Experimental measurement of surface strains and local lattice rotations combined with 3D microstructure reconstruction from deformed polycrystalline ensembles at the micro-scale
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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.
KeywordsMicro-tensile test Plastic deformation Microstructure
Many structural components are fabricated from polycrystalline materials, and the desire to both optimize the performance and extend the lifetime of metallic alloys has fostered the development of advanced micromechanical modeling and simulation tools that can accurately predict the deformation response of polycrystalline ensembles. Experimental and computational techniques working toward this goal have been the subject of numerous studies, and have evolved with increasing fidelity at decreasing length scales. One example of many approaches to address this need is crystal plasticity finite element modeling (CP-FEM) focused on explicitly representing the morphology and local crystallographic orientations of polycrystalline microstructures . These models can predict the development of intra- and inter-granular gradients in the deformation field, as well as the evolution of grain morphology and local lattice rotations, and yet at the same time have known limitations such as the inability to accurately account for length scale effects [2, 3, 4].
Experimental validation of such methods is critical to guide their further development and implementation. However, due to experimental and computational challenges, validation studies which compare experimental data to simulations which explicitly incorporate the experimental microstructure have been historically limited. These have largely involved studies where only the surface microstructure of a mechanical test specimen has been experimentally determined and subsequently used as input for either 2D or quasi-3D simulations [5, 6, 7], or to approximate the 3D microstructure of a simplified material (i.e., very large grain materials where the sub-surface microstructure is assumed to be columnar) [8, 9, 10, 11, 12]. St-Pierre collected 2D electron backscatter diffraction (EBSD) scans of the surface microstructure of a tensile sample and used microstructure statistics to generate a 3D mesh of the tensile sample with the experimental surface and a realistic sub-surface virtual microstructure . Musienko utilized successive electropolishing on a post-deformation tensile specimen combined with EBSD scans to determine the 3D microstructure from a small volume in a region-of-interest near the specimen surface, which was subsequently meshed and simulated to compare to the tensile experiment .
In the present study, we demonstrate a new methodology for generating mechanical test datasets combined with explicit microstructure representation of the entire test specimen. We have employed in-situ SEM-based micro-scale tensile testing [15, 16, 17, 18] combined with surface strain mapping to track the evolution of surface strains throughout the mechanical test [19, 20, 21, 22, 23]. Micro-scale test volumes are amenable to 3D serial sectioning in focused ion beam-scanning electron microscopes (FIB-SEM), and performing such experiments while incorporating EBSD mapping allows for capturing the post-deformation microstructure, including local lattice rotations [24, 25, 26, 27]. The combination of all of these techniques allows the collection of rich datasets for model development and validation studies; these efforts are described in other publications .
Methods, results and discussion
The material selected for this work was a 99.0% purity annealed Ni foil with a nominal thickness of 50 μm. The foil contained no appreciable texture and was comprised of equiaxed grains with an average diameter of approximately 10 μm. Micro-tensile samples were fabricated from the foil by implementing a stencil mask technique . This technique involves using standard microelectronics processing methods to produce high aspect-ratio stencil masks from a Si wafer. Once fabricated, the stencil masks are placed on top of the foil and the mask-and-foil are co-sputtered using a broad ion beam milling system. This ultimately transfers the pattern of the stencil mask into the foil, creating an array of test structures. For the present experiments, the Si wafer was 200 μm in thickness and the pattern consisted of an array of tensile samples integrally attached to the bulk substrate. Milling was conducted with a Gatan Precision Etching Coating System, operated with a 6 kV Ar+ broad ion beam for approximately 40 hours.
Three samples were fabricated with a final specimen geometry consisting of a rectangular cross section, a gage width of 21 μm, a thickness of 38 μm, and a gage length of 80 μm. Images of the samples prior to testing can be seen in Figure 1. The flat sample surfaces were conducive to collecting EBSD patterns before and after mechanical testing, and also for making surface strain measurements throughout the mechanical test. The choice of material, grain size and specimen dimensions allowed for roughly 200 grains to be included in the gage volume. This allowed the experiment to include a sufficient number of grains such that the results would be relevant to interrogating a polycrystalline response, yet have the total number of grains be small enough such that the test could still be directly simulated using a CP-FEM model instantiated with the explicit 3D microstructure . Furthermore, the specimen dimensions are appropriate for micro-tensile testing and post-test 3D-EBSD serial sectioning in the FIB-SEM.
In-situ SEM-based micro-tensile testing was conducted using a custom-built mechanical testing device [18, 30, 31]. Selected details of the device construction have been reported elsewhere . The device is displacement-controlled using a piezoelectric actuator, and load is measured with a strain-gage-based load cell. The local sample displacements are calculated from SEM images by tracking the positional change of distinct features on the specimen surface. An alignment flexure ensures linear motion of the loading train [32, 33], and the samples are precisely positioned for testing by attaching the bulk substrate to a piezoelectric controlled x-y-z micro-positioning stage. The FIB-SEM was used to manufacture a tensile grip into the end of a SiC fiber which was 8 mm in length and 0.1 mm in diameter, and attached at the other end to the load cell. The 80:1 aspect ratio of the SiC fiber enables the tensile grip to have an extremely low lateral stiffness, thus minimizing the lateral constraints imposed on the specimen during mechanical testing [18, 31]. As a result, the imposed boundary conditions are different from that in a traditional tensile test.
The three samples were tested to different strain levels (~ 1.1, 2.5, and 11.9% axial engineering strain), as shown in Figure 2. Despite the limited number of grains within the gage volume and expected variation in local grain configurations among the three samples, the three engineering stress–strain curves are very similar. This agreement highlights the potential limitation of using the global stress–strain response as a sole validation metric, and thus other measures are required for interrogating the plastic deformation behavior of polycrystalline ensembles.
Surface strain mapping
The evolution and distribution of surface strains is typically a direct output of modeling tools such as CP-FEM, and these quantities are also measurable using modern digital image correlation (DIC) methods [8, 10, 12, 13, 14]. Both random and regular patterns can be used for DIC analysis, and for the present study a regular grid of points was milled onto the top surface of the micro-tensile samples prior to testing using the FIB-SEM. The markers (points) were circular with an approximate diameter of 30 nm and a point-to-point spacing of 2.3 μm. An example of this marker pattern can be seen in Figure 1A.
The distortion of the grid throughout an experiment was measured from the individual images and used to determine local surface strains, following a methodology similar to that described by Biery et al. . First, marker positions in each image were determined using a script that quickly found rough marker coordinates by performing a binary segmentation with a threshold intensity value that highlighted the markers, and then calculated the centroid of the resulting cluster of pixels at each marker. Refined coordinates were subsequently determined with sub-pixel accuracy by calculating the peak positions of a 2D Gaussian fit around each marker in the original non-segmented images. Marker positions in the image prior to testing were taken as a reference, and second order polynomial fits were calculated that mapped the positions of a central marker and the nearest surrounding markers in the reference image to those in the distorted image. Strain values were then determined from the coefficients of the polynomial fits following equations 1–3 from Biery et al. .
3D-EBSD serial sectioning
The internal microstructures of the deformed samples were characterized following mechanical testing by 3D-EBSD serial sectioning using the aforementioned FIB-SEM equipped with a TSL Hikari EBSD detector. The 3D-EBSD serial sectioning process has been described in detail elsewhere [24, 25, 26, 27]. Briefly, the process consisted of repeated cross-section milling of the sample using the ion beam, followed by repositioning the sample via tilt, rotation and translation of the 5-axis microscope stage to collect a variety of images or crystallographic (EBSD) maps for each section. This process has been fully automated with the development of custom codes that utilize FEI RunScript software to control the FIB-SEM, and AutoIt automation software to initiate the collection of EBSD maps and facilitate communication between the FIB-SEM control computer and the EBSD acquisition system.
Additionally, for one of the samples the raw EBSD patterns were saved for every pixel within a scan. Enabling this option significantly slows the acquisition process, in part because of the requirement to not use pattern binning and additionally to allow time for the computer to store large quantities of image data. As such, the raw EBSD pattern data was collected with a reduced resolution of 1 μm voxels by using an in-plane pixel size of 1 μm and only collecting this data for every fourth cross-section. The resolution of the pattern images was 640 × 480, an example of which can be seen in Figure 4D. A single crystal Si rod was extracted from a wafer and placed on top of the sample using an Omniprobe micro-manipulator to be used as a pattern center reference (as can be seen in Figure 4B and C), however, differences between Si and Ni diffraction pattern intensities made it difficult to find a set of camera parameters optimized for both and as such the pattern quality in this experiment was insufficient for this application. Currently, the raw EBSD patterns are not being used, however, in the future we hope to use this data to extract residual strains along with more precise crystallographic orientations .
After completing the registration process, the internal grain structure was segmented in DREAM.3D using a disorientation criteria, where sample voxels were iteratively grouped into fields (grains) when the disorientation between neighboring voxels was less than a user-defined angular threshold, here 5 degrees. This segmentation resulted in the definition of the internal grain structure, however, additional clean-up steps were required to re-assign internal data points that were deemed as erroneous, often the result of indexing errors or from identification as bad data via the original multi-threshold criteria. These features were removed from the data volume and the corresponding voxels were re-assigned using minimum size filters in DREAM.3D, where these filters were set to an ad-hoc threshold size of 16 voxels, corresponding to a volume of 0.25 μm3. Lastly, a combination of a 1 voxel erosion/dilation morphological filter and a surface smoothing filter were used to eliminate one-voxel wide lines and trenches on the surface of the sample. This latter filter operates by iteratively examining the coordination number of all surface voxels, and altering them by either removing voxels that have a high coordination number with the empty space, or by performing the reverse by filling empty space voxels that have a high coordination number with the sample. The 3D reconstruction of the sample deformed to 2.5% axial strain, along with engineering stress – engineering strain data and SEM images from the micro-tensile test used to calculate surface strain maps, have been made publically available .
Additional file 6: Montage of example data metrics that can be generated from the 3D EBSD characterization experiments using DREAM.3D, which have been subsequently rendered using the open-source visualization software ParaView. The data shown corresponds to the 11.9% axial strain sample. Clockwise starting from the upper left: Inverse Pole Figure coloring, where the reference orientation is the tensile axis, and the colors correspond to the standard IPF color triangle for the FCC crystal structure; Schmid factor for each grain; the Image Quality parameter reported by the EBSD mapping system used in this study; the Grain Reference Misorientation in degrees, where the reference orientation is the average orientation for the grain associated with each voxel; the Kernel Average Misorientation in degrees, calculated using a 3 × 3 × 3 voxel kernel; the L1 (Manhattan) distance relative to the grain boundary network, reported in units of pixels (1 pixel = 0.25 μm). (MOV 19 MB)
In the present study, we demonstrated a new methodology for generating high-fidelity mechanical test data sets combined with explicit 3D microstructure representation of the entire test specimen, with the intent to couple this data to simulations for model validation and development. This was accomplished utilizing a micro-scale mechanical test specimen, so that the test volumes were amenable to examination via an established 3D microstructure characterization technique, 3D-EBSD serial sectioning with a FIB-SEM. Future studies may collect similar data on larger (mm-scale) samples by utilizing emerging destructive  and nondestructive  microstructure characterization techniques.
Surface strain distributions and internal lattice rotations were measured, and will serve as metrics from which to compare to simulations in future validation studies. One caveat to using this data for validation studies is that only the microstructure from the deformed specimen can be measured, as 3D-EBSD serial sectioning is a destructive process. Hence, some assumptions will have to be made in terms of assigning initial orientations to the individual grains (removing internal lattice rotations due to deformation), and also the initial grain morphology (since the measured microstructure will be distorted due to the deformation). The usefulness of this technique for validation studies is therefore likely best at lower total strain values.
Availability of supporting data
The 3D reconstruction of the sample deformed to 2.5% axial strain, along with engineering stress – engineering strain data and SEM images from the micro-tensile test used to calculate surface strain maps, have been made publically available .
The authors would like to thank Dr. R. Wheeler (UES Inc., MicroTesting Solutions LLC) who developed the micro-testing device used in these experiments, and Adam Shiveley (UES, Inc.) for help setting up communication between various instrument computers. The authors would also like to acknowledge useful discussions with Drs. D.M. Dimiduk (Air Force Research Laboratory), T.J. Turner (Air Force Research Laboratory), and Y.S. Choi (UES Inc.). The authors acknowledge support from the Air Force Office of Scientific Research (AFOSR, program managers Dr. Joan Fuller and Dr. Ali Sayir) and the Materials & Manufacturing Directorate of the Air Force Research Laboratory.
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