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 ωω is related to the viscosity ηη for steady-state Coble creep and the (unrelaxed) rigidity μμ through a dimensionless relation of the form Q=F(ωη/μ)Q=F(ωη/μ). Using existing measurements of ηη 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 ηη 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.