ANALYSIS OF INTERNAL STRUCTURES OF COMPOSITE-MATERIALS BY 2ND-ORDER PROPERTY OF MOSAIC PATTERNS

Properties of composite materials depend on their internal structures which in most cases are highly random. Therefore, high-order informati on is often required for quantitative characterization of morphologica l features in spatial distributions of the constituent phases. The pre sent study develops a general expression for a second-order moment, th at is, autocorrelation function R(x)(upsilon), of multiphase heterogen eous composites. The obtained R(x)(upsilon) depends on three types of parameters: volume fractions of the constituent phases, values of the phase function, and pi (the probability that two points with distance upsilon are in the same basic cell). pi depends on the constitution of the basic cell, and thus the specific characteristics of the internal structure of the material. To determine completely the autocorrelatio n function, probability pi is derived based on a morphological model c alled mosaic patterns. Derivation of pi for two types of mosaic patter ns indicates that pi [and thus R(x)(upsilon)] has different formulatio ns for different internal structures, although all of them depend on t he same set of parameters: coarseness of microstructures, lambda, volu me fraction of constituent phases, phi, and values of the chosen phase function. For a two-phase composite, with increasing phi(1) (volume f raction of phase 1), the value of R(x)(upsilon) increases; while, with increasing lambda, the structure of the composite becomes more and mo re fine grained, and thus the correlation between two points with a fi xed distance upsilon becomes weaker. As an example of applications of the present result, the autocorrelation function is applied to predict the fluctuation of local volume fractions of two-phase composite mate rials.