Chapter 8: Dislocations and Strengthening

Chapter 8: Dislocations and Strengthening

CHAPTER 8: DEFORMATION AND 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? 1 DISLOCATIONS & MATERIALS CLASSES Metals: Disl. motion easier. -non-directional bonding -close-packed directions electron cloud for slip. + + + + + + + + + + + + + + + + + + + + + + + + ion cores Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) Ionic Ceramics (NaCl): bonding Motion hard. -need to avoid ++ and -neighbors.

+ - + - + - + - + - + - + - + - + - +

- + 2 DISLOCATION MOTION Produces plastic deformation, Depends on incrementally breaking bonds. Adapted from Fig. 7.1, Callister 6e. (Fig. 7.1 is adapted from A.G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, 1976. p. 153.) If dislocations don't move, deformation doesn't happen! 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.) Adapted from Fig. 7.8, Callister 6e.

3 INCREMENTAL SLIP Dislocations slip planes incrementally... The dislocation line (the moving red dot)... ...separates slipped material on the left from unslipped material on the right. Simulation of dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) 4 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 DISLOCATIONS & CRYSTAL STRUCTURE view onto two Structure: closeclose-packed planes.

packed planes & directions are preferred. close-packed directions close-packed plane (bottom)close-packed plane (top) Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none Mg (HCP) Results of tensile testing. tensile direction Al (FCC) 6 STRESS AND DISLOCATION MOTION Crystals slip due to a resolved shear stress, R. Applied tension can produce such a stress. Applied tensile stress: = F/A F A o ip cti l s re di Resolved shear stress: R=Fs /As

slip plane normal, ns F on i p t i sl rec di R R=Fs/As R As Fs n Relation between and R Fcos A/cos F ns n o i ip t sl rec di

Fs A As R cos cos 7 CRITICAL RESOLVED SHEAR STRESS Condition for dislocation motion: R CRSS Crystal orientation can make it easy or hard to move disl. R cos cos R = 0 =90 typically 10-4G to 10-2G R =/2 =45 =45 R = 0 =90 8

DISL. MOTION IN POLYCRYSTALS Slip planes & directions (, ) change from one crystal to another. Adapted from Fig. 7.10, Callister 6e. (Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) R will vary from one crystal to another. The crystal with the largest R yields first. Other (less favorably oriented) crystals yield later. 300 m 9 4 STRATEGIES FOR STRENGTHENING: 1: REDUCE GRAIN SIZE ai n

gr Grain boundaries are barriers to slip. Barrier "strength" slip plane B n ai increases with r g misorientation. grain A Adapted from Fig. 7.12, Callister 6e. Smaller grain size: (Fig. 7.12 is from A Textbook of Materials Hall-Petch Equation: Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.) yield o k yd 1/2 ry da un bo more barriers to slip. 10 GRAIN SIZE STRENGTHENING: AN EXAMPLE 70wt%Cu-30wt%Zn brass alloy

yield o k yd 1/2 Data: grain size, d (mm) yield(MPa) 200 10-1 10-2 5x10-3 150 ky 100 1 50 0 0 4 8 12 16 Adapted from Fig. 7.13, Callister 6e. (Fig. 7.13 is adapted from H. Suzuki, "The Relation Between the Structure and Mechanical Properties of Metals", Vol. II, National Physical

Laboratory Symposium No. 15, 1963, p. 524.) 0.75mm Adapted from Fig. 4.11(c), Callister 6e. (Fig. 4.11(c) is courtesy of J.E. Burke, General Electric Co. [grain size (mm)]-0.5 11 ANISOTROPY IN yield Can be induced by rolling a polycrystalline metal -before rolling -after rolling Adapted from Fig. 7.11, Callister 6e. (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.) rolling direction 235 m -isotropic since grains are approx. spherical & randomly oriented. -anisotropic

since rolling affects grain orientation and shape. 12 ANISOTROPY IN DEFORMATION 3. Deformed cylinder side view rolling direction 1. Cylinder of 2. Fire cylinder Tantalum at a target. machined from a rolled plate: end view The noncircular end view shows: Photos courtesy of G.T. Gray III, Los Alamos National Labs. Used with permission. plate thickness direction anisotropic deformation of rolled material. 13

STRENGTHENING STRATEGY 2: SOLID SOLUTIONS Impurity atoms distort the lattice & generate stress. Stress produce a barrier to dislocation Smallercan substitutional Larger substitutional motion. impurity impurity A C B Impurity generates local shear at A and B that opposes disl motion to the right. D Impurity generates local shear at C and D that opposes disl motion to the right. 14 EX: SOLID SOLUTION STRENGTHENING IN COPPER 400 300 200 0 10 20 30 40 50

Yield strength (MPa) Tensile strength (MPa) Tensile strength & yield strength increase w/wt% Ni. 180 Adapted from Fig. 7.14 (a) and (b), Callister 6e. 120 60 wt. %Ni, (Concentration C) 0 10 20 30 40 50 wt. %Ni, (Concentration C) 1/2 Empirical relation: y ~C Alloying increases y and TS. 15 STRENGTHENING STRATEGY 4: COLD WORK (%CW) Room temperature deformation. Common forming operations change the cross sectional area: -Forging force die

A o blank -Drawing die Ao die -Rolling Ad Ao Adapted from Fig. 11.7, Callister 6e. Ao tensile force Ad roll force Ad roll force -Extrusion container ram billet container

Ao Ad %CW x100 Ao die holder extrusion Ad die 16 DISLOCATIONS DURING COLD WORK Ti alloy after cold working: Dislocations entangle with one another during cold work. Dislocation motion becomes more difficult. 0.9 m Adapted from Fig. 4.6, Callister 6e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) 17 RESULT OF COLD WORK Dislocation density (d) goes up: Carefully prepared sample: d ~ 103 mm/mm3

Ways of measuring dislocation 10 Heavily deformed sample: 40m d ~ 10 density: Volume, V Area, A 3 mm/mm length, l1 length, l2 length, l3 d l1 l2 l3 V OR N d A Yield stress increases y1 as d increases: y0 dislocation pit N dislocation pits (revealed by etching) Micrograph adapted from

Fig. 7.0, Callister 6e. (Fig. 7.0 is courtesy of W.G. Johnson, General Electric Co.) large hardening small hardening 18 SIMULATION: DISLOCATION MOTION/GENERATION Tensile loading (horizontal dir.) of a FCC metal with notches in the top and bottom surface. Over 1 billion atoms modeled in 3D block. Note the large increase in disl. density. Simulation courtesy of Farid Abraham. Used with permission from International Business Machines Corporation. Click on image to animate 19 DISLOCATION-DISLOCATION TRAPPING Dislocation generate stress. This traps other dislocations. Red dislocation generates shear at pts A and B that

opposes motion of green disl. from left to right. A B 20 IMPACT OF COLD WORK Stress Yield strength ( y ) increases. Tensile strength (TS) increases. Ductility (%EL or %AR) decreases. % co ld Adapted from Fig. 7.18, Callister 6e. (Fig. 7.18 is from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 221.) wo rk Strain 21

COLD WORK ANALYSIS What is the tensile strength & ductility after cold working? ro2 rd2 %CW x10035.6% 2 ro yield strength (MPa) 700 500 600 100 0 20 Cu 40 60 % Cold Work y=300MPa Do=15.2mm Dd=12.2mm tensile strength (MPa) 800 300 300MPa Copper

Cold work -----> 60 40 400 340MPa 200 0 ductility (%EL) 20 Cu 40 60 % Cold Work TS=340MPa 20 Cu 7% 00 20 40 60 % Cold Work

%EL=7% Adapted from Fig. 7.17, Callister 6e. (Fig. 7.17 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.) 22 - BEHAVIOR VS TEMPERTURE Adapted from Fig. 6.14, Callister 6e. 800 Stress (MPa) Results for polycrystalline iron: 600 -200C -100C 400 25C 200 0 0 0.1 0.2

0.3 Strain 0.4 0.5 y and TS decrease with increasing test temperature. %EL increases with increasing test temperature. 3. disl. glides past obstacle Why? Vacancies 2. vacancies help dislocations replace atoms on the past obstacles. obstacle disl. half plane 1. disl. trapped by obstacle 23 EFFECT OF HEATING AFTER %CW 1 hour treatment at Tanneal... decreases TS and increases %EL. Annealing Temperature (C) 100 300 500 700 60

600 tensile strength 50 500 40 400 30 ductility 20 ductility (%EL) tensile strength (MPa) Effects of cold work are reversed! 300 R Re Gr ec ain c ov ry sta ery Gr ow lliz th

ati on 3 Annealing stages to discuss... Adapted from Fig. 7.20, Callister 6e. (Fig. 7.20 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 RECOVERY Annihilation reduces dislocation density. Scenario 1 extra half-plane of atoms atoms diffuse to regions of tension extra half-plane of atoms Disl. annhilate and form a perfect atomic plane. Scenario 2 3. Climbed disl. can now

move on new slip plane 2. grey atoms leave by vacancy diffusion allowing disl. to climb 1. dislocation blocked; cant move to the right R 4. opposite dislocations meet and annihilate obstacle dislocation 25 RECRYSTALLIZATION New crystals are formed that: --have a small disl. density --are small --consume cold-worked crystals. 0.6 mm 0.6 mm Adapted from Fig. 7.19 (a), (b), Callister 6e. (Fig. 7.19 (a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after

3 sec. at 580C. 26 FURTHER RECRYSTALLIZATION All cold-worked crystals are consumed. 0.6 mm 0.6 mm Adapted from Fig. 7.19 (c), (d), Callister 6e. (Fig. 7.19 (c),(d) are courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds 27 GRAIN GROWTH At longer times, larger grains consume smaller ones. Why? Grain boundary area (and therefore 0.6 mm 0.6 mm energy) Adapted from is reduced. Fig. 7.19 (d),

After 8 s, 580C After 15 min, 580C Empirical Relation: exponent typ. ~ grain 2 diam. n d at time t. dn o Kt (e), Callister 6e. (Fig. 7.19 (d),(e) are courtesy of J.E. Burke, General Electric Company.) coefficient dependent on material and T. elapsed time 28 TENSILE RESPONSE: BRITTLE & (MPa) PLASTIC Near Failure brittle failure x

60 40 Initial 20 0 0 onset of necking near failure plastic failure x unload/reload 2 4 aligned,networked crosscase linked case 6 8 crystalline regions slide

semicrystalline case amorphous regions elongate crystalline regions align Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve (purple) adapted from Fig. 15.12, Callister 6e. (Fig. 15.12 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.) 29 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 Adapted from Fig. 15.12, Callister 6e. (Fig. 15.12 is stretching dir. from J.M. Schultz, Polymer Materials Science, Prentice--decreases ductility (%EL) Hall, Inc., 1974, pp. 500-501.) Annealing after drawing... --decreases alignment --reverses effects of drawing. Compare to cold working in metals! 30

THERMOPLASTICS VS THERMOSETS Thermoplastics: --little cross linking --ductile --soften w/heating --polyethylene (#2) polypropylene (#5) polycarbonate polystyrene (#6) T mobile liquid viscous liquid crystalline solid Callister, rubber Fig. 16.9 tough plastic Tm Tg partially crystalline solid Molecular weight Thermosets: Adapted from Fig. 15.18, Callister 6e. (Fig. 15.18 is from F.W.

Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.) --large cross linking (10 to 50% of mers) --hard and brittle --do NOT soften w/heating --vulcanized rubber, epoxies, polyester resin, phenolic resin 31 TENSILE RESPONSE: ELASTOMER CASE (MPa) 60 xbrittle failure plastic failure 40 x 20 0 0 elastomer 2 initial: amorphous chains are kinked, heavily cross-linked. 4 6

x 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. 15.14, Callister 6e. (Fig. 15.14 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) Deformation is reversible! Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) 32

SUMMARY Dislocations are observed primarily in metals and alloys. Here, strength is increased by making dislocation motion difficult. Particular ways to increase strength are to: --decrease grain size --solid solution strengthening --precipitate strengthening --cold work Heating (annealing) can reduce dislocation density and increase grain size. 33 ANNOUNCEMENTS Reading: Core Problems: Self-help Problems: 0

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