Research Papers

Inferring the Size Distribution of 3D Particle Clusters in Metal Matrix Nanocomposites

[+] Author and Article Information
Heping Liu

e-mail: hepingliu@yahoo.com

Shiyu Zhou

e-mail: szhou@engr.wisc.edu
Department of Industrial and Systems Engineering,
University of Wisconsin-Madison,
3270 Mechanical Engineering,
1513 University Avenue,
Madison, WI 53706

Xiaochun Li

Department of Mechanical Engineering,
University of Wisconsin-Madison,
1035 Mechanical Engineering,
1513 University Avenue,
Madison, WI 53706
e-mail: xcli@engr.wisc.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 9, 2011; final manuscript received November 18, 2012; published online January 24, 2013. Assoc. Editor: Yong Huang.

J. Manuf. Sci. Eng 135(1), 011013 (Jan 24, 2013) (9 pages) Paper No: MANU-11-1388; doi: 10.1115/1.4023268 History: Received December 09, 2011; Revised November 18, 2012

Metal matrix nanocomposites (MMNCs) are produced by dispersing reinforcing nanoparticles into metal matrix. It is a type of emerging materials with high strength and light weight and draws significant attentions in recent years. If the particles are not well dispersed, they will form particle clusters in the metal matrix. These clusters will detrimentally impact on the final quality of MMNCs. This paper proposes a statistical approach to estimating the parameters of the size distribution of clusters in MMNCs. One critical challenge is that the clusters are distributed in a three-dimensional (3D) space, while the observations we have are two-dimensional (2D) cross-section microscopic images of these clusters. In the proposed approach, we first derived the probability distribution of the observed sizes of the 2D cross sections of the clusters and then a maximum likelihood estimation (MLE) method is developed to estimate the 3D cluster size distribution. Computational efficient algorithms are also established to make computational load manageable. The case studies based on simulation and real observed data are conducted, which demonstrates the effectiveness of the proposed approach.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


NSTC Committee on Technology, 2010, “National Nanotechnology Initiative Signature Initiative: Sustainable Nanomanufacturing—Creating the Industries of the Future,” http://www.nano.gov/sites/default/files/pub_resource/nni_siginit_sustainable_mfr_revised_nov_2011.pdf
He, J., Ice, M., Lavernia, E. J., and Dallek, S., 2000, “Synthesis of Nanostructured WC-12 pct Co Coating Using Mechanical Milling and High Velocity Oxygen Fuel Thermal Spraying,” Metall. Mater. Trans. A, 31, pp. 541–553. [CrossRef]
Yamasaki, T., Zheng, Y. J., Ogino, Y., Terasawa, M., Mitamura, T., and Fukami, T., 2003, “Formation of Metal-TiN/TiC Nanocomposite Powders by Mechanical Alloying and Their Consolidation,” Mater. Sci. Eng. A, 350, pp. 168–172. [CrossRef]
Yang, Y., Lan, J., and Li, X., 2004, “Study on Bulk Aluminum Matrix Nanocomposite Fabricated by Ultrasonic Dispersion of Nano-Sized SiC Particles in Molten Aluminum Alloy,” Mater. Sci. Eng. A, 380, pp. 378–383. [CrossRef]
Camesasca, M., Kaufman, M., and Manas-Zloczower, I., 2006, “Quantifying Fluid Mixing With the Shannon Entropy,” Macromol. Theory Simul., 15, pp. 595–607. [CrossRef]
Ganguly, P., and Poole, W. J., 2002, “Characterization of Reinforcement Distribution Inhomogeneity in Metal Matrix Composites,” Mater. Sci. Eng. A, 332, pp. 301–310. [CrossRef]
Hashim, J., Looney, L., and Hashmi, M. S. J., 2002, “Particle Distribution in Cast Metal Matrix Composites—Part I,” J. Mater. Process. Technol., 123, pp. 251–257. [CrossRef]
Hashim, J., Looney, L., and Hashmi, M. S. J., 2002, “Particle Distribution in Cast Metal Matrix Composites—Part II,” J. Mater. Process. Technol., 123, pp. 258–263. [CrossRef]
Tzamtzis, S., Barekar, N. S., Hari Babu, N., Patel, J., Dhindaw, B. K., and Fan, Z., 2009, “Processing of Advanced Al/SiC Particulate Metal Matrix Composites Under Intensive Shearing—A Novel Rheo-Process,” Composites, Part A, 40, pp. 144–151. [CrossRef]
Cressie, N. A. C., 1993, Statistics for Spatial Data, Rev. ed., John Wiley & Sons, New York.
Diggle, P. J., 2003, Statistical Analysis of Spatial Point Patterns, 2nd ed., Oxford University Press, New York.
Zhou, Q., Zhou, J., De Cicco, M. P., Zhou, S., and Li., X., “Detecting Particle-Clustering in Metal Matrix Nanocomposites Using Microscopic Image Samples,” Technometrics (to be published).
Boal, A. K., Ilhan, F., DeRouchey, J. E., Thurn-Albrecht, T., Russell, T. P., and Rotello, V. M., 2000, “Self-Assembly of Nanoparticles Into Structured Spherical and Network Aggregates,” Nature, 404, pp. 746–748. [CrossRef] [PubMed]
Alabrudzinski, S., Ekiel-Jezewska, M. L., Chehata-Gomez, D., and Kowalewski, T. A., 2009, “Particle Clusters Settling Under Gravity in a Viscous Fluid,” Phys. Fluids, 21, p. 073302. [CrossRef]
Pratt, J. W., 1976, “F. Y. Edgeworth and R. A. Fisher on the Efficiency of Maximum Likelihood Estimation,” Ann. Stat., 4(3), pp. 501–514. [CrossRef]
Dempster, A. P., Laird, N. M., and Rubin, D. B., 1977, “Maximum Likelihood From Incomplete Data via the EM Algorithm (With Discussion),” J. R. Statist. Soc. B, 39, pp. 1–38.
Chan, K. S., and LedolterJ., 1995, “Monte Carlo EM Estimation for Time Series Models Involving Counts,” J. Am. Stat. Assoc., 90(429), pp. 242–252. [CrossRef]
Booth, J. G., Hobert, J. P., and Jank, W., 2001, “A Survey of Monte Carlo Algorithms for Maximizing the Likelihood of a Two-Stage Hierarchical Model,” Stat. Model., 1(4), pp. 333–349. [CrossRef]
Wu, C. F. J., 1983, “On the Convergence Properties of the EM Algorithm,” Ann. Stat., 11(1), pp. 95–103. [CrossRef]
Booth, J. G., and Hobert, J. P., 1999, “Maximizing Generalized Linear Mixed Model Likelihoods With an Automated Monte Carlo EM Algorithm,” J. R. Stat. Soc., Ser. B, 61, pp. 265–285. [CrossRef]
McLachlan, G., and Krishnan, T., 1996, The EM Algorithm and Extensions, John Wiley & Sons, New York.
Banks, J., Carson, J. S., II, Nelson, B. L., and Nicol, D. M., 2004, Discrete-Event System Simulation, 4th ed., Prentice-Hall, New Jersey, pp. 327–329.
Chan, J. S. K., and Kuk, A. Y. C., 1997, “Maximum Likelihood Estimation for Probit-Linear Mixed Models With Correlated Random Effects,” Biometrics, 53, pp. 86–97. [CrossRef]
Lange, K., 1995, “A Gradient Algorithm Locally Equivalent to the EM Algorithm,” J. R. Statist. Soc. B, 57, pp. 425–437.
McCulloch, C. E., 1994, “Maximum Likelihood Variance Components Estimation for Binary Data,” J. Am. Stat. Assoc., 89, pp. 330–335. [CrossRef]
McCulloch, C. E., 1997, “Maximum Likelihood Algorithms for Generalized Linear Mixed Models,” J. Am. Stat. Assoc., 92, pp. 162–170. [CrossRef]


Grahic Jump Location
Fig. 1

Clustered nanoparticles within metal matrix (A206 3v 1mic Al2O3)

Grahic Jump Location
Fig. 2

Particles on randomly sampled images: (a) no clustering and (b) clustered

Grahic Jump Location
Fig. 3

The relationship among D, R, and Rc

Grahic Jump Location
Fig. 4

The eight images with 30 clusters from a nanocomposite fabrication process

Grahic Jump Location
Fig. 5

The maximum log-likelihood function based on the observed sample data




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In