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Stereological Estimation of Orientation Distribution of Generalized Cylinders from a Unique 2D Slice

  • Jean-Pierre Da Costa (a1) (a2), Stefan Oprean (a2), Pierre Baylou (a1) (a2) and Christian Germain (a1) (a2)

Abstract

Though three-dimensional (3D) imaging gives deep insight into the inner structure of complex materials, the stereological analysis of 2D snapshots of material sections is still necessary for large-scale industrial applications for reasons related to time and cost constraints. In this paper, we propose an original framework to estimate the orientation distribution of generalized cylindrical structures from a single 2D section. Contrary to existing approaches, knowledge of the cylinder cross-section shape is not necessary. The only requirement is to know the area distribution of the cross-sections. The approach relies on minimization of a least squares criterion under linear equality and inequality constraints that can be solved with standard optimization solvers. It is evaluated on synthetic data, including simulated images, and is applied to experimental microscopy images of fibrous composite structures. The results show the relevance and capabilities of the approach though some limitations have been identified regarding sensitivity to deviations from the assumed model.

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Corresponding author

* Corresponding author. E-mail: jean-pierre.dacosta@ims-bordeaux.fr

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Badel, P., Vidal-Sallé, E., Maire, E. & Boisse, P. (2009). Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale. Int J Mater Forming 2, 189192.
Bale, H., Blacklock, M., Begley, M.R., Marshall, D.B., Cox, B.N. & Ritchie, R.O. (2012). Characterizing three-dimensional textile ceramic composites using synchrotron X-ray micro-computed-tomography. J Am Ceram Soc 95, 392402.
Ballard, D.H. & Brown, C.M. (1982). Computer Vision, Chap. 9.1, pp. 274275. Englewood Cliffs, NJ: Prentice Hall.
Blanc, R., Baylou, P., Germain, C. & Da Costa, J.P. (2010). Confidence bounds for the estimation of the volume phase fraction from a single image in a nickel base superalloy. Microsc Microanal 16, 273281.
Blanc, R., Germain, C., Da Costa, J.P., Baylou, P. & Cataldi, M. (2006). Fiber orientation measurements in composite materials. Composites Part A 37, 197206.
Chapoullié, C., Germain, C., Da Costa, J., Vignoles, G.L. & Cataldi, M. (2013). Multiscale extraction of morphological features in woven cmcs. In Proceedings of ICACC, Daytona Beach, FL, USA.
Clarke, A., Eberhardt, C. & Davidson, N. (2012). 3D characterisation of glass fibers in composites by confocal microscopy. In Proceedings of ICCM12, Paris.
Coindreau, O. & Vignoles, G.L. (2005). Assessment of structural and transport properties in fibrous c/c composite preforms as digitized by X-ray CMT. Part I: Image acquisition and geometrical properties. J Mater Res 20, 23282339.
Couégnat, G., Martin, E. & Lamon, J. (2010). 3D Multiscale Modeling of the Mechanical Behavior of Woven Composite Materials, pp. 185194. Hoboken, NJ: John Wiley & Sons Inc.
Davidson, N., Clarke, A. & Archetypal, G. (1997). Large-area, high-resolution image analysis of composite materials. J Microsc 185, 233242.
Eberhardt, C. & Clarke, A. (2001). Fiber-orientation measurements in short-glass-fibre composites. Part I. Automated, high-angular-resolution measurement by confocal microscopy. Composites Sci Technol 61, 13891400.
Germain, C., Blanc, R., Donias, M., Lavialle, O., Da Costa, J.P. & Baylou, P. (2005). Estimating the section elevation angle of cubes on a cubic mesh. Application to nickel microstructure size estimation. Image Anal Stereol 24, 127134.
Harris, J.W. & Stocker, H. (1998). Handbook of Mathematics and Computational Science, Chapter 4.6, pp. 102104. New York: Springer-Verlag.
Hivet, G., Wendling, A., Vidal-Salle, E., Laine, B. & Boisse, P. (2010). Modeling strategies for fabrics unit cell geometry application to permeability simulations. Int J Mater Form 3, 727730.
Kern, W.F. & Bland, J.R. (1948). Solid Mensuration with Proofs, chapters 16–17, pp. 3642. New York: Wiley.
Kim, J., Liaw, P.K., Hsu, D.K. & McGuire, D.J. (1997). Nondestructive evaluation of nicalon/sic composites by ultrasonics and X-ray computed tomography. Ceram Eng Sci Proc 18, 287296.
Lee, K.S., Lee, S.W., Youn, J., Kang, T. & Chung, K. (2001). Confocal microscopy measurement of the fiber orientation in short fiber reinforced plastics. Fibers Polym 2, 4150.
Lee, Y.H., Lee, S.W., Youn, J., Chung, K. & Kang, T. (2002). Characterization of fiber orientation in short fiber reinforced composites with an image processing technique. Mater Res Innov 6, 6572.
Martín-Herrero, J. & Germain, C. (2007). Microstructure reconstruction of fibrous c/c composites from X-ray microtomography. Carbon 45, 12421253.
Miao, J., Charalambous, P., Kirz, J. & Sayre, D. (1999). Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342344.
Miao, J., Sandberg, R. & Song, C. (2012). Coherent X-ray diffraction imaging. Selected topics in quantum electronics, IEEE J Sel Topics Quantum Electron 18, 399410.
Mlekusch, B. (1999). Fiber orientation in short-fiber-reinforced thermoplastics. II. Quantitative measurements by image analysis. Compos Sci Technol 59, 547560.
Oakeshott, R.B.S. & Edwards, S.F. (1992). On the stereology of ellipsoids and cylinders. Phys A 189, 208233.
Russ, J. & Dehoff, R. (2000). Practical Stereology. New York: Plenum Press.
Sterio, D. (1984). The unbiased estimation of number and sizes of arbitrary particles using the dissector. J Microsc 134, 127136.
Weisstein, E.W. (2013). Cylinder, from Mathworld—A Wolfram web resource. Available at http://mathworld.wolfram.com/Cylinder.html.

Keywords

Stereological Estimation of Orientation Distribution of Generalized Cylinders from a Unique 2D Slice

  • Jean-Pierre Da Costa (a1) (a2), Stefan Oprean (a2), Pierre Baylou (a1) (a2) and Christian Germain (a1) (a2)

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