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A Simple Algorithm to Eliminate Ambiguities in EBSD Orientation Map Visualization and Analyses: Application to Fatigue Crack-Tips/Wakes in Aluminum Alloys

Published online by Cambridge University Press:  25 October 2010

Vipul K. Gupta  and
Sean R. Agnew
Vipul K. Gupta*
Affiliation:
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904-4745, USA
Sean R. Agnew
Affiliation:
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904-4745, USA
*
Corresponding author. E-mail: vipul.gupta@nianet.org
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Abstract

A simple algorithm is developed and implemented to eliminate ambiguities, in both statistical analyses of orientation data (e.g., orientation averaging) and electron backscattered diffraction (EBSD) orientation map visualization, caused by symmetrically equivalent orientations and the wrap-around or umklapp effect. Using crystal symmetry operators and the lowest Euclidian-distance criterion, the orientation of each pixel within a grain is redefined. An advantage of this approach is demonstrated for direct determination of the representative orientation of a grain within an EBSD map by mean, median, or quaternion-based averaging methods that can be further used within analyses or visualization of misorientation or geometrically necessary dislocation (GND) density. If one also considers the lattice curvature tensor, five components of the dislocation density tensor—corresponding to a part of the GND content—may be inferred. The methodology developed is illustrated using EBSD orientation data obtained from the fatigue crack-tips/wakes in aerospace aluminum alloys 2024-T351 and 7050-T7451.

Keywords

wrap-aroundcrystal symmetryquaternionorientation maplattice curvatureNye tensor
Type
Instrumentation and Software Developments
Information
Microscopy and Microanalysis , Volume 16 , Issue 6 , December 2010 , pp. 831 - 841
Copyright
Copyright © Microscopy Society of America 2010

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References

REFERENCES

Ashby, M.F. (1970). The deformation of plastically non-homogeneous materials. Philos Mag 21(170), 399–424.CrossRefGoogle Scholar
Barton, N. & Dawson, P. (2001). A methodology for determining average lattice orientation and its application to the characterization of grain substructure. Metallurg Mater Trans A 32(8), 1967–1975.CrossRefGoogle Scholar
Cheong, K.-S. & Busso, E.P. (2006). Effects of lattice misorientations on strain heterogeneities in FCC polycrystals. J Mech Phys Solids 54(4), 671–689.CrossRefGoogle Scholar
Cho, J.-H., Rollett, A.D. & Oh, K.H. (2005). Determination of a mean orientation in electron backscatter diffraction measurements. Metallurg Mater Trans A 36(12), 3427–3438.CrossRefGoogle Scholar
Cortie, M.B. (1997). Calculation of texture volume fractions by integration and Gaussian fitting. Texture Microstruct 29(3–4), 155–183.CrossRefGoogle Scholar
Demir, E., Raabe, D., Zaafarani, N. & Zaefferer, S. (2009). Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography. Acta Mater 57(2), 559–569.CrossRefGoogle Scholar
Demir, E., Raabe, D. & Roters, F. (2010). The mechanical size effect as a mean-field breakdown phenomenon: Example of microscale single crystal beam bending. Acta Mater 58(5), 1876–1886.CrossRefGoogle Scholar
El-Dasher, B.S., Adams, B.L. & Rollett, A.D. (2003). Viewpoint: Experimental recovery of geometrically necessary dislocation density in polycrystals. Scripta Mater 48(2), 141–145.CrossRefGoogle Scholar
Field, D.P., Trivedi, P.B., Wright, S.I. & Kumar, M. (2005). Analysis of local orientation gradients in deformed single crystals. Ultramicroscopy 103(1), 33–39.CrossRefGoogle ScholarPubMed
Glez, J.C. & Driver, J. (2001). Orientation distribution analysis in deformed grains. J Appl Crystallogr 34, 280–288.CrossRefGoogle Scholar
Gupta, V.K. (2009). Diffraction based study of fatigue crack initiation and propagation in aerospace aluminum alloys. PhD Thesis. Charlottesville, VA: University of Virginia.Google Scholar
Gupta, V.K. & Agnew, S.R. (2008). Measuring the effect of environment on fatigue crack-wake plasticity in aluminum alloy 2024 using electron backscatter diffraction. Mater Sci Eng A 494(1–2), 36–46.CrossRefGoogle Scholar
Gupta, V.K. & Agnew, S.R. (2009). Indexation and misorientation analysis of low-quality Laue diffraction patterns. J Appl Crystallogr 42, 116–124.Google Scholar
HKL Technology (2001). HKL Channel 5 Users Manual. Danbury, CT: HKL Technology.Google Scholar
Humbert, M., Gey, N., Muller, J. & Esling, C. (1996). Determination of a mean orientation from a cloud of orientations: Application to electron back-scattering pattern measurements. J Appl Crystallogr 29(6), 662–666.CrossRefGoogle Scholar
Humphreys, F.J. (2001). Review grain and subgrain characterisation by electron backscatter diffraction. J Mater Sci 36(16), 3833–3854.CrossRefGoogle Scholar
Kamaya, M., Wilkinson, A.J. & Titchmarsh, J.M. (2005). Measurement of plastic strain of polycrystalline material by electron backscatter diffraction. Nucl Eng Design 235(6), 713–725.CrossRefGoogle Scholar
Krieger Lassen, N.C., Juul Jensen, D. & Conradsen, K. (1994). On the statistical analysis of orientation data. Acta Crystallogr 50(6), 741–748.CrossRefGoogle Scholar
Kröner, E. (1955). Der fundamentale zusammenhang zwischen versetzungsdichte und spannungsfunktionen. Z Phys A-Hadron Nucl 142(4), 463–475.Google Scholar
Kunze, K., Wright, S.I., Adams, B.L. & Dingley, D.J. (1993). Advances in automatic EBSP single orientation measurements. Texture Microstruct 20(1–4), 41–54.CrossRefGoogle Scholar
Kysar, J.W. & Briant, C.L. (2002). Crack tip deformation fields in ductile single crystals. Acta Mater 50, 2367–2380.CrossRefGoogle Scholar
Larson, B.C., Yang, W., Ice, G.E., Budai, J.D. & Tischler, J.Z. (2002). Three-dimensional X-ray structural microscopy with submicrometre resolution. Nature 415(6874), 887–890.CrossRefGoogle ScholarPubMed
Maitland, T. & Sitzman, S. (2007). Electron backscatter diffraction (EBSD) technique and materials characterization examples. In Scanning Microscopy for Nanotechnology: Techniques and Applications, Zhou, W. & Wang, Z.L. (Eds.), pp. 41–75. New York: Springer Science + Business Media, LLC.Google Scholar
Morawiec, A. & Pospiech, J. (1989). Some information on quaternions useful in texture calculations. Texture Microstruct 10, 211–216.Google Scholar
Nye, J.F. (1953). Some geometrical relations in dislocated crystals. Acta Metall 1(2), 153–162.CrossRefGoogle Scholar
Pantleon, W. (2008). Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scripta Mater 58(11), 994–997.CrossRefGoogle Scholar
Prior, D.J., Boyle, A.P., Brenker, F., Cheadle, M.C., Day, A., Lopez, G., Peruzzo, L., Potts, G.J., Reddy, S., Spiess, R., Timms, N.E., Trimby, P., Wheeler, J. & Zetterström, L. (1999). The application of electron backscatter diffraction and orientation contrast imaging in the SEM to textural problems in rocks. Amer Mineral 84, 1741–1759.CrossRefGoogle Scholar
Randle, V. & Engler, O. (2000). Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping, 1st ed.Amsterdam, The Netherlands: Gordon and Breach Science Publishers.CrossRefGoogle Scholar
Sun, S., Adams, B.L. & King, W.E. (2000). Observations of lattice curvature near the interface of a deformed aluminium bicrystal. Philos Mag A 80(1), 9–25.CrossRefGoogle Scholar
Tatschl, A. & Kolednik, O. (2003). On the experimental characterization of crystal plasticity in polycrystals. Mater Sci Eng A 356(1–2), 447–463.CrossRefGoogle Scholar
Wilkinson, A.J., Meaden, G. & Dingley, D.J. (2006). High resolution mapping of strains and rotations using electron backscatter diffraction. Mater Sci Technol 22, 1271–1278.CrossRefGoogle Scholar
Wilkinson, A.J. & Randman, D. (2010). Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction. Philos Mag 90(9), 1159–1177.CrossRefGoogle Scholar
Zaafarani, N., Raabe, D., Singh, R.N., Roters, F. & Zaefferer, S. (2006). Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations. Acta Mater 54(7), 1863–1876.CrossRefGoogle Scholar