Transcript Materials Engineering – Day 6 - Rose

Materials Engineering – Day 6
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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.
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.
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?
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).
• If dislocations don't move,
deformation doesn't occur!
Adapted from Fig. 7.1,
Callister 7e.
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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
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.
1. The solute atoms are not quite the right size. This
produces stress and strain in the lattice.
2. The solute atoms’s stess field attracts or repels the
stress field around the dislocation.
3. The result is that the dislocation is pinned or blocked –
It’s motion is impeded!
“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
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.
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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
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Imperfections in Solids
Application of Hume–Rothery rules – Solid Solutions
Element
1. Would you predict
more Al or Ag
to dissolve in Zn?
2. More Zn or Al
in Cu?
Cu
C
H
O
Ag
Al
Co
Cr
Fe
Ni
Pd
Zn
Atomic
Radius
(nm)
0.1278
0.071
0.046
0.060
0.1445
0.1431
0.1253
0.1249
0.1241
0.1246
0.1376
0.1332
Crystal
Structure
Electronegativity
Valence
FCC
1.9
+2
FCC
FCC
HCP
BCC
BCC
FCC
FCC
HCP
1.9
1.5
1.8
1.6
1.8
1.8
2.2
1.6
+1
+3
+2
+3
+2
+2
+2
+2
Table on p. 106, Callister 7e.
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Strengthening by Alloying
• small impurities tend to concentrate at dislocations
• reduce mobility of dislocation  increase strength
Adapted from Fig.
7.17, Callister 7e.
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Strengthening by alloying
• large impurities concentrate at dislocations on low density
side
Adapted from Fig.
7.18, Callister 7e.
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Ex: Solid Solution
Strengthening in Copper
Yield strength (MPa)
Tensile strength (MPa)
• Tensile strength & yield strength increase with wt% Ni.
400
300
200
0 10 20 30 40 50
wt.% Ni, (Concentration C)
• Empirical relation:
180
Adapted from Fig.
7.16 (a) and (b),
Callister 7e.
120
60
0 10 20 30 40 50
wt.%Ni, (Concentration C)
sy ~ C1/ 2
• Alloying increases sy and TS.
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Result
Here is the plot in the notes.
Strength
Effect depends
upon alloying
element
% alloy
Solid Solution Strengthening
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.
Adapted from Fig. 7.14, Callister 7e.
(Fig. 7.14 is from A Textbook of Materials
Technology, by Van Vlack, Pearson Education,
Inc., Upper Saddle River, NJ.)
• Hall-Petch Equation:
syield  so  ky d 1/ 2
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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.
The Hall-Petch Relationship
Yield Strength
sys =so+kyd-1/2
d -1/2
Effect of Grain Size Reduction
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.
Yield Strength
Degree of
strengthening
depends on
material
%area reduction
Effect of Plastic Deformation
Strategies for Strengthening:
Cold Work (%CW)
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
-Forging
force
die
A o blank
-Drawing
die
Ao
-Rolling
Ad
Ao
Adapted from Fig.
11.8, Callister 7e.
Ad
roll
force
Ad
roll
-Extrusion
Ao
tensile
force
force
die
container
ram
billet
container
Ao  Ad
%CW 
x 100
Ao
die holder
extrusion
Ad
die
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Dislocations During Cold Work
• Ti alloy after cold working:
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
0.9 mm
Adapted from Fig.
4.6, Callister 7e.
(Fig. 4.6 is courtesy
of M.R. Plichta,
Michigan
Technological
University.)
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Result of Cold Work
Dislocation density =
total dislocation length
unit volume
– Carefully grown single crystal
 ca. 103 mm-2
– Deforming sample increases density
 109-1010 mm-2
– Heat treatment reduces density
 105-106 mm-2
• Yield stress increases
as rd increases:
s
sy1
sy0
large hardening
small hardening
e
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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.
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Yield Strength
sys =so+kyd-1/2
d -1/2
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.
Effect of Grain Size Reduction
Strength
Effect depends
upon alloying
element
% alloy
Solid Solution Strengthening
Yield Strength
Degree of
strengthening
depends on
material
%area reduction
Effect of Plastic Deformation
Mechanism:
Number of dislocations
increases by orders of
magnitude, distorting
lattice and impeding
dislocations
Process:
Mechanically deform
plastically. (e.g. cold roll,
wire draw)