1. Goal: To understand how different deformation mechanisms control the rheological behavior of rocks Rheology and deformation mechanisms

2. Elastic rheologies — e = σ d /E

3. Griffith cracks Pre-existing flaw in crystal lattice Accounts for apparent weakness of solids

4. Crack propagation

5. Tensile stress concentration

6. Failure 1. Cracks coalesce to form fractures 2. Fractures coalesce to form fault zones

7. Cataclastic flow Cataclastic flow: Combination of pervasive fracturing, frictional sliding, and rolling of fragments in fault zone Most frictional-brittle faults operate by cataclastic flow

8. 1 2

9. 3 4

10. Linear-viscous rheologies — ė = σ d /η 1.Dry diffusion creep: Diffusion (movement) of atoms in the crystal lattice accommodated by shuffling of vacancies 2.Dissolution-reprecipitation creep: dissolving material at high-stress areas and reprecipitating it in low-stress areas

11. 1. Dry diffusion creep Volume diffusion: movement of atoms through the crystal Grain-boundary diffusion: movement of atoms around the crystal

12. Crystal defects

14. Diffusion creep

15. Volume diffusion Volume diffusion governed by: ė = σ d x [(α L x V L x μ L ) x e^(-Q/RT) x (1/d 2 ) ] d = average grain diameter T = temperature Constants: α L = constant V L = lattice volume μ L = lattice diffusion coefficient R = gas constant Q = constant Natural log base, not elongation

16. ė = σ d x [(α L x V L x μ L ) x e^(-Q/RT) x (1/d 2 ) ] 1/viscosity (1/η) So, ė = σ d /η Therefore, viscosity is proportional to temperature and inversely proportional to (grain size) 2

17. Grain-boundary diffusion governed by the equation: ė = σ d x (α GB x V L x μ GB ) x e^(-Q/RT) x (1/d 3 ) α GB = constant μ GB = lattice diffusion coefficient

18. ė = σ d x [(α GB x V L x μ GB ) x e^(-Q/RT) x (1/d 3 )] 1/viscosity (1/η) So, ė = σ d /η Therefore, viscosity is proportional to temperature and inversely proportional to (grain size) 3

19. Diffusion creep Favored by: High T Very small grain sizes Low σ d –Dominant deformation mechanism in the mantle below ~100–150 km

20. Material dissolved at high-stress areas and reprecipitated in low-stress areas 2. Dissolution-reprecipitation creep Reprecipitation Dissolution

21. Probably diffusion limited Also ~linear-viscous rheology Viscosity proportional to 1/d 3

22. Often involved with metamorphic reactions Important deformation mechanism in middle third of continental crust Forms dissolution seams (cleavages), veins, and pressure shadows

23. Nonlinear rheologies — ė = (σ d ) n /η n = stress exponent — typically between 2.4 and 4 Small increases in σ d produce large changes in ė

24. Dislocation creep Dislocation: linear flaw in a crystal lattice Can be shuffled through the crystal

26. Dislocation glide

27. TEM image of dislocations in olivine

28. Dynamic recrystallization driven by dislocations

29. Dislocation tangle in olivine Show recrystallization movie

30. Dynamically recrystallized quartz