2. Constant stress experiment ductile elastic

3. Constant stress (strain varies) Constant strain (stress varies)

4. Constant stress (strain varies) Constant strain (stress varies)

5. Constant stress (strain varies) Constant strain (stress varies)

6. Constant stress (strain varies) Constant strain (stress varies)

7. Constant stress (strain varies) Constant strain (stress varies)

8. deformation occurs throughout crust, therefore yield stress (σ y ) reached at all depths. ductile elastic Boundary condition = Plate motion! Beneath brittle-ductile transition, deformation described by ductile flow law: ε = A s σ s n FLOW STRESS YIELD STRESS

9. deformation occurs throughout crust, therefore yield stress (σ y ) reached at all depths. ductile elastic Boundary condition = Plate motion! Beneath brittle-ductile transition, deformation described by ductile flow law: ε = A s σ s n FLOW STRESS YIELD STRESS Constant strain experiment?... (constant plate velocities) σ y = σ s

10. Constant strain experiment?... (constant plate velocities) Undeformed rock Shear zone σyσy σyσy σsσs w v ε = v / w Therefore, increase w = decrease ε ε = A s σ s n Therefore, increase w = decrease σ s σ y > σ s - deformation migrates into shear zone Therefore, w decreases until σ y = σ s

11. Constant strain experiment?... (constant plate velocities) Undeformed rock Shear zone σyσy σyσy σsσs w v ε = v / w Therefore, decrease w = increase ε ε = A s σ s n Therefore, decrease w = increase σ s σ y < σ s - deformation migrates outwards Therefore, w decreases until σ y = σ s

12. Constant strain experiment?... (constant plate velocities) Undeformed rock Shear zone σyσy σyσy σsσs w v ε = v / w Therefore, decrease w = increase ε ε = A s σ s n Therefore, decrease w = increase σ s σ y < σ s - deformation migrates outwards Constant stress experiment... i.e. σ y = σ s (due to the buffering effect of the yield stress in the surrounding rock)

13. Problems: 1. If plate velocity changes, strain rate (and therefore flow stress) decreases, resulting in w being too large. 2. pre-existing structure might result in the yield stress being relatively low, therefore w can be higher than predicted. 3. Normal and reverse faulting result in temperature changes, leading to microstructural changes which weaken/strengthen the shear zone localizing or distributing the shear. Conclusion: Strength of lithosphere controlled by yield strength of undeformed rock making up the plate (and NOT the weak shear zone).

14. w = v / A s σ y n i.e. width of the shear zone is a function of the plate velocity / ductile flow law Extrapolated from flow laws for feldspar and olivine

15. Rheology Implications: 1.The microstructures of shear zones evolve differently depending on if they are constant strain rate or constant stress! 2.Dominant mechanism of weakening/localizing in ductile shear zone is grain size reduction (by dynamic recrystallization). Grain size reduction: (= function of stress) 1. Dynamic recrystallization reduces dislocation density (counteracts work hardening) 2. Results in increased grain boundary sliding 3. Results in switch to grain boundary diffusion creep (= grain size sensitive)

16. Rheology Implications: 1.Constant strain experiments: these grain size reduction mechanisms result in decreasing flow stress which in turn decrease the rate of grain size reduction. (A to C) 2.Grain growth driven by surface energy counteracts grain size reduction, shifting the deformation mechanism to dislocation creep (C to D). Therefore weakening is not permanent! Grain size reduction: (= function of stress) 1. Dynamic recrystallization reduces dislocation density (counteracts work hardening) 2. Results in increased grain boundary sliding 3. Results in switch to grain boundary diffusion creep (= grain size sensitive)

17. Rheology Implications: 1.Constant stress experiments: flow stress is maintained. Therefore, the rate of grain size reduction does NOT decrease, and there is no stress drop. (A to B) 2.Grain growth driven by surface energy is inhibited by the faster grain boundary migration. Therefore, no further evolution of grain size. Therefore grain size reduction = dominant cause of strain localization in the lithosphere! Grain size reduction: (= function of stress) 1. Dynamic recrystallization reduces dislocation density (counteracts work hardening) 2. Results in increased grain boundary sliding 3. Results in switch to grain boundary diffusion creep (= grain size sensitive)