A dataset for the development, verification, and validation of microstructure-sensitive process models for near-alpha titanium alloys

The datasets supporting the results of this article are available in the NIST repository, https://​doi.​org/​hdl.​handle.​net/​11256/​647 [12]. When using the results of the present work, please cite the dataset and this manuscript as they are mutually dependent on one another for meaning. The principal components of the dataset [12] include results from (i) the characterization of the microstructure of billet material on three orthogonal planes via scanning electron microscopy (SEM) and EBSD; (ii) the plastic flow behavior derived from isothermal hot-compression tests performed on Ti-6242Si at three different temperatures, three different angles to the axis of the initial cylindrical billet, and one strain rate; (iii) the finite-element method (FEM) simulations of the hot-compression tests; (iv) the characterization of the 899 °C compression samples on three orthogonal planes with SEM and EBSD; and (v) the distributions of the MTR sizes on each plane in (iv). The above data is divided into the following subsections based on the type of information, i.e., isothermal hot compression, FEM, microscopy, and segmentation and quantification of microstructure and MTRs.

To develop an orientation- and temperature-dependent flow-stress database, isothermal hot-compression tests were performed on 25.4-mm-diameter × 38.1-mm-height cylinders cut from the mid-radius position of a 209-mm-diameter Ti-6242Si billet; the composition, microstructure, texture, and microtexture of this billet have been reported previously [13]. More specifically, the samples were cut with the compression direction oriented 0° (axial), 45°, or 90° (radial) to the long axis of the billet and, by extension, to the long direction of the initially high-aspect-ratio MTRs in the billet. The samples were compressed isothermally at temperatures of 899 °C, 954 °C, and 982 °C on a servo-hydraulic load frame at a constant true axial strain rate of 0.01 s⁻¹ to an average true height strain of 1.07 (i.e., a 3:1 reduction). After reaching the total reduction, each sample was water quenched (within <1 s) to retain the elevated-temperature microstructure.

The load stroke and resulting average pressure-height strain data from the compression tests were corrected for machine stiffness and die-workpiece interface friction per Altan [14] (assuming a friction shear factor, m _s, of 0.4) to produce true-stress-true-strain curves. The raw and processed data are provided in a Microsoft Excel™ (Microsoft, Redmond, WA) file in which the equations are embedded so that the reader can assess the sensitivity of the friction-correction to the choice of the critical parameter, m _s. The friction-corrected flow curves (Fig. 2a) revealed a strong dependence on temperature. There was also some sensitivity of the flow stress to orientation for test temperatures of 899 °C and 954 °C, at which there is ~75 or ~50 % primary-alpha particles by volume, respectively; at both of these temperatures the axial direction was slightly stronger. At 982 °C, at which the primary-alpha phase constitutes only ~25 % of the material by volume, most deformation is accommodated by the beta phase, which is less plastically anisotropic resulting in essentially no orientation dependence of the flow behavior, at least at the macroscopic, polycrystalline scale. The subtle differences due to orientation at the highest test temperature were within the experimental error, as shown in Fig. 2b. This figure compares data for two isothermal compression tests performed on axial samples at 954 °C. The peak stress differed by less than 2 MPa, a variation which was consistently tracked throughout the entire experiment.

Two-dimensional, axisymmetric FEM simulations of the hot-compression tests were performed using the commercially available code DEFORM™ (Scientific Forming Technologies Corporation, Columbus, OH) for the purpose of understanding the spatial and temporal evolution of local strain components and rigid-body rotations due to metal flow. These data were used in turn to guide the selection of locations for microstructural characterization.

The friction-corrected flow-stress data were used to develop a database that was implemented in the FEM simulations, which were run non-isothermally. In addition, the friction shear factor was tuned iteratively in the simulations until the load-stroke data and simulated cross-section shape matched the experimentally observed stiffness-corrected load-stroke and sample cross-section results, respectively. The flow stress, friction, and various boundary conditions for the FEM code are provided as input.KEY files, which contain all of the information necessary to run the simulations inside DEFORM™. The database files (extension *.DB) are also included which contain the complete FE model. These can be loaded directly into the DEFORM™ post processor, and the thermomechanical history at each time step can be visualized. If the reader does not have access to this software, however, the other information provided in this article, including Table 1, and the corresponding supporting data are sufficient to recreate the model in any FEM package. As an example of the results from DEFORM™, the initial and final sample meshes and the final effective Von Mises strain contours for the axial compression at 899 °C are shown in Fig. 3. Simulation results for the other samples looked very similar with only very minor variations in the magnitude of local strains and hence are not shown here.

Based on the strain distributions predicted by the FEM simulations (with special attention to local strain gradients), a region of interest (ROI) was defined to do microstructure and texture characterization. Because MTRs can measure multiple millimeters in one or more dimensions and the size and shape of an MTR following a forming operation is a strong function of the strain path experienced during deformation, we selected ROIs near the center of each compression sample for detailed characterization. The material elements at such locations had experienced essentially axisymmetric compression with no shear strain (Table 2) and minimal rigid-body rotation. The near equality of the Von Mises effective strains and the imposed axial strain underscore the near perfect uniaxial-compression assumption. In view of sample symmetry, the ROI thus comprised a 15-mm-diameter × 3-mm-height cylinder centered in the bulk of each compression sample. Due to practical limitations, however, it was only possible to perform a detailed examination on three mutually perpendicular planes within the ROI. For this purpose, each sample was sectioned via electric-discharge machining to expose three orthogonal faces. The imaging planes, the locations of EBSD analyses, and the corresponding reference frames for the billet and compression samples are shown schematically in Figs. 4 and 5, respectively. This approach provided a statistically averaged sense of the three-dimensional shape of the MTRs before and after compression and the relative amount of rotation of the principal axes of the MTRs during the imposed strain. While this is a reasonable approach for modeling the average response, it does neglect the possibly important contribution of the local neighborhood to the development of intragranular strains, which may be relevant to the spheroidization process and the concomitant randomization of orientations within an individual MTR during forging. Two additional EBSD scans covering significantly larger areas are also included in the dataset. These include a scan of the full cross-section of face 1 for the 45° compression sample and a scan of half the sample of the axial-compression specimen.

Backscattered-electron micrographs were acquired on a FEI XL30 or a FEI Sirion SEM. Both SEMs were equipped with field-emission-gun (FEG) sources. To facilitate strong contrast within the microstructure, each SEM was operated at 20 kV with a spot size of “5” and a 30-μm aperture producing ~2.5 nA of current. Images were collected at multiple magnifications (×250, ×500, ×1000, and ×2000) from approximately the center of the forging in the highly compressed region of each sample. Additional ×500 images were collected on each sample elsewhere within the previously defined characterization volume to assess microstructural variability. A magnification-calibration standard image collected during each SEM session is provided to facilitate accurate quantitative measurements. Representative micrographs of the as-received billet material are shown in Fig. 6 while examples from the compression samples are shown in Fig. 7. These images reveal the extent of the changes to the size, shape, and volume fraction of primary-alpha particles during heat-up, soaking for 3 min, and the ~107 s necessary to complete the compression test.

The extent of texture and microtexture were assessed with EBSD. These data were collected on the FEI XL30 SEM with a FEG source using a Hikari camera. Beam conditions were chosen to provide a high probe current to enhance pattern quality; for this purpose, an accelerating voltage of 20 kV with a spot size of 5 and a 100-μm final aperture were employed to produce nearly 50 nA. Using a custom batch-scan program [15], EBSD data were collected over relatively large areas using a combination of beam scans and automated stage movements. Table 3 provides a summary of the scans collected for this work and which are included in the dataset. The individual tiles in their native binary *.osc format are provided in the “RawData” folder for each sample. While there is a MATLAB (The MathWorks, Inc., Natick, MA) function that can unpack the binary files and read them into a variable in the MATLAB workspace, we have also provided the entire stitched dataset as a single ASCII file (file extension *.ang) that resulted as an output of a previously published code [16]. All of the subsequent data shown here were generated from the stitched file after having been cropped to the dimensions shown in Fig. 5b–d. The .ang files are the standard ASCII format for the commercial EBSD vendor EDAX/TSL (EDAX, Mahwah, NJ). The files contain 10 columns of data that are, in order, the crystal orientation in “active” Bunge Euler angles (phi₁, PHI, phi₂) (following the so-called Z-X-Z convention, i.e., active rotations from the “initial” sample axes to the “new” crystal axes), spatial coordinates (x,y), image quality (IQ), confidence index (CI), phase identification, detector intensity, and fit. For ease of visualization, we have also provided JPEG images of the crystal orientation maps and the resulting textures derived from them for the 0001, \( 10\overline{1}0 \), \( 2\overline{1}\overline{1}0 \), and \( \overline{2}113 \) poles of the hexagonal alpha phase.

EBSD data are provided in the native reference frame, the “RD-TD-ND” coordinate system from the EDAX/TSL software, which are equivalent to the “X-Y-Z” axes of a right-handed orthonormal reference system. The relationship between these axes and the EBSD scans performed on the as-received billet and the compression samples are illustrated in Figs. 4 and 5. It is noteworthy that the reference frame used for crystallographic orientations is not the same reference frame used to denote the spatial coordinates of the pixels [17] and that the orientation of the hexagonal alpha phase at the Euler angle (0,0,0) has the \( \left[2\overline{1}\overline{1}0\right] \) parallel to “RD” or the X-axis of the sample reference frame while \( \left[01\overline{1}0\right] \) is parallel to “TD” or the Y-axis. The same billet material was used for all of the compression experiments. Hence, it was assumed that the as-measured billet texture reasonably approximated the starting condition for each experiment since all compression samples were cut from the same radial position in the billet. As a result, it is necessary to rotate the morphological and crystallographic orientations of the MTRs for the 45° and 90° (radial) compression specimens prior to simulating the respective deformation experiments. Special attention should be paid to face 1 in the billet (Fig. 4) as it was physically oriented 90° relative to face 3 when the data was collected.

If one is interested in assessing the global texture evolution in the final forgings by combining the measurements from the three mutually perpendicular faces, it is necessary to apply additional transformations to the post-compression datasets. The following rotation matrices, R _i, should be used to transform the as-collected orientation, g, to the new orientation, g′ = R _ig, which coincides with the face 1 reference frame.

The stitched, but otherwise raw, EBSD data were further processed for the purposes of feature identification and segmentation of MTRs. For this purpose, a new DREAM.3D (BlueQuartz Software, Springboro, OH) filter [18] was developed to overcome the shortcomings of current algorithms. Presently, most EBSD analysis software utilizes a so-called “burn” algorithm to group pixels of discrete measurements into grains (features) based on a user-defined misorientation criterion. The misorientation operator acts on only first-nearest-neighbor pixels and therefore requires contiguity of similarly oriented pixels to form a grain. Such an approach is incapable of properly segmenting MTRs, however, because adjacent alpha particles may not necessarily be interconnected, either in reality or due to the scan resolution. This is especially true after solution heat treatment high in the alpha+beta-phase field where primary-alpha particles are effectively insulated from one another by a matrix of transformed beta. There are rare instances in which the primary-alpha particles and adjacent secondary alpha adopt a similar orientation such that the classic burn algorithm can capture the MTRs; however, this is a rare exception. Despite an absence of connectivity, similarly oriented alpha particles tend to behave as a single microstructural unit as evidenced by observations of large, faceted initiation sites on dwell-fatigue fracture surfaces of alloys with low volume fractions of primary alpha. Such observations raise two important questions that impact the choice of segmentation parameters, which are founded in the context of material behavior, i.e.,: (i) at what distance do two alpha particles of the same orientation no longer interact with one another and (ii) how does this value change with misorientation and particle size? Therefore, in the present work and the work by Tucker et al. [19], a two-step feature identification process was used.

First, alpha particles are identified using the classical misorientation parameter with a relatively tight tolerance, ~2°, similar to the 1.25° used in the pioneering work of Woodfield et al. [4]. Second, the alpha particles are considered for grouping as MTRs in a burn algorithm that operates on the previously identified particles. The contiguity requirement is not enforced here; instead, the “burn” is performed within a user-specified search radius, which looks at centroid-to-centroid distances of neighboring alpha particles (so-called neighborhoods). The search radius is entered as a multiple of the average alpha-particle diameter, and alpha particles satisfying these criteria are grouped into MTRs based on a moderately wide c-axis misorientation tolerance, viz, 20°. The second-tier search proceeds until all previously identified particles are assigned to a parent MTR or left as an individual feature. The c-axis is used as opposed to the classic misorientation because the elastic and plastic response varies strongly with changes in c-axis orientation relative to the stress axis per se, whereas no or very minor changes are observed for rotations about [0001] at a constant orientation. Moreover, crack propagation occurs on or near basal planes [20] at small-crack lengths, so tilt boundaries offer resistance to crack propagation through deflection of the crack path and the development of roughness-induced closure. Basal twist boundaries, on the other hand, offer no such similar resistance to small fatigue-crack growth as evidenced by previous marker band studies [21].

It is noteworthy that this filter can be used within other pipelines in the DREAM.3D application suite and therefore has broad applicability to the study of “neighborhood-sensitive” properties in other materials. We have used a factor of five times the average particle size for this work which, due to the coarse resolution, was essentially the step size of the scan (5 × 5 μm = 25 μm search radius). As illustrated in Fig. 8, the upper tail of the measured MTR size distribution, which is typically the region responsible for life-limiting dwell-fatigue failures, is quite sensitive to the search-radius parameter, which, at present, does not have a physical basis for its specification. Saint-Venant’s principle may serve as a working hypothesis, which indicates that the influence of a given object ceases at approximately three times the feature size. For this analysis, we have used a set of empirically determined segmentation parameters, and thus, we have also provided the raw data and the associated pipeline to process the data using DREAM.3D such that the reader can test other segmentation parameters. Furthermore, all identified features with semi-major (ellipse fit) axes less than 100 μm, corresponding to approximately seven average alpha particles, have been thresholded to define the lower-bound dimension of the MTR. For other purposes, the threshold value may need to be considerably larger depending on the problem of interest.

Example crystal orientation maps and the corresponding segmented MTRs (colored by equivalent diameter) are shown in Figs. 9 and 10. The size and shape of the MTRs in each two-dimensional plane were approximated as ellipses quantified using the length of their major and minor axes and the inclination of the major axis with respect to the billet or forging direction. Table 4 shows basic statistics for the MTR sizes on face 1 of the 45° compression sample. The statistics were applied to independent quartiles of the data based on the MTR major-axis lengths. Figures 11 and 12 depict the effect of strain on the evolution of major and minor MTR axis lengths as a function of MTR aspect ratio and inclination angle for face 1 in the billet and following hot compression in the 45° direction. The aspect ratio is defined as the major/minor axis lengths while the inclination angle reported is relative to a direction perpendicular to the compression axis. Figure 11a shows that the great majority (~80 %) of the MTRs have aspect ratios less than ~5. The MTR major-axis inclination angle data in Fig. 11b has been rotated into the same reference frame as the 45° compression sample, and hence, the initial billet axis is located at 45°. Following compression at 45° to the billet axis (Fig. 12), one can see that the major axes of most MTRs were rotated nearly perpendicular to the compression direction and were reduced in size. The MTR aspect ratios were only moderately impacted, exhibiting a slight increase, as indicated by the similar shape and position of the cumulative distributions. The Excel™ file in the MTR processing folder contains this information for all datasets.

Crystal orientation maps of the full cross-section of the 45° and half cross-section of the axial-compression samples are shown in Figs. 13 and 14, respectively. These datasets show the interaction of the MTRs with the continuum-scale metal flow. For instance, Fig. 13 shows the retention of larger MTRs in the dead metal zone while there is clear bending and distortion of the MTRs in Fig. 14.