Which rule of mixture is the best for predicting the overall elastic properties of polyphase rocks based on the elasticities and volume fractions of their constituents? In order to address this question, we sintered forsterite-enstatite polycrystalline aggregates with a varied forsterite volume fraction (0, 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0). Elastic properties of these synthesized composites were measured as a function of pressure up to 3.0 GPa in a liquid-medium piston cylinder apparatus using a high precision ultrasonic interferometric technique. The experimental data can be much better described by the shear-lag model than by the commonly used simple models such as Voigt, Reuss and Hill averages, Hashin-Shtrikman bounds, Ravichandran bounds, Halpin-Tsai equations, and Paul's calculations. We interpret this as an indication that the elastic interaction and stress transfer between phases are neglected in all models except the shear-lag model. In particular, the present study suggests that olivine in the mantle may be more abundant than previously inferred from the comparison between seismic Earth model velocities and calculated overall elastic properties of mantle mineral composites according to the Hill average or Hashin-Shtrikman bounds.
Ji, S., & Wang, Z. (1999). Elastic properties of forsterite-enstatite composites up to 3.0 GPa. Journal of Geodynamics, 28(2–3), 147–174. https://doi.org/10.1016/S0264-3707(98)00034-9