Topological characterization of second-phase structure in heterogeneous materials

Abstract

A topology-based method originally used by astrophysicists for studying the large-scale structure of star clusters is adopted here to characterize the spatial arrangement of second-phase particles in heterogeneous materials. The microstructure inside a representative unit is smoothed into a continuum density field. Using a density threshold the material can be separated into two parts. Then the genus, a topological measure of surfaces, is calculated for the interface between the two parts. A curve of the genus versus the normalized density is plotted using a series of values of the density threshold. It is shown that this curve can be used to identify the spatial arrangement of the second-phase particles. Several typical arrangements are studied using this method to demonstrate its effectiveness. The characterization method can be used to analyze microstructure data obtained using experimental techniques, e.g. X-ray tomography. It can also be further simplified to provide a set of internal variables for constitutive modelling of the material.

Acknowledgements

The authors are grateful to Professor D. H. Weinberg at the Ohio State University who kindly provided us with a computer program and instructions in using the program for calculating the G_s –ν _V curves. This project is financially funded by the EPSRC (S97996).