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? Chapter 7: Dislocations & Strengthening Mechanisms

Dislocations & Materials Classes Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) bonding Ionic Ceramics (NaCl): Motion hard. -need to avoid ++ and - - neighbors Metals: Disl. motion easier. -non-directional bonding -close-packed directions for slip. electron cloudion cores

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). If dislocations don't move, deformation doesn't occur! Adapted from Fig. 7.1, Callister 7e.

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 (relatively close-packed) in directions (close-packed) => total of 12 slip systems in FCC –in BCC & HCP other slip systems occur Deformation Mechanisms Adapted from Fig. 7.6, Callister 7e.

Slip Systems in Cubic Metals:

Note: By definition is the angle between the stress direction and Slip direction;  is the angle between the normal to slip plane and stress direction Stress and Dislocation Motion Crystals slip due to a resolved shear stress,  R. Applied tension can produce such a stress. slip plane normal, n s Resolved shear stress: RR =F s /A/A s slip direction ASAS RR RR FSFS slip direction Relation between  and RR RR = FSFS /AS/AS Fcos A/cos  F FSFS  nSnS ASAS A Applied tensile stress: = F/A  slip direction F A F

Condition for dislocation motion: Crystal orientation can make it easy or hard to move dislocation GPa to GPa typically Critical Resolved Shear Stress RR = 0 =90°  RR =  /2 =45°   RR = 0  =90° 

Generally: Resolved  (shear stress) is maximum at =  = 45º And  CRSS =  y /2 for dislocations to move (in single crystals)

Determining  and angles for Slip in Crystals (single X-tals this is easy!)  and angles are respectively angle between tensile direction and Normal to Slip plane and angle between tensile direction and slip direction (these slip directions are material dependent) In General for cubic xtals, angles between directions are given by: Thus for metals we compare Slip System (normal to slip plane is a direction with exact indices as plane) to applied tensile direction using this equation to determine the values of  and to plug into the  R equation to determine if slip is expected

Stronger since grain boundaries pin deformations Slip planes & directions (,  ) change from one crystal to another.  R will vary from one crystal to another. The crystal with the largest  R yields first. Other (less favorably oriented) crystals yield (slip) later. Adapted from Fig. 7.10, Callister 7e. (Fig is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) Slip Motion in Polycrystals  300  m

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

Hall-Petch equation:

Grain Size Reduction Techniques: Increase Rate of solidification from the liquid phase. Perform Plastic deformation followed by an appropriate heat treatment. Notes:  Grain size reduction also improves toughness of many alloys.  Small-angle grain boundaries are not effective in interfering with the slip process because of the small crystallographic misalignment across the boundary.  Boundaries between two different phases are also impediments to movements of dislocations.

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

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

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 7e.

Strengthening by alloying Large impurities concentrate at dislocations on “Tensile Stress” side – pinning dislocation Adapted from Fig. 7.18, Callister 7e.

Ex: Solid Solution Strengthening in Copper Tensile strength & yield strength increase with wt% Ni. Empirical relation: Alloying increases  y and TS. Adapted from Fig (a) and (b), Callister 7e. Tensile strength (MPa) wt.% Ni, (Concentration C) Yield strength (MPa) wt.%Ni, (Concentration C)

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

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

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

Ti alloy after cold working: Dislocations entangle and multiply Thus, Dislocation motion becomes more difficult. Adapted from Fig. 4.6, Callister 7e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) During Cold Work 0.9  m

Result of Cold Work Dislocation density = –Carefully grown single crystal  ca mm -2 –Deforming sample increases density  mm -2 –Heat treatment reduces density  mm -2 Yield stress increases as  d increases: total dislocation length unit volume large hardening small hardening    y0y0  y1y1

Impact of Cold Work Lo-Carbon Steel! Adapted from Fig. 7.20, Callister 7e. Yield strength (  y ) increases. Tensile strength (TS) increases. Ductility (%EL or %AR) decreases. As cold work is increased

What is the tensile strength & ductility after cold working? Cold Work Analysis D o =15.2mm Cold Work D d =12.2mm Copper

What is the tensile strength & ductility after cold working to 35.6%? Adapted from Fig. 7.19, Callister 7e. (Fig 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.) Cold Work Analysis % Cold Work Cu yield strength (MPa) % Cold Work tensile strength (MPa) 200 Cu MPa TS = 340MPa ductility (%EL) % Cold Work Cu 7% %EL= 7% YS = 300 MPa

Results for polycrystalline iron:  y and TS decrease with increasing test temperature. %EL increases with increasing test temperature. Why? Vacancies help dislocations move past obstacles. Adapted from Fig. 6.14, Callister 7e.  -  Behavior vs. Temperature 2. vacancies replace atoms on the disl. half plane 3. disl. glides past obstacle -200  C -100  C 25  C Strain Stress (MPa) disl. trapped by obstacle obstacle

1 hour treatment at T anneal... decreases TS and increases %EL. Effects of cold work are reversed! 3 Annealing stages to discuss... Adapted from Fig. 7.22, Callister 7e. (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.) Effect of Heating After %CW tensile strength (MPa) ductility (%EL) tensile strength ductility Recovery Recrystallization Grain Growth annealing temperature (ºC)

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

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

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

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

TRTR Adapted from Fig. 7.22, Callister 7e. º º T R = recrystallization temperature

Recrystallization Temperature, T R T R = recrystallization temperature = point of highest rate of property change 1.T R  T m (K) 2.Due to diffusion  annealing time  T R = f(t) shorter annealing time => higher T R 3.Higher %CW => lower T R – strain hardening 4.Pure metals lower T R due to dislocation movements Easier to move in pure metals => lower T R

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.

Coldwork Calculations Solution If we directly draw to the final diameter what happens? D o = 0.40 in Brass Cold Work D f = 0.30 in

Coldwork Calc Solution: Cont. For %CW = 43.8% Adapted from Fig. 7.19, Callister 7e –  y = 420 MPa –TS = 540 MPa > 380 MPa 6 –%EL = 6< 15 This doesn’t satisfy criteria…… what can we do?

Coldwork Calc Solution: Cont. Adapted from Fig. 7.19, Callister 7e For %EL > 15 For TS > 380 MPa > 12 %CW < 27 %CW  our working range is limited to %CW = 12 – 27%

This process Needs an Intermediate Recrystallization i.e.: Cold draw-anneal-cold draw again For objective we need a cold work of %CW  –We’ll use %CW = 20 Diameter after first cold draw (before 2 nd cold draw)? –must be calculated as follows:  Intermediate diameter =

Summary: 1.Cold work D 01 = 0.40 in  D f1 = in 2.Anneal above D s2 = D f1 3.Cold work D s2 = in  D f 2 =0.30 in Therefore, meets all requirements Coldwork Calculations Solution  Fig 7.19

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. Summary