1. ME 330 Engineering Materials
Lecture 9
Dislocations & Strengthening Mechanisms
Strengthening Mechanisms
Grain boundary Refinement
Solid-solution Hardening
Precipitation Hardening
Strain Hardening
Cold Work
Annealing and Recrystallization
Please read sections

2. Making the Connection We have learned ...
Theoretical strengths are not met for engineering materials
Dislocations ease deformation of material
Carpet ruck, caterpillar locomotion, planking boards ….
Allow planes of atoms to move at lower stresses than predicted
Results in permanent deformation prior to tensile failure
Today, we will look at how we can regain some strength
No dislocations, no plastic deformation
If dislocations cannot move, no plastic deformation
No plastic deformation, close in on theory
But … we loose something … deformation
How do we get it back?

3. Strengthening Mechanisms
Eliminate dislocations
No mechanism for plastic deformation in metals
Whiskers and fibers
Eliminate dislocation movement
If they can’t move, they can’t carry plastic deformation
Introduce barriers to movement
Grain boundaries
Solid-solution strengthening (alloying)
Precipitates can pin dislocations
Increase dislocation density
Solutes cause multiplication
Strain hardening
Cold work

4. Dislocation Interactions
Dislocations have built-in stress/strain fields
Explains interactions (repel, immobilize)
Unless dislocations are of opposite sign, on same slip plane, interaction will cause changes in microstructure
Same is true if dislocations interact with some other lattice distortion
Grain boundary
Solid solution particles
Precipitates
Slip
Planegrain2
Grain Boundary
Slip Planegrain1 T C C T T C

5. Grain Boundary Strengthening
Slip
Planegrain2
Slip Planegrain1
Grain Boundary
Remember: Dislocation motion impeded at grain boundaries
Dislocation has to change slip planes in different grains
Boundaries posses atomic scale disorder - pins dislocation
Smaller grains provide more barriers to dislocation motion - stronger, harder, tougher

6. Hall-Petch (or Petch-Hall)
Yield strength related to grain size
o = lattice resistance to motion
ky =dislocation locking term
d = average grain size
Empirical fit!
May not hold for very large or small grained materials
Dislocation pile-up effects also important at:
Phase boundaries
Twin boundaries
As grains get smaller,
Strength increases
Toughness increases so k
Intrinsic lattice resistance is quite a bit higher for BCC than FCC/HCP … that is why BCC is not 4x as ductile. Same for FCC and HCP
note we are plotting inverse root of grain diameter … as we move right, grains are getting smaller
From: Hertzberg, p.455

7. Dislocations & Strengthening
Dislocation motion limits strength
To increase strength
Remove dislocations
Don’t allow them to move
Impede dislocations with point, line, or planar obstacles
“whiskers”
Cold worked metals
Tensile Strength (MPa)
Annealed metals
Dislocation Density
100
106
1012

8. “Whiskers” Extremely small, thin, defect free
No dislocations to carry plastic deformation
Usually metallic or ceramic
Single crystal, may be grown around screw dislocation
Applications primarily in composites

9. Solid Solution Hardening
Impurity (alloying) elements are incorporated into crystal structure in orderly manner.
Can have substitutional or interstitial solid solutions
Substitutional alloys formed when
Same crystal structure
Atomic sizes are similar
Often two or more metals
Interstitial alloys usually formed when
Alloying agent is of much smaller atomic size
Carbon, nitrogen, oxygen in metal
Common Alloys
Steel
Iron, <2% Carbon
Gold
18K 75% Au 20% Ag 5% Cu
14K 58% Au 22% Ag 20% Cu
Brass
60 – 80% Cu 20 – 40% Zn
Bronze
60 – 70% Cu 30 – 40% Sn
Stainless Steel
74% Fe 18% Ni 8% Cr

10. Definitions
Alloy – metals which are not pure; impurities are added intentionally
Solvent – element or compound present in greater amount (host atoms)
Solute – element present in minor concentration
Solid solution – addition of impurity into metal
solute atoms are added to the host material
crystal structure is maintained
no new structure is formed
atoms are intermixed so composition is uniform
(liquid analogy: mixing of two liquids)
Two types of solid solutions
Substitutional solution – solute atoms replace or substitute host atoms
Interstitial solution – impurity atoms fill voids or interstices
Read Section 4.3

11. Substitutional solution
Atomic size factor – difference in atomic radii is less than 15%
Crystal structure – should be same for solute and solvent atoms
Example: copper and nickel
Radius of copper = nm
Radius of nickel = nm
Both have FCC structure
Interstitial solution
Atomic diameter of intersticial impurity atoms is much smaller that of host atoms
Example: Carbon added to iron
Radius of carbon = 0.071
Radius of iron = 0.124

12. Compositions In wt% In at% nm1 = number of moles
m1 and m2, weights (or masses)
In at%
nm1 = number of moles
A = atomic weight

13. Conversion of atom percent to weight percent
Eqn 4.7
Conversion of weight percent to atom percent
Eqn 4.6

14. Solid Solution Strengthening
Interstitials and solutes distort the lattice
Introduce lattice strains
Solutes diffuse toward dislocations
Stress fields interact with dislocations
Lattice strains increase if dislocations are torn from solutes
Greater stress necessary to initiate movement (i.e. higher yield)
Greater stress to continue deformation (i.e. more hardening)
For solid solutions, larger size mismatch  larger induced stresses
Solute
Tension
Compression
Interstitial

15. Effect of Alloying Strength (tensile and ultimate) increases70
Copper-Nickel
Brass (Copper-Zinc)
400 60
UTS, MPa 50
300
Elongation, % 40 30
200 20 25 50
Nickel / Zinc, % 25 50
Nickel / Zinc, %
Strength (tensile and ultimate) increases
Hardness increases
Ductility can increase or decrease
Modulus remains unchanged!

16. Precipitation Hardening
Precipitates form when solubility of a particular impurity is low
Solubility usually increases with temperature
Add second phase to saturation (or less) at high temperature
Cool to room temperature and impurity will precipitate out to form a second phase
Rate of cooling is critical … need precipitation time (aging) to give ideal properties
i.e. aluminum alloys -T4, -T6 indicates different aging conditions
Precipitates act to impede dislocation motion
If dislocations loop, multiplication occurs (Frank-Reed, Orowan)
If dislocation cuts through precipitate, loses a lot of energy
Looping and cutting can occur simultaneously

17. Strain Hardening
Metal strengthens and becomes harder through “cold work”
Also known as “work hardening” (brass specimen in lab):
Self-feeding process
Dislocations multiply,
Average spacing decreases
Motion is impeded
Dislocations multiply
Stress needed to move dislocations goes up
 (MPa) E
 (%)
Power-law hardening

18. Strain Hardening in Industrial Processes
Cold Rolling:
Large change in cross-sectional area
Changes size of grains
Work hardens material by strain hardening
% Cold Work
Sheet metal forming
Very large strains at corners t r

19. Cold Rolling Ao Af Equiaxed grains Low dislocation density
Elongated Grains
High dislocation density

20. Mechanical Properties & Cold Work75
1000 Cu
800
1040 Steel 50
600
Brass
Elongation, %
Tensile Strength, MPa
Brass 25
1040 Steel
400 Cu
200 25 50 75
% Cold Work 25 50 75
% Cold Work
Cold Work  Higher strength, lower ductility

21. Strengthening Methods Specifically for Metals & Alloys
Adapted from: N.E. Dowling, Mechanical Behavior of Materials, Prentice Hall, 1993, p. 52

22. Annealing Process
Cold work  dislocation interactions  high strain energy
Structure wants to reduce total energy
Raise temperature  facilitates atomic motion
Material is heated to a high temperature and held for time:
Atoms to rearrange themselves into a lower energy state
Diffusion driven process
Governed by both time and temperature:
High temperatures and short times
Lower temperatures and longer times.
Removes the effects of cold work
Dislocation density will decrease
Grains become equiaxed.
Cold work uses mechanical energy to change microstructure. However, this also locks a lot of energy in the material
Annealing uses thermal energy to enable the materials to use its own stored strain energy to again reshape microstructure

23. Stages of Annealing Recovery Stresses around dislocations are relieved
Dislocations move to lower energy configurations, annihilate
Recrystallization
Strained material still has trapped internal energy
New equiaxed grains nucleate from dislocations
Return to nearly pre-cold worked structure & mechanical properties
Recrystallization temperature - complete recrystallization in 1 hour
Typically
Increased prior cold work will lower this temperature
Will not occur unless certain level of prior cold work has been achieved
Grain Growth
Grains grow to reduce overall grain boundary area
Grain boundaries have high energy: less boundaries  less total energy  energetically more favorable
Grain boundaries migrate - atoms diffuse from one side to other
Grain diameter
Dislocation climb is important during recovery … slip planes change, reorient and allow for some annihilation and lower energy states
cold work necessary to increase dislocatoin density and cause driving force for recrystallization

24. Changing Mechanical Properties Temperature/Time Effects
As Annealing temperature (time) increases:
Increase ductility
Decrease tensile strength
As temperature (time) continues to increase, grain size increases
Strong relation between time & temperature
Annealing a Brass Alloy for 1 hour,
varying temperature

25. Micrographs of Annealing Process
From: Callister
Different materials, but same basic concept
Looking at last micrograph, you should be able to tell me what kind of crystal structure this material has. Annealling twins!
From: Hull & Bacon, p.178-9