Implications of the similarity principle relating creep and attenuation in finely grained solids

The Raj-Ashby model of diffusionally accommodated grain-boundary sliding implies the existence of similitude in the mechanical loss spectrum of finely grained solids: the quality factor Q of a shear wave propagating with angular frequency ω is related to the viscosity η for steady-state Coble creep and the (unrelaxed) rigidity μ through a dimensionless relation of the form Q = F (ω η / μ). Using existing measurements of η and Q obtained respectively from uniaxial creep tests, and forced torsional oscillation tests, we test that prediction. Though the similarity principle appears to hold, definitive proof will require further measurements of Q and η over a larger range of grain sizes. With that proviso, we conclude that the Raj-Ashby model includes the basic physical mechanisms acting in the experiments underlying two existing data sets on attenuation in the geological material olivine.