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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.

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Figures

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Fig. 1

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

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Fig. 2

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

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Fig. 3

The relationship among D, R, and Rc

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Fig. 4

The eight images with 30 clusters from a nanocomposite fabrication process

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Fig. 5

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

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