DOI: 10.5061/dryad.xsj3tx9tn
title: High-resolution deformation mapping of martensitic transformation and plasticity in superelastic Nickel-Titanium

description: Shape-memory alloys (SMAs) such as nitinol (NiTi) can recover large
 strains through a reversible stress- or temperature-induced martensitic
 transformation, but cyclic transformation degrades reversibility. Recent
 experimental evidence has linked this functional fatigue to the emission
 of dislocations from the fine martensitic microstructure that forms near
 the phase boundary, but the precise coupling mechanism between dislocation
 slip and martensitic microstructure is still widely debated. This creates
 a mesoscale gap in the understanding of SMAs and their fatigue: multiscale
 simulation is prohibitively expensive, while experimental methods that can
 spatially resolve fine microstructure and individual dislocations (e.g.,
 transmission electron microscopy) cannot capture bulk mechanical behavior.
 In biomedical applications, understanding and modeling the mechanisms of
 slip localization and functional fatigue will be particularly crucial for
 the newest generations of ultra-high-purity nitinol, with flaw sizes below
 the theoretical crack length threshold. In the work to which this dataset
 is linked, we develop a new framework (MMICROSTRUCTURE) to reconstruct the
 geometrically necessary martensitic transformation and plastic slip in
 polycrystalline SMAs from high-resolution, full-field deformation maps.
 Using digital image correlation in a scanning electron microscope
 (SEM-DIC), we experimentally measure deformation with approximately 200
 nanometer spatial resolution over a 0.5-millimeter field of view. We align
 this deformation data to austenite grain structure mapped via electron
 backscatter diffraction (EBSD). Using the MMICROSTRUCTURE framework, we
 quantitatively map the activity of individual slip systems and martensitic
 variants in each DIC subset. We show that localized networks of coupled
 slip and martensitic reorientation form microstructural
 "bridges" that propagate transformation through clusters of
 poorly oriented grains. The energy dissipated during bridging may be the
 origin of the unusual prestrain effects in nitinol, where higher
 prestrains (for example, crimping of a medical device) have been
 correlated to increased fatigue strength. Contrary to recent theories of
 functional fatigue focusing on a Type II twin interface, we observe that
 the most intense slip localization events are coupled to the development
 of Type I twins with a finite width.
description: # High-resolution deformation mapping of martensitic transformation and
 plasticity in superelastic Nickel-Titanium Dataset DOI:
 [10.5061/dryad.xsj3tx9tn](https://doi.org/10.5061/dryad.xsj3tx9tn) ##
 Dataset overview This study investigated the interactions between
 martensitic phase transformation and plastic slip in superelastic
 Nickel-Titanium (NiTi, or nitinol). The experiment was designed to be
 analogous to the early-stage duty cycle of a nitinol cardiovascular
 implant. The dataset comprises the following: 1. **SEM-DIC (HR-DIC)**:
 high-resolution, sub-grain deformation maps obtained via in situ scanning
 electron microscopy digital image correlation (SEM-DIC, sometimes called
 HR-DIC) 2. **EBSD**: orientation maps obtained via electron backscatter
 diffraction (EBSD) 3. **MMICROSTRUCTURE**: activity fields for each slip
 system and martensitic variant reconstructed via the MMICROSTRUCTURE
 framework, which is developed and presented in the accompanying
 publication Full experimental details are available in the linked
 publications. ## File structure ### SEM-DIC (HR-DIC) Nanopatterned tensile
 samples were loaded in situ in an FEI Teneo FEG-SEM with a Kammrath and
 Weiss tensile-compressive module. At different macroscopic strain levels,
 loading was paused for image acquisition. Each file is labeled with a
 string "e_", which refers to the macroscopic strain: * Cycle 0:
 e1 (2.5% strain), e2 (5.5% strain), e3 (8.5% strain) * Cycle 1: e4 (3.5%
 strain), e5 (5.5% strain) * Cycle 2: e6 (3.5% strain), e7 (5.5% strain),
 e8 (unloaded) **sem_dic_images.zip** contains the raw SEM image data from
 the tensile test. * Tiled images were acquired in a 7x7 grid at 20 kV and
 1.6 nA, with a 3.2-microsecond dwell time. * SEM images are (4096, 4096)
 16-bit grayscale TIF, with a resolution of 19 nm/px. Images were captured
 with a custom scan controller
 ([DOI: 10.1016/j.ultramic.2018.08.025](https://doi.org/10.1016/j.ultramic.2018.08.025)) to avoid beam artifacts. * Each of the subfolders (e0-e8) contains the tiled images from one of the macroscopic strain levels described above. Each image is named according to both the strain index and the row/column indices; for example, "e3_r0c1.tif" should be read as "strain level 3, row 0, column 1". **e1.mat, e2.mat, e3.mat, e4.mat, e5.mat, e6.mat, e7.mat, e8.mat**: these files contain the stitched displacement and deformation fields formatted as Matlab structs.  * Displacements are "u" and "v"; positions in the original images are "x" and "y"; Lagrange-Green strains are "exx", "eyy", and "exy"; displacement gradients are "fxx", "fxy", "fyx", "fyy"; the correlation confidence index is "sigma" - Displacements were obtained by digital image correlation in VIC-2D, using 25-pixel (475 nm) subsets and 5-pixel (95 nm) step size. DIC was performed with first-order shape functions and the normalized SSD error metric. Each image tile was correlated independently. - Strains and displacement gradients were calculated in VIC-2D with 5-pixel Gaussian prefiltering. - We have presented all DIC quantities in the coordinate systems defined by VIC-2D. Please note that "exy," "fxy", and "fyx" must be multiplied by -1 to match the EBSD coordinate system. - After correlation, the fields were stitched together using cross-correlation ([DOI: 10.1007/s11340-018-0419-y](https://doi.org/10.1007/s11340-018-0419-y)). The stitching code is available on Github at [andrewchristison/dic-stitching](https://github.com/andrewchristison/dic-stitching). **dds.txt** contains the raw force and displacement measured by the load cell (1 kN) and extensometer (LVDT), respectively, as a function of time. Please note that the LVDT extensometer is somewhat unreliable. For the published stress-strain curves, these displacement data were rescaled using the SEM-measured end-to-end displacement of the gauge section. * Stress data were scaled using the upper plateau stress. In our material, this was 309 MPa (65 N). * The maximum end-to-end strain measured in the gauge section was 8.54%. ### EBSD Austenite grain orientation maps were obtained prior to the tensile test via EBSD. Diffraction patterns were acquired at 30 kV with an EDAX camera at a 1-micron step size, then indexed with the Hough transform in OIM Analysis. The orientation map was aligned to the DIC data by manually selecting control points and warping with a third-order polynomial. * **oima_orientations.ang** is the orientation data exported from OIM Analysis. Diffraction patterns were acquired at 30 kV with an EDAX camera at a 1-micron step size, then indexed with the Hough transform in OIM analysis. * **mtex_orientations.mat** is the EBSD orientations after alignment with the DIC data. Note that these two datasets do *not* have the same resolution; instead, each EBSD data point contains a saved position (x, y), which corresponds to the pixel location in the DIC data. Data are saved in the format of the MTEX library. * **mtex_grains.mat** contains the grains calculated in MTEX, with a misorientation threshold of 0.5 degrees. ### MMICROSTRUCTURE The MMICROSTRUCTURE framework allows users to simultaneously reconstruct martensitic transformation and plastic slip from SEM-DIC and EBSD data. **mmicrostructure.mat** is a Matlab struct containing: * The **activity** fields stored as a 3D array (4944, 4873, 18). Here, we include the data for strain levels e1, e2, e3, and e8. Each page of the array contains either the volume fraction of a martensitic variant (1:12) or the activity of a slip system (13:18). This reconstruction was obtained with alpha = 0.05 and epsilon = 0.02, as described in the linked publication. * The kinematics **eta** stored as a 3D array (3, 3, 18). Each page contains the full displacement gradient tensor of a martensitic variant (1:12) or slip system (13:18). Note that each tensor *must* be rotated into the coordinate system of the grain before reconstruction.