Chapter 8 Deformation Strengthening Mechanisms ISSUES TO ADDRESS

Chapter 8: Deformation & Strengthening Mechanisms ISSUES TO ADDRESS. . . • Why are the number of dislocations present greatest in metals ? • How are strength and dislocation motion related? • Why does heating alter strength and other properties? Chapter 8 - 1

Dislocations & Materials Classes • Metals (Cu, Al): Dislocation motion easiest + + + + - non-directional bonding + + + + - close-packed directions ion cores electron cloud for slip + + • Covalent Ceramics (Si, diamond): Motion difficult - directional (angular) bonding • Ionic Ceramics (Na. Cl): Motion difficult - need to avoid nearest neighbors of like sign (- and +) + - + - + - + Chapter 8 - 2

Dislocation Motion Dislocation motion & plastic deformation • Metals - plastic deformation occurs by slip – an edge dislocation (extra half-plane of atoms) slides over adjacent plane half-planes of atoms. • If dislocations can't move, plastic deformation doesn't occur! Adapted from Fig. 8. 1, Callister & Rethwisch 3 e. Chapter 8 - 3

Dislocation Motion • A dislocation moves along a slip plane in a slip direction perpendicular to the dislocation line • The slip direction is the same as the Burgers vector direction Edge dislocation Adapted from Fig. 8. 2, Callister & Rethwisch 3 e. Screw dislocation Chapter 8 - 4

Deformation Mechanisms Slip System – Slip plane - plane on which easiest slippage occurs • Highest planar densities (and large interplanar spacings) – Slip directions - directions of movement • Highest linear densities Adapted from Fig. 8. 6, Callister & Rethwisch 3 e. – FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed) => total of 12 slip systems in FCC – For BCC & HCP there are other slip systems. Chapter 8 - 5

Stress and Dislocation Motion • Resolved shear stress, R – results from applied tensile stresses Applied tensile stress: = F/A A F Resolved shear stress: R =Fs /A s slip plane normal, ns n F n p ctio i l s re R di R = FS /AS R FS p io sli rect di Relation between and R AS Fcos F p sli rec di n tio FS A/cos n. S A AS Chapter 8 - 6

Critical Resolved Shear Stress • Condition for dislocation motion: • Ease of dislocation motion depends on crystallographic orientation typically 10 -4 GPa to 10 -2 GPa R = 0 =90° R = /2 =45° maximum at = = 45º R = 0 =90° Chapter 8 - 7

Single Crystal Slip Adapted from Fig. 8. 9, Callister & Rethwisch 3 e. Adapted from Fig. 8. 8, Callister & Rethwisch 3 e. Chapter 8 - 8

Ex: Deformation of single crystal = 60° a) Will the single crystal yield? b) If not, what stress is needed? = 35° crss = 20. 7 MPa Adapted from Fig. 8. 7, Callister & Rethwisch 3 e. = 6500 psi So the applied stress of 6500 psi will not cause the crystal to yield. Chapter 8 - 9

Ex: Deformation of single crystal What stress is necessary (i. e. , what is the yield stress, y)? So for deformation to occur the applied stress must be greater than or equal to the yield stress Chapter 8 - 10

Slip Motion in Polycrystals • Stronger - grain boundaries pin deformations • Slip planes & directions ( , ) change from one crystal to another. Adapted from Fig. 8. 10, Callister & Rethwisch 3 e. (Fig. 8. 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 mm Chapter 8 - 11

Anisotropy in sy • Can be induced by rolling a polycrystalline metal - before rolling - after rolling Adapted from Fig. 8. 11, Callister & Rethwisch 3 e. (Fig. 8. 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 mm - isotropic since grains are approx. spherical & randomly oriented. - anisotropic since rolling affects grain orientation and shape. Chapter 8 - 12

Anisotropy in Deformation 2. Fire cylinder at a target. 3. Deformed cylinder side view rolling direction 1. Cylinder of tantalum 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. Chapter 8 - 13

4 Strategies for Strengthening Metals: 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. Adapted from Fig. 8. 14, Callister & Rethwisch 3 e. (Fig. 8. 14 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc. , Upper Saddle River, NJ. ) • Hall-Petch Equation: Chapter 8 - 14

4 Strategies for Strengthening Metals: 2: Solid Solutions • Impurity atoms distort the lattice & generate stress. • Stress can produce a barrier to dislocation motion. • Smaller substitutional impurity • Larger substitutional impurity A C B Impurity generates local stress at A and B that opposes dislocation motion to the right. D Impurity generates local stress at C and D that opposes dislocation motion to the right. Chapter 8 - 15

Stress Concentration at Dislocations Adapted from Fig. 8. 4, Callister & Rethwisch 3 e. Chapter 8 - 16

Strengthening by Alloying • small impurities tend to concentrate at dislocations • reduce mobility of dislocation increase strength Adapted from Fig. 8. 17, Callister & Rethwisch 3 e. Chapter 8 - 17

Strengthening by Alloying • large impurities concentrate at dislocations on low density side Adapted from Fig. 8. 18, Callister & Rethwisch 3 e. Chapter 8 - 18

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 with wt% Ni. 180 Adapted from Fig. 8. 16 (a) and (b), Callister & Rethwisch 3 e. 120 60 wt. % Ni, (Concentration C) 0 10 20 30 40 50 wt. %Ni, (Concentration C) • Empirical relation: • Alloying increases y and TS. Chapter 8 - 19

4 Strategies for Strengthening Metals: 3: Precipitation Strengthening • Hard precipitates are difficult to shear. Ex: Ceramics in metals (Si. C in Iron or Aluminum). precipitate Large shear stress needed to move dislocation toward precipitate and shear it. Side View Top View Unslipped part of slip plane S Dislocation “advances” but precipitates act as “pinning” sites with spacing S. Slipped part of slip plane • Result: Chapter 8 - 20

Application: Precipitation Strengthening • Internal wing structure on Boeing 767 Adapted from chapteropening photograph, Chapter 11, Callister & Rethwisch 3 e. (courtesy of G. H. Narayanan and A. G. Miller, Boeing Commercial Airplane Company. ) • Aluminum is strengthened with precipitates formed by alloying. Adapted from chapteropening photograph, Chapter 11, Callister & Rethwisch 3 e. (courtesy of G. H. Narayanan and A. G. Miller, Boeing Commercial Airplane Company. ) 1. 5 mm Chapter 8 - 21

4 Strategies for Strengthening Metals: 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 force Ad Ao Adapted from Fig. 14. 2, Callister & Rethwisch 3 e. Ad roll -Extrusion Ao tensile force roll force container ram billet container die holder extrusion die Chapter 8 - 22 Ad

Dislocations During Cold Work • Ti alloy after cold working: • Dislocations entangle with one another during cold work. • Dislocation motion becomes more difficult. 0. 9 mm Adapted from Fig. 5. 11, Callister & Rethwisch 3 e. (Fig. 5. 11 is courtesy of M. R. Plichta, Michigan Technological University. ) Chapter 8 - 23

Result of Cold Work Dislocation density = total dislocation length unit volume – 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 y 1 as rd increases: y 0 large hardening small hardening e Chapter 8 - 24

Effects of Stress at Dislocations Adapted from Fig. 8. 5, Callister & Rethwisch 3 e. Chapter 8 - 25

Impact of Cold Work As cold work is increased • Yield strength ( y) increases. • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. Adapted from Fig. 8. 20, Callister & Rethwisch 3 e. Chapter 8 - 26

Cold Work Analysis • What is the tensile strength & ductility after cold working? Copper Cold Work Do =15. 2 mm yield strength (MPa) tensile strength (MPa) 60 700 800 500 600 300 MPa 100 0 20 Cu 40 % Cold Work y = 300 MPa 60 0 ductility (%EL) 40 20 400 340 MPa 200 Dd =12. 2 mm 20 Cu 40 60 % Cold Work TS = 340 MPa Cu 7% 00 20 40 60 % Cold Work %EL = 7% Adapted from Fig. 8. 19, Callister & Rethwisch 3 e. (Fig. 8. 19 is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9 th ed. , B. Bardes (Ed. ), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9 th ed. , H. Baker (Managing Ed. ), American Society for Metals, 1979, p. 276 and 327. ) Chapter 8 - 27

s- e Behavior vs. Temperature Adapted from Fig. 7. 14, Callister & Rethwisch 3 e. Stress (MPa) 800 • Results for polycrystalline iron: -200 C 600 -100 C 400 25 C 200 0 0 0. 1 0. 2 0. 3 0. 4 Strain • 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 move past obstacles. atoms on the obstacle disl. half plane 0. 5 1. disl. trapped by obstacle Chapter 8 - 28

Effect of Heating After %CW • 1 hour treatment at Tanneal. . . decreases TS and increases %EL. • Effects of cold work are reversed! 100 200 300 400 500 600 700 60 tensile strength 50 ductility (%EL) tensile strength (MPa) annealing temperature (ºC) 500 40 400 30 ductility 20 300 Re co ve ry Re c rys tal liza Gr ai n. G tio n row th • 3 Annealing stages to discuss. . . Adapted from Fig. 8. 22, Callister & Rethwisch 3 e. (Fig. 8. 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. ) Chapter 8 - 29

Recovery Annihilation reduces dislocation density. • Scenario 1 Results from diffusion • Scenario 2 extra half-plane of atoms diffuse to regions of tension extra half-plane of atoms 3. “Climbed” disl. can now move on new slip plane 2. grey atoms leave by vacancy diffusion allowing disl. to “climb” 1. dislocation blocked; can’t move to the right Dislocations annihilate and form a perfect atomic plane. R 4. opposite dislocations meet and annihilate Obstacle dislocation Chapter 8 - 30

Recrystallization • New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains. 0. 6 mm Adapted from Fig. 8. 21 (a), (b), Callister & Rethwisch 3 e. (Fig. 8. 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. Chapter 8 - 31

Further Recrystallization • All cold-worked grains are consumed. 0. 6 mm Adapted from Fig. 8. 21 (c), (d), Callister & Rethwisch 3 e. (Fig. 8. 21 (c), (d) are courtesy of J. E. Burke, General Electric Company. ) After 4 seconds After 8 seconds Chapter 8 - 32

Grain Growth • At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced. 0. 6 mm After 8 s, 580ºC 0. 6 mm After 15 min, 580ºC • Empirical Relation: exponent typ. ~ 2 grain diam. at time t. Adapted from Fig. 8. 21 (d), (e), Callister & Rethwisch 3 e. (Fig. 8. 21 (d), (e) are courtesy of J. E. Burke, General Electric Company. ) coefficient dependent on material and T. elapsed time Ostwald Ripening Chapter 8 - 33

º TR = recrystallization temperature TR Adapted from Fig. 8. 22, Callister & Rethwisch 3 e. º Chapter 8 - 34

Recrystallization Temperature, TR TR = recrystallization temperature = point of highest rate of property change 1. Tm => TR 0. 3 -0. 6 Tm (K) 2. Due to diffusion annealing time TR = f(time) shorter annealing time => higher TR 3. Higher %CW => lower TR – strain hardening 4. Pure metals lower TR due to dislocation movements • Easier to move in pure metals => lower TR Chapter 8 - 35

Coldwork Calculations A cylindrical rod of brass originally 0. 40 in (10. 2 mm) in diameter is to be cold worked by drawing. The circular cross section will be maintained during deformation. A cold-worked tensile strength in excess of 55, 000 psi (380 MPa) and a ductility of at least 15 %EL are desired. Further more, the final diameter must be 0. 30 in (7. 6 mm). Explain how this may be accomplished. Chapter 8 - 36

Coldwork Calculations Solution If we directly draw to the final diameter what happens? Brass Cold Work Do = 0. 40 in Df = 0. 30 in Chapter 8 - 37

Coldwork Calc Solution: Cont. 420 540 6 Adapted from Fig. 8. 19, Callister & Rethwisch 3 e. • For %CW = 43. 8% – y = 420 MPa – TS = 540 MPa > 380 MPa – %EL = 6 < 15 • This doesn’t satisfy criteria…… what can we do? Chapter 8 - 38

Coldwork Calc Solution: Cont. 15 380 27 12 For TS > 380 MPa > 12 %CW For %EL > 15 < 27 %CW Adapted from Fig. 8. 19, Callister & Rethwisch 3 e. our working range is limited to %CW = 12 -27 Chapter 8 - 39

Coldwork Calc Soln: Recrystallization Cold draw-anneal-cold draw again • For objective we need a cold work of %CW 12 -27 – We’ll use %CW = 20 • Diameter after first cold draw (before 2 nd cold draw)? – must be calculated as follows: Intermediate diameter = Chapter 8 - 40

Coldwork Calculations Solution Summary: 1. Cold work D 01= 0. 40 in Df 1 = 0. 335 m 2. Anneal above D 02 = Df 1 3. Cold work D 02= 0. 335 in Df 2 =0. 30 m Fig 7. 19 Therefore, meets all requirements Chapter 8 - 41

Rate of Recrystallization start 50% finish • Hot work above TR • Cold work below TR • Smaller grains – stronger at low temperature – weaker at high temperature log t Chapter 8 - 42

Mechanical Properties of Polymers – Stress-Strain Behavior brittle polymer plastic elastomer elastic moduli – less than for metals Adapted from Fig. 7. 22, Callister & Rethwisch 3 e. • Fracture strengths of polymers ~ 10% of those for metals • Deformation strains for polymers > 1000% – for most metals, deformation strains < 10% Chapter 8 - 43

Mechanisms of Deformation—Brittle Crosslinked and Network Polymers Initial Near Failure (MPa) Initial x brittle failure Near Failure x plastic failure aligned, crosslinked polymer e network polymer Stress-strain curves adapted from Fig. 7. 22, Callister & Rethwisch 3 e. Chapter 8 - 44

Mechanisms of Deformation — Semicrystalline (Plastic) Polymers (MPa) Stress-strain curves adapted from Fig. 7. 22, Callister & Rethwisch 3 e. Inset figures along plastic response curve adapted from Figs. 8. 27 & 8. 28, Callister & Rethwisch 3 e. (Figs. 8. 27 & 8. 28 are from J. M. Schultz, Polymer Materials Science, Prentice. Hall, Inc. , 1974, pp. 500 -501. ) fibrillar structure x brittle failure onset of necking plastic failure x unload/reload e undeformed structure near failure amorphous regions elongate crystalline block segments separate crystalline regions align Chapter 8 - 45

Predeformation by Drawing • Drawing…(ex: monofilament fishline) -- stretches the polymer prior to use -- aligns chains in the stretching direction • Results of drawing: -- increases the elastic modulus (E) in the stretching direction -- increases the tensile strength (TS) in the stretching direction Adapted from Fig. 8. 28, Callister & Rethwisch 3 e. (Fig. 8. 28 is -- decreases ductility (%EL) from J. M. Schultz, Polymer Materials Science, Prentice-Hall, • Annealing after drawing. . . Inc. , 1974, pp. 500 -501. ) -- decreases chain alignment -- reverses effects of drawing (reduces E and TS, enhances %EL) • Contrast to effects of cold working in metals! Chapter 8 - 46

Mechanisms of Deformation— Elastomers (MPa) x brittle failure x plastic failure elastomer x e initial: amorphous chains are kinked, cross-linked. final: chains are straighter, still cross-linked Stress-strain curves adapted from Fig. 7. 22, Callister & Rethwisch 3 e. Inset figures along elastomer curve (green) adapted from Fig. 8. 30, Callister & Rethwisch 3 e. (Fig. 8. 30 is from Z. D. Jastrzebski, The Nature and Properties of Engineering Materials, 3 rd ed. , John Wiley and Sons, 1987. ) deformation is reversible (elastic)! • Compare elastic behavior of elastomers with the: -- brittle behavior (of aligned, crosslinked & network polymers), and -- plastic behavior (of semicrystalline polymers) (as shown on previous slides) Chapter 8 - 47

Summary • Dislocations are observed primarily in metals and alloys. • 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. This decreases the strength. Chapter 8 - 48