1. Plastic deformation Extension of solid under stress becomes
permanent when s exceeds elastic limit se L DL s
Ductile solids: able for plastic deformation
(metals, plastics)
Brittle solids: break suddenly without being
deformed (ionic and covalent crystals) s
elastic
region
fracture se sM
DL/L
plastic
deformation
Ductility grows with
temperature: metals
can be shaped easily
at high temperatures

2. Ductility Solids change shape without appreciable change in volume
The maximum extension can be from a few to 50%
Work hardening: elastic limit of metal can be
increased by plastic deformation s s1 se
new
elastic
region
original
elastic
region e1
DL/L

3. Slip in metals to each other, but solid remains crystalline
Planes of atom in crystal slip with respect
to each other, but solid remains crystalline
Slip planes are seen on a surface as slip
lines
Slip planes are parallel to lattice planes
(HCP has 3 slip systems, FCC has 12 slip
systems) Al, Ag, Au, Pb, Cu A d B C a s sM x A B C
d/2 d

4. Slip in metals m , dyn/cm2 sM , dyn/cm2 m/ sM Sn Ag Al Duralumin Fe
1.9x1011
1.3x107
15000 Ag
2.8x1011
6x106
45000 Al
2.5x1011
4x106
60000
Duralumin
9.9x108
250 Fe
8x1011
1.5x109
500

5. Slip in metals: Schmid’s law
normal
“Slip begins on a given slip system, when the
shear stress resolved on that system reaches
a critical value” S f F a
slip direction
Slip lines on Al
crystal
50 mm

6. Dislocations:edge Edge dislocation in simple cubic crystal
line
Burger vector
^ dislocation
Burger circuit- path around
dislocation line: 3 steps to->,
3 steps down, 3 steps to <-,
3 steps up. “Failure” to close
this circuit is Burger vector b
Dislocation may “glide”- little
energy should be supply to
slip crystal. Elastic limit in real
crystal << ideal crystal.

7. Dislocations: screw dislocation line Atoms/ molecules bond to
screw dislocation during
crystal growth.
Burger vector II dislocation line
Density of dislocations: from 102 dislocations/cm2 in the best Ge and Si
to 1012 dislocations/cm2 in heavily deformed
metals
Motion of dislocation can be blocked by: another dislocation, grain boundary,
point defect
Work-hardening: annealing decrease dislocation density to 106 dislocations/cm2.
After plastic deformation density increases to 1012 dislocations/cm2, but motion of
the dislocation can be blocked by pinning at other dislocations

8. Dislocations: grain boundaries
grain boundary
Dislocations are blocked by grain
boundaries -> slip is blocked
Smaller grain size-> larger surface of grain
boundaries -> larger elastic limit
Empirical equation for maximum elastic
stress (Petch) sM =A+Bd-1/2, d -grain
diameter
Elastic limit in cooper doubles when grain
size falls from 100 mm to 25 mm
dislocations

9. Alloys Substitutional solution: dissolve atoms replace
Alloys contain several mixed constituent metals
Substitutional solution: dissolve atoms replace
those of basic metal (Cu in Ni )
Interstitual solution: added elements are lodged in
in interstitial sites (C in Fe)
Motion of dislocations is impeded by irregularities
-> elastic limit increases
Elastic limit
Concentration of
alloyed element %
C,N Si Mn Mo Ni 1 2

10. Alloys with precipitates
Alloy contains two phases: predominant phase of matrix and
precipitated phase is dispersed in form of fine grains.
This take place at high concentration of added element
Motion of dislocations are blocked by this grains -> larger
elastic limit.
Dislocation can pass the
precipitated grains

11. Alloys with Guinier-Preston zones
Alloy with GP zones is intermediate between homogeneous
and precipitated phases: added element is concentrated
in ~10nm GP zones. These zones block motion of dislocation
Structure hardening
Al+ 5% Cu alloy is
homogeneous at 550 OC
Cooled by quenching
to room temperature
Alloy with GP
zones: high
elastic limit
Alloy in Concord: Al +2% Cu +1.5% Mg+1% Ni has sM~450Mpa with
operation temperature up to 120O C

12. Steel and martensitic transformation
–Fe ferrite
BCC
–Fe austenite
FCC
Martensite:
needle crystals of a
form aligned in g form
C is diluted in a form
hard but brittle
New phase:
Fe3C cementit
in a-ferrite
hard and ductile
Fe – 0.5% C alloy at
950OC has g form
quench
to room
temperature
annealing
T<800OC

13. Interaction of dislocation with impurities
elastic
region sL sU
DL/L U L
plastic
deformation
work
hardening
Impurities diffuse to dislocations
and form “clouds”-> dislocations
are pinned -> higher elastic limit
When s exceeds sU dislocations
escapes impurities -> stress needed
for plastic deformation decreases