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### Dislocation

Dr. Richard Chung

Department of Chemical and Materials Engineering

San José State University

Learning Objectives

- Describe the types of line defects (dislocations) and their relationships between the microstructure and the movement of dislocations
- Distinguish the difference between perfect slips and atomic distortions associated with dislocation motion
- Explain the slip processes in edge and screw dislocations
- Illustrate the interrelationships among structural irregularities, strain energy and stress field with respect to dislocations
- Define different terms involved in dislocations such as Frank-Read mechanisms, kinks, jogs, climb, cross-slip, twinning, cell structure, etc.

Dislocations

- Dislocations are types of line defect.
- Dislocations usually appear in low- stressed crystalline material.
- Dislocations are responsible for a plastic flow in a material.
- The number of dislocation, the deformation mechanisms, the stress field, and strain energies are all associated with the key role dislocations play in a crystal material.

Some Useful Web Pages

- Defects in Crystals
Prof. Helmut Föll, University of Kiel

http://www.techfak.uni-kiel.de/matwis/amat/def_en/makeindex.html

- Dislocation Movement Across Grain Boundaries
http://www.jwave.vt.edu/crcd/farkas/lectures/dislocations/tsld023.htm

- Kinks and Jogs
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_3_1.html

Inter-atomic Distance, b

- The shear stress is responsible for displacing atoms.
- Assume two rows of atoms are moving against each other in opposite directions. The distance between the center of an atom to the center of another atom is defined as the inter-atomic distance b.
- At x= b/2, the crystal (lattice) energy is at a maximum, whereas the shear stress is at a minimum.
- At x= b/4 the shear stress reaches a maximum value, max

- Stress-displacement curve in a sinusoidal function.
Where b is atomic separation distance, and a is the spacing between slip planes

Large Discrepancy between Theoretical Values and Experimental Values

- The theoretical value of maximum shear stress is based on the order of G/2
- The relationship between the applied force and the atomic separation is not in a symmetry the sinusoidal curve is not valid
- Atomic shear is not the driving force for the plastic deformation in a crystal

Motion of Edge Dislocations Experimental Values

Edge Dislocation Experimental Values

Frictional stress Experimental Values

- Peierls and Nabarro developed the equation for calculating the frictional stress:
- is the Possion’s ratio
The formula can also be expressed by the width (w)of a dislocation

Climb of A Dislocation Experimental Values

- The core of a dislocation can move into an adjacent atomic vacancy dislocation climbs
- An adjacent atom can move into the core of a dislocation a lattice vacancy

- Kinks and Jogs Experimental Values
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_3_1.html

Jogs and Slip Vector Experimental Values

- Jogs are continuously created and destroyed in an edge dislocation by randomly exchange its atoms with the surrounding

Shear Stress and Jogs Experimental Values

Twinning Experimental Values

Properties of Dislocations Experimental Values

- Dislocation stress fields
- Dislocation energies
- Dislocation interactions (forces in between)
- Dislocation kinks and velocities

Dislocation Stress fields Experimental Values

Conclusion Experimental Values

- Burgers vector indicate the slip direction
- Burgers vector is normal to an edge dislocation line, but parallel to a screw dislocation line
- A screw dislocation can cross slip from one slip plane to another
- An edge dislocation can move out of its slip plane by moving upward, normal to it
- Dislocation energy is proportional to the square of its Burgers vector

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