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A machine component fabricated by additive manufacturing (AM) of metal powders often possesses steep residual stress gradients with significant magnitudes due to large temperature gradients that transpire within a localized area during fabrication. These processing-induced residual stresses can cause distortion of the part, and if they are of significant magnitude, they could induce cracking of the component, degrade printability, and/or diminish subsequent mechanical performance. The ability to predict these residual stresses imparted by AM is an important step in permeating AM technology for advanced manufacturing. Calibration and validation of AM process models used for prediction are, therefore, a critical step in understanding the origin and mitigating the challenges associated with residual stresses inherent to the AM process. In the present work, the residual strain distributions in components with simple geometries fabricated by a laser powder bed fusion (LBPF) process were characterized non-destructively using energy-dispersive X-ray diffraction in support of the US Air Force Research Laboratory Additive Manufacturing Modeling Challenge Series Groeber et al. (JOM 70:441-448, 2018). The measurement setup and approach are described in detail so that the data can be used as a benchmark to calibrate and validate models for the prediction of macro-scale residual stresses due to the LPBF process.

We describe 3D characterization of an additively manufactured Inconel 625 nickel-base superalloy specimen conducted during a uniaxial tension test using a suite of nondestructive x-ray techniques. High-energy diffraction microscopy in both near- and far-field modalities are employed in situ to track evolution of the material orientation and stress–strain fields at six points during the mechanical test, and these data streams are registered with micro-computed tomography reconstructions which probe the material density. This data volume was matched to a multi-modal serial sectioning characterization of the specimen taken after loading, described in this article’s companion. Twenty-eight grains which were monitored throughout the experiment were selected to form the basis for AFRL AM Modeling Series Challenge 4, Microscale Structure-to-Properties.

High-energy diffraction microscopy (HEDM) in-situ mechanical testing experiments offer unique insight into the evolving deformation state within polycrystalline materials. These experiments rely on a sophisticated analysis of the diffraction data to instantiate a 3D reconstruction of grains and other microstructural features associated with the test volume. For microstructures of engineering alloys that are highly twinned and contain numerous features around the estimated spatial resolution of HEDM reconstructions, the accuracy of the reconstructed microstructure is not known. In this study, we address this uncertainty by characterizing the same HEDM sample volume using destructive serial sectioning (SS) that has higher spatial resolution. The SS experiment was performed on an Inconel 625 alloy sample that had undergone HEDM in-situ mechanical testing to a small amount of plastic strain (~ 0.7%), which was part of the Air Force Research Laboratory Additive Manufacturing (AM) Modeling Series. A custom-built automated multi-modal SS system was used to characterize the entire test volume, with a spatial resolution of approximately 1 µm. Epi-illumination optical microscopy images, backscattered electron images, and electron backscattered diffraction maps were collected on every section. All three data modes were utilized and custom data fusion protocols were developed for 3D reconstruction of the test volume. The grain data were homogenized and downsampled to 2 µm as input for Challenge 4 of the AM Modeling Series, which is available at the Materials Data Facility repository.

Elastic micromechanical fields are tracked for a nickel-based superalloy polycrystal via high energy X-ray diffraction microscopy (HEDM) and corresponding intragranular deformation metrics are determined with peak broadening analysis during cyclic high temperature loading. A low solvus, high refractory (LSHR) sample with 252 grains was subjected to uniaxial tension and held under fixed displacement while thermally cycling between 460 °C and 770 °C with intermittent HEDM characterization to study the grain average response to thermo-mechanical deformation. Elevated temperatures were found to allow for heterogeneous amounts of recovery amongst distinct grains within the sampled region, indicating complex grain interactions; the extent of recovery was greater at higher temperatures.

Polycrystalline alloys are used pervasively across structural applications contingent upon extensive experimental testing. A statistically representative number of tests are necessary to expose the variability in the material's performance, as a result of non-uniform microstructures and associated micromechanical fields. In a more direct means of capturing this pertinent information, multi-modal experimental techniques are presented to measure and track the complete micromechanical state, evolving during loading, of each and every grain within the regions of interest. Specifically, a combination of high-energy X-ray diffraction microscopy and digital image correlation coupled with electron backscatter diffraction are conducted on a specimen for each of the alloys, Haynes 282 and Ti7Al. The results of the multi-modal analysis definitively demonstrate that the degree of heterogeneity increases with deformation level and is used to assess the number of grains necessary for a representative volume element description of the stress state for each of these materials. Moreover, higher resolution imaging is used for identification of the slip system activity and subsequently used to study slip transmission events. An accurate knowledge of the resolved shear stress in adjacent grains (grain interactions) is demonstrated to be a key descriptor of the slip transmission events.

The accuracy of the near-field high-energy diffraction microscopy (nf-HEDM) technique is evaluated by directly comparing an nf-HEDM reconstructed microstructure with an electron backscatter diffraction (EBSD) characterization of the same microstructure. A high-purity gold oligocrystal was chosen for characterization in order to facilitate direct one-to-one comparison between the reconstructions given by each technique. By using the comparatively high spatial resolution of the EBSD reconstruction as the ground truth for the grain-boundary network's morphology, it is determined that nf-HEDM locates internal grain boundaries with an accuracy on average better than the resolution of the imaging detector used or within the reconstruction voxel size, whichever is larger. By taking the intragranular misorientation in well ordered grains as a proxy for orientation resolution, it is determined that standard data collection procedures determine crystallographic orientations to better than 0.1°. The effects of various modified data collection procedures are also examined.

The small fatigue crack (SFC) growth regime in polycrystalline alloys is complex due to the heterogeneity in the local micromechanical fields, which result in high variability in crack propagation directions and growth rates. In this study, we employ a suite of techniques, based on high-energy synchrotron-based X-ray experiments that allow us to track a nucleated crack, propagating through the bulk of a Ni-based superalloy specimen during cyclic loading. Absorption contrast tomography is used to resolve the intricate 3D crack morphology and spatial position of the crack front. Initial near-field high-energy X-ray diffraction microscopy (HEDM) is used for high-resolution characterization of the grain structure, elucidating grain orientations, shapes, and boundaries. Cyclic loading is periodically interrupted to conduct far-field HEDM to determine the centroid position, average orientation, and average lattice strain tensor for each grain within the volume of interest. Reciprocal space analysis is used to further examine the deformation state of grains that plasticize in the vicinity of the crack. Analysis of the local micromechanical state in the grains ahead of the crack front is used to rationalize the advancing small crack path and growth rate. Specifically, the most active slip system in a grain, determined by the maximum resolved shear stress, aligns with the crack growth direction; and the degree of microplasticity ahead of the crack tip helps to identify directions for potential occurrences of crack arrest or propagation. The findings suggest that both the slip system level stresses and microplasticity events within grains are necessary to get a complete description of the SFC progression. Further, this detailed dataset, produced by a suite of X-ray characterization techniques, can provide the necessary validation, at the appropriate length-scale, for SFC models.

The kinetics of the dissolution of the equiaxed alpha phase into the beta matrix in Ti-6Al-4V were established and modeled for both isothermal (constant temperature) and transient/continuous heating conditions. For the isothermal experiments, samples were solution treated at a subtransus temperature to equilibrate the microstructure followed by rapid, direct-resistance heating to a temperature either 25 K or 78 K (25 °C or 78 °C) above the equilibrium beta transus and held for times ranging from 1 to 32 seconds. Dissolution behavior under transient conditions was determined in-situ using an indirect-resistance furnace and X-ray (synchrotron) source; these trials comprised a similar initial subtransus solution heat treatment followed by continuous heating at a constant rate in the range between 15 and 135 K/min (15 and 135 °C/min) to a temperature lying 25 K (25 °C) above the transus. Measurements of the temporal evolution of the volume fraction of alpha were interpreted using numerical simulations based on the Whelan dissolution model modified to treat a distribution of particle sizes and the possible interaction of the concentration gradients developed around adjacent particles; i.e., soft impingement. The isothermal dissolution measurements were bounded by predictions from simulations with and without the soft-impingement assumption. Similar trends were found for continuous-heating behavior. In particular, slow or fast heating-rate observations were replicated by simulation predictions with or without the soft-impingement constraint, respectively.

A validation is reported for micromechanical simulation using a reimplementation of an elasto-viscoplastic FFT-based (EVPFFT) formulation, i.e., the Micromechanical Analysis of Stress-strain Inhomogeneities with fast Fourier transform (MASSIF) code, against experimental data obtained from synchrotron x-ray diffraction. The experimental data was collected during in-situ deformation of a titanium alloy specimen by High Energy Diffraction Microscopy (HEDM), which provided the average elastic strain tensor and orientation of each grain in a polycrystalline sample. MASSIF was used to calculate the local micromechanical fields in a Ti-7Al polycrystalline sample at different load levels. The initially attempted simulation showed that, although the effective response was calibrated to reproduce the experiment, MASSIF was not able to reproduce the micromechanical fields at the scale of individual grains. The differences between calculated and measured averages at the grain scale were related to initial residual strains resulting from the prior processing of the material, which had not been incorporated in the original calculation. Accordingly, a new simulation was instantiated using information on the measured residual strains to define a set of eigenstrains, calculated via an Eshelby approximation. This initialization significantly improved the correlation between calculated and simulated fields for all strain and stress components, for measurements performed within the elastic regime. For the measurements at the highest load, which was past plastic yield, the correlations deteriorated because of plastic deformation at the grain level and the lack of an accurate enough constitutive description in this deformation regime.

High-energy synchrotron x-rays are used to track grain-averaged lattice reorientation and stress-state evolution in Ti-7Al as it is cyclically loaded to 90% of its macroscopic yield stress. This evolution provides clear indication of accumulating plastic strain even though the sample never exceeded the elastic limit. The largest changes in lattice orientation and stress state are observed following the first cycle then evolution continues at a lower rate with subsequent cycles. Variation of the axes about which lattice reorientation occurs is found to be highly dependent on the maximum resolved shear stress and corresponding activation of various families of slip systems.

A novel in situ scanning electron microscope (SEM), high frequency fatigue testing methodology is developed using a combination of laser milling, focused ion beam fabrication and nanoindentation. This methodology is used to investigate crack initiation, propagation, fracture, fatigue life, and the mechanical response of microcantilever samples of a Ni-based superalloy (Rene-N5) under different cyclic strain amplitudes. The crack initiation and propagation in the microcantilever is monitored by observing changes in the beam's dynamic stiffness and continuous SEM imaging. The dynamic stiffness response of the micro-beams exhibits a transition from softening to hardening at a critical strain amplitude of 7 × 10 − 3 . Theoretical analysis indicates that this transition corresponds to the stress required to shear γ ′ precipitates. SEM imaging reveals the evolution of significant extrusions, intrusions, and slip traces during cyclic loading above this critical strain amplitude. Below this strain amplitude, very little surface roughening is observed. In addition, the measured dynamic stiffness is observed to exhibit two regimes of decrease after crack initiation. These two regimes correspond to short and large crack propagation. Finally, an overall increase in fatigue life is observed when comparing to bulk scale experiments on nickel-base superalloys. It is proposed that this is an inherent size effect in the small-volume, single crystal specimens tested.

Full stress tensors of over four hundred individual grains in a titanium alloy specimen (Ti-7Al) are tracked during continuous uniaxial deformation through the elasto-plastic transition at 355°C. The experiment is facilitated by a unique radiative heating furnace and load frame designed for in-situ high-energy X-ray diffraction measurements. Average strengths of multiple slip system families are calculated directly from the ensemble grain stress data. Results show that elevated temperature lowers the strength of basal slip systems relative to prismatic slip systems, reduces the degree of flow softening due to precipitate shearing, and decreases the first-order pyramidal slip system work-hardening rate.

Additive manufacturing offers enhanced design and topological complexity over traditional manufacturing and is well suited to fabricate complex structures. Here, we present a new milli-scale test method to assess the location-specific mechanical response of laser powder-bed printed Inconel 625 thin-walled structures. High-resolution digital image correlation was coupled with ambient temperature milli-scale tests to understand the progression of plastic deformation in T-shaped specimens. Plastic strains were concentrated around the intersection of the horizontal and vertical ligaments, emphasizing their importance in the design process. EBSD scans elucidated the role of geometry in the development of in-plane texture. Isotropic finite element models were unable to fully predict the response of printed specimens, but anisotropic models, motivated by the texture measurements, resulted in much better agreement. This work illustrates the importance of local processing and microstructure on the mechanical response of additively manufactured components.

A finite element framework is developed to resolve the intragranular fields of incompatible deformation generated intrinsically in response to applied deformation, through linear elasticity complemented by the theory of continuous distribution of dislocations and experimental grain-scale observations. Discrete grain-averaged lattice strains, characterized along with grain orientations via X-ray diffraction microscopy, enable high fidelity continuous solutions anchored to measured response and satisfy boundary conditions, mechanical equilibrium, and strain compatibility within a finite element model. A continuous distribution of strain fields in a nickel-based superalloy, evaluated periodically during R = 0 cyclic loading, exposes the fundamental heterogeneity in polycrystalline response which creates locations of high stress gradients and potential sites of failure. Incompatibility is shown to be an effective measure driving the spatial concentration of stress with loading, particularly at twin and high angle grain boundaries. Furthermore, incompatible deformation is shown, through both specific examples and statistically, to be predominantly preserved upon elastic recovery improving our understanding of the history dependence of residual stresses. Positive correlation between residual stress & incompatible deformation and saturation of material response or shakedown in response to cyclic loading is revealed. The scalability of the framework with experiments at multiple length scales are discussed.

Improvements to synchrotron-based micro-computed tomography scanning capabilities have gifted researchers the ability to characterize 4D material thermomechanical responses more thoroughly than ever before. These advancements, however, have brought about new challenges in analyzing the resulting deluge of data. We report on a nickel-based superalloy specimen imaged 26 times in-situ during cyclic loading at Argonne National Laboratory Advanced Photon Source beamline 1ID, in order to monitor crack growth within the microstructure. Several deep learning approaches which utilize convolutional neural networks are implemented to segment crack features from reconstructed tomography scans. U-Net architecture implementations are found to be especially effective, achieving IoU = 0.995 ± 0.004 and Matthews correlation coefficient scores of ϕ = 0.826 ± 0.085 . These advancements broaden possibilities for scientists seeking to automate segmentation analyses of similar large datasets.

The full three-dimensional stress state of 172 individual bulk grains in austenitic stainless steel 316 L at 0.1 and 1% sample elongation has been determined with sufficient accuracy to allow comparison with the theoretical Bishop-Hill stress states for plastically deforming grains as well as calculation of the resolved shear stresses on the individual slip systems. At 0.1%, the resolved shear stresses exhibit quite large variations between grains of similar orientation. When averaging over similarly oriented grains, the resolved shear stresses correspond to the Schmid factors for uniaxial tension. At 1%, only about half of the grains were close to a Bishop-Hill stress state. The stress state of the other half of the grains was closer to the applied uniaxial stress, in between Bishop-Hill states, or in some cases none of these. The orientation dependence of the assigned stress states deviate somewhat from the theoretical expectation. These deviations are found to originate from a larger tensile stress component than in the theoretical Bishop-Hill stress states and to be associated also with deviations from axisymmetric plastic strain. This conclusion was supported by finite-element crystal plasticity simulations.

Crack initiation at inclusions is a dominant, unavoidable and life-limiting failure mechanism of important structural materials. Fatigue progresses in a complex manner to find the ‘weakest link’ in the microstructure, leading to crack nucleation. In this study, fully 3-D characterization methods using high energy synchrotron x-rays are combined with in-situ mechanical testing to study the crack initiation mechanism in a Ni-based superalloy specimen. The specimen was produced via powder metallurgy and seeded with a non-metallic inclusion. Two x-ray techniques were employed: absorption contrast computed micro-tomography (μ-CT) to determine the morphology of the inclusion and its location in the gauge section of the specimen; and far-field high energy diffraction microscopy (FF-HEDM) to resolve the centroids, average orientations, and lattice strains of the individual grains comprising the microstructure surrounding the inclusion. Sequential μ-CT and FF-HEDM scans were carried out at both peak and zero applied stress following schedules of cyclic deformation. The μ-CT data showed the onset and location of crack initiation, and the FF-HEDM data provided temporal and spatial evolution of the intergranular strains. Strain partitioning and the associated stress heterogeneities that develop are shown to stabilize within a few loading cycles. Elasto-viscoplastic fast Fourier transform simulations were utilized to supplement interpretation of the experimental stress distributions and compared with the experimental stress distributions. Appropriate conditions for crack nucleation in the form of stress gradients were demonstrated and created by virtue of the inclusion, specifically the residual stress state and local bonding state at the inclusion-matrix interface.

Far-field high-energy X-ray diffraction microscopy is used to asses the evolution of slip system strengths in hexagonal close-packed (HCP) Ti-7Al during tensile deformation in-situ. The following HCP slip system families are considered: basal 〈 a 〉 , prismatic 〈 a 〉 , pyramidal 〈 a 〉 , and first-order pyramidal 〈 c + a 〉 . A 1 mm length of the specimen's gauge section, marked with fiducials and comprised of an aggregate of over 500 grains, is tracked during continuous deformation. The response of each slip system family is quantified using ‘slip system strength curves’ that are calculated from the average stress tensors of each grain over the applied deformation history. These curves, which plot the average resolved shear stress for each slip system family versus macroscopic strain, represent a mesoscopic characterization of the aggregate response. A short time-scale transient softening is observed in the basal 〈 a 〉 , prismatic 〈 a 〉 , and pyramidal 〈 a 〉 slip systems, while a long time-scale transient hardening is observed in the pyramidal 〈 c + a 〉 slip systems. These results are used to develop a slip system strength model as part of an elasto-viscoplastic constitutive model for the single crystal behavior. A suite of finite element simulations is performed on a virtual polycrystal to demonstrate the relative effects of the different parameters in the slip system strength model. The model is shown to accurately capture the macroscopic stress-strain response using parameters that are chosen to capture the mesoscopic slip system responses.

The implementation of saw-tooth refractive lenses at the APS 1-ID high-energy X-ray beamline is presented., The Advanced Photon Source 1-ID beamline, operating in the 40–140 keV X-ray energy range, has successfully employed continuously tunable saw-tooth refractive lenses to routinely deliver beams focused in both one and two dimensions to experiments for over 15 years. The practical experience of implementing such lenses, made of silicon and aluminium, is presented, including their properties, control, alignment, and diagnostic methods, achieving ∼1 µm focusing (vertically). Ongoing development and prospects towards submicrometre focusing at these high energies are also mentioned.

The desire to improve the performance and lifetime of polycrystalline components has fueled the development of advanced micromechanical modeling tools. Multiscale modeling approaches, such as Crystal Plasticity Finite Element Methods (CPFEM), now possess the ability to illuminate the link between material processing, microstructure, and properties [1]. Whereas traditional FE modeling relies on convergent macroscale properties, the ability of CPFEM to explicitly represent the morphology and local crystallographic orientations of polycrystalline microstructures requires scale-specific, quantitative microstructural information for both input and validation. The development and implementation of experimental techniques for capturing behavior and microstructural properties at salient length scales are needed to inform the determination of representative volume elements (RVEs). Here, accurately capturing microstructural details and observing size effects on material properties are both important. Simply extrapolating from average microstructure descriptors does not provide information about the relative importance of specific grain size, shape, and configuration with neighbors. These are features that can be captured experimentally through advanced characterization techniques, such as 3D serial sectioning [2].

The advancement of microstructure-sensitive models for elevated temperature applications requires experimental data at the relevant length scales and usage environments. Towards this goal, we studied the evolution of grain-level strains in a Ni-based superalloy during heating and subsequent loading at elevated temperature. The specimen was heated using two halogen lamps in a furnace designed explicitly for the special load frame used for the synchrotron-based experiment. High energy X-ray diffraction was used to non-destructively characterize the initial 3D microstructure, confirm the temperature of the specimen, and monitor the evolution of grain-level strains, stresses, and orientations through the elastic-plastic transition. The distributions of grain-level normal strains were observed to broaden with elastic loading, whereas elastic-plastic loading led to development of local intergranular “hotspots”, or activation of plastic slip within select grains, that both broaden and skew the grain-level strain distributions. These grain-level strain distributions were fit to a generalized extreme value (GEV) distribution function. The GEV shape parameter is observed to change significantly at the onset of macroscopic plasticity. At the grain scale, more grain reorientation (plasticity) occurred for grains oriented for lower strength-to-stiffness ratios. During the onset of plastic deformation for LSHR at 660 ∘ C load shedding from lower strength-to-stiffness-oriented grains to higher strength-to-stiffness-oriented grains was observed. Additionally, based on the grain-averaged reorientation axis, it was found that LSHR has a preference for activation of multiple slip systems at 660 ∘ C. We conclude with a discussion on the critical need for statistical analysis of such mesoscale data obtained in situ at elevated temperature for the verification/validation of the next generation of microstructure-sensitive models.

Hexagonal metals have anisotropic coefficients of thermal expansion causing grain-level internal stresses during heating. High energy x-ray diffraction microscopy, a non-destructive, in situ, micromechanical and microstructural characterization technique, has been used to determine the anisotropic coefficients of thermal expansion (CTEs) for Ti-7Al. Two samples of polycrystalline $\alpha$-phase Ti-7Al were continuously heated from room temperature to 850 $^\circ$C while far-field HEDM scans were collected. The results showed a change in the ratio of the CTEs in the 'a' and 'c' directions which explains discrepancies found in the literature. The CTE additionally appears to be affected by the dissolution of $\alpha_2$ precipitates. Analysis of the grain-resolved micromechanical data also shows reconfiguration of the grain scale stresses likely due to anisotropic expansion driving crystallographic slip., Comment: 22 pages, 12 figures, Submitted for peer review

Ti-7Al is a good model material for mimicking the α phase response of near-α and α+β phases of many widely used titanium-based engineering alloys, including Ti-6Al-4V. In this study, three model structures of Ti-7Al are investigated using atomistic simulations by varying the Ti and Al atom positions within the crystalline lattice. These atomic arrangements are based on transmission electron microscopy observations of short-range order. The elastic constants of the three model structures considered are calculated using molecular dynamics simulations. Resonant ultrasound spectroscopy experiments are conducted to obtain the elastic constants at room temperature and a good agreement is found between the simulation and experimental results, providing confidence that the model structures are reasonable. Additionally, energy barriers for crystalline slip are established for these structures by means of calculating the γ-surfaces for different slip systems. Finally, the positions of Al atoms in regards to solid solution strengthening are studied using density functional theory simulations, which demonstrate a higher energy barrier for slip when the Al solute atom is closer to (or at) the fault plane. These results provide quantitative insights into the deformation mechanisms of this alloy.

High-Energy Diffraction Microscopy (HEDM) is a 3-d X-ray characterization method that is uniquely suited to measuring the evolving micro-mechanical state and microstructure of polycrystalline materials during in situ processing. The near-field and far-field configurations provide complementary information; orientation maps computed from the near-field measurements provide grain morphologies, while the high angular resolution of the far-field measurements provides intergranular strain tensors. The ability to measure these data during deformation in situ makes HEDM an ideal tool for validating micro-mechanical deformation models that make their predictions at the scale of individual grains. Crystal Plasticity Finite Element Models (CPFEM) are one such class of micro-mechanical models. While there have been extensive studies validating homogenized CPFEM response at a macroscopic level, a lack of detailed data measured at the level of the microstructure has hindered more stringent model validation efforts. We utilize an HEDM dataset from an alpha-titanium alloy (Ti-7Al), collected at the Advanced Photon Source, Argonne National Laboratory, under in situ tensile deformation. The initial microstructure of the central slab of the gage section, measured via near-field HEDM, is used to inform a CPFEM model. The predicted intergranular stresses for 39 internal grains are then directly compared to data from 4 far-field measurements taken between ~4 and ~80 pct of the macroscopic yield strength. The evolution of the elastic strain state from the CPFEM model and far-field HEDM measurements up to incipient yield are shown to be in good agreement, while residual stress at the individual grain level is found to influence the intergranular stress state even upon loading. Implications for application of such an integrated computational/experimental approach to phenomena such as fatigue are discussed.

Combined application of a near-field High Energy Diffraction Microscopy measurement of crystal lattice orientation fields and a tomographic measurement of pore distributions in a sintered nickel-based superalloy sample allows pore locations to be correlated with microstructural features. Measurements were carried out at the Advanced Photon Source beamline 1-ID using an X-ray energy of 65 keV for each of the measurement modes. The nickel superalloy sample was prepared in such a way as to generate significant thermally induced porosity. A three-dimensionally resolved orientation map is directly overlaid with the tomographically determined pore map through a careful registration procedure. The data are shown to reliably reproduce the expected correlations between specific microstructural features (triple lines and quadruple nodes) and pore positions. With the statistics afforded by the 3D data set, we conclude that within statistical limits, pore formation does not depend on the relative orientations of the grains. The experimental procedures and analysis tools illustrated are being applied to a variety of materials problems in which local heterogeneities can affect materials properties.

In austenite, the twin boundary normal is a common elastically stiff direction shared by the two twins, which may induce special interactions. By means of three-dimensional X-ray diffraction this elastic interaction has been analysed and compared to grains separated by conventional grain boundaries. However, the components of the Type II stress normal to the twin boundary plane exhibit the same large variations as for the grain boundaries. Elastic grain interactions are therefore complex and must involve the entire set of neighbouring grains. The elastic-regime stress along the tensile direction qualitatively depends on the grain orientation, but grain-to-grain variations are large.

The angular precision of crystal orientation determination by cross-correlating dynamically simulated electron diffraction patterns with experimental patterns via spherical harmonic analysis is investigated. The best precision found in this study is 0.016°, which approaches the level reported in the literature for other high-precision electron backscatter diffraction implementations. At this angular precision, the noise floor for geometrically necessary dislocation density calculations is found to be approximately 5×1013 m−2 at a 200 nm step size. Conventional Hough-transform indexing of the same raw patterns gave an angular precision of 0.156° and a dislocation noise floor of 6×1014 m−2, an order of magnitude larger for both parameters, albeit better than is typical for Hough indexing due to the high-quality patterns used. Experimental trade-off curves of precision versus exposure time, pattern resolution (i.e. camera binning), and analysis bandwidth are also presented, allowing for optimization of data collection and analysis rates once the desired level of precision has been determined.

A suite of finite element simulations was executed to find optimal values for high-temperature single crystal elastic moduli of low solvus high refractory (LSHR) nickel super alloy from high energy x-ray diffraction microscopy (HEDM) measurements. In the experiment, a polycrystalline specimen was scanned in an unloaded state to determine a three-dimensional spatial map of lattice orientations in the gauge volume. The specimen was then heated and loaded while performing in situ X-ray measurements to determine grain-averaged elastic strain tensors at several macroscopic loads. The finite element simulations, utilizing three meshes of increasing resolution, mimicked the experimental loading. Initial simulations were conducted to find a box containing the optimal moduli, from which a finer grid of trial moduli was created. A suite of simulations was then executed using these meshes and moduli. For each simulation, an error was determined by comparing the simulated strain field to the measured one, with the resulting data set providing rich information about this fitting process. Anisotropy of the optimal moduli was studied relative to the level of mesh refinement, and a tendency for the anisotropy to decrease as the mesh refinement increases was found. Optimal values of anisotropic moduli and isotropic moduli were determined using the presented optimization methodology; the anisotropic moduli gave appreciably better results. Furthermore, we examined the sensitivity of the error to changes in the moduli; the takeaway was that size of the modulus had a primary effect on the sensitivity, with larger moduli being harder to fit.

An evolving suite of X-ray characterization methods are presently available to the materials community, providing a great opportunity to gain new insight into material behavior and provide critical validation data for materials models. Two critical and related issues are sample repositioning during an in situ experiment and registration of multiple data sets after the experiment. To address these issues, a method is described which utilizes a focused ion-beam scanning electron microscope equipped with a micromanipulator to apply gold fiducial markers to samples for X-ray measurements. The method is demonstrated with a synchrotron X-ray experiment involving in situ loading of a titanium alloy tensile specimen.

An important advance in understanding the mechanics of solids over the last 50 years has been development of a suite of models that describe the performance of engineering materials while accounting for internal fluctuations and anisotropies (ex., anisotropic response of grains) over a hierarchy of length scales. Only limited engineering adoption of these tools has occurred, however, because of the lack of measured material responses at the length scales where the models are cast. Here, we demonstrate an integrated experimental capability utilizing high energy X-rays that provides an in situ , micrometer-scale probe for tracking evolving microstructure and intergranular stresses during quasi-static mechanical testing. We present first-of-a-kind results that show an unexpected evolution of the intergranular stresses in a titanium alloy undergoing creep deformation. We also discuss the expectation of new discoveries regarding the underlying mechanisms of strength and damage resistance afforded by this rapidly developing X-ray microscopy technique.

Focused ion beam (FIB) based serial sectioning was utilized to characterize the morphology of two high angle grain boundaries (HAGB) in a nickel based superalloy, one that experienced grain boundary sliding (GBS) and the other experienced strain accumulation, during elevated temperature constant stress loading conditions. A custom script was utilized to serial section and collect ion-induced secondary electron images from the FIB-SEM system. The MATLAB based MIPAR TM software was utilized to align, segment and reconstruct 3D volumes from the sectioned images. Analysis of the 3D data indicates that the HAGB that exhibited GBS had microscale curvature that was planar in nature, and local serrations on the order of ±150 nm. In contrast, the HAGB that exhibited strain accumulation was not planar and had local serrations an order of magnitude greater than the other grain boundary. It is hypothesized that the serrations and the local grain boundary network are key factors in determining which grain boundaries experience GBS during creep deformation.

Resonant ultrasound spectroscopy (RUS) is a nondestructive evaluation (NDE) method that uses measured resonance frequencies of a solid to estimate its complete set of elastic moduli. One of the advantages of the RUS method is its applicability to small single crystals. The goal of this project is to measure elastic properties of micrometer sized pillars (micro-pillars) of single crystals and to quantify the level of uncertainties in the measurement. To achieve this goal of resonance frequencies measurements for a micrometer sized specimen, a non-contact detecting technique was needed. A new LASER-based non-contact detecting technique was developed and demonstrated using millimeter sized samples. The measured resonances and the estimated elastic moduli obtained with the LASER-based system are comparable to the results obtained in the traditional contact RUS measurements. In order to determine the level of uncertainties in the estimated elastic moduli using the RUS-based technique, a framework of error propagation for RUS measurement technique was developed and applied to four specimens with different complexities in crystal structures and orientations. The results show that the level of uncertainty increases with increase in material complexities.Resonant ultrasound spectroscopy (RUS) is a nondestructive evaluation (NDE) method that uses measured resonance frequencies of a solid to estimate its complete set of elastic moduli. One of the advantages of the RUS method is its applicability to small single crystals. The goal of this project is to measure elastic properties of micrometer sized pillars (micro-pillars) of single crystals and to quantify the level of uncertainties in the measurement. To achieve this goal of resonance frequencies measurements for a micrometer sized specimen, a non-contact detecting technique was needed. A new LASER-based non-contact detecting technique was developed and demonstrated using millimeter sized samples. The measured resonances and the estimated elastic moduli obtained with the LASER-based system are comparable to the results obtained in the traditional contact RUS measurements. In order to determine the level of uncertainties in the estimated elastic moduli using the RUS-based technique, a framework of error prop...

The plastic deformation of crystalline materials is usually modeled as smoothly progressing in space and time, yet modern studies show intermittency in the deformation dynamics of single-crystals arising from avalanche behavior of dislocation ensembles under uniform applied loads. However, once the prism of the microstructure in polycrystalline materials disperses and redistributes the load on a grain-by-grain basis, additional length and time scales are involved. Thus, the question is open as to how deformation intermittency manifests for the nonuniform grain-scale internal driving forces interacting with the finer-scale dislocation ensemble behavior. In this work we track the evolution of elastic strain within individual grains of a creep-loaded titanium alloy, revealing widely varying internal strains that fluctuate over time. The findings provide direct evidence of how flow intermittency proceeds for an aggregate of $\ensuremath{\sim}700$ grains while showing the influences of multiscale ensemble interactions and opening new avenues for advancing plasticity modeling.

Residual stress in an engineering component induced from processing is pervasive and can impact the component’s performance significantly. There are numerous destructive and non-destructive techniques that are available to determine the residual stresses in a component. In this work, an interference fit sample was manufactured from a titanium alloy. The sample was equipped with a set of strain gauges to measure the strains induced by the interference process used for sample assembly. Energy dispersive diffraction experiment using synchrotron radiation was conducted to measure the lattice strains in the interference fit sample. Hole drilling measurements were also conducted on the sample. The non-destructive X-ray result is compared with strain gauge measurements, and found to be in good agreement when appropriately averaged.

During cyclic loading, localization of intragranular deformation due to crystallographic slip acts as a precursor for crack initiation, often at coherent twin boundaries. A suite of high-resolution synchrotron X-ray characterizations, coupled with a crystal plasticity simulation, was conducted on a polycrystalline nickel-based superalloy microstructure near a parent-twin boundary in order to understand the deformation localization behavior of this critical, 3D microstructural configuration. Dark-field X-ray microscopy was spatially linked to high energy X-ray diffraction microscopy and X-ray diffraction contrast tomography in order to quantify, with cutting-edge resolution, an intragranular misorientation and high elastic strain gradients near a twin boundary. These observations quantify the extreme sub-grain scale stress gradients present in polycrystalline microstructures, which often lead to fatigue failure., Structural alloys have distinct microstructural features known as twins that are preferential sites for fatigue crack initiation and need to be better understood to mitigate catastrophic failures. Here, the authors show unusually large stress gradients near a twin boundary, using X-ray techniques and modelling.

A micro-tensile test system equipped with in situ monitoring of the in-plane displacements of a surface and an electron backscattered diffraction-based serial-sectioning technique were used to study the deformation (up to 2.4 pct axial plastic strain in tension) of a polycrystalline nickel micro-specimen. The experimental data include the global engineering stress-engineering strain curve, the local mesoscopic in-plane displacement and strain fields, the three-dimensional microstructure of the micro-specimen reconstructed after the tensile test, and the kernel-average misorientation distribution. The crystal plasticity finite element method using elasto-viscoplastic constitutive formulations was used to simulate the global and local deformation responses of the micro-specimen. Three different boundary conditions (BCs) were applied in simulation in order to study the effects of the lateral displacement (perpendicular to the loading direction) of the top and bottom faces of the specimen gage section. The simulation results were compared to the experimental results. The comparison between experiment and simulation results is discussed, based upon their implications for understanding the deformation of micro-specimens and the causes associated with uncertainties embedded in both experimental and numerical approaches. Also, the sensitivity of BCs to near-field and far-field responses of the micro-specimen was systematically studied. Results show that the experimental methodology used in the present study allows for limited but meaningful comparisons to crystal plasticity finite element simulations of the micro-specimen under the small plastic deformation.

Summary The prior β grain structure and orientations in the central stir zone of friction stir–processed Ti–6Al–4V were reconstructed from measured α phase orientations obtained by three-dimensional serial sectioning in a dual-beam focused ion beam scanning electron microscope. The data were processed to obtain the α colony and β grain size distributions in the volume. Several β grains were individually analysed to determine the total number of unique α variants and the respective volume fractions of each. The analysis revealed that some grains experienced overwhelming variant selection (i.e. one variant dominated) whereas other β grains contained a more evenly distributed mixture of all 12 variants.

The advancement and transition of computational materials models requires corresponding developments in experimental methods to provide new phenomenological insights as well as quantification of model performance. In this article, we explore the natural links between crystal plasticity modeling and a suite of high-energy X-ray diffraction experimental techniques referred to as high-energy diffraction microscopy (HEDM). HEDM methods provide information such as the elastic strain state of individual grains and the distribution of crystallographic orientations. As a non-destructive characterization method, pairing HEDM with in situ mechanical testing enables tracking of material state evolution through quantitative measurements that may be directly compared to a simulation. We highlight some recent successes in this area and provide suggestions for future research.

Under high cycle and very high cycle fatigue (HCF and VHCF) conditions, scatter in fatigue lifetimes is substantial; often 2–3 orders of magnitude. Characterization of fatigue crack initiation sites in laboratory scale fatigue specimens has led to the identification of characteristic initiation sites and microstructural arrangements. Despite these observations, in some cases, it is still unclear how apparently similar initiation sites exhibit such different total fatigue lifetimes. Differences in crack-initiation mechanisms can be further revealed if specific microstructural arrangements are isolated within a micro-specimen. Towards this end, an in situ microscale tension testing technique was adapted to enable microscale fatigue testing on tensile dog-bone specimens. Microscale tensile fatigue specimens with approximate gage diameters of 20 μm were prepared with a focused ion beam (FIB) microscope. Initial tensile experiments were conducted to characterize the mechanical behavior of microscale specimens for this microstructure. The microscale tensile specimens were observed to exhibit reduced yield and flow stresses in comparison to bulk tensile specimens. However, in this feasibility demonstration of in situ microscale fatigue testing, microscale specimens exhibit enhanced fatigue properties relative to conventional specimens, which may result from the differences in strain rate and, potentially, the method of test control (load vs. displacement) between these two testing methods. Both tensile and fatigue specimens have been characterized with electron backscatter diffraction to identify the neighborhood and the specific slip systems that were activated under local deformation conditions within the microstructure. Both basal and prism slip were observed, although prism slip was more prevalent. Results of the tension and fatigue experiments are discussed in the context of the growing body of literature on microscale testing, and avenues for future work are highlighted.

This article describes a new approach to characterize the deformation response of polycrystalline metals using a combination of novel micro-scale experimental methodologies. An in-situ scanning electron microscope (SEM)-based tension testing system was used to deform micro-scale polycrystalline samples to modest and moderate plastic strains. These tests included measurement of the local displacement field with nm-scale resolution at the sample surface. After testing, focused ion beam serial sectioning experiments that incorporated electron backscatter diffraction mapping were performed to characterize both the internal 3D grain structure and local lattice rotations that developed within the deformed micro-scale test samples. This combination of experiments enables the local surface displacements and internal lattice rotations to be directly correlated with the underlying 3D polycrystalline microstructure, and such information can be used to validate and guide further development of modeling and simulation methods that predict the local plastic deformation response of polycrystalline ensembles.

In this paper, we introduce an apparatus to perform microtensile tests at elevated temperatures inside a scanning electron microscope. The apparatus has a stroke of 250 μm with a displacement resolution of 10 nm and a load resolution of 9.7 μN. Measurements at elevated temperatures are performed through use of two silicon-based micromachined heaters that support the sample. Each heater consists of a tungsten heating element that also serves as a temperature gauge. To demonstrate the testing capabilities, tensile tests were performed on submicron Cu films at various temperatures up to 430 °C. Stress–strain curves show a significant decrease in yield strength and initial slope for the samples tested at elevated temperature, which we attribute to diffusion-facilitated grain boundary sliding and dislocation climb.

Resonant ultrasound spectroscopy (RUS) measures the mechanical resonance of solids and uses the resonance frequencies to extract a complete set of elastic constants of the solid material. One of the advantages of the RUS method is its applicability to small single crystals. In the past two decades, the RUS technique has gained more acceptance as a nondestructive method to measure elastic properties. The inherent assumptions in the conventional RUS algorithm include free boundary condition on the specimen faces and the faces of the specimens are normal/parallel to the principal crystallographic axes. This assumption is fulfilled through a time consuming procedure that typically involves multiple iterations of sample cutting and inspection using an x-ray Laue method. Such an intensive method is not suitable for many samples in engineering applications. To estimate the elastic constants of such samples, a modified RUS algorithm has been developed to incorporate the sample crystallographic orientation express...

We report experimental and three-dimensional discrete dislocation dynamics measurements to characterize the effect of high starting dislocation density on size-affected flow. Microcrystals were focused ion beam milled into a pre-strained bulk Ni single crystal to obtain a dense heterogeneous dislocation cell structure. The strength-scaling exponent is shown to decreases considerably with increasing dislocation density. Cutting the pre-existing forest during microcrystal fabrication can lead to alternate pathways for the advancing slipped areas to defeat the forest, resulting in a lower strength than the pre-strained bulk crystal.

Ni3Al alloys exhibit remarkable deformation characteristics at small scales that are tied to their unique dislocation core structures. The present work examines microcrystal strengthening and flow for a binary Ni3Al alloy and two alloys containing −0.25% Hf and −1.0% Ta, and evaluates their response relative to known dislocation mechanisms for this material and sample size effects in other materials. The work includes analysis of the flow-stress anomaly mechanisms, dislocation velocity, the single-arm source model, exhaustion strengthening and dislocation multiplication for describing the response of Ni3Al alloy microcrystals. Primary remaining needs are to understand the nature of double cross slip and dislocation sources that trigger the onset of flow and limit size-dependent strengthening.

Summary A method for automatically aligning consecutive data sets of large, two-dimensional multi-tile electron backscatter diffraction (EBSD) scans with high accuracy was developed. The method involved first locating grain and phase boundaries within search regions containing overlapping data in adjacent scan tiles, and subsequently using cross-correlation algorithms to determine the relative position of the individual scan tiles which maximizes the fraction of overlapping boundaries. Savitzky-Golay filtering in two dimensions was used to estimate the background, which was then subtracted from the cross-correlation to enhance the peak signal in samples with a high density of interfaces. The technique was demonstrated on data sets with a range of interface densities. The equations were implemented as enhancements to a recently published open source code for stitching of multi-tile EBSD data sets.