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Research Papers

# Multiscale Characterization of Spatial Heterogeneity in Multiphase Composite Microstructures

[+] Author and Article Information
M. A. Tschopp

Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39762

G. B. Wilks

Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RX, Wright Patterson AFB, OH 45433; General Dynamics Corporation, Dayton, OH 45431

J. E. Spowart

Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RX, Wright Patterson AFB, OH 45433

Since the chemical reaction units are in moles and the amounts of A and B from an image will be in units of area (volume in 3D), there will be a constant for each reactant relating the area (volume) to the number of moles. To simplify, here we have used 1 pixel of A or B is equal to 1 mol of A or B.

A cubic spline fit may be used to interpolate values between data points, as shown in Fig. 5. The intersection points for $RY0.05$, $RY0.50$, and $RY0.95$ are shown as triangles in Fig. 5.

J. Eng. Mater. Technol 133(1), 011004 (Dec 01, 2010) (5 pages) doi:10.1115/1.4002639 History: Received February 08, 2010; Revised June 22, 2010; Published December 01, 2010; Online December 01, 2010

## Abstract

A computational characterization technique is presented for assessing the spatial heterogeneity of two reactant phases in a three-phase chemically reactive composite. This technique estimates the reaction yield on multiple microstructure length scales based on the segregation of the two reactant phases and the expected reaction stoichiometry. The result of this technique is a metric, quantifying the effectiveness of phase mixing in a particular microstructure as a function of length scale. Assuming that the proportionate mixing of reactant phases on multiple length scales will enhance reaction kinetics and the overall level of reaction completion, this tool can subsequently be used as a figure-of-merit for optimizing microstructure via appropriate processing. To illustrate this point, an example is shown where a bimodal three-phase microstructure has a higher reaction yield at every length scale when compared with a monomodal three-phase microstructure with the same constituent loading.

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## Figures

Figure 3

The evolution of the coefficient of variation as a function of length scale for the ϕ=0.50, d=42 pixel two-phase microstructure (Fig. 1) using the isotropic MSAAF technique. The inset image is a lower resolution image of the analyzed two-phase microstructure.

Figure 4

The evolution of the area fractions of A and B, the reaction product (γ), and unreacted fraction (δ,ε) as a function of length scale, Q, according to the three-phase MSAAF technique

Figure 5

The evolution of the reaction yield as a function of the length scale for a monomodal (dA=dB=42 pixels) and bimodal (dA=14 pixels and dB=42 pixels) three-phase composite with ϕA=0.30 and ϕB=0.20. The red and black triangles mark the length scales associated with RY0.05, RY0.50, and RY0.95 for the monomodal and bimodal cases, respectively.

Figure 1

Subregions (1024 pixel×1024 pixel) of various microstructures generated using the random sequential adsorption technique: (a) a two-phase microstructure with ϕ=0.50, d=42 pixels, (b) a three-phase monomodal (dA=dB=42 pixels) microstructure with ϕA=0.30 and ϕB=0.20, and (c) a three-phase bimodal (dA=14 pixels and dB=42 pixels) microstructure with ϕA=0.30 and ϕB=0.20

Figure 2

The evolution of the area fraction of second phase (depicted by gray level intensity) as a function of length scale, Q, according to the isotropic MSAAF technique (1-2)

Figure 6

The evolution of the reaction yield as a function of the length scale for monomodal (dA=dB=42 pixels) and bimodal (dA=42 pixels and dB=14 pixels) three-phase composites with ϕA=0.10 and ϕB=0.10, 0.20, and 0.30

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