MATERIALS ENGINEERING – DAY 7
Complete Strengthening Mechanisms
 Cold Work
 Annealing

SOLID SOLUTION STRENGTHENING
AND GRAIN SIZE REFINEMENT
Why are alloys stronger than the base metal
alone?
 What is the advantage of having a fine-grained
crystalline structure?

THE HALL-PETCH RELATIONSHIP
Yield Strength
sys =so+kyd-1/2
d -1/2
Effect of Grain Size Reduction
EXAMPLE

Assume that a metal has a yield stress of 20 ksi
if the grain size is 10-4 mm, and 32 ksi if the
grain size is 10-6 mm. What will be the yield
stress if the grain size was 10-5 mm, all other
things being equal?
20   0  k 10000
Solving, we find that
k=0.01333 and 0 = 18.67
32   0  k 1000000
 y  18.67  0.01333 100000 22.9 ksi
ANOTHER BLOCKER: OTHER
DISLOCATIONS
Recall that as plastic deformation proceeds the
density of dislocations increases by several orders
of magnitude.
 So dislocations block each other. 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
WHAT ABOUT DUCTILITY?

A trade off is taking place. As we block
dislocations, and the material gets stronger, we
lose the capacity for plastic deformation. In other
words, the ductility is decreased.
AS WE BLOCK DISLOCATIONS, STRENGTH
INCREASES AND DUCTILITY DECREASES.

Exception: Fine grain size gives strength
without significant decrease in ductility.
FOR COLD WORK AND ANNEALING
BE ABLE TO:
Calculate %cold work from change in crosssectional geometry
 Describe the microstructural and property
changes during Recovery, Recrystallization and
Grain Growth, and the relationship between
microstructure and properties

COLD WORK



In cold work, metals are strengthened at the expense
of ductility.
Cold refers to the fact that the material is plastically
deformed at a temperature below it
“recrystallization” temperature. (More on this later.)
Also called strain hardening.
A0
Rolling: very
common CW
Af
okasatria.blogspot.com/
The grain structure of a low carbon steel produced by
cold working: (a) 10% cold work, (b) 30% cold work,
(c) 60% cold work, and (d) 90% cold work (250).
(Source: From ASM Handbook Vol. 9, Metallography
and Microstructure, (1985) ASM International,
Materials Park, OH 44073.
HOW COLD WORK IS MEASURED

It is measured as the percentage in area
reduction during the deformation process.
%CW 
A0  Af
A0
100%
This is calculated in the same way that %RA ductility is
calculated. BUT, the CW produced in some
manufacturing process, not the tension test.
4 STRATEGIES FOR STRENGTHENING:
4: 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
Ad
extrusion
die
11
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.)
12
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:

y1
y0
large hardening
small hardening
e
13
IMPACT OF COLD WORK
As cold work is increased
• Yield strength (y) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases.
Adapted from Fig. 7.20,
Callister 7e.
14
WHY DO COLD WORK…
It’s about several issues…
1. Strengthening the manufactured part
2. Shaping the manufactured part
3. Cold Work can be used to impart a nice surface
finish
 Often we can’t complete the shaping process
with just one step of cold work. There just isn’t
enough ductility in the metal. Plus, we need to
get the material back to a state of 0% CW.
(While keeping the new shape, of course!)
 How might we do that? First, think of what we
have.

WHAT COLD WORKED METAL IS LIKE
Dislocation density very high.
 Residual stresses are very commonly
encountered.
 The original grain structure is still in existence.
But the grains have been stretched in the
direction of the deformation.
 Electrical conductivity and thermal conductivity
may be reduced.
 The state of internal energy is high.
 So what can be done to diminish these effects?

ANNEALING


1.
2.
3.
Annealing – a thermal process – we heat the cold
worked metal. BUT WE DO NOT MELT IT
Three phenomena are observed. Here is the order in
which they are known to happen.
Recovery. Enough energy is supplied so that
dislocations can spontaneously move to lower
residual stresses.
Recrystallization. In the middle of the old,
elongated grains, new small equi-axed grains begin
to form, until we have a completely new grain
structure.
Grain growth. If more heat is supplied over time the
grains grow, smaller ones eaten by bigger ones.
FIGURES FROM TEXT SHOWING THE
RECRYSTALLIZATION SEQUENCE. (BRASS –
33% CW) HEAT TO 580C.
start
After 8 s
After 3 s
After 15 min
After 4 s
After 10 min at 700C
HERE’S HOW THE PROPERTIES CHANGE AS
CHANGE ANNEALING TEMPERATURE
Metal is Brass.
This is based on
an annealing
time of 1 hour.
Similar looking
plots could be
produced for a
constant
temperature with
time as the
independent
variable.
http://info.lu.farmingdale.edu/depts/met/met205/annealingstages.html
“LAWS” OF RECRYSTALLIZATION
Thermally activated.
 Critical temperature.
 Critical deformation.
 Deformation affects the critical temperature.
 Initial grain size affects the critical temperature.
Grain boundaries are good sites for nuclei to
form.

RECRYSTALLIZATION TEMPEPATURE
Depends on Alloy Content. Lower for pure
metals.
 Depends on the amount of previous CW.

Metal is iron (Fe). Note
that for less than about
5% CW, there will be no
recrystallization.
Final note:
Recrystallization is very
useful in grain size
control.
REVIEW OF THREE STRENGTHENING
MECHANISMS
1.
2.
3.
Solute Atoms. (Alloying)
Grain boundaries. (Grain boundary refinement)
Dislocations. (Cold Work, i.e. plastic
deformation done on purpose.
THERE ARE OTHER STRENGTHENING
MECHANISMS WHICH WE WILL ALSO
TALK ABOUT.