A generalized mixture rule for estimating the viscosity of solid-liquid suspensions and mechanical properties of polyphase rocks and composite materials

摘要

A simple phenomenological formula is proposed to predict the mechanical properties of isotropic multiphase materials in terms of component properties, volume fractions, and microstructures. The formula is regarded as a generalized mixture rule (GMR) because it works equally well for various mechanical properties ( e. g., Young's modulus, viscosity, hardness, yield, and flow strengths) and for wide ranges of multiphase systems. The GMR can be readily utilized to polyphase systems having either weak-phase supported structure ( e. g., solid-liquid suspensions) or strong-phase supported structure (e.g., porous materials). Various well-known expressions (e.g., Einstein, Roscoe, Voigt, Reuss, and geometrical mean) are special cases of the GMR and can be derived from the master equation using different values of the single microstructural coefficient J. It is believed that the GMR will facilitate further understanding of the statistical effects of arbitrarily complex microstructures ( e. g., phase continuity and connectivity, particle shape, and size distribution) on the overall mechanical properties of composite materials including polymineralic and partially melted rocks. The formula has a particular advantage if it is desired to invert the mechanical data to the volume fractions of the composite constituent phases and microstructure.