Why are dislocations observed primarily in metals CHAPTER 8: DEFORMATION AND STRENGTHENING MECHANISMS

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1 Why are dislocations observed primarily in metals CHAPTER 8: and alloys? DEFORMATION AND STRENGTHENING MECHANISMS How are strength and dislocation motion related? How do we manipulate properties? Strengthening Heat treating 1

2 Slip on close packed planes In a given crystal, slip is easiest on the most densely packed plane in the most densely packed direction Single crystal Zn (hcp)

3 DISLOCATIONS Edge Screw Produce plastic deformation, Incrementally breaking/reforming bonds. 3

4 Stress at dislocation From: Van Vlack, 1985 Highest stress with no impurity at core Under shear, atoms in the highly strained area will shift more easily

5 BOND BREAKING AND REMAKING Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) 5

6 DISLOCATIONS & MATERIALS CLASSES Metals: Disl. motion easier. -non-directional bonding -close-packed directions for slip. electron cloud ion cores Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) bonding Ionic Ceramics (NaCl): Motion hard. -need to avoid ++ and -- neighbors

7 DISLOCATION MOTION - SLIP Strain field around dislocation core Interaction between strain fields can effect motion Edge Dislocations allow slip at lower shear stress, but when they become entangled the metal is stronger. 3

8 DISLOCATIONS & CRYSTAL STRUCTURE close-packed planes & directions are preferred. WHY? more nearest neighbors, easier to transfer bond from one atom to next 6

9 FCC slip directions Ex.: In (111) plane Along [10-1] direction How many slip directions? (100)<011> FCC (110)<-110>

10 Slip plane/directions Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none NO CLOSE-PACKED PLANES, but still has preferred slip directions and planes

11 Shear stress Applied tensile stress produces shear on internal planes Resolved components of pure shear and pure tension for the plane of interest σ = σ cos 2 θ τ = σ sin θ cos θ shear and normal stress on plane Max shear stress at this angle (45) 3

12 STRESS AND DISLOCATION MOTION Crystals slip due to a resolved shear stress, τ R. on favorably oriented plane/direction τ R = σcos λcos φ for shear stress on particular plane and direction Plastically stretched zinc single crystal. Adapted from Fig. 7.9, Callister 6e. (Fig. 7.9 is from C.F. Elam, The Distortion of Metal Crystals, Oxford University Press, London, 1935.) 7

13 CRITICAL RESOLVED SHEAR STRESS (CRSS) Condition for dislocation motion Orientation of slip system (crystal orientation) can make it easy or hard to move dislocation on that system τ R =σcos λcos φ σ σ τ R > τ CRSS typically 10-4 G to 10-2 G σ Material property τ R = 0 λ=90 τ R = σ/2 λ=45 φ=45 τ R = 0 φ=90 8

14 DISL. MOTION IN POLYCRYSTALS σ Slip planes & directions (λ, φ) change from one crystal to another. τ R for most favorable direction will vary from one crystal to another. The crystal with the largest τ R yields first. Other (less favorably oriented) crystals yield later. Unfavorably oriented grains inhibit deformation of favorably oriented grains 300 μm Adapted from Fig. 7.10, Callister 6e. (Fig is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) 9

15 Manipulation of properties 1. Strengthening 2. Heat treating

16 3 STRATEGIES FOR STRENGTHENING: 1: REDUCE GRAIN SIZE Grain boundaries are barriers to slip. Barrier "strength" increases with misorientation. Smaller grain size: more barriers to slip. Hall-Petch Equation: slip plane grain A Adapted from Fig. 7.12, Callister 6e. (Fig is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.) σ yield =σ o + k y d 1/2 grain B grain boundary Example: Solidification conditions can change grain size 10

17 Can be induced by rolling a polycrystalline metal -before rolling ANISOTROPY IN σ yield -after rolling rolling direction Adapted from Fig. 7.11, Callister 6e. (Fig 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 μm -isotropic since grains are approx. spherical & randomly oriented. -anisotropic since rolling affects grain orientation and shape. 12

18 STRENGTHENING STRATEGY 2: SOLID SOLUTIONS Impurity atoms distort the lattice & generate stress. Stress can produce a barrier to dislocation motion. Smaller substitutional impurity A Larger substitutional impurity C B D Impurity generates local shear at A and B that opposes disl motion to the right. Impurity generates local shear at C and D that opposes disl motion to the right. 14

19 STRENGTHENING STRATEGY 2: SOLID SOLUTIONS Impurity atoms distort the lattice & generate stress. Stress can produce a barrier to dislocation motion. 14

20 Solid Solution: Stress at dislocation From: Van Vlack, 1985 Highest stress with no impurity at core Under shear, atoms in the highly strained area will shift more easily Effect of adding impurity at core of dislocation added stress needed to move dislocation past the impurity

21 EX: SOLID SOLUTION STRENGTHENING IN COPPER Tensile strength & yield strength increase w/wt% Ni. Tensile strength (MPa) Yield strength (MPa) wt. %Ni, (Concentration C) Adapted from Fig (a) and (b), Callister 6e. wt. %Ni, (Concentration C) Empirical relation: 1/ 2 ~ impurity σ y C Alloying increases σ y and TS. 15

22 STRENGTHENING STRATEGY 3: COLD WORK (%CW) Room temperature deformation. increase # of dislocations Common forming operations change the cross sectional area: -Forging Ao die blank -Drawing Ao die die force force Ad Ad tensile force Adapted from Fig. 11.7, Callister 6e. Ao force -Rolling Ao roll roll -Extrusion container ram billet container Ad die holder extrusion Ad die %CW = A o A d A o x100 16

23 DISLOCATIONS DURING COLD WORK Ti alloy after cold working: Dislocations entangle with one another during cold work. Dislocation motion becomes more difficult. 0.9 μm Adapted from Fig. 4.6, Callister 6e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) 17

24 RESULT OF COLD WORK Dislocation density (ρ d ) goes up: Carefully prepared sample: ρd ~ 10 3 mm/mm 3 Heavily deformed sample: ρd ~ mm/mm 3 Measuring dislocation density: 40μm Area, A dislocation pit Yield stress increases as ρ d increases: ρ d = N A σ σ y1 σ y0 N dislocation pits (revealed by etching) large hardening small hardening ε 18

25 IMPACT OF COLD WORK Yield strength (σ y ) increases. Tensile strength (TS) increases. Ductility (%EL or %AR) decreases. Stress % cold work Strain Adapted from Fig. 7.18, Callister 6e. (Fig is from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 221.) 21

26 COLD WORK ANALYSIS What is the tensile strength & ductility after cold working? Copper Cold work -----> Do=15.2mm Dd=12.2mm %CW = πr o 2 πr d 2 πr o 2 x100 = 35.6% Ductility decreased, Tensile strength increased 22

27 Effect of Temperature on Strength

28 σ-ε BEHAVIOR VS TEMPERTURE Results for polycrystalline iron: Stress (MPa) Strain σ y and TS decrease with increasing test temperature. %EL increases with increasing test temperature. Why? Vacancies 3. disl. glides past obstacle help dislocations past obstacles. 2. vacancies replace atoms on the disl. half plane -200 C -100 C obstacle 1. disl. trapped by obstacle 25 C 23

29 Heat treatment: EFFECT OF HEATING AFTER %CW 1 hour treatment at Tanneal... decreases TS and increases %EL. Effects of cold work are reversed! tensile strength (MPa) Annealing Temperature ( C) tensile strength Recovery ductility Recrystallization ductility (%EL) Grain Growth 3 Annealing stages to discuss... Recovery Recrystallization Grain growth Adapted from Fig. 7.20, Callister 6e. (Fig 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.) 24

30 RECOVERY Dislocation motion without externally applied stress Annihilation reduces dislocation density. diffusion extra half-plane of atoms atoms diffuse to regions of tension extra half-plane of atoms Disl. annhilate and form a perfect atomic plane. Reduction of dislocation density reduces strength 25

31 RECRYSTALLIZATION New crystals are formed that: --have a small disl. density --are small --consume cold-worked crystals. 0.6 mm 0.6 mm The higher the internal strain, the faster recrystallization will occur Adapted from Fig (a),(b), Callister 6e. (Fig (a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580C. 26

32 FURTHER RECRYSTALLIZATION All cold-worked crystals are consumed. 0.6 mm 0.6 mm Adapted from Fig (c),(d), Callister 6e. (Fig (c),(d) are courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds 27

33 At longer times, larger grains consume smaller ones. Why? 0.6 mm 0.6 mm GRAIN GROWTH Grain boundary area (and therefore internal energy) is reduced. After 8 s, 580C After 15 min, 580C Adapted from Fig (d),(e), Callister 6e. (Fig (d),(e) are courtesy of J.E. Burke, General Electric Company.) 28

34 Heat Treatment of cold worked metal Grain growth and recovery have a moderate effect on properties compared to recrystallization where disclocation density is more severely affected One hour of baking at each temperature 28

35 Deformation and strengthening of polymers

36 TENSILE RESPONSE: BRITTLE & PLASTIC Near Failure σ(mpa) 60 x 40 brittle failure onset of necking plastic failure x near failure Initial aligned, networked cross- case linked case semicrystalline case unload/reload amorphous regions elongate 8 ε crystalline regions align crystalline regions slide Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve (purple) adapted from Fig , Callister 6e. (Fig is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp ) 29

37 PREDEFORMATION BY DRAWING Drawing... --stretches the polymer prior to use --aligns chains to the stretching direction Results of drawing: --increases the elastic modulus (E) in the stretching dir. --increases the tensile strength (TS) in the stretching dir. --decreases ductility (%EL) Annealing after drawing... --decreases alignment --reverses effects of drawing. Compare to cold working in metals! Adapted from Fig , Callister 6e. (Fig is from J.M. Schultz, Polymer Materials Science, Prentice- Hall, Inc., 1974, pp ) 30

38 TENSILE RESPONSE: ELASTOMER CASE σ(mpa) 60 x initial: amorphous chains are kinked, heavily cross-linked. brittle failure plastic failure x elastomer Deformation is reversible! ε 8 final: chains are straight, still cross-linked Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig , Callister 6e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) x 32