Chapter 7: Dislocations & Strengthening Mechanisms

1. Chapter 7: Dislocations & Strengthening Mechanisms ISSUES TO ADDRESS... • Why are dislocations observed primarily in metals and alloys? • How are strength and dislocation motion related? • How do we increase strength? • How can heating change strength and other properties?

2. Dislocations & Materials Classes • Metals: Disl. mvt easier. -non-directional bonding -close-packed directions for slip. + + + + + + + + + + + + + + + + + + + + + + + + electron cloud ion cores • Covalent Ceramics (Si, diamond): Movement difficult. -directional (angular) bonding • Ionic Ceramics (NaCl): Movement difficult. -need to avoid ++ and - - neighbors. - - - + + + + - - - - + + + - - - + + + +

3. Dislocation Motion Dislocations & plastic deformation • Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations). • If dislocations don't move, deformation doesn't occur! Adapted from Fig. 7.1, Callister 7e.

4. Dislocation Motion • Dislocation moves along slip plane in slip direction perpendicular to dislocation line • Slip direction same direction as Burgers vector Edge dislocation Adapted from Fig. 7.2, Callister 7e. Screw dislocation

5. photomicrograph of a lithium fluoride (LiF) single crystal, the small pyramidal pits represent those positions at which dislocations intersect the surface. The surface was polished and then chemically treated; these “etch pits” result from localized chemical attack around the dislocations and indicate the distribution of the dislocations. 750X

6. f03_07_pg177 Dislocation Motion

7. Deformation Mechanisms Slip System • Slip plane - plane allowing easiest slippage • Wide interplanar spacings - highest planar densities • Slip direction- direction of movement - Highest linear densities • FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed) => total of 12 slip systems in FCC • in BCC & HCP other slip systems occur Adapted from Fig. 7.6, Callister 7e.

8. Resolved Shear Stress Resolved shear stress is the shear component of an applied tensile (or compressive) stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The critical resolved shear stress is the value of resolved shear stress at which yielding begins; it is a property of the material.

9. Critical Resolved Shear Stress typically 10-4GPa to 10-2 GPa • Condition for dislocation motion: • Crystal orientation can make it easy or hard to move dislocation  = 60°  = 35°

10. Single Crystal Slip Adapted from Fig. 7.9, Callister 7e. Adapted from Fig. 7.8, Callister 7e.

11. Slip Motion in Polycrystals s 300 mm • Stronger - grain boundaries pin deformations • Slip planes & directions (l, f) change from one crystal to another. • tRwill vary from one crystal to another. • The crystal with the largest tR yields first. • Other (less favorably oriented) crystals yield later. Adapted from Fig. 7.10, Callister 7e. (Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)

12. Anisotropy in sy - after rolling rolling direction - anisotropic since rolling affects grain orientation and shape. • Can be induced by rolling a polycrystalline metal - before rolling Adapted from Fig. 7.11, Callister 7e. (Fig. 7.11 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure, p. 140, John Wiley and Sons, New York, 1964.) 235 mm - isotropic since grains are approx. spherical & randomly oriented.

13. f12_07_pg187 Deformation by Twinning HRTEM Image of Si

14. Difference between Slip and Twinning

15. Difference Between Slip and Twinning • Slip occurs in distinct atomic spacing multiples, whereas the atomic displacement for twinning is less than the inter-atomic separation, usually proportional to their distances from the twin plane. • for slip, the crystallographic orientation above and below the slip plane is the same both before and after the deformation; for twinning, there will be a reorientation across the twin plane. • The amount of bulk plastic deformation from twinning is normally small relative to that resulting from slip; twinning may however place new slip systems in orientations that are favorable relative to the stress axis such that the slip process can now take place.

16. 4 Strategies for Strengthening: 1: Reduce Grain Size • Grain boundaries are barriers to slip. • Barrier "strength" increases with Increasing angle of misorientation. • Smaller grain size: more barriers to slip. • Hall-Petch Equation: Adapted from Fig. 7.14, Callister 7e. (Fig. 7.14 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)

17. 4 Strategies for Strengthening: 2: Solid Solutions • Smaller substitutional impurity • Larger substitutional impurity A C D B Impurity generates local stress at A and B that opposes dislocation motion to the right. Impurity generates local stress at C and D that opposes dislocation motion to the right. • Impurity atoms distort the lattice & generate stress. • Stress can produce a barrier to dislocation motion.

18. Stress Concentration at Dislocations Adapted from Fig. 7.4, Callister 7e.

19. Strengthening by Alloying • small impurities tend to concentrate at dislocations • reduce mobility of dislocation  increase strength Adapted from Fig. 7.17, Callister 7e.

20. Strengthening by alloying • large impurities concentrate at dislocations on low density side Adapted from Fig. 7.18, Callister 7e.

21. 180 400 120 Yield strength (MPa) Tensile strength (MPa) 300 60 200 0 10 20 30 40 50 0 10 20 30 40 50 wt.% Ni, (Concentration C) wt.%Ni, (Concentration C) Ex: Solid SolutionStrengthening in Copper • Tensile strength & yield strength increase with wt% Ni. Adapted from Fig. 7.16 (a) and (b), Callister 7e. • Empirical relation: • Alloying increases sy and TS.

22. 4 Strategies for Strengthening: 3: Precipitation Strengthening precipitate Side View Unslipped part of slip plane Top View S spacing Slipped part of slip plane • Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum). Large shear stress needed to move dislocation toward precipitate and shear it. Dislocation “advances” but precipitates act as “pinning” sites with spacing S . • Result:

23. Application:Precipitation Strengthening 1.5mm • Internal wing structure on Boeing 767 Adapted from chapter-opening photograph, Chapter 11, Callister 5e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) • Aluminum is strengthened with precipitates formed by alloying. Adapted from Fig. 11.26, Callister 7e. (Fig. 11.26 is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)

24. force -Forging -Rolling roll die A d A A A o blank o d Adapted from Fig. 11.8, Callister 7e. roll force -Drawing -Extrusion A o die container A d die holder tensile force A o ram A billet extrusion d force die die container 4 Strategies for Strengthening: 4: Cold Work (%CW) • Room temperature deformation. • Common forming operations change the cross sectional area:

25. Dislocations During Cold Work 0.9 mm • Ti alloy after cold working: • Dislocations entangle with one another during cold work. • Dislocation motion becomes more difficult. Adapted from Fig. 4.6, Callister 7e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.)

26. total dislocation length unit volume s large hardening s y1 s small hardening y0 e Result of Cold Work Dislocation density = • Carefully grown single crystal  ca. 103 mm-2 • Deforming sample increases density 109-1010 mm-2 • Heat treatment reduces density  105-106 mm-2 • Yield stress increases as rd increases:

27. Impact of Cold Work As cold work is increased • Yield strength (sy) increases. • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. Adapted from Fig. 7.20, Callister 7e.

28. Cold Work Analysis Copper Cold Work D =15.2mm D =12.2mm o d tensile strength (MPa) yield strength (MPa) ductility (%EL) 60 800 700 40 600 500 Cu 300MPa 300 Cu 20 400 340MPa Cu 7% 100 200 0 0 20 40 60 0 20 40 60 0 20 40 60 % Cold Work % Cold Work % Cold Work s = 300MPa TS = 340MPa %EL = 7% y • What is the tensile strength & ductility after cold working? Adapted from Fig. 7.19, Callister 7e. (Fig. 7.19 is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, 1979, p. 276 and 327.)

29. s-e Behavior vs. Temperature 800 -200C 600 -100C Stress (MPa) 400 25C 200 0 0 0.1 0.2 0.3 0.4 0.5 Strain 3 . disl. glides past obstacle 2. vacancies replace atoms on the obstacle disl. half 1. disl. trapped plane by obstacle • Results for polycrystalline iron: Adapted from Fig. 6.14, Callister 7e. • sy and TS decrease with increasing test temperature. • %ELincreases with increasing test temperature. • Why? Vacancies help dislocations move past obstacles.

30. Effect of Heating After %CW annealing temperature (ºC) 100 200 300 400 500 600 700 600 60 tensile strength 50 500 ductility (%EL) 40 tensile strength (MPa) 400 30 ductility 20 300 Recovery Grain Growth Recrystallization • 1 hour treatment at Tanneal... decreases TS and increases %EL. • Effects of cold work are reversed! • 3 Annealing stages to discuss... Adapted from Fig. 7.22, Callister 7e. (Fig. 7.22 is adapted from G. Sachs and K.R. van Horn, Practical Metallurgy, Applied Metallurgy, and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, American Society for Metals, 1940, p. 139.)

31. Recovery & Dislocation Movement Adapted from Fig. 7.5, Callister 7e.

32. Recovery • Scenario 1 extra half-plane of atoms Dislocations Results from diffusion annihilate atoms and form diffuse a perfect to regions atomic of tension plane. extra half-plane of atoms tR 3 . “Climbed” disl. can now move on new slip plane 2 . grey atoms leave by 4. opposite dislocations vacancy diffusion meet and annihilate allowing disl. to “climb” Obstacle dislocation 1. dislocation blocked; can’t move to the right Annihilation reduces dislocation density. • Scenario 2

33. f08_04_pg94

34. Recrystallization 0.6 mm 0.6 mm Adapted from Fig. 7.21 (a),(b), Callister 7e. (Fig. 7.21 (a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580C. • New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains.

35. Further Recrystallization 0.6 mm 0.6 mm After 8 seconds After 4 seconds • All cold-worked grains are consumed. Adapted from Fig. 7.21 (c),(d), Callister 7e. (Fig. 7.21 (c),(d) are courtesy of J.E. Burke, General Electric Company.)

36. Grain Growth 0.6 mm 0.6 mm After 8 s, 580ºC After 15 min, 580ºC coefficient dependent on material and T. • Empirical Relation: exponent typ. ~ 2 elapsed time grain diam. at time t. Ostwald Ripening • At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced. Adapted from Fig. 7.21 (d),(e), Callister 7e. (Fig. 7.21 (d),(e) are courtesy of J.E. Burke, General Electric Company.)

37. Grain Growth • Occurs by grain boundary migration. • Large grains grow at the expense of smaller grains. • Grain Boundary movement occurs by short range diffusion of atoms from one side of the boundary to the other.

38. Grain Growth • Atoms and Grain Boundaries move in opposite directions!!!

39. TR º TR = recrystallization temperature Adapted from Fig. 7.22, Callister 7e. º

40. Recrystallization Temperature, TR TR= Recrystallization temperature = point of highest rate of property change • Tm => TR 0.3-0.6 Tm (K) • Due to diffusion  annealing time TR = f(t) shorter annealing time => higher TR • Pure metals lower TR due to dislocation movements easier to move in pure metals => lower TR • Cold work  below TR • Hot work above TR

41. Recrystallization Temperature for Metals

42. Summary • Dislocations are observed primarily in metals and alloys. • Strength is increased by making dislocation movement difficult. • Particular ways to increase strength are to: --decrease grain size --solid solution strengthening --precipitation strengthening --cold work • Heating (annealing) can reduce dislocation density and increase grain size. This decreases the strength.