3D Grain Research Articles

A new method to create of the plane section standards of grain metal structures

A new method to create of the plane section standards of grain metal structures with a previously known size distribution of 3D grains is proposed. A quantitative analysis of G3, G4, G5 indices of the standard ISO 643:2012 was performed. The stereological modeling method taking into account the polyhedral shape of 3D grains was used to create new versions of plane section standards. Versions of 3D grains structures as the diameter size distributions of 3D grains, plane sections of which correspond to the main quantitative characteristics of existing G3, G4, G5 indices have been created. It was shown that these versions should contain 3D grain more than 1.5 times the mean diameter of the corresponding plane sections. Choosing the diameter size distributions of 3D grains, necessary for the standard, its possible to create a visual index as a picture, as it done on the existing standard, and also to give the parameters of 3D structure, plane section of which corresponds to this standard. Using a new approach to creating standards will increase the accuracy of the grain structure parameters determining.

A Method to Incorporate Grain Boundary Strength and its Effects on Plastic Deformation in FCC Polycrystals

A three-dimensional (3D) crystal plasticity finite element method (CPFEM) is developed to investigate the effect of grain boundary strength on heterogeneous strain partitioning in FCC polycrystals. The proposed method incorporates electron backscatter diffraction (EBSD) maps into finite element analyses. The numerical analysis accounts for crystallographic texture, its evolution and 3D grain morphologies. Furthermore, grain boundaries are also mapped with a special finite element framework that allows material properties to be assigned to the grain boundaries. The material parameters and the grain boundary strengths are obtained by calibration to experimental uniaxial tension curves for single and polycrystals. Numerical simulations of uniaxial tension are performed and the effects of grain boundary strength on the onset of non-uniform deformation is investigated. The predicted local strain evolution is compared with corresponding experimental results from digital image correlation (DIC) measurements of an AA5754 aluminium sheet. The results showed that an excellent agreement was reached when the grain boundary properties were set so that the hardness was five times that of the average polycrystal response.

3D grain structure of an extruded 6061 Al alloy by lab-scale X-ray diffraction contrast tomography (DCT)

In this work, lab-scale X-ray diffraction contrast tomography (DCT) was conducted to investigate the 3D grain structure of α-Al in an extruded 6061 Al alloy. The morphological statistics of α-Al grains and the crystallographic characteristics including grain orientation, misorientation, and grain boundary plane orientation were analyzed. Grain boundary plane distributions of all grain boundaries or grain boundaries with specific misorientations were also revealed. A thorough understanding of the crystallographic characteristics of 6061 Al alloy is key to unlocking a more robust understanding of material performance.

A multiscale study of hot-extruded CoNiGa ferromagnetic shape-memory alloys

Ferromagnetic shape-memory CoNiGa alloys have attracted much scientific interest due to their potential alternative use as high-temperature shape-memory alloys, bearing a high prospect for actuation and damping applications at elevated temperatures. Yet, polycrystalline CoNiGa, due to strong orientation dependence of transformation strains, suffers from intergranular fracture. Here, two multi-grain CoNiGa samples were prepared by a novel hot extrusion process that can promote favourable grain-boundary orientation distribution and improve the material's mechanical behaviour. The samples were investigated by multiple methods and their microstructural, magnetic, and mechanical properties are reported. It is found that a post-extrusion solutionising heat treatment leads to the formation of a two-phase oligocrystalline homogeneous microstructure consisting of an austenitic parent B2 phase and γ-CoNiGa precipitates. Reconstruction of the full 3D grain morphology revealed large, nearly spherical grains with no low-angle grain boundaries throughout the entire sample volume. The presence of γ precipitation affects the transformation behaviour of the samples, by lowering the martensitic transformation temperature, while, in conjunction with the oligocrystalline microstructure, it improves the ductility. Controlling the composition of the B2 matrix, as well as the phase fraction of the γ phase, is thus crucial for the optimal behaviour of the alloys.

Effects of transition metals on the evolution of polymer-derived SiOC ceramics

This study focuses on catalytic graphitization from different metals, iron (Fe), cobalt (Co), and nickel (Ni), for inducing carbon growth in silicon oxycarbides (SiOCs) during the pyrolysis. Fe, Co, and Ni-modified SiOCs were synthesized by pyrolysis to 900, 1100, and 1300 °C respectively in Ar. The transition metals induced the formation of the corresponding metal silicides, β-SiC, and graphitic carbon with the catalytic activity in the order of Fe > Co > Ni, in agreement with the activation energy calculation based on the carbon types and amounts. Lateral growth of turbostratic carbon followed a 2D grain growth process and its point-like defect density decreased based on the catalytic order of the transition metals, with SiOC/Fe having the lowest defect density. Quantitative analysis of the XPS results with Rietveld refinement illustrated that the phase separation of SiOC is more dominant than local carbothermal reduction between SiO2 and C in the SiOC/M (M = Ni, Co, or Fe) systems. Understanding the catalytic graphitization effect of Ni, Co, and Fe on polymer derived ceramics offers new strategies in increasing high-temperature phase amounts and thus creating novel materials for heterogeneous catalysis, magnetic, and other applications.

X-ray orientation microscopy using topo-tomography and multi-mode diffraction contrast tomography

Polycrystal orientation mapping techniques based on full-field acquisition schemes like X-ray Diffraction Contrast Tomography and certain other variants of 3D X-ray Diffraction or near-field High Energy Diffraction Microscopy enable time efficient mapping of 3D grain microstructures. The spatial resolution obtained with this class of monochromatic beam X-ray diffraction imaging approaches remains typically below the ultimate spatial resolution achievable with X-ray imaging detectors. Introducing a generalised reconstruction framework enabling the combination of acquisitions with different detector pixel size and sample tilt settings provide a pathway towards 3D orientation mapping with a spatial resolution approaching the one of state of the art X-ray imaging detector systems.

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

ABSTRACT We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling before. We illustrate the speed and accuracy of the algorithm by generating RVEs with user-defined volume distributions with up to 20,000 grains in 3D. We can achieve volume percentage errors of less than 1% in the order of minutes on a standard desktop PC. We also give examples of polydisperse microstructures with bands, clusters and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements of an IF steel.

Quantification of the morphology of gold grains in 3D using X-ray microscopy and SEM photogrammetry

ABSTRACT The shape of gold is widely used in mineral exploration and in sedimentology to estimate the distance of transport from the source to the site of deposition. However, estimation of the morphology is based on qualitative observations or on the quantification of shape in 2D. The 3D analysis of grain shape is useful for accurate morphometric quantification and to evaluate its volume, which is related to particle size. This study compares X-ray 3D microscope and 3D SEM photogrammetry to reconstruct the shape of gold particles. These new methods are exploited to quantify the shape of gold grains 85 to 300 μm in size. The shape parameters, such as axial lengths, surface area, volume, diameter of curvature of all corners, and diameter of the largest inscribed sphere and smallest circumscribed sphere are measured on a particle in order to estimate shape factors such as flatness ratios, shape indices, sphericity, and roundness. Most shape parameters and shape factors estimated on the same gold grain with simple geometry are similar between the two approaches. This result validates these methods for the 3D description of gold particles with simple morphology, while providing a methodology for describing grains with more complex geometry.

Grain Orientation Optimization of Two-Dimensional Grain Selector during Directional Solidification of Ni-Based Superalloys.

The grain selection method is widely used in industry to produce Ni-based single crystal superalloys. A Z-form two-dimensional (2D) grain selector was designed to obtain high-quality single crystals. To control grain orientation deviation, one of the most important defects of the single crystal superalloys in casting, Z-form 2D grain selectors with different take-off angle were investigated in this study. The MM247LC superalloy single crystal samples were obtained by the Bridgman method modified by the Z-form grain selectors in this study. The Electron Backscattered Diffraction (EBSD) and the Optical Microscopy (OM) were used to observe and measure the grain selection growth and the microstructural evolution and orientation of the single crystal were also discussed. The results show that a Z-form 2D grain selector with an appropriate take-off angle can significantly reduce the deviation of the grain orientation. A single crystal superalloy with a deviation angle less than 6° can be obtained effectively when the take-off angle was 40°.

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Random tessellations are well suited for probabilistic modeling of three-dimensional (3D) grain microstructures of polycrystalline materials. The present paper is focused on so-called Gibbs-Laguerre tessellations, in which the generators of the Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process such that the resulting tessellation matches some desired geometrical properties. Since the model is analytically intractable, our main tool of analysis is stochastic simulation based on Markov chain Monte Carlo. Such simulations enable us to investigate the properties of the models, and, in the next step, to apply the knowledge gained to the statistical reconstruction of the 3D microstructure of an aluminum alloy extracted from 3D tomographic image data.

Nondestructive 3D Image Analysis Pipeline to Extract Rice Grain Traits Using X-Ray Computed Tomography

The traits of rice panicles play important roles in yield assessment, variety classification, rice breeding, and cultivation management. Most traditional grain phenotyping methods require threshing and thus are time-consuming and labor-intensive; moreover, these methods cannot obtain 3D grain traits. In this work, based on X-ray computed tomography, we proposed an image analysis method to extract twenty-two 3D grain traits. After 104 samples were tested, the R2 values between the extracted and manual measurements of the grain number and grain length were 0.980 and 0.960, respectively. We also found a high correlation between the total grain volume and weight. In addition, the extracted 3D grain traits were used to classify the rice varieties, and the support vector machine classifier had a higher recognition accuracy than the stepwise discriminant analysis and random forest classifiers. In conclusion, we developed a 3D image analysis pipeline to extract rice grain traits using X-ray computed tomography that can provide more 3D grain information and could benefit future research on rice functional genomics and rice breeding.

Exploring the effect of 3D grain shape on the packing and mechanical behaviour of sands

This paper investigated the dependence of three-dimensional grain shape characteristics on particle size by applying X-ray micro-computerized tomography. A series of packing and triaxial shearing experiments are performed, which suggest that the macroscale behaviour of sands at different scales of stress states progressively correspond to the characteristic scales of the microscale morphological descriptors of particles. That is, the packing behaviour are more reliant on grain aspect ratio (AR), whereas the critical state mechanical behaviour are more reliant on grain sphericity. As the AR of particulates increases, the extreme void ratios and packing index decrease. The shearing friction angles at the critical state decrease as the sphericity of grains increases and the intercept void ratios become smaller. The drained peak friction angles and maximum friction angles of undrained stable and strain-hardening specimens of angular sands are larger than those of rounded sands at the same state parameter level because the interlocking of angular sands with many projecting corners is stronger than that of rounded sands during shearing. At the same initial state level, rounded sands are more susceptible to softening and liquefaction than angular sands under undrained conditions, because smooth corners permit easier grain rotations in undrained unstable specimens.

Development of a vector‐based 3D grain entrainment model with application to X‐ray computed tomography scanned riverbed sediment

AbstractSediment transport equations typically produce transport rates that are biased by orders of magnitude. A causal component of this inaccuracy is the inability to represent complex grain‐scale interactions controlling entrainment. Grain‐scale incipient motion has long been modelled using geometric relationships based on simplified particle geometry and two‐dimensional (2D) force or moment balances. However, this approach neglects many complexities of real grains, including grain shape, cohesion and the angle of entrainment relative to flow direction. To better represent this complexity, we develop the first vector‐based, fully three‐dimensional (3D) grain rotation entrainment model that can be used to resolve any entrainment formulation in 3D, and which also includes the effect of matrix cohesion. To apply this model we use X‐ray computed tomography to quantify the 3D structure of water‐worked river grains. We compare our 3D model results with those derived from application of a 2D entrainment model. We find that the 2D approach produces estimates of dimensionless critical shear stress ( ) that are an order of magnitude lower than our 3D model. We demonstrate that it is more appropriate to use the c‐axis when calculating 2D projections, which increases values of to more closely match our 3D estimates. The 3D model reveals that the main controls on critical shear stress in our samples are projection of grains, cohesive effects from a fine‐grained matrix, and bearing angle for the plane of rotation (the lateral angle of departure from downstream flow that, in part, defines the grain's direction of pivot about an axis formed by two contact points in 3D). The structural precision of our 3D model demonstrates sources of geometric error inherent in 2D models. By improving flow properties to better replicate local hydraulics in our 3D model, entrainment modelling of scanned riverbed grains has the potential for benchmarking 2D model enhancements. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.

A morphologic and crystallographic comparison of CV chondrite matrices

AbstractMeteoritic matrices are commonly classified by their modal mineralogy, alteration, and shock levels. Other “textural” characteristics are not generally considered in classification schemes, yet could carry important information about their genesis and evolution. Terrestrial rocks are routinely described by grain morphology, which has led to morphology‐driven classifications, and identification of controlling processes. This paper investigates three CV chondrites—Allende (CV3.2oxA), Kaba (CV3.0oxB), and Vigarano (CV3.3red)—to determine the morphologic signature of olivine matrix grains. 2D grain size and shape, and crystallographic preferred orientations (CPOs) are quantified via electron backscatter diffraction mapping. Allende contains the largest and most elongate olivine grains, while Vigarano contains the least elongate, and Kaba contains the smallest grains. Weak but notable CPOs exist in some regions proximal to chondrules and one region distal to chondrules, and CPO geometries reveal a weak flattening of the matrix grains against the edge of chondrules within Allende. Kaba contains the least plastically deformed grains, and Allende contains the most plastically deformed grains. We tentatively infer that morphology is controlled by the characteristics of the available population of accreting grains, and aqueous and thermal alteration of the parent body. The extent of overall finite deformation is likely dictated by the location of the sample with respect to compression, the localized environment of the matrix with respect to surrounding material, and the post deformation temperature to induce grain annealing. Our systematic, quantitative process for characterizing meteorite matrices has the potential to provide a framework for comparison within and across meteorite classes, to help resolve how parent body processing differed across and between chondritic asteroids.

Integral mean curvature analysis of 3D grain growth: Linearity of dV/dt and grain volume

The volumetric growth rate of individual grains has been found to be directly proportional to the individual grain volume V as dV/dt = β(Vo-V). This simple result is explained through the DeHoff relationship dV/dt = −kMs between growth rate and the integral mean curvature of individual grains, Ms, combined with the experimentally observed relationship between Ms and grain volume, Ms = α(Vo-V). These relationships have now been observed consistently in both 3D grain growth simulations and experiments. This paper describes the relationships among these kinetic and geometric grain characteristics that provide this simple description of 3D grain growth.

Statistics and Reproducibility of Grain Morphologies and Crystallographic Orientations Mapped by Laboratory Diffraction Contrast Tomography

Laboratory diffraction contrast tomography (LabDCT) enables a user to reconstruct 3D grain maps of polycrystalline materials non-destructively. For each grain, the morphology and crystallographic orientation, as well as derived properties such as grain boundary properties can be determined. Through two application examples this paper demonstrates the capabilities and potential of the current LabDCT implementation. Firstly, for well-annealed grain structures the reproducibility of LabDCT for more than 95% of the grains was found to be 5 μm on grain center-of-mass positions and 0.02° on orientations, while 90% of the grain boundary locations are determined with an accuracy better than 4 μm. The second example highlights the available statistics on thousands of grains, as well as the complementarity between LabDCT and absorption contrast tomography, readily available due to the integration of LabDCT on a commercial X-ray microscope

Numerical simulation of complicated grains with 3D burnback and Quasi-One-Dimensional flow field of solid rocket motors

In this research, the 3D grain burnback with quasi-one-dimensional internal ballistic in a solid rocket motor is simulated using the Level set theory and the utilization of Sections method, while achieving high accuracy in the simulation of green's post-back analysis time can also be significantly reduced. By using Section method, 3D grains are divided to many 2D grain, then 2D Level set is utilized to analyse grain burnback. Finally, the burning port of 3D grains are calculated by means of Interpolation. Also, to predict the internal pressure of the motor and the burning rate, a numerical code is written and coupled with grain burnback programme.

Integrated Computational Materials Engineering to Predict Melt-Pool Dimensions and 3D Grain Structures for Selective Laser Melting of Inconel 625

This work presents a comparison of simulation results with the experimental data for four of the six challenges within the National Institute of Standards and Technology (NIST) Additive Manufacturing (AM) Benchmark Test Series (AM Bench) problem AMB2018-02. This comparison is akin to a test case to assess the technology maturity level (TML) for the AM predictive capabilities that can be utilized to improve AM products in the industry. The solutions are for the prediction of melt-pool geometry, cooling rate, solidification grain shapes, and their 3D structure. These results were obtained using the Additive Manufacturing Parameter Predictor (AMP2) software. AMP2 is an Integrated Computational Materials Engineering (ICME) suite of software developed by Applied Optimization, Inc. (AO). The melt-pool geometry is obtained using a thermal-computational fluid dynamics (CFD) solution of melt-pool physics. The melt-pool geometry, mean track cross section, 3D distribution of thermal gradient, and the liquid-to-solid interface velocity are predicted by the thermal-CFD model and utilized as input for the solidification grain structure computation. The grain shapes and 3D structure are modeled using cellular automata (CA). AO received a second-place award for predicting the grain structure within three single laser tracks on a bare plate of alloy Inconel 625 (IN625).

Phase-field study of grain growth in porous polycrystals

During sintering, a multitude of mechanisms act in different ways resulting in densification and coarsening. Since the material properties depend on the microstructure, the manufacturing of advanced ceramics requires a deep understanding of the sintering process. The present study focuses on the occurrence of grain growth during final stage sintering. In a porous microstructure, the pores exert a dragging force to grain boundary motion retarding the grain growth. However, as soon as the porosity becomes low enough, the grain growth exceeds the dragging force and the microstructure starts to coarsen. This interdependency of densification and grain growth is still not fully understood. The present study uses a 3D phase-field model to investigate grain growth in porous microstructures during final stage sintering. A model extension treats pore dynamics under consideration of pressure stability as well as pore coalescence. To account for the size effect of pores on its dragging force, a surface diffusion based mobility approache is incorporated. Large-scale 3D grain growth simulations are conducted to analyze the effect of different porosities and pore sizes with statistical relevance comparable to real microstructures. Depending on the porosity, two dominating effects on the reduction of grain growth rate are found. For low porosities, the growth rate depends on the number of pores whereas for higher porosities the pore size and their mobility dominate the process. The results show the need to consider the effects of the pore size and their distribution during final stage sintering.

Using a Three-Dimensional Reduction Method in the High-Efficiency Grain Selector and Corresponding Grain Selection Mechanism.

In the development of a high-efficiency grain selector, the spiral selectors are widely used in Ni-based single crystal (SX) superalloys casting to produce single crystal turbine blades. For the complex three-dimensional structure of the spiral, a 2D grain selector was designed to investigate in this paper. As a result, the parameters of two-dimensional grain selection bond and the corresponding grain selection mechanism were established, and the three-dimensional grain selection bond was designed again by means of two-dimensional coupling optimization parameters.