Rheology and deformation mechanisms

Goal: To understand how different deformation mechanisms control the rheological behavior of rocks

Rheology and deformation mechanisms

Elastic rheologies — e = σd/E

Griffith cracks• Pre-existing flaw in crystal lattice

• Accounts for apparent weakness of solids

Crack propagation

Tensile stress concentration

Failure

1. Cracks coalesce to form fractures

2. Fractures coalesce to form fault zones

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

1 2

3 4

Linear-viscous rheologies — ė = σd/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

1. Dry diffusion creep

Volume 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:

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

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

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

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

Diffusion creepFavored by:• High T

• Very small grain sizes

• Low σd

– Dominant deformation mechanism in the mantle below ~100–150 km

Material dissolved at high-stress areas and reprecipitated in low-stress areas

2. Dissolution-reprecipitation creep

Reprecipitation

Dissolution

• Probably diffusion limited

• Also ~linear-viscous rheology

• Viscosity proportional to 1/d3

• Often involved with metamorphic reactions

• Important deformation mechanism in middle third of continental crust

• Forms dissolution seams (cleavages), veins, and pressure shadows

Nonlinear rheologies — ė = (σd)n/η

n = stress exponent — typically between 2.4 and 4

Small increases in σd produce large changes in ė

Dislocation creep

Dislocation: linear flaw in a crystal lattice

Can be shuffled through the crystal

Dislocation glide

TEM image of dislocations in olivine

Dynamic recrystallization driven by dislocations

Dislocation tangle in olivine

Show recrystallization movie

Dynamically recrystallized quartz