Grain Boundary Misorientation Distribution Research Articles

Crystal plasticity finite element analysis of size effect on the formability of ultra-thin ferritic stainless steel sheet for fuel cell bipolar plate

The present study investigated the size effect on the formability of ultra-thin metallic bipolar plate for proton exchange membrane (PEM) fuel cell by crystal plasticity finite element method (CPFEM) in conjunction with the Marciniak-Kuczynski (MK) model. Mechanical behavior and crystallographic texture of a 0.08 mm-thick ferritic stainless steel (FSS) sheet were characterized by uniaxial tensile test and electron backscatter diffraction (EBSD) measurement. Nakazima formability test was carried out to measure the forming limit diagram (FLD) of ultra-thin FSS sheet. A hybrid cellular automata–Monte Carlo (CA–MC) model was developed to generate a ‘realistic’ representative volume element (RVE) that accurately reconstructed the measured texture and grain boundary misorientation distribution (GBMD). The predicted FLD by the CPFEM–MK model with the realistic RVE shows a good agreement with the experimental results. In order to explore the size effect on the formability, the forming limit analyses were performed using RVEs with various thickness-to-grain size ratios (t/d = 2∼10). The results reveal a significant degradation of the formability of the ultra-thin FSS sheet as t/d decreases. With decreasing number of grains through the thickness, the stress and strain heterogeneities in the surface grains are noticeably increased due to the less constraint by the subsurface grains, which plays an important role in the size effect. Furthermore, it is found that the surface strain hot spots in the material with low t/d can act as the geometrical imperfection to accelerate the failure, together with the increased stress triaxiality in the surface grains as the results of the localized strains and premature necking during the deformation. This attributes the decrease of forming limit strains to the early plastic flow instability in the ultra-thin sheet material with low thickness-to-grain size ratio.

Interface stress in nanocrystalline materials

Abstract Based on a generalization of a capillary equation for solids, we develop a method for measuring the absolute value of grain-boundary stress in polycrystalline samples having a large interface-to-volume ratio. The grain-boundary stress in nanocrystalline Pd is calculated from X-ray diffraction measurements of the average grain size and the residual-strain-free lattice spacings, yielding a value of 1.2 ± 0.1 N /m. The random distribution of crystallite orientations in the sample in conjunction with calorimetric data for the area-averaged interfacial energy and knowledge of the grain-boundary misorientation distribution function suggest that this value is characteristic of random high-angle grain boundaries in Pd.

A study of the static recrystallization behaviour of cast Alloy 825 after hot-compressions

The static recrystallization behaviour of a columnar and equiaxed Alloy 825 material was studied on a Gleeble-3800 thermo-simulator by single-hit compression experiments. Deformation temperatures of 1000-1200 °C, a strain of up to 0.8, a strain rate of 1s−1, and relaxation times of 30, 180, and 300 s were selected as the deformation conditions to investigate the effects of the deformation parameters on the SRX behaviour. Furthermore, the influences of the initial grain structures on the SRX behaviors were studied. The microstructural evolution was studied using optical microscopy and EBSD. The EBSD measurements showed a relaxation time of 95 % for fractional recrystallization grains, t95, in both structures, was less than 30 seconds at the deformation temperatures 1100 °C and 1200 °C. However, fewer than 95% of recrystallized grains recrystallized when the deformation temperature was lowered to 1000 °C. From the grain-boundary misorientation distribution in statically recrystallized samples, the fraction of high-angle grain boundaries decreased with an increasing deformation temperature from 1000 °C to 1200 °C for a given relaxation time. This was attributed to grain coarsening.

Helium bubble nucleation at grain boundaries and its influence on intergranular fracture

ABSTRACTAn in-depth understanding of the formation of intergranular helium bubbles and its relation to embrittlement is an important issue in the nuclear industry. In this paper, a thermodynamic model is developed to analyze the nucleation of intergranular helium bubbles. Microstructural observation using scanning electron microscopy and electron backscatter diffraction gives a detailed description for the relation between the bubble formation and the grain-boundary (GB) misorientation in helium-implanted nickel and Inconel X750. The theoretical and the experimental results confirm that the nucleation of intergranular helium bubbles is GB structure-dependent, the helium-to-vacancy ratio plays an important role in the bubble precipitation, and the interfacial tension of bubbles cannot be approximated to be the interfacial energy. The bubble-induced intergranular embrittlement in a polycrystal is modelled. The GB misorientation distribution, the intergranular bubble nucleation and growth and the GB connectivity are the key factors affecting the GB fracture toughness. The hoop ductility of the cladding tubes containing helium is analyzed. The hoop stress-induced increase in the GB energy promotes the precipitation of bubbles at the radial GBs and lead to the loss of tube ductility. Based on this work, the complicated correlation among the intergranular helium bubbles, the GB structure, the helium concentration, the applied stress and the helium embrittlement is clarified.

Texture and grain-boundary misorientation distributions in Y123 ceramics deformed by torsion under pressure

Texture and grain-boundary misorientation distributions in different parts of the sample of the high-Tc superconductor Y123 deformed by torsion under pressure at 1008 °C to a twist angle of 30° were investigated. The average levels of the basal plane texture (the Lotgering factor F) of undeformed and deformed samples were F = 0.25 and 0.965, respectively. In the undeformed sample, the fraction of low-angle grain boundaries (LAGBs) with misorientation angles from 2° to 10° does not exceed 5%. The deformation led to the formation of a strong, but non-uniform texture along the radius of the sample. In the center of the sample, a strong fiber texture is formed with the [001]-axis parallel to the axis of compression / torsion, and the fraction of LAGBs is about 20%. At a distance of 2 mm from the center of the sample there is a ring with a non-basal texture, where the fraction of LAGBs reaches 30%. A biaxial texture is formed at the edge of the sample: the [001] axis is parallel to the axis of compression / torsion, and the [110] axis is oriented along the radius of the sample. The fraction of LAGBs at the edge of the sample is 56%.

Structure Evolution and Distributions of Grain-Boundary Misorientainons in Submicrocrystalline Molybdenum Irradiated with a Pulsed Electron Beam

Using the methods of electron backscatter diffraction, electron microscopy and X-ray diffraction analysis, it is demonstrated that irradiation of the surface of a submicrocrystalline molybdenum specimen with a pulsed electron beam in a non-melt regime results in the formation of a gradient structure in its bulk. The irradiation temperature is shown to affect the density of defects, the value of stress, and the distributions of grain-boundary misorientations in the surface and bulk of the submicrocrystalline molybdenum specimens.

Effect of the Grain-boundary Misorientation Distribution on the Intergranular Voltage Relaxation of Bi1.65Pb0.35Sr2Ca2Cu3 O 10+δ Ceramic Samples

The impact of the grain boundary misorientation distribution (GBMD) on the intergranular voltage relaxation (V − t) curves at zero applied magnetic field in Bi1.65Pb0.35Sr2Ca2Cu3O10+δ (Bi-2223) ceramic samples has been investigated. Changes in the GMBD were realized by subjecting powders of Bi-2223 to two different uniaxial compacting pressures (UCP) before the last heat treatment of the samples. The GBMD was then determined from X-ray rocking curves and revealed significant differences between intergranular media of the specimens. It was found that the UCP results in a two-time reduction in the population of high-angle grain boundaries (𝜃 > 12∘) while the orientation homogeneity of the grain boundaries rises ∼ 30 %, indicating an improvement of the degree of texture of the materials. Such changes are mirrored in the behavior of the V − t curves which are explained by invoking differences in the rearrangement of the transport current driven by the angular dependence of the critical current density along grain boundaries. Numerical simulations of the V − t curves support the experimental V − t results and further suggest the occurrence of current localization in conductive paths within the materials.

Homology metrics for microstructure response fields in polycrystals

Quantitative homology metrics are proposed for characterizing the thermal–elastic response of polycrystalline materials. Simulations for a calcite-based polycrystal, marble, are used as an illustrative example. The homology metrics are based on topological measurements, such as the number of components and the number of handles of the thermal–elastic response fields for a complex microstructure. These homology metrics are applied to characterize not only the elastic energy density and maximum principal stress response fields in a polycrystal but also the correlated grain-boundary misorientation distributions that influenced the formation of these response fields. It is demonstrated that the topological analysis can quantitatively distinguish between different types of grain-boundary misorientations, as well as between differences in the resulting response fields.

Particle-associated misorientation distribution in a nickel-base superalloy

An approach was developed to quantify the relationship between the location of carbide particles and grain boundaries during the annealing of a typical nickel-base superalloy, Waspaloy. The average grain size increased during supersolvus heat treatment at 1100 °C for 1 h despite an absence of carbide coarsening and changes in the global texture. It was determined that the spatial distribution of carbides which developed during annealing was correlated to the grain-boundary misorientation distribution.

Evolution of microstructure and microtexture in fcc metals during high-pressure torsion

Pure nickel and commercially pure (CP) aluminium were selected as model fcc materials for a detailed investigation of the experimental parameters influencing grain refinement and evolution of microstructure and microtexture during processing by high-pressure torsion (HPT). Samples were examined after HPT using microhardness measurements, transmission electron microscopy and orientation imaging microscopy. Processing by HPT produces a grain size of ∼170 nm in pure Ni and ∼1 μm in CP aluminium. It is shown that homogeneous and equiaxed microstructures can be attained throughout the samples of nickel when using applied pressures of at least ∼6 GPa after 5 whole revolution. In CP aluminium, a homogeneous and equiaxed microstructure was achieved after 2 whole revolutions under an applied pressure of 1 GPa. For these conditions, the distributions of grain boundary misorientations are similar in the centre and at the periphery of the samples. It is shown that simple shear texture develops in fcc metals subjected to high-pressure torsion. Some grain growth was detected at the periphery of the Al disk after 8 revolutions. The factors influencing the development of homogeneous microstructures in processing by HPT are discussed.

Experimental parameters influencing grain refinement and microstructural evolution during high-pressure torsion

Pure nickel was selected for a detailed investigation of the experimental parameters influencing grain refinement and microstructural evolution during processing by high-pressure torsion (HPT). Samples were examined after HPT using microhardness measurements, transmission electron microscopy and orientation imaging microscopy. Processing by HPT produces a grain size of ~170 nm in pure Ni, and homogeneous and equiaxed microstructures are attained throughout the samples when they are subjected to at least ~5 whole revolutions under applied pressures of at least ~6 GPa. For these conditions, the distributions of grain boundary misorientations are similar in the center and at the periphery of the samples. A simple model is proposed to explain the development of a homogeneous microstructure in HPT.

Evolution of submicrocrystalline iron containing dispersed oxides under mechanical milling followed by consolidation

The structural changes in an Fe-0.6 pct O alloy during mechanical milling followed by consolidation through rolling were studied. The iron-iron oxide powders were mechanically milled in an argon atmosphere for various times from 20 to 300 hours. The powders were then canned into a steel pipe and multiple rolled at 700 °C for consolidation. The microstructure of the final product depended significantly on the milling time. The volume fraction of the dispersed oxides (10 nm in diameter) increased from about 0.3 to 2.5 pct when the milling time was increased from 20 to 300 hours. The relatively short milling time of 20 hours resulted in the evolution of elongated grains (an average size of about 1.2 µm) with a large fraction of low-angle grain boundaries after consolidation. In contrast, much finer grains (about 0.2 µm in size) with a near random grain-boundary misorientation distribution evolved in the samples milled for 300 hours.

Orientation imaging microscopy of ultrafine-grained nickel

Orientation imagining microscopy was used to measure the distributions of grain boundary misorientations in ultrafine-grained nickel processed by high-pressure torsion and equal-channel angular pressing. Both procedures give high fractions of high-angle boundaries but also higher fractions of low-angle boundaries than anticipated from a random distribution.

Microstructure evolution in Zr under equal channel angular pressing

Pure polycrystalline Zr was deformed by equal channel angular pressing (ECAP), and the microstructural characteristics were analyzed. By repeated alternating ECAP, it was possible to, refine the grain size from 200 to 0.2 μm. Subsequent annealing heat treatment at 550°C resulted in a grain growth of up to 6 μm. Mechanical twinning was an important deformation mechanism, particularly during the early stage of deformation. The most active twinning system was identified as 85.2 deg \(\left\{ {10\bar 12} \right\}\left\langle {\bar 1011} \right\rangle \) tensile twinning, followed by 57.1 deg \(\left\{ {10\bar 11} \right\}\left\langle {\bar 1012} \right\rangle \) compressive twinning. Crystal texture as well as grain-boundary misorientation distribution of deformed Zr were analyzed by X-ray diffraction (XRD) and electron backscattered diffraction (EBSD). The ECAP-deformed Zr showed a considerable difference in the crystallographic attributes from those of cold-rolled Zr or Ti, in that texture and boundary misorientation-angle distribution tend toward more even distribution with a slightly preferential distribution of boundaries of a 20 to 30 deg misorientation angle. Furthermore, unlike the case of cold rolling, the crystal texture was not greatly altered by subsequent annealing heat treatment. Overall, the present work suggests ECAP as a viable method to obtain significant grain refining in hexagonal close-packed (hcp) metals.

Directional and single-crystal solidification of Ni-base superalloys: Part II. Coincidence site lattice character of grain boundaries

The development of grain boundary misorientations with an evolving axial texture during directional solidification has been examined using the electron backscattered diffraction (EBSD) technique on the Ni-base superalloys, CMSX4 and CM186LC. A preferred grain boundary misorientation distribution (GBMD) for a sharp 〈001〉 axial texture in CM186LC was associated with a clustering of misorientation axes (MAx) in the proximity of 〈001〉. This is accompanied by an enhanced distribution of coincidence site lattice (CSL) boundaries. The increased distribution of low angle boundaries, Σ1 and Σ5, can be attributed to the existence of a preferred MAx and accommodation by secondary intrinsic grain boundary dislocations. The more diffuse 〈001〉 axial texture in CMSX4 is associated with a significant proportion of MAx deviating from 〈001〉 and a dramatic reduction in the proportion of CSL boundaries.

On the correlation of grain boundary misorientation distribution with critical current in bulk processed YBa2Cu3O7-δ

Abstract The grain boundary misorientation distribution of bulk processed high-T c superconductor YBa2Cu3O7-δ was studied as a function of processing conditions. The deviation of the grain boundary misorientation distribution (GBMD) from the random distribution, was tested using a χ2 analysis, and a grain boundary character distribution (GBCD) based upon the coincidence site lattice (CSL) model was developed and applied. The GBMD and GBCD both showed evolution departing from a random distribution for processing temperatures above 935°C. The GBCD analysis suggests an increase in the population of CSL-related boundaries with annealing time and temperature; and, in particular, the population of boundaries related to CSLs derived from a crystal with c/a > 3 continued to increase with annealing, while the population of boundaries related to other CSLs (c/a = 3) remained essentially constant. Comparison of the GBCD with the volume-averaged J c for each processing condition, indicates that the increasing proportion of 'c/a > 3' boundaries is related to a reduction in J c.

Grain boundary studies of high-temperature superconducting materials using electron backscatter Kikuchi diffraction

Grain orientation and grain boundary misorientation distributions in high critical current density, high-temperature superconductors were determined using electron backscatter Kikuchi diffraction. It is found that depending on the type of superconductor and the processing method used to fabricate it, there exist different scales of biaxial texture from no biaxial texture, local biaxial texture, to complete biaxial texture. Experimentally obtained grain boundary misorientation distributions (GBMDs) were found to be skewed significantly to low angles in comparison to what is expected on the basis of macroscopic texture alone, suggesting that minimization of energy may be a driving force during the processing of high critical current density materials. In addition, a higher than expected fraction of coincident-site lattice boundaries is observed. Examination of maps of grain boundary misorientations in spatially correlated grains, i.e. the grain boundary mesotexture, suggests the presence of percolative paths of high critical current density. A combination of orientation measurements, theoretical modeling of GBMDs and modeling of percolative current flow through an assemblage of grain boundaries is performed to gain an insight into the important microstructural features dictating the transport properties of high-temperature superconductors. It is found that maximization of low energy, in particular, low-angle boundaries, is essential for higher critical currents. The combination of experimental and analytical techniques employed are applicable to other materials where physical properties are dominated by intergranular characteristics.

Analyses of the Grain Boundary Misorientation and Oxygen Content of Bulk Processed YBa2Cu3O7-δ

ABSTRACTThe grain boundary misorientation distribution of 203 grain boundaries in bulk processed high Tc superconductor YBa2Cu3O7-δ with five processing conditions, was studied. Two complementary analytical approaches, Grain Boundary Misorientation Distribution (GBMD) from the random description, using a hypothesis test and X2 analysis, and Grain Boundary Character Distribution (GBCD), using the Coincidence Site Lattice (CSL) model, were applied. The GBMD and GBCD both showed grain boundary evolution departing from a random distribution above 935°C processing temperature. The GBCD analyses indicated an approximately linear increase in the population of CSL-related boundaries, among which the tetragonal CSL (c/a ≠ 3) boundaries grew in the same trend while orthorombic boundaries (c/a = 3) became stagnated. The results from comparing the corresponding GBCD and volume averaged Jc for each batch indicated that the tetragonal CSL boundaries were oxygen deficient and accounted for, among other current limiting factors, lower current carrying ability.

Statistical Analysis of Boundaries in NiO Films Grown on Ni Single Crystals

ABSTRACTAn attempt was made to apply the statistical analysis of NiO grain boundaries to explain the dependence of NiO growth kinetics on the crystallographic orientation of Ni substrate. Study was conducted for two crystals faces of Ni, (100) and (111), which exhibits a difference in oxidation rate constants at 1073 K, over one order of magnitude. The orientation distribution functions (ODF), calculated from X-ray measurements for NiO grown on both Ni faces, were analyzed numerically to assess the grain boundary character. The grain boundary misorientation distribution (GBMD) and grain boundary character distribution (GBCD), used to describe oxide structure, were derived using three different assumptions regarding the spatial correlation in orientation of neighbouring grains. Grain boundary network was created to analyze the high temperature diffusion properties through the oxide using diffusion constants available in the literature under assumption of various contribution of bulk and grain boundary diffusion paths to overall transport of ionic species. The growth parameters obtained were finally verified by comparison with experimentally measured oxidation kinetics.

Effect of texture on grain boundary misorientation distributions in polycrystalline high temperature superconductors

Computer simulations were performed to determine the most probable grain boundary misorientation distribution (GBMD) in model polycrystalline superconductors. GBMDs in polycrystalline superconductors can be expected to dictate the macroscopic transport critical current density, Jc. Calculations were performed by simulating model polycrystals and then determining the GBMD. Such distributions were calculated for random materials having cubic, tetragonal, and orthorhombic crystal symmetry. In addition, since most high temperature superconductors are tetragonal or pseudotetragonal, the effect of macroscopic uniaxial and biaxial grain orientation texture on the GBMD was determined for tetragonal materials. It is found that macroscopic texture drastically alters the grain boundary misorientation distribution. The fraction of low angle boundaries increases significantly with uniaxial and biaxial texture. The results of this study are important in correlating the macroscopic transport Jc with the measured grain orientation texture as determined by x-ray diffraction