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Combined near- and far-field high-energy diffraction microscopy dataset for Ti-7Al tensile specimen elastically loaded in situ
High-energy diffraction microscopy (HEDM) constitutes a suite of combined X-ray characterization methods, which hold the unique advantage of illuminating the microstructure and micromechanical state of a material during concurrent in situ mechanical deformation. The data generated from HEDM experiments provides a heretofore unrealized opportunity to validate meso-scale modeling techniques, such as crystal plasticity finite element modeling (CPFEM), by explicitly testing the accuracy of these models at the length scales where the models predict their response. Combining HEDM methods with in situ loading under known and controlled boundary conditions represents a significant challenge, inspiring the recent development of a new high-precision rotation and axial motion system for simultaneously rotating and axially loading a sample. In this paper, we describe the initial HEDM dataset collected using this hardware on an alpha-titanium alloy (Ti-7Al) under in situ tensile deformation at the Advanced Photon Source, Argonne National Laboratory. We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.
Minimizing Experimental Setup Time and Effort at APS beamline 1-ID through Instrumentation Design
Sector 1-ID at the APS accommodates a number of dif-ferent experimental techniques in the same spatial enve-lope of the E-hutch end station. These include high-energy small and wide angle X-ray scattering (SAXS and WAXS), high-energy diffraction microscopy (HEDM, both near and far field modes) and high-energy X-ray tomography. These techniques are frequently combined to allow the users to obtain multimodal data, often attaining 1 μm spatial resolution and <0.05º angular resolution. Furthermore, these techniques are utilized while the sam-ple is thermo-mechanically loaded to mimic real operat-ing conditions. The instrumentation required for each of these techniques and environments has been designed and configured in a modular way with a focus on stability and repeatability between changeovers. This approach allows the end station to be more versatile, capable of collecting multi-modal data in-situ while reducing time and effort typically required for set up and alignment, resulting in more efficient beam time use. Key instrumentation de-sign features and layout of the end station are presented.
Crystal Plasticity Model Validation Using Combined High-Energy Diffraction Microscopy Data for a Ti-7Al Specimen
High-Energy Diffraction Microscopy (HEDM) is a 3-d x-ray characterization method that is uniquely suited to measuring the evolving micromechanical 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 provide 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. Here, we utilize an HEDM dataset from an alphatitanium 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% of the macroscopic yield strength. In conclusion, the intergranular stresses from the CPFEM model and far-field HEDM measurements up to incipient yield are shown to be in good agreement, and implications for application of such an integrated computational/experimental approach to phenomena such as fatigue and crack propagation is discussed.
High-energy diffraction microscopy at the advanced photon source
The status of the High Energy Diffraction Microscopy (HEDM) program at the 1-ID beam line of the Advanced Photon Source is reported. HEDM applies high energy synchrotron radiation for the grain and sub-grain scale structural and mechanical characterization of polycrystalline bulk materials in situ during thermomechanical loading. Case studies demonstrate the mapping of grain boundary topology, the evaluation of stress tensors of individual grains during tensile deformation and comparison to a finite element modeling simulation, and the characterization of evolving dislocation structure. Complementary information is obtained by post mortem electron microscopy on the same sample volume previously investigated by HEDM.
BraggNN : fast X-ray Bragg peak analysis using deep learning
X-ray diffraction based microscopy techniques such as high-energy diffraction microscopy (HEDM) rely on knowledge of the position of diffraction peaks with high precision. These positions are typically computed by fitting the observed intensities in detector data to a theoretical peak shape such as pseudo-Voigt. As experiments become more complex and detector technologies evolve, the computational cost of such peak-shape fitting becomes the biggest hurdle to the rapid analysis required for real-time feedback in experiments. To this end, we propose BraggNN, a deep-learning based method that can determine peak positions much more rapidly than conventional pseudo-Voigt peak fitting. When applied to a test dataset, peak center-of-mass positions obtained from BraggNN deviate less than 0.29 and 0.57 pixels for 75 and 95% of the peaks, respectively, from positions obtained using conventional pseudo-Voigt fitting (Euclidean distance). When applied to a real experimental dataset and using grain positions from near-field HEDM reconstruction as ground-truth, grain positions using BraggNN result in 15% smaller errors compared with those calculated using pseudo-Voigt. Recent advances in deep-learning method implementations and special-purpose model inference accelerators allow BraggNN to deliver enormous performance improvements relative to the conventional method, running, for example, more than 200 times faster on a consumer-class GPU card with out-of-the-box software.
3D Reconstruction of a High-Energy Diffraction Microscopy Sample Using Multi-modal Serial Sectioning with High-Precision EBSD and Surface Profilometry
High-energy diffraction microscopy (HEDM) combined with in situ mechanical testing is a powerful nondestructive technique for tracking the evolving microstructure within polycrystalline materials during deformation. This technique relies on a sophisticated analysis of X-ray diffraction patterns to produce a three-dimensional reconstruction of grains and other microstructural features within the interrogated volume. However, it is known that HEDM can fail to identify certain microstructural features, particularly smaller grains or twinned regions. Characterization of the identical sample volume using high-resolution surface-specific techniques, particularly electron backscatter diffraction (EBSD), can not only provide additional microstructure information about the interrogated volume but also highlight opportunities for improvement of the HEDM reconstruction algorithms. In this study, a sample fabricated from undeformed “low solvus, high refractory” nickel-based superalloy was scanned using HEDM. The volume interrogated by HEDM was then carefully characterized using a combination of surface-specific techniques, including epi-illumination optical microscopy, zero-tilt secondary and backscattered electron imaging, scanning white light interferometry, and high-precision EBSD. Custom data fusion protocols were developed to integrate and align the microstructure maps captured by these surface-specific techniques and HEDM. The raw and processed data from HEDM and serial sectioning have been made available via the Materials Data Facility (MDF) at https://doi.org/10.18126/4y0p-v604 for further investigation.
Direct numerical simulation of deformation twinning in polycrystals
Abstract not provided
High-Energy X-Ray Diffraction Microscopy in Materials Science
High-energy diffraction microscopy (HEDM) is an implementation of three-dimensional X-ray diffraction microscopy. HEDM yields maps of internal crystal orientation fields, strain states, grain shapes and locations as well as intragranular orientation distributions, and grain boundary character. Because it is nondestructive in hard materials, notably metals and ceramics, HEDM has been used to study responses of these materials to external fields including high temperature and mechanical loading. Currently available sources and detectors lead to a spatial resolution of ~1 μm and an orientation resolution of <0.1°. With the penetration characteristic of high energies ( E ≥ 50 keV), sample cross-section dimensions of ~1 mm can be studied in materials containing elements across much of the Periodic Table. This review describes hardware and software associated with HEDM as well as examples of applications. Overall, these applications include studies of grain growth, recrystallization, texture development, orientation gradients, deformation twinning, annealing twinning, plastic deformation, and additive manufacturing. We also describe relationships to other X-ray-based methods as well as prospects for further development.
In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading
The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σ θZ ) and axial (σ ZZ ) stress tensor components, stress and stress deviator tensor invariants (I 1 , J 2 , and J 3 ), von Mises equivalent stress (σ$^{grain}_{VM}$), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter ($\barθ$) values were tracked for ~300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σ θZ , σ$^{grain}_{VM}$, and J 2 ; by comparison, I 1 , J 3 , η, and $\barθ$ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I 1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.
Evaluating the grain-scale deformation behavior of a single-phase FCC high entropy alloy using synchrotron high energy diffraction microscopy
We report although the deformation behavior of high-entropy alloys (HEAs) has been extensively studied at the macroscale, many important properties have yet to be explored for these alloys at the microscale, thus hampering accurate prediction of damage and failure processes. Synchrotron high-energy diffraction microscopy (HEDM) and fast-Fourier transform-based crystal plasticity modeling was conducted to investigate the three-dimensional (3D) grain-resolved micromechanical response for approximately 1,900 constituent grains within a single-phase FCC HEA up to 1% applied strain. The evolution of grain-resolved elastic strains, lattice reorientations, and maximum resolved shear stresses (mRSS) were evaluated to quantify elastic, yield, and fully plastic behavior. Overall, the initial critical resolved shear stress (CRSS), determined via in situ HEDM and companion modeling, was found to be > 20% higher than estimated using the classical polycrystalline Taylor factor (M = 3.06). However, a descriptive parameter based on the average grain-resolved Taylor factor ($\overline{M}$) was found to show excellent agreement with plastic yielding behavior observed within HEDM datasets. Noticeable deviations in HEDM lattice reorientations compared to both EVP-FFT simulations and classical predictions for FCC polycrystals were discovered, highlighting the complexity in correlating local lattice reorientations, Taylor, and Schmid factors with plastic response for this material at the grain-scale. Therefore, it is anticipated that the overall trends and parameter identification of 3D grain-resolved properties in this study can serve as an important foundation for continued mesoscale investigation on both well-established and newly developed Cantor-like HEAs.
Processing and consolidation of copper/tungsten
Here, we developed a copper/tungsten (Cu/W) composite for mesoscale Materials Science applications using the novel High-Energy Diffraction Microscopy (HEDM) technique. Argon-atomized copper powder was selected as the starting raw powder and screened to remove the extremely large particle fraction. Tungsten particles were collected by milling and screening the -325 mesh tungsten powder between 500 and 635 mesh sieves. Hot pressing of screened Cu powder was performed at 900 °C in Ar/4 %H 2 atmosphere. XRD and ICP results show that the hot-pressed Cu sample consists of about 5 vol% Cu 2 O, which is caused by the presence of oxygen on the surface of the starting Cu powder. Hot pressing the copper powder in a pure hydrogen atmosphere was successful in removing most of the surface oxygen. Our process was also implemented for hot pressing the Cu/W composite. The density of the Cu/W composites hot pressed at 950 °C in pure hydrogen was about 94 % of the theoretical density (TD). The hot-pressed Cu/W composites were further hot isostatic pressed at 1050 °C in argon atmosphere, which results in 99.6 % of the TD with the designed Cu grain size and W particle distribution. Tensile specimens with D-notch were machined using the wire EDM method. Furthermore, the processing and consolidation of these materials will be discussed in detail. The HEDM images are also showed and discussed.
Validation of micro-mechanical FFT-based simulations using High Energy Diffraction Microscopy on Ti-7Al
Abstract not provided
Four-dimensional microstructurally small fatigue crack growth in cyclically loaded nickel superalloy specimen
Here, we nondestructively image a low-solvus high refractory (LSHR) nickel base specimen microstructure during cyclic loading to characterize crack propagation during the microstructurally small crack (MSC) growth regime. Micro-computed tomography (uCT) is used to characterize the material density and identify crack interfaces, while high-energy diffraction microscopy (HEDM) provides snapshots of the microstructural orientation field changes. From these measurements, data are computationally reconstructed and coregistered to describe the specimen’s configuration before load, before crack nucleation, and throughout the crack propagation/loading process. An MSC forms at a FIB-cut notch, which was previously placed to concentrate stress at the center of the specimen gauge, and propagates along a facet parallel to the local {1 1 1} crystallographic plane. Analysis of available crystallographic slip directions and measured point-to-point disorientation axes indicate probable single and coplanar slip activity along FCC octahedral planes within this region. Similar analyses of other crack propagation facets reveal generally slower growth along directions favoring zig-zag cross and codirectional cross slip, which are often disfavored at room temperature.
Experimental determination of critical resolved shear stress for strain-induced phase transformation
The current investigation reports the first attempt to measure the critical resolved shear stress to initiates strain-induced phase transformation in a three-dimensional polycrystalline aggregate using high-energy diffraction microscopy (HEDM). In situ tensile testing was performed on a Fe38.5Mn20Co20Cr15Si5Cu1.5 metastable alloy exhibiting transformation-induced plasticity (TRIP). Grains with a higher propensity for strain-induced phase transformation were tracked using HEDM. A sharp drop in grain specific stress, coinciding with the appearance of a new ε-hcp grain oriented relative to the parent γ-fcc phase, was taken as evidence of grain-specific stress required to trigger phase transformation. The highest resolved shear stress on the potential transformation systems was identified as the critical resolved shear stress (CRSS) for strain-induced phase transformation. For the studied metastable alloy, CRSS for transformation was determined to be 86±3 MPa which was very close to theoretical CRSS value determined using Schmid factor (89±12 MPa) compared to the value determined using Taylor factor (62±7 MPa).
3D In-situ Stop Action Study of Recrystallization in Additively Manufactured 316L Stainless Steel: Reconstruction Optimization and Observations
A volume of an additively manufactured 316L stainless steel sample has been tracked during its recrystallization using near-and far-field High Energy Diffraction Microscopy (HEDM) and absorption tomography at Advanced Photon Source beamline 1-ID. A nearfield compatible in situ furnace allows monitoring of Bragg diffraction signals as they evolve out of a weak and diffuse background while the sample temperature is approximate to 1250 degrees C. The sample is rapidly cooled to room temperature after observation of significant signal evolution and ti similar to 0.035 mm(3) is mapped by the near-field method. Four cycles of heat treatment follow the structure from a state of small, isolated grains through impingement of domains to near completion of recyrstallization. Here, the experiment and reconstructions are described, and recrystallized fractions, twin domains, and distributions of grain boundary types are discussed.
Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals
As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.
Overview of High-Energy X-Ray Diffraction Microscopy (HEDM) for Mesoscale Material Characterization in Three-Dimensions
Abstract not provided