Scaling of internal dissipation of polycrystalline solids on grain-size and frequency

Abstract

Internal friction is essential for nearly all solids to dissipate kinetic energy through internal mechanisms. The pioneering analyses by Zener (Phys. Rev. 60 (1941) 906-908) and Kê (Phys. Rev. 71 (1947) 533-546) demonstrated the existence of a single friction peak in the loss modulus spectrum of polycrystalline solids, which is attributed to viscous sliding in grain boundaries. In this study, we establish a continuum model coupled elastic deformation, viscous creep and diffusion in grain boundaries and reveal the existence of a second loss modulus peak resulted from viscous deformation within grain boundaries. The corresponding two frequencies when internal dissipation reaches its local maximum depend on grain size d, one is inversely proportional to d, and the other is proportional to d−3. The effects of local elasticity and diffusion in grain boundaries on the loss modulus spectrum are examined and the condition when the two peaks emerge is identified. The findings can be applied to granular and porous materials, and complex rheology in geosciences, where internal dissipation is momentous for waves and seismic activities.