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Research Papers

Dislocation Density Tensor Characterization of Deformation Using 3D X-Ray Microscopy

[+] Author and Article Information
B. C. Larson1

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831bcl@ornl.gov

J. Z. Tischler

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

Anter El-Azab2

Mechanical Engineering Department, Florida State University, Tallahassee, FL 32310

Wenjun Liu

Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439

1

Corresponding author.

2

Also at School of Computational Science, Florida State University, Tallahassee FL 32306.

J. Eng. Mater. Technol 130(2), 021024 (Apr 02, 2008) (10 pages) doi:10.1115/1.2884336 History: Received September 20, 2007; Revised January 04, 2008; Published April 02, 2008

Three-dimensional (3D) X-ray microscopy with submicron resolution has been used to make spatially resolved measurements of lattice curvature and elastic strain over two-dimensional slices in thin deformed Si plates. The techniques and capabilities associated with white-beam 3D X-ray microscopy are discussed, and both theoretical and experimental considerations associated with the measurement of Nye dislocation density tensors in deformed materials are presented. The ability to determine the local geometrically necessary dislocation (GND) density in the form of a dislocation density tensor, with micron spatial resolution over mesoscopic length scales, is demonstrated. Results are shown for the special case of an elastically bent (dislocation free) thin Si plate and for a similar thin Si plate that was bent plastically, above the brittle-to-ductile transition temperature, to introduce dislocations. Within the uncertainties of the measurements, the known result that GND density is zero for elastic bending is obtained, and well-defined GND distributions are observed in the plastically deformed Si plate. The direct and absolute connection between experimental measurements of GND density and multiscale modeling and computer simulations of deformation microstructures is discussed to highlight the importance of submicron-resolution 3D X-ray microscopy for mesoscale characterization of material defects and to achieve a fundamental understanding of deformation in ductile materials.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic view of the beamline configuration for the XOR/UNI Sector 34 3D X-ray microscopy facility at the APS. White synchrotron radiation is incident onto upper and lower slits that pass either white radiation directly to the crossed K-B mirrors (top) or, reflecting off the two-bounce monochromator (bottom), deliver a scanning monochromatic beam to the mirrors. The beam is focused to ∼0.5μm at the position of the schematic bent-plate sample. A CCD area X-ray detector is mounted at 90deg to the incident microbeam, and the depth-profiler wire is advanced with submicron steps through the diffracted beams to obtain 3D spatial resolution.

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Figure 2

Color-coded grain structure measured on commercial purity (1% Si,Fe) polycrystalline Al using 3D X-ray microscopy. The individual voxels represent micron spaced points in three dimensions at which local orientations were determined; one of the grains has been separated from its position in the sample to illustrate the use of electronic orientation grouping.

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Figure 3

Optical photographs of cylindrically bent single crystal Si plates indicating the surface-normal direction z, surface bend tangent direction y, and cylindrical bend axis x. (a) 42μm thick Si plate bent elastically into the form of an arch; (b) 25μm thick plastically bent Si plate after annealing to 700°C while in an elastically bent state, where the schematic drawing illustrates that the microbeam enters the sample at a 45deg angle to the surface at or near the apex of the arch; and (c) optical image showing typical slip trace patterns present on the surface of the plastically bent Si plate.

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Figure 4

Energy-scanning monochromatic microbeam measurements of surface-normal lattice strains in the elastically bent (thick line, open circles) and plastically bent (thin lines) Si samples and on a flat, undeformed Si plate (thick line, open squares) as a strain-free reference. The measurements were made at the apex of the elastically bent sample. The measurements on the plastically deformed sample were made near its apex at five separate positions across the sample width, chosen to represent a range of Laue spot streaking. Each of the plastically bent sample strain measurements show some broadening compared to that for the perfect, flat sample; however, all of the plastically deformed sample strain widths are much narrower than that for the elastically bent sample.

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Figure 5

Color-coded mapping of local orientations, elastic strain tensors, and dislocation density tensors over a vertical slice perpendicular to the bend axis of the elastically bent Si arch in Fig. 3. (a) x, y, and z components of the rotation vector θ=(θx,θy,θz) relative to the orientation at the “+” in the figure; (b) the elastic strain tensor mapping for the elastically bent Si sample; (c) GND dislocation density tensor mapping for elastically bent Si, showing no statistically significant GNDs. Full-scale colors correspond to ±5mrad in (a), ±3×10−3 strain in (b), and 3mrad∕μm=0.95×109cm−2 in (c). In addition to the 20μm length bar at the top that pertains to all graphs in the figure, tick marks with 2μm spacing are included on each axis to further define the length scale.

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Figure 6

Color-coded mapping of local rotations and dislocation density tensors on a slice perpendicular to the bend axis of the 700°C annealed plastically deformed Si sample in Fig. 3. (a) x, y, and z components of the rotation vector θ=(θx,θy,θz) relative to the orientation at the “+” in the figure; (b) dislocation density tensor mapping of the plastic deformation-induced GNDs showing αxy to be the dominant component. Full-scale colors correspond to ±20mrad in (a) and 3mrad∕μm=0.95×109cm−2 in (b). In addition to the 20μm length bar at the top of the figure that pertains to all graphs, tick marks with 2μm spacing are included on each axis to further define the length scale.

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