1. Materials Science
Metals and alloys

2. Types of imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects (0D)
• Dislocations
Line defects (1D)
• Grain Boundaries
Area defects (2D)
• Precipitates / cracks /
porosity
Volume defects (3D)

3. Line defects in solids (1D)
1-D defect in which atoms are mispositioned.

4. Dislocation motion • Incrementally breaking bonds
• If dislocations don't move, deformation doesn't happen! (But it will fracture like a ceramic)

5. Dislocations in materials
• 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 (NaCl):
Motion hard.
-need to avoid ++ and --
neighbors.

6. Stress-Strain curves σUTS σYIELD σFAILURE or σFRACTURE εYIELD εUTS
Necking starts
STRESS
σUTS
REGION I
REGION III
σYIELD
REGION II
HARDENING OCCURS
DISLOCATION MOTION
AND GENERATION !
l0 + le
σFAILURE or σFRACTURE
Region I : Elastic Deformation
Hooke’s Law
Region II: Uniform Plastic Deformation
Strain is uniform across material
Region III: Non-uniform Plastic Deformation
Deformation is limited to “neck” region E
l0 + le + lp
STRAIN
εYIELD
εUTS l0

7. Plastic deformation (Metals)
1. Initial
2. Small load
3. Unload p
lanes
still
sheared F d
elastic + plastic
bonds
stretch
& planes
shear
plastic F d
linear
elastic
plastic

8. Atomic origin of elastic properties
Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of material s e
High E
Low E

9. Modulus vs Yield Strength

10. Mechanical properties – objectives
Strength (tensile and yield strength)
Stiffness (elastic or Young’s modulus)
Ductility (plastic deformation) vs Brittleness
Resilience (capacity to absorb and recover elastic energy)
Hardness
Toughness (energy absorption / impact)

11. Dislocations – local strain fields
Edge dislocation: compression (above dislocation line) & tension (below dislocation line)
Screw dislocation: shear
Stress & strain fields decrease with radial distance from dislocation line
Symbol
Symbol

12. Dislocation interaction
Strain field from one dislocation can affect a neighboring dislocation
Two like dislocations can repel each other
Unlike dislocations attract and annihilate each other

13. Strengthening mechanisms (metals)
Macroscopic plastic deformation corresponds to the motion of large numbers of dislocations
The ability of a metal to plastically deform depends on the ability of dislocations to move
Virtually all strengthening techniques rely on restricting or hindering dislocation motion
We will look at 4 such mechanisms
Reduce grain size
Solid-solution strengthening
Precipitation strengthening
Strain hardening (or cold working)

14. Strategy 1: Grain size reduction
• Grain boundaries are barriers to slip
- dislocation has to change directions
- grain boundary region disordered, so discontinuity in slip planes
• Barrier "strength” increases with misorientation
• Smaller grain size: more barriers to slip

15. Strategy 1: Grain size reduction
Small grains increase strength, but decrease ductility (many barriers to dislocations)
Controlled by casting conditions (slow/ fast cooling)
Can also be altered by processing –
Can be induced by rolling a polycrystalline metal
-before rolling
-anisotropic
since rolling affects grain
orientation and shape.
-after rolling
-isotropic
since grains are
approx. spherical
& randomly
oriented.
235 mm
rolling direction

16. Strategy 2: Solid-solution strengthening
Deliberately alloy metal with impurity atoms
Substitutional or interstitial
Impurity atoms produce lattic strains
Strain fields interact with dislocations restricting movement
‘Dislocation atmosphere’ pins the dislocations OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)

17. Strategy 2: Solid-solution strengthening
• Impurity atoms distort the lattice & generate stress.
• Stress can produce a barrier to dislocation motion.
• Smaller substitutional
impurity
• Larger substitutional
impurity

18. Strategy 2: Solid-solution strengthening
Degree of strengthening depends on relative atomic size
Size difference between Cu and Sn is large
Large lattice strain
Greater strengthening by concentration

19. Strategy 3: Precipitation strengthening
Hard precipitates are difficult to shear
E.g. Ceramics in metals (SiC in Iron or Aluminum)
• Result:

20. Strategy 3: Precipitation strengthening
E.g. Aluminum is strengthened with precipitates formed by alloying.
1.5mm
Internal wing structure on Boeing 767

21. Strategy 4: Cold work strengthening
Dislocations entangle with one another during cold work.
Dislocation motion becomes more difficult.
Ti alloy after cold working:

22. SUMMARY • Dislocations are observed primarily in metals and alloys.
• Here, 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. 29