Transcript MICROMECHANICS II: DUCTILE DEFORMATION

MICROMECHANICS II: CRYSTAL PLASTICITY
This presentation relies on:
1) www.tf.uni-kiel.de/matwis/amat/def\_en
2) www.iap.tuwien.ac.at/www/surface/STM\_Gallery
3) http://www.geo.cornell.edu/geology/classes/RWA
Review of deformation styles:
Brittle: failure that occurs during elastic deformation and is localized
along a single plane.
Ductile: when the rock undergoes a large change in shape without
breaking. At the grain scale, the deformation may occur by cracking
and/or fracturing, or it may occur as plastic deformation.
While brittle deformation is localized, ductile deformation is distributed.
Cataclastic flow: refers to
distributed microfractures at
grain level such that at a
mesoscopic level or hand
specimen scale the rock
appears to flow, and
therefore is "ductile".
Pressure solution
A common deformation
mechanism in the upper crust,
which involves the solution and
re-precipitation of minerals.
This process is
accelerated in the
presence of water.
Slide taken from: http://www.erictwelker.com/pressuresolution.htm
Diffusion and creep:
Micromechanics defects play a central role not only in brittle
deformation (why?), but also in crystal plasticity.
0-Dimensional defects and diffusion creep
Vacancies are missing atoms.
Interstitials are atoms that are
sitting not in their regular place.
Point defects generally are mobile - at least at high temperatures. The
migration of point defects in crystalline solids are referred to as creep
deformation.
Vacancy diffusion
Interstitial diffusion
1-Dimensional defects and dislocation creep
Dislocations are linear defects in lattice structure. These are the
most important defects for the understanding of deformation
under crustal conditions - including the rupture of earthquakes.
STM (Scanning Tunneling
Microscope) image of a
dislocation.
The Burger vector and the Burger circuit
All dislocations may be described by a combination of 2 end-members:
1) Edge dislocation: when the Burger vector is oriented
perpendicular to the dislocation line.
2) Screw dislocation: when the Burger vector is oriented parallel
to the dislocation line.
Dislocation creep proceeds atomic step by atomic step and
finite strain is the result of this process repeated billions of
times!
Edge dislocation
Screw dislocation
Question: Is this an elastic deformation?
Edge dislocation is analogous to a carpet wrinkle
Figure taken from: http://ic.ucsc.edu/~casey/eart150/Lectures/DefMech/14deformationmechanisms.htm
The rheology of dislocation creep
eÝ C0 (1   3 ) n exp( Q
RT
),
where:

eÝ
C0
1   3
n
Q
R
T
is the strain rate
is a constant
is the differential stress
is a constant
is the activation energy
is the universal gas constant
is the temperature
(parameters in red are experimentally determined)
The strength of minerals
Based on the above equation, it is possible to construct
differential stress versus temperature for a variety of rock types.
An important conclusion is that only olivine would have significant
strength at the base of continental crust!
The brittle-ductile transition and the “jelly sandwich” model
The transition between brittle and ductile deformations occurs
when the ductile strain rate is fast enough to prevent the stress
from becoming large enough to reach the brittle strength.
Continental geothermal gradient.
Composition of crust is quartz-dominated.
Composition of mantle is olivine-dominated.
This may explain why earthquakes are confined
to shallow depths.
I'm not aware of field evidence for brittle
deformation below the Moho
Figure from http://peterbird.name/guide/Step_19.htm
The strength profile
depends on the
geothermal gradient and
the mineralogical
composition.
A word of caution: This model
relies entirely on the results of
laboratory experiments that
were conducted on tiny
rock/mineral samples and were
subjected to strain rates that are
up to 7 orders of magnitude
smaller than typical tectonic
rates. Thus, the extrapolation of
these results to geological scale
is non-trivial!