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Geometrically necessary dislocations (GNDs) play a key role in accommodating strain incompatibility between neighboring grains in polycrystalline materials. One critical step toward accurately capturing GNDs in deformation models involves studying the microstructural features that promote GND accumulation and the resulting character of GND fields. This study utilizes high-resolution electron backscatter diffraction to map GND populations in a large polycrystalline sample of pure tantalum, under simple tension. A total of 1,989 grains, 3,518 grain boundaries (GBs), and 3,207 triple junctions (TJs) were examined in a subsurface region of the sample. Correlations between GND density and GB character, and to some extent, TJ character, are investigated. Statistical geometrical relationships between these entities are quantified, and also visualized, using a novel application of two-point statistics. The nature of GNDs across the sample is also visualized and assessed using a recently developed method of mapping the local net Burgers vectors. The different approaches to characterizing GND distribution are compared in terms of how they quantify the size of near boundary gradient zones.

SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.

Observations of microstructural coarsening at cryogenic temperatures, as well as numerous simulations of grain boundary motion that show faster migration at low temperature than at high temperature, have been troubling because they do not follow the expected Arrhenius behavior. This work demonstrates that classical equations, that are not simplified, account for all these oddities and demonstrate that non-Arrhenius behavior can emerge from thermally activated processes. According to this classical model, this occurs when the intrinsic barrier energies of the processes become small, allowing activation at cryogenic temperatures. Additional thermal energy then allows the low energy process to proceed in reverse, so increasing temperature only serves to frustrate the forward motion. This classical form is shown to reconcile and describe a variety of diverse grain boundary migration observations.

Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (body centred cubic and body centred tetragonal, with small tetragonality) phases in steels using standard EBSD software. One method to tackle the problem of phase distinction is to measure the tetragonality of the phases, which can be done using simulated patterns and cross-correlation techniques to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both kinetically simulated and dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate ∼0.2% error in carbon content estimation. Such an error makes the technique unsuitable for estimation of total carbon content of most commercial steels, which often have carbon levels below 0.1%. However, even in the DP steel for this study (0.1 wt.% carbon) it can be used to map carbon in regions with higher accumulation (such as in martensite with nonhomogeneous carbon content). LAY DESCRIPTION: Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (BCC and BCT) phases in steels using standard EBSD software due to the small difference in crystal structure. One method to tackle the problem of phase distinction is to measure the tetragonality, or apparent 'strain' in the crystal lattice, of the phases. This can be done by comparing experimental EBSD patterns with simulated patterns via cross-correlation techniques, to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both simple kinetically simulated and more complex dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate error in carbon content estimation. Such an error makes an estimate of total carbon content particularly unsuitable for low carbon steels; although maps of local carbon content may still be revealing. Application of the method developed in this paper will lead to better understanding of the complex microstructures of steels, and the potential to design microstructures that deliver higher strength and ductility for common applications, such as vehicle components.

A study of 346 computed [1 0 0] disorientation axis grain boundaries provides insight into grain boundary energy structure-property relationships. The grain boundaries come from 6 coincidence site lattice misorientations at regularly spaced disorientation angles, and cover the full range of boundary plane orientations. The computed energy has clear trends in disorientation angle and boundary plane orientation. The data are used to reexamine the ‘special’ attribute frequently applied to low Σ coincidence site lattice misorientations and low-angle boundaries and to assess the accuracy of a face-centered cubic grain boundary energy function developed by Bulatov, Reed, and Kumar (Acta Mater. 65 (2014) 161-175).

Improved plasticity models require simultaneous experimental local strain and microstructural evolution data. Microscopy tools, such as electron backscatter diffraction (EBSD), that can monitor transformation at the relevant length-scale, are often incompatible with digital image correlation (DIC) techniques required to determine local deformation. In this paper, the viability of forescatter detector (FSD) images as the basis for the DIC study is investigated. Standard FSD and an integrated EBSD/FSD approach (Pattern Region of Interest Analysis System: PRIAS™) are analyzed. Simultaneous strain and microstructure maps are obtained for tensile deformation of Q&P 1180 steel up to ~14% strain. Tests on an undeformed sample that is simply shifted indicate a standard deviation of error in strain of around 0.4% without additional complications from a deformed surface. The method resolves strain bands at ~2 μm spacing but does not provide significant sub-grain strain resolution. Similar resolution was obtained for mechanically polished and electropolished samples, despite electropolished surfaces presenting a smoother, simpler topography. While the resolution of the PRIAS approach depends upon the EBSD step size, the 80 nm step size used provides seemingly similar resolution as 8,000× (22.7 nm) FSD images. Surface feature evolution prevents DIC analysis across large strain steps (>6% strain), but restarting DIC, using an FSD reference image from an interim strain step, allows reasonable DIC across the stress–strain curve. Furthermore, the data are obtained easily and provide complementary information for EBSD analysis.

The deformation of materials at cryogenic temperature is of interest for space, arctic, and fundamental science applications. In this work, a custom-built cooling system attached to a commercial picoindenter was used for in situ cryogenic microcompression testing of equal-channel angular-pressed copper with real-time electron backscatter diffraction. Stress-driven grain growth at cryogenic temperatures was observed during a series of elastic and plastic deformations. These results provide direct evidence for the previously predicted phenomenon, whereas previous ex situ examinations demonstrated coarsening after cryogenic loading when samples were not maintained at cryogenic temperatures between deformation and characterization.

We apply a newly developed Voronoi fundamental zone (VFZ) framework to gain insights about grain boundary (GB) structure-property relationships in the five degree-of-freedom (5DOF) space of cubic GBs. We analyze the shape and size of a 5DOF fundamental zone (FZ), molecular statics energy uncertainty, property similarity of GBs that are crystallographically \close" (i.e. correlations), and energy pathways through 5DOF space. Considered together, these insights are important for managing tradeoffs between accuracy, complexity, and design considerations for electron backscatter diffraction/serial sectioning, high-energy diffraction microscopy, molecular statics, and density-functional theory. In terms of the shape and size of a 5DOF FZ, we discover that a FZ is smaller than expected at only ∼65° in the largest principal component. Thus, a 10° difference between two GBs, which may have previously been considered small, is actually quite large. We represent a GB by five transformed Cartesian coordinates equipped with a Euclidean distance metric. Using this representation, we find that the FZ has a low aspect-ratio shape (i.e. width, length, height, etc. are similar) which is important for 5DOF numerical differentiation. Semivariogram and numerical optimization methods reveal that grain boundary energy (GBE) in Ni and Fe are globally correlated within ∼6° to 8° in the grain boundary octonion (GBO) sense (multiply by 2 to convert to misorientation angle). For local correlation lengths of high-symmetry GBs of interest, we notice significant variation relative to global correlation lengths and an inverse relationship with the Brandon criterion. We suggest that property data with no more than ± ∼3 % error and point sets with GBs that are no more than ∼3−4° apart should be used and then paired with high-fidelity interpolation strategies. Finally, in terms of dynamic material behavior, geodesic paths through 5DOF space for Ni suggest that, under appropriate conditions, a certain low-energy Σ7 GB may transform into the frequently observed Σ3 coherent-twin GB which may be interesting to verify by experiment or simulation.

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 minutes annealing at 400{\deg}C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum {\Sigma}3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials., Comment: The document contains the manuscript, figure captions, and a short supplemental document with further details

Yield point phenomena (YPP) are widely attributed to discrete dislocation locking by solute atmospheres. An alternate YPP mechanism was recently suggested by simulations of Ta single crystals without any influence of solutes or discrete dislocations. The general meso-scale (GM) simulations consist of crystal plasticity (CP) plus accounting for internal stresses of geometrically necessary dislocation content. GM predicted the YPP while CP did not, suggesting a novel internal stress mechanism. The predicted YPP varied with crystal orientation and boundary conditions, contrary to expectations for a solute mechanism. The internal stress mechanism was probed by experimentally deforming oligocrystal Ta samples and comparing the results with independent GM simulations. Strain distributions of the experiments were observed with high-resolution digital image correlation. A YPP stress–strain response occurred in the 0–2% strain range in agreement with GM predictions. Shear bands appeared concurrent with the YPP stress–strain perturbation in agreement with GM predictions. At higher strains, the shear bands grew at progressively slower rates in agreement with GM predictions. It was concluded that the internal stress mechanism can account for the existence of YPP in a wide variety of materials including ones where interstitial-dislocation interactions and dislocation transient avalanches are improbable. The internal stress mechanism is a CP analog of various micro-scale mechanisms of discrete dislocations such as pile-up or bow-out. It may operate concurrently with strain aging, or either mechanism may operate alone. A suggestion was made for a future experiment to answer this question.

Efforts to construct predictive grain boundary (GB) structure–property models have historically relied on property measurements or calculations made on bicrystals. Experimental bicrystals can be difficult or expensive to fabricate, and computational constraints limit atomistic bicrystal simulations to high-symmetry GBs (i.e., those with small enough GB periodicity). Although the use of bicrystal property data to construct GB structure–property models is more direct, in many experimental situations the only type of data available may be measurements of the effective properties of polycrystals. In this work, we investigate the possibility of inferring GB structure–property models from measurements of the homogenized effective properties of polycrystals when the form of the structure–property model is unknown. We present an idealized case study in which GB structure–property models for diffusivity are inferred from noisy simulation results of two-dimensional microstructures, under the assumption that the number of polycrystal measurements available is larger than the number of parameters in the inferred model. We also demonstrate how uncertainty quantification for the inferred structure–property models is easily performed within this framework.

High-throughput simulations can be a powerful tool in the discovery of new materials and behaviors. As part of a special issue on Rising Stars in Computational Materials Science, this article uses the work of the author to show how high-throughput simulations have had an impact in grain boundary structure-property relationships and other complex microstructural phenomena. The work demonstrates how new tools designed to analyze large datasets produced by high-throughput simulations are enabling comprehensive grain boundary structure-property relationships to be obtained. High-throughput simulations are also used to demonstrate the impact descriptive and inferential statistics has had in extracting key aspects of deformation in metallic glasses. Finally, several different examples are used to show a balanced approach between simulations designed to survey and simulations designed for detailed analysis. Together, the two approaches provide a comprehensive picture of the variety of behaviors that exist, while ensuring that the physics underlying the behaviors are thoroughly understood.

The space of possible grain boundary structures is vast, with 5 macroscopic, crystallographic degrees of freedom that define the character of a grain boundary. While numerous datasets of grain boundaries have examined this space in part or in full, we present a computed dataset of over 7304 unique aluminum grain boundaries in the 5D crystallographic space. Our sampling also includes a range of possible microscopic, atomic configurations for each unique 5D crystallographic structure, which total over 43 million structures. We present an overview of the methods used to generate this dataset, an initial examination of the energy trends that follow the Read-Shockley relationship, hints at trends throughout the 5D space, variations in GB energy when non-minimum energy structures are examined, and insights gained in machine learning of grain boundary energy structure-property relationships. This dataset, which is available for download, has great potential for insight into GB structure-property relationships., Comment: 16 pages, 10 figures

Molecular dynamics simulations are used to examine the migration behavior of one incoherent twin, a Σ3 (11 8 5) / (8 11 5) grain boundary. The boundary is known to exhibit non-Arrhenius boundary migration that slows as temperature increases. This behavior is examined in 165 metastable structures of the same boundary and in a large simulation cell where smaller length scales can have less of an effect. The metastable boundaries show diverse migration behaviors from non-Arrhenius to Arrhenius, though the majority of them exhibit non-Arrhenius behavior. The large simulation cell sizes show no dependence on system size, eliminating concerns about the effect of facet nucleation on the migration in periodic simulation cells. However, facet structures play an important role in the migration of the metastable boundaries. Boundaries with larger facets typically migrate faster than those with smaller facets and with defects in the boundary structure.

Recent synchrotron X-ray measurements examined three-dimensional boundary migration during recrystallization [Scripta Mater 205 (2021) 114187]. To analyze possible correlations between grain boundary mobility and the observed heterogeneous boundary migration, molecular dynamics simulations were carried out. Migration of two selected boundary segments were simulated in both planar and spherical bicrystal atomistic models. These two segments were chosen because in the experiment one was observed to migrate much faster than the other. The simulations reveal that mobility cannot account for the experimentally observed heterogeneous migration. The result points to the possibility that recrystallization boundary migration strongly depends on features within the deformed microstructure.

We introduce the Voronoi fundamental zone octonion interpolation framework for grain boundary (GB) structure-property models and surrogates. The VFZO framework offers an advantage over other five degree-of-freedom based property interpolation methods because it is constructed as a point set in a manifold. This means that directly computed Euclidean distances approximate the original octonion distance with significantly reduced computation runtime (~7 CPU minutes vs. 153 CPU days for a 50000x50000 pairwise-distance matrix). This increased efficiency facilitates lower interpolation error through the use of significantly more input data. We demonstrate grain boundary energy interpolation results for a non-smooth validation function and simulated bi-crystal datasets for Fe and Ni using four interpolation methods: barycentric interpolation, Gaussian process regression (GPR), inverse-distance weighting, and nearest-neighbor interpolation. These are evaluated for 50000 random input GBs and 10 000 random prediction GBs. The best performance was achieved with GPR, which resulted in a reduction of the root mean square error (RMSE) by 83.0% relative to RMSE of a constant, average model. Likewise, interpolation on a large, noisy, molecular statics Fe simulation dataset improves performance by 34.4% compared to 21.2% in prior work. Interpolation on a small, low-noise MS Ni simulation dataset is similar to interpolation results for the original octonion metric (57.6% vs. 56.4%). A vectorized, parallelized, MATLAB interpolation function (interp5DOF.m) and related routines are available in our VFZO repository (github.com/sgbaird-5dof/interp) which can be applied to other crystallographic point groups. The VFZO framework offers advantages for computing distances between GBs, estimating property values for arbitrary GBs, and modeling surrogates of computationally expensive 5DOF functions and simulations., Comment: main: 22 pages, 10 figures; appendices: 5 pages, 3 figures; supp: 13 pages, 12 figures

Antithermal grain boundary migration is an interesting phenomenon that has been recently discovered. These grain boundaries behave opposite to what is expected of thermally activated grain boundary migration; the antithermal grain boundaries exhibit mobility that decreases with increasing temperature. Two recent studies have provided insight into important behaviors correlated with antithermal migration. O'Brien and Foiles (J Mater. Sci. Vol. 51, p. 6607–6623, 2016) demonstrated that the high mobility exhibited by an antithermal Σ7 grain boundary is enabled by ordered atomic motions. Ulomek and Mohles (Acta Mater. Vol. 103, p. 424–432, 2016) demonstrated that the thermal migration of a different Σ7 grain boundary exhibited a two-step migration process. In this work, we demonstrate that the antithermal temperature dependence exhibited by these types of grain boundaries is caused by a combination of these two discoveries. Specifically, ordered atomic motions about Coincidence Site Lattice atoms (atoms common to the lattices on either side of the grain boundary), seen by O'Brien and Foiles, are interrupted by additional thermal energy at higher temperature. This is the source of the two-step process seen by Ulomek and Mohles. This two-step process is akin to stick-slip behaviors observed in shear coupled grain boundary migration. As temperature is increased, the duration of the stagnant portion increases and the mobility decreases. This behavior is demonstrated through molecular dynamics simulations in nickel bicrystals over temperatures ranging from 100 to 1400 K for Σ7 and Σ9 grain boundaries. For these Σ7 and Σ9 grain boundaries, those that have ordered atomic mechanisms are almost exclusively antithermal, while those that do not have ordered atomic mechanisms are thermally activated.

U-Pu-Zr alloys are considered ideal metallic fuels for experimental breeder reactors because of their superior material properties and potential for increased burnup performance. However, significant constituent redistribution has been observed in these alloys when irradiated, or subject to a thermal gradient, resulting in inhomogeneity of both composition and phase, which, in turn, alters the fuel performance. The hybrid Potts-phase field method is reformulated for ternary alloys in a thermal gradient and utilized to simulate and predict constituent redistribution and phase transformations in the U-Pu-Zr nuclear fuel system. Simulated evolution profiles for the U-16Pu-23Zr (at. pct) alloy show concentric zones that are compared with published experimental results; discrepancies in zone size are attributed to thermal profile differences and assumptions related to the diffusivity values used. Twenty-one alloys, over the entire ternary compositional spectrum, are also simulated to investigate the effects of alloy composition on constituent redistribution and phase transformations. The U-40Pu-20Zr (at. pct) alloy shows the most potential for compositional uniformity and phase homogeneity, throughout a thermal gradient, while remaining in the compositional range of feasible alloys.

Forming limits and retained austenite (RA) transformation in Q&P 1180 steel are quantified as a function of plastic strain levels for three different strain paths. In-plane uniaxial tension testing was performed in a standard test frame, while limiting dome height tooling was employed for out-of-plane biaxial and plane strain tension experiments. Sheet specimens were tested incrementally for each strain path, and the RA content at each level of strain was measured using electron backscatter diffraction (EBSD). The biaxial tension strain path resulted in the greatest effective strain prior to necking at 0.355, compared to 0.123 for plane strain and 0.142 for uniaxial tension. EBSD measurements for various levels of plastic strain reveal a clear dependence of RA rate of transformation on strain path for the three linear strain paths that were employed in this work. Thinning strains appear to provide a slightly better correlation to RA transformation than effective strain levels, where biaxial tension achieved the greatest level just prior to necking, followed by plane-strain tension, and then uniaxial tension.

We present a method for performing efficient barycentric interpolation for large grain boundary octonion point sets which reside on the surface of a hypersphere. This method includes removal of degenerate dimensions via singular value decomposition (SVD) transformations and linear projections, determination of intersecting facets via nearest neighbor (NN) searches, and interpolation. This method is useful for hyperspherical point sets for applications such as grain boundaries structure-property models, robotics, and specialized neural networks. We provide a case study of the method applied to the 7-sphere. We provide 1-sphere and 2-sphere visualizations to illustrate important aspects of these dimension reduction and interpolation methods. A MATLAB implementation is available at github.com/sgbaird-5dof/interp.•Barycentric interpolation is combined with hypersphere facet intersections, dimensionality reduction, and linear projections to reduce computational complexity without loss of information•A max nearest neighbor threshold is used in conjunction with facet intersection determination to reduce computational runtime.

In this work we present a non-parametric Bayesian approach for developing structure-property models for grain boundaries (GBs) with built-in uncertainty quantification (UQ). Using this method we infer a structure-property model for H diffusivity in [100] tilt GBs in Ni at 700 K based on molecular dynamics (MD) data. Once a GB structure-property model is developed, it can be used as an input to mesoscale simulations of the effective properties of polycrystals, microstructure evolution, etc. A significant advantage of the Bayesian approach presented here is that it facilitates propagation of uncertainties from the underlying structure-property model to the output predictions from mesoscale modeling. Leveraging this capability, we perform mesoscale simulations of the effective diffusivity of polycrystals to investigate the interaction between structure-property model uncertainties and GB network structure. We observe a fundamental interaction between crystallographic correlations and spatial correlations in GB networks that causes certain types of microstructures (those with large populations of J 2 - and J 3 -type triple junctions) to exhibit intrinsically larger uncertainty in their effective properties. Data and code are provided in supplementary materials.

With twin grain boundaries playing an important role in numerous materials, it is important to understand their behavior across the full range of possible boundary plane orientations. This work examines the migration of 41 computed ∑3 nickel grain boundaries over a range of temperatures. The boundary plane orientation appears to play the determining role in the nature of the migration observed, which is evident when the data are plotted in the fundamental zone of possible boundary plane orientations. GBs whose boundary plane lie between ( 1 1 1 ) and ( 2 1 ¯ 1 ¯ ) exhibit thermally activated migration and the atoms do not move in a coordinated fashion. The remaining GBs, including the ( 1 0 1 ¯ ) GB, exhibit some form of thermally damped migration. The thermally damped migration is characterized by inverse temperature dependence where the GBs migrate faster at lower temperatures and move in a coordinated fashion involving Shockley partial dislocations. The inverse temperature dependence, which is confirmed by random walk simulations, appears to be consistent with dislocation drag, which could be related to the Shockley partial dislocations. At least one GB exhibits mixed mobility trends due to the presence of both thermally activated and thermally damped migration characteristics.

A “bottom-up” representative volume element (RVE) for a dual phase steel was constructed based on measured microstructural properties (“microproperties”). This differs from the common procedure of inferring hypothetical microproperties by fitting to macroscopic behavior using an assumed micro-to-macrolaw. The bottom-up approach allows the assessment of the law itself by comparing RVE-predicted mechanical behavior with independent macroscopic measurements, thus revealing the nature of the controlling micromechanisms. An RVE for DP980 steel was constructed using actual microproperties. Finite element (FE) simulations of elastic-plastic transitions were compared with independent loading-unloading-loading and compression-tension experiments. Constitutive models of three types were utilized: 1) a standard continuum model, 2) a standard Crystal Plasticity (CP) model, and 3) a SuperDislocation (SD) model similar to CP but including the elastic interactions of discrete dislocations. These comparisons led to following conclusions: 1) While a constitutive model that ignores elastic interaction of defects can be fit to macroscopic or microscopic behavior, it cannot represent both accurately, 2) Elastic interactions among dislocations are the predominant source of nonlinearity in the nominally-elastic region (i.e. at stresses below the standard yield stress), and 3) Continuum stress inhomogeneity arising from the hard martensite / soft ferrite microstructure has a minor role in the observed transitional nonlinearity in the absence of discrete dislocation interactions.

Grain boundary dislocation nucleation is simulated in a Nickel bicrystal with Σ21b (211)/(211) grain boundaries. Using molecular dynamics, 386 different triaxial stress states are examined for their effect on dislocation nucleation on different slip systems. The approach leads to dislocation nucleation on six of the twelve partial slip systems, enabling a study of conditions leading to nucleation. The criteria for nucleation on each of the slip systems is shown to have a linear dependence on the resolved shear, normal, and co-slip stresses, though the constants for this linear dependence are unique for each slip system. The combined nucleation criteria are used to construct a theoretical nucleation surface. The surface is reminiscent of a Mohr-Coulomb yield surface, except that in the present case the facets of the surface correspond to nucleation on different slip systems.

Grain boundaries are known to act as important diffusion pathways in metals. Here we examine how hydrogen diffusion in nickel grain boundaries is affected by different grain boundary types. We simulate 26 [ 1 0 0 ] symmetric tilt grain boundaries at several temperatures and develop a modified mean squared displacement method for isolating the grain boundary diffusivity from the bulk diffusivity. We analyze the diffusivity data for the different boundaries and find the grain boundary diffusivity to be higher than the bulk diffusivity up to a temperature where the two converge. We test a model developed by Borisov et al. (Phys. Met. Metallogr. 17, 1964, 80-84) that relates grain boundary diffusion to grain boundary interfacial energy. Despite the fact that the Borisov relationship has never been used to examine solute interstitial diffusion before, it fits the simulated diffusion data well for temperatures where the grain boundary diffusivity is higher than the bulk diffusivity. Some parameters in the Borisov relationship, related to the geometry of the grain boundary and its activated states, have always taken on assumed values because they are hard to measure or acquire. The fit of the simulated data provides estimates for these values that are physically realistic and provides evidence that the use of the traditionally assumed values should be reconsidered. This work also demonstrates that while there is a need for further validation, the Borisov relationship can reasonably relate solute interstitial diffusivity of hydrogen to the interfacial energy of individual [ 1 0 0 ] symmetric tilt nickel grain boundaries, whereas in the past it has been used to relate self diffusion and interfacial energy of a grain boundary network as a whole.

Historically, attempts to correlate grain boundary (GB) structure and properties have relied on experimental measurements and computational calculations performed on bicrystals. While the resulting data can be precise, it is usually severely limited in quantity due to the cost and/or computational expense of sampling the full 5D GB character space. As a result, existing data is concentrated around highly-symmetric sub-regions. In contrast, polycrystals are ubiquitous, inexpensive, and contain a broad range of GB characters. However, extracting GB properties from the effective properties of polycrystals requires the solution of an inverse problem. In this work, we present a Bayesian framework, that we call GB property localization, to address both of these challenges by facilitating the inference of GB structure-property models from indirect polycrystal measurements and severely limited data (i.e. when the system is strongly underdetermined). The method naturally provides uncertainty quantification for the resulting inferences. We present the results of validation tests using 1DOF and 3DOF structure-property models for GB diffusivity in 2D (or columnar) microstructures, and we investigate the influence of the number of observations and the number of grains in a polycrystal on the inference quality. We identify a transition in the preferred type of data as a function of the number of observations: when data is abundant bicrystals lead to more accurate inferences; however when data is severely limited, polycrystals may provide more accurate results.

The properties of TRIP-assisted steels are influenced by the transformation of retained austenite into martensite during deformation via the mechanically-induced martensite transformation. In the present work the effect of strain path on isothermal stress-assisted martensite nucleation and variant selection are studied by the coupling of the kinetic Monte Carlo method with the finite element method. This coupled model centers on a thermomechanical model of the martensitic transformation, and the model is tuned and validated against transformation data gathered experimentally for a TRIP-assisted dual phase steel (Ennis et al. (2017)). The effect of the proximity of adjacently transforming regions (kinematic coupling) is also studied as a function of strain path. The model results demonstrate how the rate of martensite nucleation is affected by the strain path (uniaxial tension, biaxial tension, and plane strain) and how the kinematic coupling between adjacent transforming regions is unique to each path. These phenomena are discussed in the context of the Magee effect, which is the relationship between stress state and the suppression/assistance of the nucleation of specific variants of martensite. The implications of martensite nucleation’s sensitivity to strain path and kinematic coupling are discussed for TRIP-assisted steels that transform by isothermal stress-assisted nucleation.

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effort to better inform mesoscale models of dislocation movement within polycrystals. It is found that the ability to predict the slip system of a transmitted dislocation using common geometric criteria is confirmed. Furthermore, machine learning processes are implemented revealing that geometric properties, such as the minimum potential residual Burgers vector (RBV) and the disorientation between the two grains, are stronger indicators of whether or not a dislocation would transmit than other properties, such as the resolved shear stress.

The effects of using a traction-free (plane-stress) assumption to obtain the full distortion tensor from high-resolution EBSD measurements are analyzed. Equations are derived which bound the traction-free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum 'safe' angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction-free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction-free assumption appears to be admirably robust.

Metallic glass matrix (MGM) composites demonstrate impressive plasticity over monolithic metallic glasses due to their ability to delocalize strain and inhibit shear band propagation. This work investigates various microstructural factors (volume fraction, length scale and yield strength) influencing strain delocalization in a model MGM composite. Shear transformation zone dynamics is utilized to model the amorphous phase while a local Taylor dislocation model is used for the crystalline phase. An N-factorial experiment examines replicates for various macro- and microscopic measures of strain delocalization and regression analysis is used to identify statistically significant trends in the data. The experiment shows that strain delocalization and the consequent ductility are most strongly influenced by a crystalline phase with a substantially lower yield stress than that of the amorphous matrix. It also shows that increased crystalline volume fraction alone is insufficient to promote strain delocalization in the case of a crystalline phase with high relative yield stress, and that a lower yield stress for the crystalline phase implies lower maximum stresses supported by the composite. Examination of shear band–inclusion interactions indicate that the nucleation and diffuse transmission of numerous shear bands is critical to the strain delocalization. The regression analysis provides continuous functional forms for the various relationships between properties that can be exploited to optimize the microstructure of MGM composites.

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large data set in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical “building blocks” that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.

Twin detection via EBSD can be particularly challenging due to the fine scale of certain twin types - for example, compression and double twins in Mg. Even when a grid of sufficient resolution is chosen to ensure scan points within the twins, the interaction volume of the electron beam often encapsulates a region that contains both the parent grain and the twin, confusing the twin identification process. The degradation of the EBSD pattern results in a lower image quality metric, which has long been used to imply potential twins. However, not all bands within the pattern are degraded equally. This paper exploits the fact that parent and twin lattices share common planes that lead to the quality of the associated bands not degrading; i.e. common planes that exist in both grains lead to bands of consistent intensity for scan points adjacent to twin boundaries. Hence, twin boundaries in a microstructure can be recognized, even when they are associated with thin twins. Proof of concept was performed on known twins in Inconel 600, Tantalum, and Magnesium AZ31. This method was then used to search for undetected twins in a Mg AZ31 structure, revealing nearly double the number of twins compared with those initially detected by standard procedures.

Studies of dislocation density evolution are fundamental to improved understanding in various areas of deformation mechanics. Recent advances in cross-correlation techniques, applied to electron backscatter diffraction (EBSD) data have particularly shed light on geometrically necessary dislocation (GND) behavior. However, the framework is relatively computationally expensive—patterns are typically saved from the EBSD scan and analyzed offline. A better understanding of the impact of EBSD pattern degradation, such as binning, compression, and various forms of noise, is vital to enable optimization of rapid and low-cost GND analysis. This paper tackles the problem by setting up a set of simulated patterns that mimic real patterns corresponding to a known GND field. The patterns are subsequently degraded in terms of resolution and noise, and the GND densities calculated from the degraded patterns using cross-correlation ESBD are compared with the known values. Some confirmation of validity of the computational degradation of patterns by considering real pattern degradation is also undertaken. The results demonstrate that the EBSD technique is not particularly sensitive to lower levels of binning and image compression, but the precision is sensitive to Poisson-type noise. Some insight is also gained concerning effects of mixed patterns at a grain boundary on measured GND content.

This study explores the evolution of GNDs and their effects on back stress through experimental and computational methods. Four large-grained tantalum tensile specimens were strained in uniaxial tension, electron backscatter diffraction (EBSD) data were collected, and geometrically necessary dislocation (GND) maps of the four specimens in the unloaded state were produced. EBSD-based GND maps revealed several types of features with high GND content which caused back stress in the specimens. Correlations between five geometrically-based grain boundary (GB) transmission factors and the GB GND content were evaluated, and statistically significant correlations were found for transmission factors based on Livingston and Chalmer's N factor, Werner and Prantl's slip transfer number, and GB misorientation. The sign of individual components of the Nye tensor were used to visually and quantitatively identify clustering of GNDs of the same sign, thus giving additional evidence of increasing back stress due to deformation. Deformation of one of the specimens was simulated using multiple CPFEM based modeling approaches and predicted stress-strain responses are compared. The super dislocation model (SD model) — a crystal plasticity finite element method (CPFEM) which incorporates elastic dislocation interactions — was able to isolate impact of back stress on the overall flow stress. The SD model predicted correct stresses when compared with experimental data; however, when the elastic interactions in the SD model were turned off, stress predictions were 25% too low. Thus, demonstrating the importance of incorporating back stress into the model.

Compliant mechanisms rely on the elastic bending of thin members to generate motion. In the paper by Homer, et al., bulk metallic glasses (BMGs) are shown to have an optimal combination of mechanical properties and processing ability, making them ideal for complex, low-cost compliant mechanisms.

A mesoscale simulation by shear transformation zone (STZ) dynamics is used to analyze the initial stages of shear localization in amorphous metals, of which many details remain unresolved due to the difficulty in accessing the appropriate time- and length-scales. Examination of a constant strain-rate tensile test of a model amorphous metal reveals four different stages in the microscopic processes that lead to formation of a shear band. These stages are identified as: (i) STZ clustering, where potential nucleation sites form as STZ activations cluster in space; (ii) growth following nucleation, where a nascent shear band exhibits a propagating front that defines the shear band path; (iii) relaxation thickening, where the shear band thickens and relaxes the system down to the flow stress; and (iv) flow thickening, where the shear band exhibits prolonged thickening at the flow stress. The results are consistent with the literature but suggest that a shear band is defined by a front that propagates very quickly with negligible accumulated strain. This propagating front likely occurs below the resolution of current methods that only observe simultaneous slip in a shear band where significant strain can be accumulated at much slower rates. Analysis of a thermodynamic model also suggests a specific critical stress that is required to nucleate a shear band, after which the shear band is allowed to grow unconstrained.

Grain boundary (GB) motion in polycrystalline materials is expected and observed to be dominated by thermally activated processes. This has important implications for properties influenced by the presence of GBs. Here, the GB motions of a catalog of 388 simulated nickel boundaries reveal a rich set of behaviors, which demonstrate that the temperature dependencies of GB mobility are far more complex than originally believed. In the set of 388 boundaries, four different general classes were observed with the following percentages: (I) ~57% exhibited traditional thermally activated mobility; (II) ~20% exhibited non-thermally activated mobility, where mobility was either independent of temperature or mobility decreased with increasing temperature (i.e., not thermally activated); (III) ~14% exhibited mixed modes of mobility, where different trends were exhibited over different temperature regimes (e.g., thermally activated at low temperature and non-thermally activated at high temperature); and (IV) ~9% exhibited unclassifiable mobility trends or were immobile over the studied temperature range. Thus, although the studied set of boundaries is not statistically representative of all GBs, it indicates that we must expand our preconceived notions to include new and interesting phenomena.

A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye’s GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye’s tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal’s electron opacity by combining experimentally-accessible Nye’s tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye’s tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors.

A mesoscale model, shear transformation zone dynamics (STZ dynamics), is employed to investigate the connections between the structure and deformation of metallic glasses. The present STZ dynamics model is adapted to incorporate a structure-related state variable, and evolves via two competing processes: STZ activation, which creates free volume, vs. diffusive rearrangement, which annihilates it. The dynamical competition between these two processes gives rise to an equilibrium excess free volume that can be connected to flow viscosity via the phenomenological Vogel–Fulcher–Tammann relation in relaxed structures near the glass transition temperature. On the other hand, the excess free volume allows glasses to deform at low temperatures via shear localization into shear bands, even in the presence of internal stress distributions that arise upon cooling after processing., Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies, United States. Defense Threat Reduction Agency (Contract HDTRA-11-1-0062)

In this work, we introduce and demonstrate a hybrid model that combines elements of the Monte Carlo Potts Model with those of the phase field model. This hybrid model is introduced as a method to simulate microstructural evolution processes that are kinetically controlled by long-range diffusion in multi-component systems. The hybrid model uses a digitized microstructure with each site characterized by its microstructural features and its composition. The total free energy of the system is defined by bulk chemical free energy as well as interfacial energy. The coupling between the microstructure and composition is achieved by using the total free energy to drive the evolution in both fields. The kinetics are simulated by a combination of Monte Carlo methods and solution of the Cahn–Hilliard equation. This model is applied to several example problems to demonstrate its capabilities. These are diffusion in single- and two-phase diffusion couples, grain growth in a two-phase system controlled by diffusion and diffusion phase transformation by nucleation and growth of a second phase.

Shear-coupled grain boundary motion is examined for a large number of grain boundaries including 73 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 symmetric tilt boundaries. In the present work, the grain boundary motion is induced by a synthetic driving force as opposed to prior studies of shear coupling induced by applied shear. For those boundaries that are observed to undergo shear-coupled motion, the results based on the two driving forces agree well, both for experiments and simulations. This agreement also confirms the generality of the shear coupling mechanism over numerous boundaries and boundary types. The examination of boundary structure provides insight into the different trends that are observed. Shear coupling according to modes not predicted by the Frank–Bilby equation are also demonstrated. The temperature dependence of shear coupling is examined, and is consistent with prior work for symmetric tilt boundaries. While prior studies have emphasized symmetric tilt boundaries, some general grain boundaries exhibit shear coupling as well. In these boundaries, it is found that the shear coupling is either temperature independent, decreases in magnitude with increasing temperature or, in some cases, changes direction with temperature.

High-resolution (or “cross-correlation”) electron backscatter diffraction analysis (HR-EBSD) utilizes cross-correlation techniques to determine relative orientation and distortion of an experimental electron backscatter diffraction pattern with respect to a reference pattern. The integrity of absolute strain and tetragonality measurements of a standard Si/SiGe material have previously been analyzed using reference patterns produced by kinematical simulation. Although the results were promising, the noise levels were significantly higher for kinematically produced patterns, compared with real patterns taken from the Si region of the sample. This paper applies HR-EBSD techniques to analyze lattice distortion in an Si/SiGe sample, using recently developed dynamically simulated patterns. The results are compared with those from experimental and kinematically simulated patterns. Dynamical patterns provide significantly more precision than kinematical patterns. Dynamical patterns also provide better estimates of tetragonality at low levels of distortion relative to the reference pattern; kinematical patterns can perform better at large values of relative tetragonality due to the ability to rapidly generate patterns relating to a distorted lattice. A library of dynamically generated patterns with different lattice parameters might be used to achieve a similar advantage. The convergence of the cross-correlation approach is also assessed for the different reference pattern types.

Low-load nanoindentation can be used to assess not only the plastic yield point, but the distribution of yield points in a material. This paper reviews measurements of the so-called nanoscale strength distribution (NSD) on two classes of materials: crystals and metallic glasses. In each case, the yield point has a significant spread (10–50% of the mean normalized stress), but the origins of the distribution are shown to be very different in the two materials classes. In crystalline materials the NSD can arise from thermal fluctuations and is attended by significant rate and temperature dependence. In metallic glasses well below their glass-transition temperature, the NSD is reflective of fluctuations in the sampled structure and is not very sensitive to rate or temperature. Computer simulations using shear transformation zone dynamics are used to separate the effects of thermal and structural fluctuations in metallic glasses, and support the latter as dominating the NSD of those materials at low temperatures. Finally, the role of the NSD as a window on structural changes due to annealing or prior deformation is discussed as a direction for future research on metallic glasses in particular.

A combined program of experiments and simulations is used to study the problem of cyclic indentation loading on metallic glasses. The experiments use a spherical nanoindenter tip to study shear band formation in three glasses (two based on Pd and one on Fe), after subjecting the glass to cycles of load in the nominal elastic range. In all three glasses, such elastic cycles lead to significant increases in the load required to subsequently trigger the first shear band. This cyclic hardening occurs progressively over several cycles, but eventually saturates. The effect requires cycles of sufficient amplitude and is not induced by sustained loading alone. The simulations employed a new shear transformation zone (STZ) dynamics code to reveal the local STZ operations that occur beneath an indenter during cycling. These results reveal a plausible mechanism for the observed cyclic hardening: local regions of confined microplasticity can develop progressively over several cycles, without being detectable in the global load–displacement response. It is inferred that significant structural change must attend such microplasticity, leading to hardening of the glass., United States. Office of Naval Research (Grant No. N00014-08-10312), United States. Army Research Office (National Defense Science and Engineering Graduate Fellowship), King Fahd University of Petroleum and Minerals

A new mesoscale modeling technique for the thermo-mechanical behavior of metallic glasses is proposed. The modeling framework considers the shear transformation zone (STZ) as the fundamental unit of deformation, and coarse-grains an amorphous collection of atoms into an ensemble of STZs on a mesh. By employing finite element analysis and a kinetic Monte Carlo algorithm, the modeling technique is capable of simulating glass processing and deformation on time and length scales greater than those usually attainable by atomistic modeling. A thorough explanation of the framework is presented, along with a specific two-dimensional implementation for a model metallic glass. The model is shown to capture the basic behaviors of metallic glasses, including high-temperature homogeneous flow following the expected constitutive law, and low-temperature strain localization into shear bands. Details of the effects of processing and thermal history on the glass structure and properties are also discussed., United States. Office of Naval Research (contract N00014-08-1-0312)