New approximate solution for N-point correlation functions for heterogeneous materials

M. Baniassadi, Said Ahzi, H. Garmestani, D. Ruch, Y. Remond

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Statistical N-point correlation functions are used for calculating properties of heterogeneous systems. The strength and the main advantage of the statistical continuum approach is the direct link to statistical information of microstructure. Two-point correlation functions are the lowest order of correlation functions that can describe the morphology and the microstructure-properties relationship. Experimentally, statistical pair correlation functions are obtained using SEM or small x-ray scattering techniques. Higher order correlation functions must be calculated or measured to increase the precision of the statistical continuum approach. To achieve this aim a new approximation methodology is utilized to obtain N-point correlation functions for non-FGM (functional graded materials) heterogeneous microstructures. Conditional probability functions are used to formulate the proposed theoretical approximation. In this approximation, weight functions are used to connect subsets of (N-1)-point correlation functions to estimate the full set of N-point correlation function. For the approximation of three and four point correlation functions, simple weight functions have been introduced. The results from this new approximation, for three-point probability functions, are compared to the real probability functions calculated from a computer generated three-phase reconstructed microstructure in three-dimensional space. This three-dimensional reconstruction was based on an experimental two-dimensional microstructure (SEM image) of a three-phase material. This comparison proves that our new comprehensive approximation is capable of describing higher order statistical correlation functions with the needed accuracy.

Original languageEnglish
Pages (from-to)104-119
Number of pages16
JournalJournal of the Mechanics and Physics of Solids
Volume60
Issue number1
DOIs
Publication statusPublished - Jan 2012
Externally publishedYes

Fingerprint

microstructure
approximation
Microstructure
continuums
statistical correlation
scanning electron microscopy
x ray scattering
set theory
Scanning electron microscopy
methodology
Set theory
estimates
Scattering
X rays

Keywords

  • Conditional probability
  • Heterogeneous medium
  • N-point correlation functions
  • Statistical information of microstructure

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

New approximate solution for N-point correlation functions for heterogeneous materials. / Baniassadi, M.; Ahzi, Said; Garmestani, H.; Ruch, D.; Remond, Y.

In: Journal of the Mechanics and Physics of Solids, Vol. 60, No. 1, 01.2012, p. 104-119.

Research output: Contribution to journalArticle

Baniassadi, M. ; Ahzi, Said ; Garmestani, H. ; Ruch, D. ; Remond, Y. / New approximate solution for N-point correlation functions for heterogeneous materials. In: Journal of the Mechanics and Physics of Solids. 2012 ; Vol. 60, No. 1. pp. 104-119.
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