Based on measured values for the stress exponent, n≈3.5, combined with the empirically determined relationship between dislocation density and stress (ρ∝σ1.37) and an analysis of diffusion kinetics in olivine, we conclude that silicon pipe diffusion limits strain rate in the dislocation creep regime. Furthermore, assuming that steady state recrystallized grain size is set by a dynamic balance between strain energy density (associated with dislocations) and surface energy density (associated with grain boundaries), the resulting dependence of recrystallized grain size on stress accurately describes experimental observations when the empirical dislocation density versus stress relationship is accounted for (d∝1/σ1.37). The improved physical understanding of the stress dependence of creep rate provides justification for incorporation of experimentally derived flow laws into models of geodynamical process and grain size evolution. These lab constraints combined with independent analyses of the stress dependence of mantle viscosity based on geophysical data provide bounds on rheological properties such as the yield stress of the lithosphere.
Bibliographical noteFunding Information:
The authors thank Reid Cooper and Mike Gurnis, amongst many others, for helpful discussions. The research was supported by NSF grants EAR-1220075 (GH) and EAR-1214876 (DLK).
- Grain size
- Mantle viscosity