The aim of this study is to explore the internal damage mechanisms of AlSi12 metal matrix syntactic foam (MMSF) with embedded ceramic hollow spheres (CHSs) to understand the damage behavior during compressive loading. To achieve this goal, in situ synchrotron X‐ray tomography is used. A qualitative and quantitative assessment of the initiation and gradual collapse of matrix, filler material, and pores is presented. The imaging‐based investigation provided detailed visualization and tracking of failure mechanisms of the MMSF, with emphasis on the collapse of hollow spheres at the microstructural level. The structural parameters describing performance limits are experimentally determined and correlated with internal mechanisms. It is concluded that a homogeneous distribution of the second‐phase filler material results in a sequential collapse in a localized region; this leads to controlled and predictable energy absorption. The CHSs rupture is found to be location dependent within the localized shear band region, with spheres of all diameters failing to a similar extent. The results from this work can be used to train or validate predictive models of MMSFs deformed under compressive loading conditions by correlating the 3D damage progression with the overall mechanical response.

Grain boundary (GB) properties in an Al-5 wt % Cu alloy have been extracted from diffraction contrast tomography images after 10 sequential annealing steps for 15 min at 630 degrees C. At the annealing temperature, a copper-rich liquid was present at the GBs. The growth and shrinkage of the grains are strongly correlated with the grain size, and the velocity of individual boundaries is strongly correlated with boundary mean curvature, as expected from the classical theory of coarsening. The experimental results compare well to a threshold dynamics grain growth simulation of the process assuming uniform grain boundary energies. The correlation of the interface velocity and curvature is observed both for the data on average and for certain commonly occurring grain boundary disorientations. It is also found that the curvatures and relative areas of GBs depend on the five grain boundary parameters, even though the GBs are formed in conditions of low energy anisotropy. The observations are compared to results from grain growth in the solid state, where strong correlations between interface velocity and curvature are not observed.

High-energy x-ray diffraction microscopy (HEDM) nondestructively maps microstructures in 3D, allowing for the same grains and boundaries to be tracked over time during annealing experiments. Here, HEDM was applied to observe grain growth in strontium titanate. These results are compared to a 3D isotropic grain growth simulation that starts from the same initial microstructure to identify potentially unknown grain boundary migration mechanisms. During the simulation, grain growth behaves as expected: the change in grain volume is correlated with the number of neighbors, and the grain boundary velocity is correlated with its local curvature. Experimentally, however, flat boundaries were found to move faster than curved boundaries, and 37% of all measured boundaries move in the direction opposite to their curvature. These unexpected observations suggest that, in materials with anisotropic grain boundary properties, mechanisms other than curvature-driven boundary migration play a role in the minimization of interfacial energy.

If variety is the spice of life, then abnormal grain growth (AGG) may be the materials processing equivalent of sriracha sauce. Abnormally growing grains can be prismatic, dendritic, or practically any shape in between. When they grow at least an order of magnitude larger than their neighbors in the matrix—a state we call extreme AGG—we can examine the abnormal/matrix interface for clues to the underlying mechanism. Simulating AGG for various formulations of the grain boundary (GB) equation of motion, we show that anisotropies in GB mobility and energy leave a characteristic fingerprint in the abnormal/matrix boundary. Except in the case of prismatic growth, the morphological signature of most reported instances of AGG is consistent with a certain degree of GB mobility variability. Open questions remain, however, concerning the mechanism by which the corresponding growth advantage is established and maintained as the GBs of abnormal grains advance through the matrix.

The movement of grain boundaries in pure metals and alloys with a low concentration of dislocations has been historically proved to follow curvature flow behavior. This mechanism is typically known as grain growth (GG). However, recent 3D in-situ experimental results tend to question this global picture concerning the influence of the curvature on the kinetics of interface migration. This article explains, thanks to 2D anisotropic full-field simulations, how the torque effects can complexify these discussions. It is then illustrated that neglecting torque effects in full-field formulations remains potentially a strong hypothesis. The apparent mobility can be much more complex than expected without necessarily questioning the influence of the curvature on the local kinetic equation.

Grain boundary velocity has been believed to be correlated to curvature, and this is an important relationship for modeling how polycrystalline materials coarsen during annealing. We determined the velocities and curvatures of approximately 52,000 grain boundaries in a nickel polycrystal using three-dimensional orientation maps measured by high-energy diffraction microscopy before and after annealing at 800°C. Unexpectedly, the grain boundary velocities and curvatures were uncorrelated. Instead, we found strong correlations between the boundary velocity and the five macroscopic parameters that specify grain boundary crystallography. The sensitivity of the velocity to grain boundary crystallography might be the result of defect-mediated grain boundary migration or the anisotropy of the grain boundary energy. The absence of a correlation between velocity and curvature likely results from the constraints imposed by the grain boundary network and implies the need for a new model for grain boundary migration.

The curvature of grain boundaries in polycrystalline materials is an important characteristic, since it plays a key role in phenomena like grain growth. However, most traditional tessellation models that are used for modeling the microstructure morphology of these materials, e.g., Voronoi or Laguerre tessellations, have flat faces and thus fail to incorporate the curvature of the latter. For this reason, we consider generalizations of Laguerre tessellations—variations of so-called generalized balanced power diagrams (GBPDs)—that exhibit non-convex cells. With as many as ten parameters for each cell, it is computationally demanding to fit GBPDs to three-dimensional image data containing hundreds of grains. We therefore propose a modification of the traditional definition of GBDPs that allows gradient-based optimization methods to be employed. The resulting reduction in runtime makes it feasible to find approximations to real experimental datasets. We demonstrate this on a three-dimensional x-ray diffraction (3DXRD) mapping of an AlCu alloy, but we also evaluate the modeling errors for simulated data. Furthermore, we investigate the effect of noisy image data and whether the smoothing of image data prior to the fitting step is advantageous.

In a nanocrystalline alloy, we recently discovered a novel form of abnormal grain growth involving the emergence of grain boundaries having fractal-like morphologies. Although abnormal growth has long presented a challenge to materials scientists, new insights into this phenomenon might be gained from a study of its extreme manifestation in nanocrystalline Pd 90Au 10, where some grains not only grow to much larger sizes than their neighbors but also take on dendritic, highly convoluted shapes. To unravel the origin and mechanism of grain growth in this case, it is essential to determine the fractal dimension of the resulting grain boundaries with high accuracy. To achieve this goal, we turn to orientation mapping based on electron backscatter diffraction, the output of which is subjected to image processing and subsequent box-counting analysis. The robustness, reproducibility, and accuracy of this protocol are ensured by optimizing parameters related to sample preparation, orientational imaging, image processing, and the box-counting algorithm. We have validated the approach against non-fractal Euclidean structures as well as a mathematical fractal, finding that the method yields values for the fractal dimension that are precise up to three decimal places. Moreover, the parameters of the methodology can be adapted readily to other scenarios in which elements of a given microstructure manifest a fractal character.

Extracting the curvature of grain boundaries from 3D voxel-based representations of microstructure is challenging. Previous investigations have concluded that the accuracy of curvature estimation depends strongly on the degree of smoothing after a microstructure has been meshed. We find that best results are obtained when the degree of smoothing is determined on a boundary-by-boundary basis. Evaluating a voxelized representation of a Reuleaux tetrahedron of known boundary curvature, we establish that, for a given boundary, the optimal smoothing power minimizes the coefficient of variation (CV) of local curvature. We apply the minimum-CV criterion to the extraction of grain boundary curvatures from a measurement of polycrystalline Al-5 wt% Cu performed by 3D x-ray diffraction (3DXRD) microscopy. The results show that grain boundaries in this sample are surprisingly flat. Moreover, boundaries of larger area manifest lower curvature, while higher curvature values are observed solely for boundaries of smaller area.

In this paper, various kinds of applications are presented, in which tomographic image data depicting microstructures of materials are semantically segmented by combining machine learning methods and conventional image processing steps. The main focus of this paper is the grain-wise segmentation of time-resolved CT data of an AlCu specimen which was obtained in between several Ostwald ripening steps. The poorly visible grain boundaries in 3D CT data were enhanced using convolutional neural networks (CNNs). The CNN architectures considered in this paper are a 2D U-Net, a multichannel 2D U-Net and a 3D U-Net where the latter was trained at a lower resolution due to memory limitations. For training the CNNs, ground truth information was derived from 3D X-ray diffraction (3DXRD) measurements. The grain boundary images enhanced by the CNNs were then segmented using a marker-based watershed algorithm with an additional postprocessing step for reducing oversegmentation. The segmentation results obtained by this procedure were quantitatively compared to ground truth information derived by the 3DXRD measurements. A quantitative comparison between segmentation results indicates that the 3D U-Net performs best among the considered U-Net architectures. Additionally, a scenario, in which "ground truth" data is only available in one time step, is considered. Therefore, a CNN was trained only with CT and 3DXRD data from the last measured time step. The trained network and the image processing steps were then applied to the entire series of CT scans. The resulting segmentations exhibited a similar quality compared to those obtained by the network which was trained with the entire series of CT scans.

Far-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries-and, therefore, individual grain shapes-are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.

Large-scale phase-field simulations were performed of the evolution of grain structures with nonuniform grain boundary energy. A novel approach is proposed to determine the average grain boundary dihedral angles between the grain faces along triple and quadruple line junctions from 3-D voxel-based microstructures. We examine the effect of grain boundary energy nonuniformity on the distributions of the grain size, number of faces per grain, and dihedral angles between grain faces. We study the effect of the initial grain size distribution on the evolution toward steady state for both nonuniform and uniform boundary energy systems. The steady-state grain size and number of faces distributions remain unimodal under all conditions investigated, whereas the dihedral angle distribution is found to become multi-modal when the ratio R=σH/σL between high and low grain boundary energies lies in the range of 1.39–1.81. In addition, when R≈2 a topological transition is observed from a structure with grain faces meeting at triple lines (which themselves terminate in quadruple points) toward one in which the grain faces meet primarily at quadruple line junctions (ending at compact regions of triple junctions or very short triple lines).

Parametric tessellation models are often used to approximate complex grain morphologies of polycrystalline microstructures. A big advantage of such models is the substantial reduction in disk space required to store large, three-dimensional data sets, especially when compared with voxel-based alternatives. By selection of an appropriate tessellation model, a reasonably small loss of information on the real grain shapes can usually be achieved. Special attention has recently been devoted to models based on ellipsoidal approximations fitted to each grain. Faces of these tessellations are portions of quadric surfaces whose parameters can be derived easily. In this paper, we deal with geometric features of the structure, notably curvatures and dihedral angles, which are closely related to the kinetics of grain growth. These characteristics are computed for ellipsoidbased tessellations fitted to two different aluminum alloys with nominal composition Al-3 wt% Mg-0.2 wt% Sc and Al-1 wt% Mg. The results are then compared with estimations based on meshed empirical data. We observe that the model offers more consistent estimations of grain shape characteristics than do the meshed empirical data. Precise description of grain boundaries by the model is also promising with respect to possible applications of these tessellations in stochastic space-time modeling of grain growth.

Sintering is a key technology for processing ceramic and metallic powders into solid objects of complex geometry, particularly in the burgeoning field of energy storage materials. The modeling of sintering processes, however, has not kept pace with applications. Conventional models, which assume ideal arrangements of constituent powders while ignoring their underlying crystallinity, achieve at best a qualitative description of the rearrangement, densification, and coarsening of powder compacts during thermal processing. Treating a semisolid Al-Cu alloy as a model system for late-stage sintering-during which densification plays a subordinate role to coarsening-we have used 3D X-ray diffraction microscopy to track the changes in sample microstructure induced by annealing. The results establish the occurrence of significant particle rotations, driven in part by the dependence of boundary energy on crystallographic misorientation. Evidently, a comprehensive model for sintering must incorporate crystallographic parameters into the thermodynamic driving forces governing microstructural evolution.

As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures-such as those obtained by modern 3D characterization techniques like X-ray microtomography or focused-ion-beam serial sectioning-is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume. In this paper, we propose an alternative to the Laguerre approach, representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3D image data. Applying our algorithm to artificial microstructures and to microtomographic data sets of an Al-5 wt% Cu alloy, we demonstrate that the new approach represents statistical features of the underlying data-like distributions of grain sizes and coordination numbers-as well as or better than a recently introduced approximation method based on the Laguerre tessellation; furthermore, our method reproduces the local arrangement of grains (i.e., grain shapes and connectivities) much more accurately. The additional computational cost associated with orthogonal regression is marginal.

Much attention has been generated by nanocrystalline materials and their promise of enhanced properties. However, this class of materials suffers from an inherent instability with respect to thermally induced grain growth. Substantial microstructural coarsening is frequently observed in elemental samples even under ambient conditions, and more often than not, the mode of grain growth in such specimens is abnormal. Although deliberately adding an atomic species that segregates to the grain boundaries has been shown to stabilize the microstructure of nanomaterials to high fractions of the melting point, once grain growth commences, it generally proceeds in a highly abnormal manner in these samples, as well. In the case of Fe-based nanocrystalline alloys, abnormal growth appears to be intimately tied to the alpha-to-gamma phase transformation just above 900°C. For Ni-based segregation-stabilized specimens, however, there is no such allotropic transformation; nevertheless, the microstructure after growth manifests the same telltale signs of abnormality.