Dislocation density evolution and its consequences for steady-state and transient creep. New theory and models.

Abstract:

Dislocations are the carriers of intracrystalline plastic deformation. Therefore, the evolution of dislocation density exerts a control on the transient mechanical behaviour of rocks. Steady-state mechanical behaviour reflects an underlying dependence on dislocation density that is often neglected. Dislocation density evolves in response to deformation and therefore it is tightly coupled with transient creep. Previous approaches have recovered either the steady-state relationship between strain rate and stress, or the steady-state relationship between dislocation density and stress. We present a consistent theory that recovers both empirically-derived relationships.

Our theory is based on approaches from the materials sciences that account for the competing processes of dislocation accumulation and recovery. We describe dislocation accumulation by a geometrical approach. We incorporate a number of dislocation recovery processes including dynamic recovery, and static recovery facilitated by both bulk and pipe diffusion. The model is closed by an experimentally calibrated flow law describing dislocation glide. Importantly, this flow law incorporates both an Orowan-type dependence, in which the rate of deformation increases with increasing dislocation density, and a Taylor-like dependence that opposes the applied stress with an internal stress due to dislocations. We calibrate our model by comparison against transient creep and stress-reduction experiments on single crystals of olivine at high temperatures.

We solve for the steady-state strain rate and dislocation density predicted at any given temperature and stress. In contrast to previous approaches, we reproduce the observed power-law relationships between strain rate and stress as well as dislocation density and stress at experimental conditions. Extrapolation to settings relevant for Earth suggests that different power-law relationships operate under these conditions. The stored elastic energy associated with dislocations represents a significant fraction of the microstructural energy budget during deformation; future work will investigate grain size evolution driven by our model of dislocation density.