Deformation Micromechanics DUCTILE DEFORMATION AND BRITTLE-DUCTILE TRANSITION

 Strain rate related to stress 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

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

[1] 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 an animated 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

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?

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? 16

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

T=12 50 °C d=15 um P=1 GPa T=1 250 °C σ=3 00 MP a P=3 00 MP a Grain size (μm) Stress (MPa) Strain rate

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