Representative volumes of composite materials

Representative volume (RV) of a composite material is important not only for experimental determination of materials properties, but also for theoretical analysis of various properties of the materials. RV is a random variable; this is especially true for the composites with heterogeneous microstructures. In the present study, RV is redefined as a relationship among three parameters: the volume under consideration, the measured or predicted value of a property corresponding to the volume, and the scattering of the property from the real effective property. There are two steps involved to determine RV. The first is to determine the relationship among the effective property, the properties of each constituents, and volume fractions, which is the topic in composite mechanics. The second is determination of the local variation of the heterogeneity of the composite because, with increasing size of the local volume, the statistics from the local volume asymptotically approaches the value from the global average. The main purpose of this study is to develop a theoretical model to determine local variation of heterogeneity, which is obviously related to the morphological features of the composites. The model accounts for coarseness of grain sizes, volume fractions, spatial arrangement of the constituents, and properties of each constituents. By combining the model with available composite models for effective properties of composites, RV for various materials properties can be developed. As an example, RV for elastic moduli of cementitious materials is demonstrated.