A Theory of Inter-Granular Transient Dislocation Creep: Implications for the Geophysical Studies on Mantle Rheology

Transient creep may play an important role in short-term (small strain) time-dependent deformation such as the post-glacial rebound and the post-seismic deformation. Among various mechanisms of transient creep, I focus on inter-granular transient dislocation creep caused by plastic anisotropy in each grain. The essence of this process is the evolution of strain accommodation across grain-boundaries from elastic to plastic (viscous) accommodation. Extending the previous studies, I show that evolution of strain accommodation leads to two asymptotic behaviors: at small strain, strain accommodation across grain-boundaries is by elastic deformation and the strength is controlled largely by that of the soft slip system. In contrast, when strain exceeds a threshold value, strain accommodation occurs mostly by plastic deformation and the strength is largely controlled by that of the hard slip system. The model predicts that the threshold strain is on the order of elastic strain (depending also on the degree of plastic anisotropy) and the strength contrast between transient and steady-state creep depends on the degree of plastic anisotropy of the crystal. Consequently, transient creep plays an important role in these short-term time-dependent processes. Since the soft and the hard slip systems have different properties, applications of rheological properties inferred from short-term time-dependent deformation to long-term geodynamic processes needs to be made with a great care. Plain Language Summary Rheological properties of Earth's interior can be inferred from the short-term time-dependent deformation such as the post- glacial crustal motion or the post-seismic deformation. These phenomena involve small strain on the order of elastic strain. In contrast, deformation in the geological time scale such as mantle convection involves much larger strain. In contrast to elastic deformation, plastic deformation of solids is not instantaneous and hence strain dependent and consequently the link between these two types of deformation is not straightforward. This paper examines the link between these two types of deformation with an emphasis on deformation of a polycrystalline aggregate made of plastically anisotropic crystals such as olivine. It is shown that those two types of deformation reflect different types of defect motion and therefore the rheological properties inferred from short-term time-dependent deformation are different from those relevant to long-term geological deformation.