1. Dislocation Interactions
Adapted from Fig. 7.5, Callister 7e.

2. Lattice Stress Fields at Dislocations
Don’t move past one another – hardens material
Adapted from Fig. 7.4, Callister 7e.

3. Polycrystalline Slip Ashby model (left) Disassemble polycrystal
Allow each to deform according to Schmid’s law – create statistically stored dislocations
Creates overlaps and voids
“Correct” overlaps with geometrically necessary dislocations until grains fit together again
Reassemble crystal
G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

4. Slip Motion in Polycrystals
300 mm
• Stronger - grain boundaries pin deformations
• Slip planes & directions
(l, f) change from one
crystal to another.
• tR will vary from one
• The crystal with the
largest tR yields first.
First crystals to yield increase stress on surrounding crystals
• Other (less favorably
oriented) crystals
yield 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].)

5. Strengthening Mechanisms
What is STRENGTH?
Ability of the material to resist deformation under applied stress
How do metal crystals deform – they shear by dislocation motion
Therefore: Anything that prevents or slows dislocation motion – increases strength

6. Present 5 Strengthening Mechanisms
Reduction in Grain Size
Substitutional Solid Solution Strengthening
Interstitial Solid Solution Strengthening
Cold Work
Precipitation Strengthening
Note:
All of these are generally operative only at
temperatures below 0.5Tm (K)

7. Grain Boundaries
High angle grain boundary represents a region of random misfit between adjoining crystals
• In a polycrystalline material continuity must be maintained
Considerable differences in the amount of deformation (dislocation density) between grains and across a single grain
More slip systems typically operate near the grain boundary because of the increased strain
Grain boundaries are dislocation sources
Fine grained materials have greater strain hardening
Hall-Petch Equation:
G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

8. Solid Solution Strengthening
• Impurity atoms distort the lattice create local stress fields
Dislocations also contain local stress fields
Interaction of these stress fields impedes dislocation motion A B C D

9. Solute Alloying Additions
The typical effect of solute additions is to raise the yield stress and the level of the stress strain curve as a whole.
Affect the entire stress-strain curve – solute atoms influence the frictional resistance to dislocation motion rather than static locking of dislocations.
Solute atoms fall into 2 broad categories:
Atoms which produce non-spherical distortions – interstitials – strengthening
effect (per unit concentration) is 3G (shear modulus)
Atoms which produce spherical distortion – substitutional atoms – G/10
G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

10. Interstitial Strengthening
Highly mobile interstitial impurities tend to concentrate at dislocations (Cottrell Atmospheres)
Reduce mobility of dislocation  increase strength
Note: Responsible for discontinuous yielding

11. 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.

12. 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

13. Plastic Deformation
Plastic deformation produces an increase in the number of dislocations
total dislocation length
unit volume
Dislocation density =
An annealed metal (undeformed) : dislocations per cm2
A severely plastically deformed metal: dislocations per cm2
Most of the energy expended during cold working is converted to heat
Roughly 10% is stored in the lattice as increased internal energy (.01 – 1 cal/g)
G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

14. Dislocations During Cold Work
• Ti alloy after cold working:
0.9 mm
• As the concentration of dislocations increases
Dislocations interact and obstruct one another. (Spaghetti)
• Dislocation motion becomes more difficult.