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

Slip SystemSlip plane - plane allowing easiest slippageWide interplanar spacings - highest planar densitiesSlip 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 FCCin BCC & HCP other slip systems occurDeformation MechanismsAdapted from Fig. 7.6, Callister 7e.

Slip Systems that can and will operate in the 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 directionStress and Dislocation Motion Crystals slip due to a resolved shear stress, tR. Applied tension can produce such a stress.

Condition for dislocation motion: Crystal orientation can make it easy or hard to move dislocationCritical Resolved Shear Stress

Generally:Resolved (shear stress) is maximum at = = 45AndCRSS = 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)And Remembering 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 (l, f) change from one crystal to another.

tR will vary from one crystal to another.

The crystal with the largest tR yields first.

Other (less favorably oriented) crystals yield (slip) later.Adapted from Fig. 7.10, Callister 7e.(Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)Slip Motion in Polycrystals

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. 7.14 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

Stress Concentration at DislocationsAdapted from Fig. 7.4, Callister 7e.

Strengthening by Alloyingsmall impurities tend to concentrate at dislocations on the Compressive stress sidereduce mobility of dislocation increase strength Adapted from Fig. 7.17, Callister 7e.

Strengthening by alloyingLarge impurities concentrate at dislocations on Tensile Stress side pinning dislocationAdapted from Fig. 7.18, Callister 7e.

Ex: Solid Solution Strengthening in Copper Tensile strength & yield strength increase with wt% Ni. Empirical relation: Alloying increases sy and TS.Adapted from Fig. 7.16 (a) and (b), Callister 7e.

Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum). Result:Strategies for Strengthening: 3. Precipitation StrengtheningSlipped part of slip planeLarge 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. 11.26, Callister 7e. (Fig. 11.26 is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)Application: Precipitation StrengtheningAdapted 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:

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

Result of Cold WorkDislocation density =

Carefully grown single crystal ca. 103 mm-2Deforming sample increases density 109-1010 mm-2Heat treatment reduces density 105-106 mm-2 Yield stress increases as rd increases:

Impact of Cold WorkLo-Carbon Steel!Adapted from Fig. 7.20, Callister 7e. Yield strength (sy) 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

What is the tensile strength & ductility after cold working to 35.6%?Adapted from Fig. 7.19, Callister 7e. (Fig. 7.19 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 AnalysisYS = 300 MPa

Results for polycrystalline iron: sy 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.s - e Behavior vs. Temperature

1 hour treatment at Tanneal... decreases TS and increases %EL. Effects of cold work are reversed! 3 Annealing stages to discuss...Adapted from Fig. 7.22, Callister 7e. (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.)Effect of Heating After %CW

Annihilation reduces dislocation density.Recovery Scenario 2

New grains are formed that: -- have a low dislocation density -- are small -- consume cold-worked grains.Adapted from Fig. 7.21 (a),(b), Callister 7e. (Fig. 7.21 (a),(b) are courtesy of J.E. Burke, General Electric Company.)Recrystallization

All cold-worked grains are consumed.Adapted from Fig. 7.21 (c),(d), Callister 7e. (Fig. 7.21 (c),(d) are courtesy of J.E. Burke, General Electric Company.)Further Recrystallization

Recrystallization Temperature, TRTR = recrystallization temperature = point of highest rate of property changeTR 0.3-0.6 Tm (K)Due to diffusion annealing time TR = f(t) shorter annealing time => higher TRHigher %CW => lower TR strain hardeningPure metals lower TR due to dislocation movementsEasier to move in pure metals => lower TR

At longer times, larger grains consume smaller ones. Why? Grain boundary area (and therefore energy) is reduced.Adapted from Fig. 7.21 (d),(e), Callister 7e. (Fig. 7.21 (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.This is: Ostwald Ripening

Adapted from Fig. 7.22, Callister 7e. TR = recrystallization temperature

Coldwork CalculationsA 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 SolutionIf we directly draw to the final diameter what happens?

Coldwork Calc Solution: Cont.For %CW = 43.8%Adapted from Fig. 7.19, Callister 7e. y = 420 MPaTS = 540 MPa > 380 MPa%EL = 6< 15This doesnt satisfy criteria what can we do?

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

This process Needs an Intermediate Recrystallizationi.e.: Cold draw-anneal-cold draw againFor objective we need a cold work of %CW 12-27Well use %CW = 20Diameter after first cold draw (before 2nd cold draw)?must be calculated as follows:

Summary:Cold work D01= 0.40 in Df1 = 0.335 inAnneal above Ds2 = Df1Cold work Ds2= 0.335 in Df 2 =0.30 in

Therefore, meets all requirementsColdwork Calculations SolutionFig 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

*************Dont move past one another hardens material********Again it propagates through til reaches the edge****************So after the cold draw & anneal D02=0.335m**