# Rheology and deformation mechanisms

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06-Jan-2016Category

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Rheology and deformation mechanismsGoal: To understand how different deformation mechanisms control the rheological behavior of rocks

Elastic rheologies e = d/E

Griffith cracksPre-existing flaw in crystal latticeAccounts for apparent weakness of solids

Crack propagation

Tensile stress concentration

Failure1. Cracks coalesce to form fractures 2. Fractures coalesce to form fault zones

Cataclastic flowCataclastic flow: Combination of pervasive fracturing, frictional sliding, and rolling of fragments in fault zoneMost frictional-brittle faults operate by cataclastic flow

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Linear-viscous rheologies = d/ 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

1. Dry diffusion creepVolume diffusion: movement of atoms through the crystal

Grain-boundary diffusion: movement of atoms around the crystal

Crystal defects

Diffusion creep

Volume diffusionVolume diffusion governed by: = d x [(L x VL x L) x e^(-Q/RT) x (1/d2)]d = average grain diameterT = temperatureConstants:L = constantVL = lattice volumeL = lattice diffusion coefficientR = gas constantQ = constant

Natural log base, not elongation

= d x [(L x VL x L) x e^(-Q/RT) x (1/d2)]

1/viscosity (1/)So, = d/Therefore, viscosity is proportional to temperature and inversely proportional to (grain size)2

Grain-boundary diffusiongoverned by the equation: = d x (GB x VL x GB) x e^(-Q/RT) x (1/d3)GB = constantGB = lattice diffusion coefficient

= d x [(GB x VL x GB) x e^(-Q/RT) x (1/d3)]

1/viscosity (1/)So, = d/Therefore, viscosity is proportional to temperature and inversely proportional to (grain size)3

Diffusion creepFavored by:High TVery small grain sizesLow d

Dominant deformation mechanism in the mantle below ~100150 km

2. Dissolution-reprecipitation creepMaterial dissolved at high-stress areas and reprecipitated in low-stress areasReprecipitationDissolution

Probably diffusion limitedAlso ~linear-viscous rheologyViscosity proportional to 1/d3

Often involved with metamorphic reactionsImportant deformation mechanism in middle third of continental crustForms dissolution seams (cleavages), veins, and pressure shadows

Nonlinear rheologies = (d)n/ n = stress exponent typically between 2.4 and 4Small increases in d produce large changes in

Dislocation creepDislocation: linear flaw in a crystal latticeCan be shuffled through the crystal

Dislocation glide

TEM image of dislocations in olivine

Dynamic recrystallization driven by dislocations

Dislocation tangle in olivineShow recrystallization movie

Dynamically recrystallized quartz

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