The development of high-fidelity mechanical property prediction models for the design of polycrystalline materials relies on large volumes of microstructural feature data. Concurrently, at these same scales, the deformation fields that develop during mechanical loading can be highly heterogeneous. Spatially correlated measurements of 3D microstructure and the ensuing deformation fields at the micro-scale would provide highly valuable insight into the relationship between microstructure and macroscopic mechanical response. They would also provide direct validation for numerical simulations that can guide and speed up the design of new materials and microstructures. However, to date, such data have been rare. Here, a one-of-a-kind, multi-modal dataset is presented that combines recent state-of-the-art experimental developments in 3D tomography and high-resolution deformation field measurements.

Material and Mechanical Testing.Wrought Inconel 718 (nominal composition in wt% Ni - 0.56%Al - 17.31%Fe - 0.14%Co - 17.97%Cr - 5.4%Nb - Ta - 1.00%Ti - 0.023%C - 0.0062%N) was subjected to a 30 minute annealing treatment at 1050 °C followed by water quenching, producing a grain size distribution centered at 62 micron with a nearly random texture. A two-step precipitation hardening treatment was conducted to form hardening precipitates. Tensile testing was performed at room temperature at a quasi-static strain rate using a custom in-situ 5000 N stage within a ThermoFisher Versa3D microscope on a flat dogbone-shaped specimen. The tensile test was interrupted at macroscopic plastic strain levels of 0.17%, 0.32%, 0.61%, and 1.26% for the collection of high-resolution images for digital image correlation (HR-DIC) measurements while loaded. 

High-Resolution Digital Image Correlation. A gold nanoparticle speckle pattern with an average particle size of 60 nanometers was deposited on the sample surface for DIC measurements. SEM image sets were acquired from the middle of the gauge length before loading and underload. Tiles of 8×8 SEM images, before and after deformation, with an image overlap of 15% were collected. Each image was acquired with a dwell time of 20 microseconds, a pixel resolution of 4096×4096, and a horizontal field width of 137 microns. Consequently, each pixel has a size of 33.4 nanometers. Regions of about 1×1 mm² were investigated for the Inconel 718 nickel-based superalloy. DIC calculations are performed on these series of images and the results are merged using a pixel resolution merging procedure. A subset size of 31×31 pixels (1036.86×1036.86 nanometers) with a step size of 3 pixels (100.34 nanometers) was used for the DIC measurements. Digital image correlation was performed using the Heaviside-DIC method. 

3D Crystallographic Orientation Measurements. The TriBeam system is used for the collection of orientation fields in 3D over a half cubic millimeter volume. After mechanical testing , the specimen is unloaded and surface EBSD measurements are performed on the surface of the specimen on the same region where the HR-DIC measurements were made. Electrical discharge machining cuts were performed to prepare a pillar with optimal geometry for a Tribeam experiment. The pillar is laser ablated with a step size of 1 micron in Z, the sectioning direction. Between each slice, EBSD measurements are collected with a step size of 1 micron (X,Y) to form cubic voxels. A set of 526 slices was obtained during the experiment and reconstructed into a 3D dataset using the DREAM.3D software. Prior to reconstruction, each EBSD slice was aligned to match the corresponding BSE image.

Correlative measurements: Multi-modal Data Merging.The strain fields obtained from DIC corresponding to the investigated free surface of the 3D dataset are provided for the different loading steps. All fields have been aligned to fit the free surface of the 3D dataset. The distortion between both datasets was modeled using a polynomial function of degree 3. Individual slip traces were segmented from the DIC maps and indexed as individual features, using the iterative Hough transformation method. The location of each slip band in the 3D volume (coordinates of its endpoints on the (XY) surface), its inclination angle relative to the loading direction, its length, and average in-plane slip intensity and direction are all calculated. 

Mesh Generation with XtalMesh. One version of a mesh structure was created with XtalMesh, a publicly available code on GitHub. XtalMesh is used to create smooth representations of voxelized microstructures and leverages the state-of-the-art tetrahedralization algorithm fTetWild to generate an analysis-ready, boundary conforming tetrahedral mesh. The base workflow of XtalMesh was modified to better preserve the many small and thin features (mainly twins) of the Inconel 718 dataset from the effects of excessive smoothing (shrinkage and/or thinning). First, the default smoothing operation of XtalMesh was applied to the parent grain surface mesh geometry rather than of all the features/twins in the 3D dataset. This had the effect of smoothing only the twinned domains that bordered neighboring parent grains, leaving the twin boundaries still partially voxelized. At this point, the twinned regions of each parent grain are re-introduced into the parent grain mesh via constructive solid geometry (CSG) technique. For each twin, in order of smallest to largest based on a number of voxels, the intersection of its convex hull and respective parent grain mesh is computed and inserted into the overall surface mesh of the microstructure. The parent grain mesh is then redefined as the difference between itself and the previously calculated intersection. This new parent grain mesh is then used for the insertion process of the next twin. After the insertion of all twins was complete, tetrahedralization was performed on the resulting surface mesh of the entire microstructure using the fTetWild meshing algorithm. 

Geometric reconstruction and mesh generation using Simmetrix’ software suite. While it is possible to directly generate a mesh from a voxel dataset it is advantageous to introduce a geometric model, specifically a non-manifold boundary representation as an intermediate representation of the analysis domain. Such a model provides an unambiguous representation of the analysis domain and provides a mechanism to associate information such as material properties in a manner that is independent of the mesh. To be able to build a valid and appropriate (based on the needs of the simulation) finite element model from a voxel dataset assembled from a serial sectioning EBSD measurement, various procedures to remove artifacts are required. This includes the elimination of small groups of disconnected voxels, and removing noise from the grain boundaries (e.g., through the use of erosion and dilation filters). For the In718 RVE, features smaller than 50 connected voxels were removed followed by an erosion/dilation step using a 3x3x3 block structuring element. Care was taken not to apply the erosion filter to grains that were very thin (1 to 2 voxels thick) to preserve the geometry of those grains.This process is followed by the elimination of physically undesirable voxel configurations (e.g., voxel clusters of the same material connecting at a single voxel corner) that could create singularities in the finite element solution. The resulting geometric model represents each grain as a region (volume) with geometric faces (surfaces) representing grain boundaries. Attributes attached to each region allow the user to retrieve the grain ID as it was defined in the originating DREAM3D \cite{2014dream3D} dataset. At this stage, the face geometry still reflects the stair-stepped boundaries between the individual voxels, therefore a geometric-based algorithm is used to create smooth geometric faces while preserving the overall shape of the grain boundaries. The resulting geometric model can be tagged with meshing and analysis attributes to generate a run-ready input deck for the finite element solver.

SEM Images. The raw SEM images used for HR-DIC calculations are 16-bit tiff images.

Full-field measurements from HR-DIC. The data is provided as 32-bit tiff images. The images can be viewed using software such as ImageJ. The values at each pixel in the images are the quantitative physical value of the displayed full fields given in unit length for the strain field, in pixels for the in-plane slip amplitude, and in radians for the in-plane slip direction. Adjacent pixels in all maps represent a physical distance of 100.34 nm. The values in the in-plane slip amplitude maps are given in pixels, where one pixel represents a shearing/displacement induced by slip of 33.45 nm.

2D crystallographic Orientation Data. The IPF maps along the loading direction X from the raw EBSD measurements and after cleaning and distortion (to match the DIC full field maps) are provided in a tiff format in a RGB color type and labeled as IPF\textunderscore Raw\textunderscore X.tif and IPF\textunderscore DistordedDIC\textunderscore X.tif respectively. The IPF map along the transverse direction Z is also provided and labeled as IPF\textunderscore Raw\textunderscore Z.tif. The raw crystallographic orientation data (Euler angle and grain structure) are provided in the .osc and .ang format and labeled as Euler\textunderscore Orientation\textunderscore Raw.osc and Euler\textunderscore Orientation\textunderscore Raw.ang. The .osc format can be opened using the TSL software from EDAX. The .ang format is a ASCII text format where the first three columns displayed the Euler angles in radians. Columns 4 and 5 display the coordinate X and Z, respectively, for a given measurement point. Columns 7 and 8 display the image quality (IQ) and confidence index (CI) associated with the collected Kikuchi patterns.

3D dataset - Voxelized structure. The raw Kikuchi patterns obtained from EBSD measurement are provided in the .up2 binary file format for each EBSD slice from the Tribeam tomography measurement, these files can be opened using EMsoft dictionary indexing , EMSphInx spherical pattern reindexing or with the commercial EDAX or Oxford EBSD analysis software. The raw EBSD pattern dataset can be found here. The indexed data from EMsoft dictionary indexing for each slide are also provided in the H5 format. The BSE and SEM images obtained after each slice during Tribeam experiment are provided in 8-bit tiff images. The reconstructed 3D data with distortion correction is provided in .Dream3D file (h5 structure). The Hierarchical Data Format version 5 (h5), is an open source file format that supports large, complex, heterogeneous data. H5 file uses a "file directory" like structure that allows one to organize data within the file in many different structured ways, as one might do with files on a computer. The h5 format also allows for embedding of metadata making it self-describing. The associated .xdmf file provides the container data descriptions. Such files can be open using the open-source software Paraview for visualization.

3D dataset - Meshed structures. The mesh generated with XtalMesh is provided in two file formats, .inp and .vtk. The .inp file, labeled XtalMesh.inp, is used as input into ABAQUS. The .inp file format is standard to ABAQUS and is an ASCII data file that consists of a series of ABAQUS keyword and data lines. In it, all nodes, elements, and element sets of the mesh are defined. The .vtk file labeled XtalMesh.vtk, is a binary Visualization Toolkit (VTK) datafile provided for ease of visualization and analysis of the mesh using ParaView by Kitware. There, the mesh is represented by four-node tetrahedral elements (C3D4) to reduce system load during visualization. The mesh generated with the software suite from Simmetrix (SimModeler Voxel), is provided in an Ansys input deck. The input deck contains the following APDL (Ansys Parametric Design Language) files: run\_Model.mac, contains all the calls to load the mesh, assign material properties, define node components, orient each grain according to the average Euler angles from the EBSD measurement and, just as an example, assign boundary conditions; In718RVE.cdb, contains element connectivity and nodal coordinates of the entire RVE model; assignWPCSYS.mac, creates coordinate systems using Euler angles (each coordinate system ID is linked to the element coordinate system defined for each grain); EulerAngles.txt, contains the averaged Euler angles (available in the dream3D file) for each grain in the reconstructed microstructure; In718RVE\_pd.cdb, assigns element coordinate systems (ESYS command in APDL) to each element cluster that defines a grain and, creates node components on each side of the RVE for an easy assignment of boundary conditions; assignMatProp.mac, assigns 718 material properties to all grains; In718RVE\_ss.cdb, performs the finite element solution.