1. ASE324: Aerospace Materials Laboratory Instructor: Rui Huang Dept of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Fall 2003

2. Lecture 4 September 9, 2003

3. Plastic deformation Material remains intact Original crystal structure is not destroyed Crystal distortion is extremely localized Possible mechanisms: –Translational glide (slipping) –Twin glide (twinning)

4. Translational glide The principle mode of plastic deformation Slip planes: preferred planes with greatest interplanar distance, e.g., (111) in fcc crystals Slip directions: with lowest resistance, e.g., closed packed direction Slip lines: intersection of a slip plane with a free surface Slip band: many parallel slip lines very closely spaced together Slip plane Slip line

5. Existence of defects Theoretical yield strength predicted for perfect crystals is much greater than the measured strength. The large discrepancy puzzled many scientists until Orowan, Polanyi, and Taylor (1934). The existence of defects (specifically, dislocations) explains the discrepancy.

6. Defects Point defects: vacancies, interstitial atoms, substitional atoms, etc. Line defects: dislocations (edge, screw, mixed) –Most important for plastic deformation Surface defects: grain boundaries, phase boundaries, free surfaces, etc.

7. Edge dislocations Burgers vector: characterizes the “strength” of dislocations Edge dislocations: b  dislocation line D.R. Askeland and P.P. Phule, The Science and Engineering of Materials, Brooks/Cole (2003).

8. Screw dislocations Burgers vector b // dislocation line D.R. Askeland and P.P. Phule, The Science and Engineering of Materials, Brooks/Cole (2003).

9. Mixed dislocation Have both edge and screw components.

10. Observation of dislocations Transmission Electron microscopy (TEM): diffraction images of dislocations appear as dark lines. M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2 nd ed. (2002)

11. Glide of an edge dislocation Break one bond at a time, much easier than breaking all the bonds along the slip plane simultaneously, and thus lower yield stress. D.R. Askeland and P.P. Phule, The Science and Engineering of Materials, Brooks/Cole (2003).

12. Motion of dislocations William D. Callister, Jr., Materials Science and Engineering, An Introduction, John Wiley & Sons, Inc. (2003)

13. Force acting on dislocations Applied shear stress (  ) exerts a force on a dislocation Motion of dislocation is resisted by a frictional force (f, per unit length) Work done by the shear stress (W  ) equals the work done by the frictional force (W f ). M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2 nd ed. (2002)

14. Lattice friction stress Theoretical shear strength: Lattice friction stress for dislocation motion: Lattice friction stress is much less than the theoretical shear strength Dislocation motion most likely occurs on closed packed planes (large a, interplanar spacing) in closed packed directions (small b, in-plane atomic spacing).

15. Interactions of dislocations Two dislocations may repel or attract each other, depending on their directions. RepulsionAttraction

16. Line tension of a dislocation Atoms near the core of a dislocation have a higher energy due to distortion. Dislocation line tends to shorten to minimize energy, as if it had a line tension. Line tension = strain energy per unit length T T

17. Dislocation bowing Dislocations may be pinned by solutes, interstitials, and precipitates Pinned dislocations can bow when subjected to shear stress, analogous to the bowing of a string.  bL TT  R  /2 R L

18. Dislocation multiplication Some dislocations form during the process of crystallization. More dislocations are created during plastic deformation. Frank-Read Sources: a dislocation breeding mechanism.

19. Frank-Read sources in Si Dash, Dislocation and Mechanical Properties of Crystals, Wiley (1957).

20. Strengthening mechanisms Pure metals have low resistance to dislocation motion, thus low yield strength. Increase the resistance by strengthening: –Solution strengthening –Precipitate strengthening –Work hardening

21. Solution strengthening Add impurities to form solid solution (alloy) Example: add Zn in Cu to form brass, strength increased by up to 10 times. Cu Zn Bigger Zn atoms make the slip plane “rougher”, thus increase the resistance to dislocation motion.

22. Precipitate strengthening Precipitates (small particles) can promote strengthening by impeding dislocation motion. Dislocation bowing and looping. Critical condition at semicircular configuration: M.F. Ashby and D.R.H. Jones, Engineering Materials 1, 2 nd ed. (2002)

23. Work-hardening Dislocations interact and obstruct each other. Accounts for higher strength of cold rolled steels.    YU  YL Strain hardening ×  UTS ff

24. Polycrystalline materials Different crystal orientations in different grains. Crystal structure is disturbed at grain boundaries. D.R. Askeland and P.P. Phule, The Science and Engineering of Materials, Brooks/Cole (2003).

25. Plastic deformation in polycrystals Slip in each grain is constrained Dislocations pile up at grain boundaries Gross yield-strength is higher than single crystals (Taylor factor) Strength depends on grain size (Hall-Petch).

26. Dislocation pile-up at grain boundaries