An experimental investigation of the Hashin-Shtrikman bounds on two-phase aggregate elastic properties

摘要: Abstract Existing data supporting or disputing the validity of Hashin-Shtrikman bounds on elastic properties multiphase aggregates often do not consider porosity, anisotropy, experimental errors. In this experiment, two-phase KCl + (NH4Br, TlBr, CsCl, NaCl, Cu, and LiF) at every 20% volume fraction were vacuum hot-pressed compressional shear velocities measured with a computer-controlled ultrasonic interferometer to ±0.2%. The ratio moduli, μ, (phase 2/KCl) varied from about 1 5, producing range separations between theoretical for composites. Samples generally 99% better density, less than 1% velocity anisotropy. Porosity corrections applied assuming spherical pores, based observed velocity-pressure behaviour. Velocities agreed HS calculated end-member single-crystal stiffnesses when anisotropy was taken into account. also used estimate bulk modulus, K, modulus second phase by means matrix method — taking K μ as known calculating moduli other that Voigt-Reuss-Hill average. A narrow estimates results only if μ's both phases are fairly closely matched. For mismatched factor uncertainty in can be 10 times larger uncertainty. Estimates using VRH average lie outside HS-based results.