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Deformation Micromechanics DUCTILE DEFORMATION AND BRITTLE-DUCTILE TRANSITION.

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Deformation Micromechanic s DUCTILE DEFORMATION AND BRITTLE-DUCTILE TRANSITION
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Deformation Micromechanics

DUCTILE DEFORMATION AND BRITTLE-DUCTILE TRANSITION

Strain rate related to stress

Dislocation Flow

nD

Dislocation Flow

Movement of line defects extra half plane of

atoms

Diffusion Creep

Motion of point defects Diffusion of through the matrix

Diffusion along grain boundaries

Reactions at grain surface

Observations Lattice-preferred orientations (LPOs)

Strain rate related to grain size:

Affected by the chemistry of point defects

m

D

d

Diffusion Flow

Movement of point defects Vacancies, impurities, etc.

Pressure Solution

General Questions

Definitions of terms What are glide, climb, creep, burgers vector, and

cross-slip?

Brittle-ductile vs. Brittle-plastic What’s the difference? Spatial, temporal

relationships, etc.?

Stress and strain relationships (modern form of constitutive law) Which stresses, which strains?

Definitions

What are glide, climb, creep, burgers vector, and cross-slip?

Still don’t understand, the difference between glide, climb, cross slip and what’s burger’s vector.

Burger’s vector – what is it?

Glide, Climb, Cross-slip, Burgers vector

Glide is the movement of edge dislocations in 1-D Single plane, in a single direction

Burgers vector (blue arrow) is magnitude and direction of lattice distortion resulting from dislocation

Propagation of an edge dislocation through a crystal lattice (neon.materials.cmu.edu)

Glide, Climb, Cross-slip, Burgers vector Climb occurs when a dislocation moves up, perpendicularly,

relative to glide Activates at higher temperature

Climb + glide = creep

www.geosci.usyd.edu.au

[1] http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_1_2.html

Motion of a mixed dislocation

[1]

We are looking at the plane of the cut (sort of a semicircle centered in the lower left corner). Blue circles denote atoms just below, red circles atoms just above the cut. Up on the right the dislocation is a pure edge dislocation

on the lower left it is pure screw. In between it is mixed. In the link this dislocation is shown moving in ananimated illustration.

Glide, Climb, Cross-slip, Burgers vector Cross-slip is similar to climb, but applies to screw-

dislocations Screw dislocations operate similar to a zipper

chemistry.tutorvista.com www.matter.org.uk

Brittle-Ductile vs. Brittle-Plastic

On page 11, they describe the transition from brittle to plastic deformation to occur in two stages. Are these two spatially or temporally distinct? Why two stages? I’m just not quite sure how ductile and plastic are different.

Does the Semibrittle stage between brittle and plastic always occur, or are there sharp transitions?

To what extent can we observe both isolated and combined effects of the various factors on Semibrittle deformation in the lab?

Why is semi-brittle failure difficult to describe? No constitutive law.

Brittle-Ductile vs. Brittle-Plastic

The brittle-ductile transition is a change from localized to distributed failure. Brittle-plastic is a change from brittle cracking to plastic flow alone.

– The Authors

Brittle-Ductile vs. Brittle-Plastic

Spatially/temporally distinct?

16

Stress/strain relationships

For the creep models, a relation between strain rate and stress is established. But, which strain or stress is used?

What does “stress” mean in the constitutive equations?

How would equation (15) be restated if we considered the six independent components of the stress tensor? Could true triaxial experiments be performed to estimate parameters for the resulting set of constitutive equations?

Stress, strain relationships

Stress (σ) is always differential stress, confining pressure is expressed in an exponential term as (P)

Strain is often expressed in terms of creep rate ( = s-1; percent change per second)

General from of most commonly used flow law:

(Hirth & Kohlstedt, 2003)

Stress, strain relationships

How would equation (15) be restated considering components of the stress tensor? Could true triaxial experiments be performed to estimate parameters constitutive equations?

Which Law?

How do people choose the evolution laws for the dislocation creep? It seems completely dependent on the rock type…

Given Tables 1, 2 and 3, how does a scientist make an informed decision on which model to use? How do they account for the assumptions and limitations?

Once the deformation mechanism of a rock sample is identified, how can the various flow-law parameters be estimated for that particular sample, given the somewhat wide range of experimentally derived values?

Which Law?

Once the deformation mechanism of a rock sample is identified, how can the various flow-law parameters be estimated? Typically, parameters are estimated prior to

determination of a dominant mechanism

Whichever is fastest

Which Law?

Whichever is fastest Experimentally determined parameters for diffusion,

dislocation, and low-T plasticity are plugged into flow law

Fastest mechanism is dominant

Grain size (μm)Stress (MPa) 1 100101 104

Stra

in ra

te

Field observations

What are the features a geologist would look for to infer the dominant mechanism? What techniques are used?

How would we recognize that one specific mechanism dominated, judging only from field samples?

What does the pressure solution deformation look like in thin section/hand sample?

Features

Most common indication is LPO Dislocations are

crystallographically controlled, and will give rise to LPO

Diffusion is not, and will typically manifest as random lattice orientation

Techniques

Most common technique is electron back-scatter diffraction (EBSD) Scattered electrons form

unique pattern based on crystal structure and orientation

Oxford Instruments


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