Abstract
X-ray tomography has provided a non-destructive means for microstructure characterization in three dimensional (3D) and four dimensional (4D) (i.e., structural evolution over time), in which projections of a material’s structure are typically reconstructed using the filtered-back-projection (FBP) method or algebraic reconstruction techniques. The reconstructed images are typically segmented to conduct microstructural quantification. The process can be quite time consuming and computationally intensive. In this paper, we present an overview of our recent work on utilizing a limited (Nyquist under-sampled) number of unique perspective radiographs for computed tomography reconstruction of heterogeneous material (e.g., composites and alloys) structural quantification, property prediction and microstructural reconstruction in 3D and 4D. The proposed approach is significantly more efficient and computationally less intensive than FBP. We first show that an inverse superposition of properly normalized attenuated intensity along different x-ray paths leads to a probability map for the material system, which provides the probability of finding a particular phase at a point in the imaged sample volume. Spatial correlation functions, which are statistical morphological descriptors of the material, are readily computed from the associated probability map. Using effective medium theory and the computed correlation functions, accurate predictions of physical properties (e.g., elastic moduli and thermal/electrical conductivity) can then be obtained. Finally, we present a stochastic reconstruction procedure that generates an accurate rendition of the 3D microstructure from a reduced number of tomographic projections. This stochastic reconstruction method can be easily adapted to reconstruct 4D structural evolution from a small number of in situ projections.
Similar content being viewed by others
References
S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (New York: Springer, 2013).
M. Sahimi, Heterogeneous Materials I: Linear Transport and Optical Properties (New York: Springer, 2003).
D. Brandon and W.D. Kaplan, Microstructural Characterization of Materials (England: Wiley, 2013).
D.T. Fullwood, S.R. Niezgoda, B.L. Adams, and S.R. Kalidindi, Prog. Mater Sci. 55, 477 (2010).
H. Xu, Y. Li, C. Brinson, and W. Chen, J. Mech. Des. 136, 051007 (2014).
Y.C. Yabansu, D.K. Patel, and S.R. Kalidindi, Acta Mater. 81, 151 (2014).
A. Gupta, A. Cecen, S. Goyal, A.K. Singh, and S.R. Kalidindi, Acta Mater. 91, 239 (2015).
H. Xu, R. Liu, A. Choudhary, and W. Chen, J. Mech. Des. 137, 051403 (2015).
L. Babout, E. Maire, J.-Y. Buffière, and R. Fougeres, Acta Mater. 49, 2055 (2001).
A. Borbely, F. Csikor, S. Zabler, P. Cloetens, and H. Biermann, Mater. Sci. Eng. A 367, 40 (2004).
P. Kenesei, H. Biermann, and A. Borbély, Scr. Mater. 53, 787 (2005).
H. Toda, S. Yamamoto, M. Kobayashi, K. Uesugi, and H. Zhang, Acta Mater. 56, 6027 (2008).
A. Weck, D. Wilkinson, E. Maire, and H. Toda, Acta Mater. 56, 2919 (2008).
J. Williams, Z. Flom, A. Amell, N. Chawla, X. Xiao, and F. De, Carlo. Acta Mater. 58, 6194 (2010).
J.J. Williams, K.E. Yazzie, N.C. Phillips, N. Chawla, X. Xiao, F. De Carlo, N. Iyyer, and M. Kittur, Metall. Mater. Trans. A 42, 3845 (2011).
J.H. Kinney and M.C. Nichols, Annu. Rev. Mater. Sci. 22, 121 (1992).
J. Baruchel, P. Bleuet, A. Bravin, P. Coan, E. Lima, A. Madsen, W. Ludwig, P. Pernot, and J. Susini, C. R. Phys. 9, 624 (2008).
A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (New York: IEEE Press, 1988).
L. Feldkamp, L. Davis, and J. Kress, JOSA A 1, 612 (1984).
S.R. Kalidindi and M. De Graef, Annu. Rev. Mater. Res. 45, 171 (2015).
S. Torquato and G. Stell, J. Chem. Phys. 77, 2071 (1982).
S. Torquato and G. Stell, J. Chem. Phys. 79, 1505 (1983).
S. Torquato and G. Stell, J. Chem. Phys. 82, 980 (1985).
H. Li, S. Singh, N. Chawla, and Y. Jiao, unpublished research (2016).
S. Torquato, Phys. Rev. Lett. 79, 681 (1997).
S. Torquato, J. Mech. Phys. Solids 45, 1421 (1997).
D. Hlushkou, H. Liasneuski, U. Tallarek, and S. Torquato, J. Appl. Phys. 118, 124901 (2015).
S. Singh, H. Li, N. Chawla, Y. Jiao, unpublished research (2016).
H. Li, N. Chawla, and Y. Jiao, Scr. Mater. 86, 48 (2014).
H. Li, S. Kaira, J. Mertens, N. Chawla, and Y. Jiao, unpublished research (Arizona State University, Tempe, AZ, 2016).
G.T. Herman and A. Kuba, Advances in Discrete Tomography and Its Applications (Springer: New York, 2008).
G.T. Herman and A. Kuba, Discrete Tomography: Foundations, Algorithms, and Applications (Springer: New York, 2012).
A.P. Roberts, Phys. Rev. E 56, 3203 (1997).
H. Okabe and M.J. Blunt, J. Pet. Sci. Eng. 46, 121 (2005).
V. Sundararaghavan and N. Zabaras, Comp. Mater. Sci. 32, 223 (2005).
Y. Jiao, F. Stillinger, and S. Torquato, Phys. Rev. E 76, 031110 (2007).
D. Fullwood, S. Kalidindi, S. Niezgoda, A. Fast, and N. Hampson, Mater. Sci. Eng. A 494, 68 (2008).
D.T. Fullwood, S.R. Niezgoda, and S.R. Kalidindi, Acta Mater. 56, 942 (2008).
Y. Jiao, F. Stillinger, and S. Torquato, Phys. Rev. E 77, 031135 (2008).
Y. Jiao, F. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. USA 106, 17634 (2009).
A. Hajizadeh, A. Safekordi, and F.A. Farhadpour, Adv. Water Resour. 34, 1256 (2011).
M. Blacklock, H. Bale, M. Begley, and B. Cox, J. Mech. Phys. Solids 60, 451 (2012).
R.G. Rinaldi, M. Blacklock, H. Bale, M.R. Begley, and B.N. Cox, J. Mech. Phys. Solids 60, 1561 (2012).
P. Tahmasebi and M. Sahimi, Phys. Rev. Lett. 110, 078002 (2013).
D. Chen, Q. Teng, X. He, Z. Xu, and Z. Li, Phys. Rev. E 89, 013305 (2014).
K.M. Gerke and M.V. Karsanina, EPL 111, 56002 (2015).
M.V. Karsanina, K.M. Gerke, E.B. Skvortsova, and D. Mallants, PLoS One 10, e0126515 (2015).
X. Liu and V. Shapiro, Comp. Mater. Sci. 99, 177 (2015).
R. Bostanabad, A.T. Bui, W. Xie, D.W. Apley, and W. Chen, Acta Mater. 103, 89 (2016).
D.M. Turner and S.R. Kalidindi, Acta Mater. 102, 136 (2016).
K.J. Batenburg and J. Sijbers, IEEE Trans. Image Process. 20, 2542 (2011).
W. van Aarle, K.J. Batenburg, and J. Sijbers, IEEE Trans. Image Process. 21, 4608 (2012).
K.J. Batenburg and J. Sijbers, Discrete Appl. Math. 157, 438 (2009).
E.Y. Sidky, C.-M. Kao, and X. Pan, J. X-Ray Sci. Technol. 14, 119 (2006).
E.Y. Sidky and X. Pan, Phys. Med. Biol. 53, 4777 (2008).
N. Robert, F. Peyrin, and M.J. Yaffe, Med. Phys. 21, 1839 (1994).
C.V. Alvino, A.J. Yezzi Jr., Proceedings of the IEEE CVPR, Vol. 1 (Washington, DC, June-July, 2004)
S. Kirkpatrick and M.P. Vecchi, Science 220, 671 (1983).
E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines (England: Wiley, 1988).
C.-R. Hwang, Acta Appl. Math. 12, 108 (1988).
Y. Jiao, E. Padilla, and N. Chawla, Acta Mater. 61, 3370 (2013).
S. Chen, H. Li, and Y. Jiao, Phys. Rev. E 92, 023301 (2015).
Acknowledgements
This work was supported by the Division of Materials Research at the National Science Foundation under Award No. DMR-1305119 (Program Manager: Dr. D. Farkas and Dr. D.W. Hess). Y. Jiao is also grateful to Arizona State University for generous start-up funds.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Li, H., Singh, S., Shashank Kaira, C. et al. Microstructural Quantification and Property Prediction Using Limited X-ray Tomography Data. JOM 68, 2288–2295 (2016). https://doi.org/10.1007/s11837-016-2024-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11837-016-2024-9