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Rheology and deformation mechanisms

Rheology and deformation mechanisms. Goal : To understand how different deformation mechanisms control the rheological behavior of rocks. Elastic rheologies — e = σ d /E. Griffith cracks. Pre-existing flaw in crystal lattice Accounts for apparent weakness of solids. Crack propagation.

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Rheology and deformation mechanisms

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

  2. Elastic rheologies — e = σd/E

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

  4. Crack propagation

  5. Tensile stress concentration

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

  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 = σd/η • Dry diffusion creep: Diffusion (movement) of atoms in the crystal lattice accommodated by shuffling of vacancies • 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

  13. Diffusion creep

  14. Volume diffusion Volume diffusion governed by: ė = σd x [(αL x VL x μL) x e^(-Q/RT) x (1/d2)] d = average grain diameter T = temperature Constants: αL = constant VL = lattice volume μL = lattice diffusion coefficient R = gas constant Q = constant Natural log base, not elongation

  15. ė = σd x [(αL x VL x μL) x e^(-Q/RT) x (1/d2)] 1/viscosity (1/η) So, ė = σd/η Therefore, viscosity is proportional to temperature and inversely proportional to (grain size)2

  16. Grain-boundary diffusion governed by the equation: ė = σd x (αGB x VL x μGB) x e^(-Q/RT) x (1/d3) αGB = constant μGB = lattice diffusion coefficient

  17. ė = σd x [(αGB x VL x μGB) x e^(-Q/RT) x (1/d3)] 1/viscosity (1/η) So, ė = σd/η Therefore, viscosity is proportional to temperature and inversely proportional to (grain size)3

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

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

  20. Probably diffusion limited Also ~linear-viscous rheology Viscosity proportional to 1/d3

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

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

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

  24. Dislocation glide

  25. TEM image of dislocations in olivine

  26. Dynamic recrystallization driven by dislocations

  27. Dislocation tangle in olivine Show recrystallization movie

  28. Dynamically recrystallized quartz

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