1. Materials Engineering – Day 6
Quiz
Review crystal structure
Review crystal defects
Review dislocations
Review the golden rule for strengthening metal.
Things that can be used to make metals strong.

2. You need to know/be able to
For the following processes, determine (from graphs and/or calculations) the strength/ductility and describe the governing microstructural mechanism
Solid Solution Strengthening
Grain Size Refinement
Cold Work and Annealing
Name the two types of solid solutions (interstitial and substitutional) and explain how they differ.

3. Crystallinity in Metals
Three types of unit cells. List in order of slip systems.
Name a point defect, a line defect, and an area defect.
What is the relationship between slip and plastic deformation?
What is the relationship between dislocation motion and slip?

4. Dislocation Motion Dislocations & plastic deformation
Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).
So we saw that above the yield stress plastic deformation occurs. But how? In a perfect single crystal for this to occur every bond connecting tow planes would have to break at once! Large energy requirement
Now rather than entire plane of bonds needing to be broken at once, only the bonds along dislocation line are broken at once.
If dislocations don't move, deformation doesn't occur!
Adapted from Fig. 7.1, Callister 7e.

5. BLOCK THAT DISLOCATION
We will tell the story of one of the earliest attempts to “block that dislocation” discovered by humans. Our story starts around 700 BC…
Chinese bronze from Spring and Autumn period
Bronze sword from Troy

6. What’s Happening?
The tin atoms dissolve in the matrix of copper. There are many, many substitutional solute atoms.
These atoms interact with dislocations, impeding their motion.
The solute atoms are not quite the right size. This produces stress and strain in the lattice.
The solute atoms’s stess field attracts or repels the stress field around the dislocation.
The result is that the dislocation is pinned or blocked – It’s motion is impeded!

7. “Rules” for substitutional and Interstitial sold solutions
Hume Rothery Rules for substitutional
Similar size
Similar crystal structure
Similar electronegativity
For Interstitial
Solute atom must be small relative to solvent atom so it can fit in the spaces between atoms

8. Point Defects in Alloys
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects) OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
--different composition
--often different structure.

9. Imperfections in Solids
Conditions for substitutional solid solution (S.S.)
W. Hume – Rothery rule
1. r (atomic radius) < 15%
2. Proximity in periodic table
i.e., similar electronegativities
3. Same crystal structure for pure metals
4. Valency
All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency

10. Imperfections in Solids
Application of Hume–Rothery rules – Solid Solutions
1. Would you predict more Al or Ag to dissolve in Zn?
2. More Zn or Al
in Cu?
Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity
Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP
Table on p. 106, Callister 7e.

11. Strengthening by Alloying
small impurities tend to concentrate at dislocations
reduce mobility of dislocation  increase strength
Adapted from Fig. 7.17, Callister 7e.

12. Strengthening by alloying
large impurities concentrate at dislocations on low density side
Adapted from Fig. 7.18, Callister 7e.

13. Ex: Solid Solution Strengthening in Copper
• Tensile strength & yield strength increase with wt% Ni.
Tensile strength (MPa)
wt.% Ni, (Concentration C)
200
300
400 10 20 30 40 50
Yield strength (MPa)
wt.%Ni, (Concentration C) 60
120
180 10 20 30 40 50
Adapted from Fig (a) and (b), Callister 7e.
• Empirical relation:
• Alloying increases sy and TS.

14. Result
Here is the plot in the notes.

15. Strategies for Strengthening: 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.)

16. Another Dislocation blocker: The grain boundary
A dislocation coming up on the grain boundary will not be able to cross easily into the adjacent grain.
It will probably stop waiting for more stress to be applied. Other dislocations will pile up behind it.

17. The Hall-Petch Relationship

18. Another Blocker: Other Dislocations
Recall that as plastic deformation proceeds the density of dislocations increases by several orders of magnitude.
So dislocations block themselves! This accounts for the strengthening that occurs during plastic deformation. (Done on purpose, we call it cold work.

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

20. Dislocations During Cold Work
• Ti alloy after cold working:
0.9 mm
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
Adapted from Fig. 4.6, Callister 7e.
(Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.)

21. Result of Cold Work Dislocation density =
total dislocation length
unit volume
Dislocation density =
Carefully grown single crystal
 ca. 103 mm-2
Deforming sample increases density
 mm-2
Heat treatment reduces density
 mm-2
Again it propagates through til reaches the edge
large hardening
small hardening s e y0 y1
• Yield stress increases
as rd increases:

22. Impact of Cold Work As cold work is increased
• Yield strength (sy) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases.
Adapted from Fig. 7.20, Callister 7e.

23. Review of three Strengthening Mechanisms
Solute Atoms. (Alloying)
Grain boundaries. (Grain boundary refinement)
Dislocations. (Cold Work, i.e. plastic deformation done on purpose.

24. Mechanism:
Grain boundaries block dislocation motion. More grains (smaller grains) means more boundaries and more blocking of dislocations
Process:
Cold work to add internal energy, anneal to recrystallize and form new small grains.
Note: Strength increases without loss of toughness
Mechanism:
Solute atoms are too big or too small and cause distortion ins the crystal lattice
Process:
Add other elements to the melt e.g. add Al and V to Ti to get Ti6Al4V.
Mechanism:
Number of dislocations increases by orders of magnitude, distorting lattice and impeding dislocations
Process:
Mechanically deform plastically. (e.g. cold roll, wire draw)