Dislocation

1. Dislocation Dr. Richard Chung Department of Chemical and Materials Engineering San José State University

2. 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.

3. 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.

4. 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

5. 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

6. Dislocations Assume Take derivative

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

8. 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

9. Motion of Edge Dislocations

10. Edge Dislocation

11. Frictional stress • 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

14. Climb of A Dislocation • 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

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

16. Jogs and Slip Vector • Jogs are continuously created and destroyed in an edge dislocation by randomly exchange its atoms with the surrounding

17. Shear Stress and Jogs

21. Twinning

22. Properties of Dislocations • Dislocation stress fields • Dislocation energies • Dislocation interactions (forces in between) • Dislocation kinks and velocities

23. Dislocation Stress fields

34. Conclusion • 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