on continuous measurements of the 3D-reciprocal space maps by high-resolution x-ray diffraction as a function of temperature along a phase transition process occurring between 1200 C and room temperature. These high precision measurements allow observing the reciprocal space node splitting and the evolution of the diffuse scattering signal around that node as a function of temperature. The capability of this experimental method is illustrated by direct in situ high temperature measurements of the 3D splitting of a reciprocal space node due to phase transition recorded on dense pure zirconia polycrystals

LaueNN: neural-network-based hkl recognition of Laue spots and its application to polycrystalline materials

A feed-forward neural-network-based model is presented to index, in real time, the diffraction spots recorded during synchrotron X-ray Laue microdiffraction experiments. Data dimensionality reduction is applied to extract physical 1D features from the 2D X-ray diffraction Laue images, thereby making it possible to train a neural network on the fly for any crystal system. The capabilities of the LaueNN model are illustrated through three examples: a two-phase nanostructure, a textured high-symmetry specimen deformed in situ and a polycrystalline low-symmetry material. This work provides a novel way to efficiently index Laue spots in simple and complex recorded images in <1 s, thereby opening up avenues for the realization of real-time analysis of synchrotron Laue diffraction data

Revealing the role of microstructure architecture on strength and ductility of Ni microwires by in-situ synchrotron X-ray diffraction

Deformation mechanisms of cold drawn and electropolished nickel microwires are studied by performing in-situ monotonous and cyclic tensile tests under synchrotron radiation. X-ray diffraction tests allow probing elastic strains in the different grain families and establishing a link with the deformation mechanisms taking place within the microwires. The measurements were carried out on several microwires with diameters ranging from as-drawn 100 mu m down to 40 mu m thinned down by electropolishing. The as-drawn wires exhibit a core-shell microstructure with <111> fiber texture dominant in core and heterogeneous dual fiber texture <111> and <100> in the shell. Reduction of specimen size by electropolishing results in a higher yield stress and tensile strength along with reduced ductility. In-situ XRD analysis revealed that these differences are linked to the global variation in microstructure induced by shell removal with electropolishing, which in turn affects the load sharing abilities of grain families. This study thus proposes a new way to increase ductility and retain strength in nickel microwires across different diameters by tuning the microstructure architecture