Rheology and deformation
mechanisms
Goal: To understand how different
deformation mechanisms control the
rheological behavior of rocks
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 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
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 creep
Favored by:
• High T
• Very small grain sizes
• Low σd
– Dominant deformation mechanism in the
mantle below ~100–150 km
2. Dissolution-reprecipitation
creep
Material dissolved at high-stress areas and
reprecipitated in low-stress areas
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