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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). more...

Shear strain profiles along slip bands in a modified Rolls-Royce nickel superalloy (RR1000) were analyzed for a tensile sample deformed by 2%. The strain increased with distance away from a grain boundary (GB), with maximum shear strain towards the center of the grain, indicating that dislocation nucleation generally occurred in the grain interior. The strain gradients in the neighborhood of the GBs were quantified and generally correlated with rotation about the active slip system line direction. This leads to an ability to determine the active slip system in these regions. The dislocation spacing and pileup stresses were inferred. The dislocation spacing closely follows an Eshelby analytical solution for a single ended pileup of dislocations under an applied stress. The distribution of pileup stress values for GBs of a given misorientation angle follows a log-normal distribution, with no correlation between the pileup stress and the GB misorientation angle. Furthermore, there is no observed correlation between various transmissivity factors and slip band pileup stress. Hence it appears that the obstacle strength of any of the observed GBs is adequate to facilitate the dislocation pileups present in the slip bands. However, slip band transmission does correlate with transmissivity factors, with the current study focusing on the Luster and Morris m’-factor. Observation of strain profiles of transmitted bands indicate dislocation nucleation locations. more...

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. more...

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. more...

Graphical abstract, One of the limitations of atomistic simulations is that many of the computational tools used to extract structural information from atomic trajectories provide metrics that are not directly compatible with experiments for validation. In this work, to bridge between simulation and experiment, a method is presented to produce simulated Kikuchi diffraction patterns using data from atomistic simulations, without requiring a priori specification of the crystal structure or defect periodicity. The Kikuchi pattern simulation is based on the kinematic theory of diffraction, with Kikuchi line intensities computed via a discrete structure factor calculation. Reciprocal lattice points are mapped to Kikuchi lines using a geometric projection of the reciprocal space data. This method is validated using single crystal atomistic models, and the novelty of this approach is emphasized by simulating kinematic Kikuchi diffraction patterns from an atomistic model containing a nanoscale dislocation loop. Deviations in kinematic Kikuchi line intensities are explained considering the displacement field of the dislocation loop, as is done in diffraction contrast theory. more...

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. more...

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. more...

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. more...

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. more...

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. more...

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. more...

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. more...

How boundaries surrounding recrystallization grains migrate through the 3D network of dislocation boundaries in deformed crystalline materials is unknown and critical for the resulting recrystallized crystalline materials. Using X-ray Laue diffraction microscopy, we show for the first time the migration pattern of a typical recrystallization boundary through a well-characterized deformation matrix. The data provide a unique possibility to investigate effects of both boundary misorientation and plane normal on the migration, information which cannot be accessed with any other techniques. The results show that neither of these two parameters can explain the observed migration behavior. Instead we suggest that the subdivision of the deformed microstructure ahead of the boundary plays the dominant role. The present experimental observations challenge the assumptions of existing recrystallization theories, and set the stage for determination of mobilities of recrystallization boundaries. more...

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. more...

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. more...