A dataset of synthetic face centered cubic 3D polycrystalline microstructures, grain-wise microstructural descriptors and grain averaged stress fields under uniaxial tensile deformation

This data article presents a data set comprised of 36 synthetic 3D equiaxed polycrystalline microstructures, the microstructural descriptors for each grain, and the stress and strain fields resulting from crystal plasticity simulations mimicking uniaxial tensile deformation to a total strain of 4%. This is related to the research article entitled “Applied Machine Learning to predict stress hotspots I: Face Centered Cubic Materials” (Mangal and Holm, 2018) [1]. The microstructures were created using an open source Dream.3D software tool, and the crystal plasticity simulations were carried out using the elasto-viscoplastic fast Fourier transform (EVPFFT) method. Six different kinds of FCC textures are represented with six stochastically different microstructures with varying texture intensity for each texture kind. This dataset is freely available in a Mendeley Data archive “A dataset of synthetic face centered cubic 3D polycrystalline microstructures, grain-wise microstructural descriptors and grain averaged stress fields under uniaxial tensile deformation” located at 〈http://dx.doi.org/10.17632/ss75fdg5dg.1〉 for any academic, educational, or research purposes.


a b s t r a c t
This data article presents a data set comprised of 36 synthetic 3D equiaxed polycrystalline microstructures, the microstructural descriptors for each grain, and the stress and strain fields resulting from crystal plasticity simulations mimicking uniaxial tensile deformation to a total strain of 4%. This is related to the research article entitled "Applied Machine Learning to predict stress hotspots I: Face Centered Cubic Materials" (Mangal and Holm, 2018) [1]. The microstructures were created using an open source Dream.3D software tool, and the crystal plasticity simulations were carried out using the elasto-viscoplastic fast Fourier transform (EVPFFT) method. Six different kinds of FCC textures are represented with six stochastically different microstructures with varying texture intensity for each texture kind. This dataset is freely available in a Mendeley Data archive "A dataset of synthetic face centered cubic 3D polycrystalline microstructures, grain-wise microstructural descriptors and grain averaged stress fields under uniaxial tensile deformation" located at 〈http://dx.doi.org/ 10

Value of the data
This simulated dataset provides a statistically significant number of microstructures and stress fields along with grain-wise microstructural descriptors to analyze microstructure-property relationships in the context of material failure.
The dataset can be used to develop and benchmark data driven analysis techniques for applications such as identifying grain size distribution from images and machine learning for understanding crystal plasticity behavior of FCC materials.
The dataset can be used to pre-train machine learning models for transfer learning on experimentally obtained high energy electron diffraction (HEDM) measurements.
The data may be compared with the tensile behavior of other face centered cubic materials.

Data
This data set consists of 36 synthetic 3D equiaxed polycrystalline microstructures with different cubic textures, associated microstructural descriptors, and the corresponding results from applying a uniaxial tensile stress through EVPFFT simulations.

Synthetic microstructure generation pipeline
A dataset of synthetic microstructure images is built to be used as input to a parallelized elastoviscoplastic Fast Fourier Transform (EVPFFT) crystal plasticity formulation [2]. Dream.3D (Digital Representation Environment for Analyzing Microstructure) is an open source software package [4,5] used to create synthetic three-dimensional polycrystalline microstructures. Dream.3D uses objects (ellipsoids, octahedrons, cylinders) to represent grains. These shapes are evolved to fill a predefined cubic volume to match the statistics specified above. The microstructure is discretized on a 128 Â 128 Â 128 grid. The first step in the pipeline is to define microstructural statistics such as grain size distribution and texture (Euler angle distribution). This is done using the Stats Generator filter inside Dream.3D. The following statistics can be generated in this program: Phase Types: primary, precipitate, matrix, transformation. Relative volume fraction of phases. Crystal structure of each phase. Grain size distribution (parameters of the lognormal distribution). Grain shape: aspect ratios of grains defining them as equiaxed or rolled. Neighbor distributions: parameters of the lognormal distribution. Texture: The crystallographic orientation in the form of orientation distribution function (ODF) or misorientation distribution function (MDF). Table 1 shows the DREAM.3D parameters used to generate the microstructures included in this data set, and the DREAM.3D workflow used is shown in Fig. 1. The representative Euler angles used to generate the texture distribution in the Stats Generator filter for the 6 microstructures are listed in Table 2. The texture intensity was varied to get 6 different instantiations within each representative texture. An example microstructure, showing the equiaxed grain geometry typical of all the samples, is shown in Fig. 3, and the six crystallographic textures are represented as pole figures in Fig. 4. Overall, 36 3D microstructures are included in the data set: Six each of the six textures.

Micromechanical modeling
We use an elasto-viscoplastic model based on fast Fourier transforms (EVPFFT) [2,6,7] to calculate the local stress and strain fields that develop in these synthetic microstructures when they are subjected to a uniaxial tensile deformation. A 4% strain was chosen so that materials would transition  from elastic to plastic deformation. The constitutive model parameters for FCC materials represent oxygen free high thermal conductivity (OFHC) copper with single crystal elastic constants given in Table 3. FCC materials deform plastically by slip on twelve {111} o 110 4 slip systems. To obtain the actual values of the critically resolved shear stress (CRSS) and the Voce hardening parameters, the Voce model was fit to an experimentally measured stress-strain curve for uniaxial tension in OFHC copper [8] using the viscoplastic single crystal (VPSC) formulation similar to [9]. The results of the fitting are shown in Fig. 2. The Voce hardening parameters for this case are shown in Table 4. The boundary conditions correspond to uniaxial tension along Z, with an applied strain rate component along the tensile axis ε3 3 ¼ 1 s À 1 . The EVPFFT simulation was carried out in 400 strain steps of 0.01%, up to a strain of 4%. The microstructure and EVPFFT results files are contained in the FCC_voxelwise   A Dream.3D filter "Find Neighbor Slip Transmission Metrics" is used to calculate the geometric compatibility factor "m prime" measuring the ease of slip transmission [11] across the grain boundaries. Schmid Factor A Dream.3D filter "Find Schmid Factors" is used to calculate the Schmid factor from the average orientation of a grain given a loading direction.

Feature type Measured by:
Grain Size measurements Different metrics of grain size such as equivalent spherical diameter, number of voxels in a grain and number of neighbors are calculated using the following Dream.3D filters: "Find Feature Sizes" and "Find Feature Neighbors" Grain shape parameters The grain shapes are measured using their aspect ratios and surface area to volume ratio. These properties are calculated using to the Dream.3D filters "Find Feature Shapes" and "Find Surface Area to Volume" Shape averaged distance from special points The Dream.3D filter "Find Euclidean Distance Map" computes the distance of each voxel from its nearest grain boundary, triple junction and quadruple point. The voxels belonging to each grain are averaged to get a shape averaged distance from the special points (grain boundary, triple junction and quadruple point). Grain fraction on the periodic boundary A Dream.3D filter "Find Feature Boundary Element Fractions" is used to calculate the fraction of voxels in each grain that lie at 3D image boundary Table 7 Dataset file structure.

Data element Description
Directory FCC_voxelwise Contains the EVPFFT plasticity simulation inputs and results, comprised of a voxel-wise representation of microstructure, stress, and strain fields. Files represent 6 kind of textures (X), with 6 stochastic instantiations per texture (Y), with filenames parsed as microX_Y_voxel. folder; Table 7 describes the data contained in these files. The EVPFFT code package can be obtained by contacting the Richard P. Feynman Center for Innovation at Los Alamos National Laboratory [10].

Microstructural descriptors
For enabling machine learning, we constructed a set of crystallography and geometry based microstructural descriptors. Dream.3D filters provide a convenient way to calculate a number of microstructural descriptors. Table 5 describes how the crystallographic descriptors were computed. Table 6 describes how the geometry based descriptors were computed. The processed grain-wise descriptors and grain-wise EVPFFT simulation results are contained in the FCC_grainwise folder; Table 7 describes the data contained in these files. .
['001_IPF_0', '001_IPF_1', '001_IPF_2'] Distance from 3 corners of the 001 inverse pole figure as described in Mangal  Contains the open source jupyter notebook in .HTML format describing the two datasets and how to read them in Python