Multiscale Analysis of Area Fractions - Example

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Characterizes a binary microstructure using the multi-scale analysis of area fractions technique.

Author(s): Mark A. Tschopp, G.B. Wilks, J.E. Spowart

Corresponding Author: Mark Tschopp


The code and instructions for the synthetic microstructure builder is available at MATLAB Central.

This GUI was built as a user-friendly tool that augments several journal papers on the MSAAF technique and microstructure characterization[1][2][3]. Please forward any criticisms with the software directly to me and I will do my best to address these.

When assessing structure-property relationships for various materials, it is often necessary to define a representative length scale or volume element for characterization or simulation. The Multi-Scale Analysis of Area Fractions (MSAAF) technique characterizes the representative length scale of a two-phase microstructure[1]. This technique can be applied in an isotropic form and a directional form; the directional form is used to assess the directional dependence of the length scale of the underlying microstructure. The directional form of the MSAAF technique has recently been applied to synthetic microstructures with second phase particles of varying area fraction, aspect ratio, and alignment[2]. Additionally, the directional form has been modified such that it can be applied to any vector within the 2D microstructure image, i.e., the vector MSAAF technique[3]. A visual representation of the vector MSAAF results has been used to show the change in the directional length scale as a function of the orientation of the vector.

This MATLAB GUI script was developed as a computationally- efficient tool for researchers that will employ the various MSAAF techniques for two-phase microstructures with little knowledge of the MATLAB programming required to obtain the results. For further information on the techniques or if you have comments, please contact Mark Tschopp at


Multi-Scale Analysis of Area Fractions GUI tool screen shot.


MAT would like to acknowledge funding through the visiting scientist contract at the Air Force Research Laboratory on "Damage Mechanics Model Development for Monocrystalline Superalloys."

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The initial methodology was used in the following papers:

  1. 1.0 1.1 Tschopp, M.A., Wilks, G.B., Spowart, J.E., "Multi-Scale Characterization of Orthotropic Microstructures," MSMSE 16 (2008) 065009,
  2. 2.0 2.1 Spowart, J.E., Maruyama, B., Miracle, D., "Multi-Scale characterization of spatially heterogeneous systems: Implications for discontinuously reinforced metal matrix composite microstructures," Materials Science & Engineering A 307 (2001) 51-66,
  3. 3.0 3.1 Wilks, G.B., Tschopp, M.A., Spowart, J.E., "Multi-Scale Characterization of Inhomogeneous Morphologically Textured Microstructures," Materials Science and Engineering: A, 527 (2010) 883-889,
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