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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Figure 6. 28 The Charpy V-notch properties for a BCC carbon steel and a FCC stainless steel. The FCC crystal structure typically leads top higher absorbed energies and no transition temperature 2

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 (Na. Cl): Motion hard. -need to avoid ++ and - neighbors. + - + - + - +

Dislocation Motion Dislocations & plastic deformation • Cubic & hexagonal metals - plastic deformation is by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations). Adapted from Fig. 7. 1, Callister 7 e. • If dislocations don't move, deformation doesn't occur!

Slip Motion in Polycrystals • Stronger since grain boundaries pin deformations s • Slip planes & directions (l, f) change from one crystal to another. Adapted from Fig. 7. 10, Callister 7 e. (Fig. 7. 10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD]. ) • t. R will vary from one crystal to another. • The crystal with the largest t. R yields first. • Other (less favorably oriented) crystals yield (slip) later. 300 mm

After seeing the effect of poly crystalline materials we can say (as related to strength): • Ordinarily ductility is sacrificed when an alloy is strengthened. • The relationship between dislocation motion and mechanical behavior of metals is significance to the understanding of strengthening mechanisms. • The ability of a metal to plastically deform depends on the ability of dislocations to move. • Virtually all strengthening techniques rely on this simple principle: Restricting or Hindering dislocation motion renders a material harder and stronger. • We will consider strengthening single phase metals by: grain size reduction, solid-solution alloying, and strain hardening

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 7 e. (Fig. 7. 14 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc. , Upper Saddle River, NJ. )

Strategies for Strengthening: 2: Solid Solutions Ø Impurity atoms distort the lattice & generate stress. Ø 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.

Stress Concentration at Dislocations Adapted from Fig. 7. 4, Callister 7 e.

Strengthening by Alloying • small impurities tend to concentrate at dislocations on the “Compressive stress side” • reduce mobility of dislocation increase strength Adapted from Fig. 7. 17, Callister 7 e.

Strengthening by alloying • Large impurities concentrate at dislocations on “Tensile Stress” side – pinning dislocation Adapted from Fig. 7. 18, Callister 7 e.

Strategies for Strengthening: 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. 8, Callister 7 e. Ad roll force Ad roll -Extrusion Ao tensile force container ram billet container die holder extrusion die Ad

During Cold Work • Ti alloy after cold working: • Dislocations entangle and multiply • Thus, Dislocation motion becomes more difficult. 0. 9 mm Adapted from Fig. 4. 6, Callister 7 e. (Fig. 4. 6 is courtesy of M. R. Plichta, Michigan Technological University. )

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 s • Yield stress increases sy 1 sy 0 as rd increases: large hardening small hardening e

Impact of Cold Work As cold work is increased • Yield strength (sy) increases. • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. Lo-Carbon Steel! Adapted from Fig. 7. 20, Callister 7 e.

Cold Work Analysis • What is the tensile strength & ductility after cold working? Copper Cold Work D o =15. 2 mm D d =12. 2 mm

Cold Work Analysis • What is the tensile strength & ductility after cold working to 35. 6%? yield strength (MPa) tensile strength (MPa) 700 800 500 600 300 100 0 Cu 20 40 % Cold Work 60 YS = 300 MPa 40 20 400 340 MPa 200 0 60 ductility (%EL) 20 Cu 40 60 % Cold Work TS = 340 MPa Cu 7% 00 20 40 60 % Cold Work %EL = 7% Adapted from Fig. 7. 19, Callister 7 e. (Fig. 7. 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. )

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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. 7. 22, Callister 7 e. (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. )

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. t. R 4. opposite dislocations meet and annihilate Obstacle dislocation

Recrystallization • New grains are formed that: -- have a low dislocation density -- are small -- consume cold-worked grains. 0. 6 mm Adapted from Fig. 7. 21 (a), (b), Callister 7 e. (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.

Further Recrystallization • All cold-worked grains are consumed. 0. 6 mm Adapted from Fig. 7. 21 (c), (d), Callister 7 e. (Fig. 7. 21 (c), (d) are courtesy of J. E. Burke, General Electric Company. ) After 4 seconds After 8 seconds

Grain Growth • At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced. 0. 6 mm Adapted from Fig. 7. 21 (d), (e), Callister 7 e. (Fig. 7. 21 (d), (e) are courtesy of J. E. Burke, General Electric Company. ) After 8 s, 580ºC After 15 min, 580ºC • Empirical Relation: exponent typ. ~ 2 coefficient dependent on material & Temp. elapsed time grain dia. At time t. This is: Ostwald Ripening

º TR = recrystallization temperature TR Adapted from Fig. 7. 22, Callister 7 e. º

Recrystallization Temperature, TR TR = recrystallization temperature = point of highest rate of property change 1. TR 0. 3 -0. 6 Tm (K) 2. Due to diffusion annealing time TR = f(t) 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

Figure 7. 9 The fibrous grain structure of a low carbon steel produced by cold working: (a) 10% cold work, (b) 30% cold work, (c) 60% cold work, and (d) 90% cold work (250). (Source: From ASM Handbook Vol. 9, Metallography and Microstructure, (1985) ASM International, Materials Park, OH 44073. Used with permission. ) 27

Example 7. 3 Design of a Stamping Process One method for producing fans for cooling automotive and truck engines is to stamp the blades from cold-rolled steel sheet, then attach the blades to a “spider’’ that holds the blades in the proper position. A number of fan blades, all produced at the same time, have failed by the initiation and propagation of a fatigue crack transverse to the axis of the blade (Figure 7. 11). All other fan blades perform satisfactorily. Provide an explanation for the failure of the blades and redesign the manufacturing process to prevent these failures. 28