ME 330 Engineering Materials
Lecture 12
Phase Diagrams, Solidification, Phase transformations




Solidification
Solidification microstructures
Iron-Carbon alloys
Phase transformations
Read Chapter 10
Chapter 9 - 1
Kinetics of phase transformations
– Reaction kinetics … what happens
when time is introduced to
solidification
– TTT curves
– CCT curve
– Hardenability and Jominy end quench
test
– Surface hardening treatments
•
Please read chapter 10
Chapter 9 - 2
Development of microstructure in single or
two phase alloys usually involves
phase transformations –
alteration in the number and/or character
of phases.
Chapter 9 - 3
Phase transformations
• At least one new phase is formed that has different
physical/chemical characteristics and/or different
structure that the parent phase
• They do not occur instantaneously
– Transformation rate (dependence of reaction progress on time)
• Phase transformations have two stages
– Nucleation
(appearance of very small particles of new phase which are capable of
growing)
– Growth
Chapter 9 - 4
Phase transformations
1. Simple diffusion-dependent transformation (no
change in either the number or composition of phases
present) Ex: solidification of pure metal,
recrystallization and grain growth
2. Diffusion dependent transformation (some
alteration in phase compositions and often in number
of phases present) Ex: eutectoid reaction
3. Diffusionless trasformation (metastable phase is
produced) Ex: martensitic transformation
Chapter 9 - 5
Nucleation
• Homogeneous phase
– Nuclei of new phase form uniformly throughout
the parent phase
• Heterogeneous phase
– Nuclei form preferentially at structural
inhomogeneities (contain surfaces, grain
boundaries, dislocations, etc)
Chapter 9 - 6
Homogeneous Nucleation
Free Energy Change
G 
4
Volume  r 3
3
4 3
r Gv  4r 2
3
4r 2
r
Solid
Solid-liquid
interface
Area  4r 2
4 3
r Gv
3
Find critical radius for maximum free energy change
d (G ) 4
 Gv (3r 2 )  4 (2r )  0
dr
3
G *
Activation free energy required
for the formation of stable nucleus
2
r*  
Gv
16 3
G* 
3(Gv ) 2
Chapter 9 - 7
Gv 
H f
H f (Tm  T )
is zero at Tm
Tm
heat given up during solidification
 2 Tm   1 
r  
 H   T  T 
f  m


*
3 2 

16

Tm
1
*
G  
 3H 2  T  T  2
f

 m
These two quantities decrease
as temperature decreases.
Lowering of temperature at temperatures below the
equilibrium solidification temperature, nucleation
occurs more easily.
Chapter 9 - 8
So far we considered temperature dependence.
Next, we consider time dependence.
Chapter 9 - 9
General Solid State Reaction Kinetics
Time split between nucleation &
growth
•
Measure transformation % versus
time for various temperatures
Transformation rate (Avrami
equation)
y  1  exp( kt )
n
rate 
1
t0.5
 Q 
rate  A exp 

 RT 
Fraction of transformation,y
•
•
Time dependence of rate
Phase transformations generally
time & temperature dependent
Typical kinetics behavior
1.0
Fraction of transformation
•
•
0.5
t0.5
0
•
Nucleation
t
0
Growth.
5
log of heating time, t
Chapter 9 - 10
Fig. 10.11 in Callister
Chapter 9 - 11
Recall:
Iron-Iron Carbide Phase Diagram
•
•
•
•
Ferrite, 
– BCC structure
– Carbon dissolved in
iron (0.02% max.)
– Soft, weak, ductile
Austenite, 
– High temperature
phase, above 727°C
– FCC crystal structure
– Carbon dissolved in
iron (2.14% max.)
Ferrite, 
– BCC structure
Cementite
– Hard, strong, brittle
, Ferrite
(BCC)
, Austenite
(FCC)
, Ferrite
(BCC)
Cementite
(Fe3C)
Chapter 9 - 12
Recall:
Eutectoid Solidification
Start with pure austenite, 
Eutectoid Reaction
–  0.76%C    0.022%C   Fe3C 6.7%C 
–
•
0.76 % Carbon at 727 °C
Develop pearlite microstructure
–
–
–
Similar to eutectic
microstructure from last time
Alternating lamellae of  and
Fe3C
Properties intermediate
between constituents
1076 Steel


1000
Temperature °C
•
•



 + Fe3C
800   
727 
Fe3C
6.70%
600
 + Fe3C
0
1%
Composition (wt % C)
Chapter 9 - 13
Recall:
Temperature °C
Eutectoid Composition
1076 Steel
1000

 + Fe3C
800   
727 
0.022
0.76
Fe3C
6.70%
600
 + Fe3C
0
• Pearlite 0.76 % C
• Ferrite (white)
• Cementite (black)
1%
Composition (wt % C)
Chapter 9 - 14
Time-Temperature-Transformation (TTT)
Eutectoid composition
•
Transformation rate has a strong
temperature dependence
– Rapidly cool to given
temperature
– Hold to solidification
•
More convenient to plot time
versus temperature
– Plot initiation and
completion lines
– Eutectoid plotted as
horizontal line
•
Valid only for
– Given composition
– Isothermal transformation
End
100
675 °C
650 °C
50
0
Begin
Austenite
(unstable)
Temperature °C
– 0.76 % C
–     Fe3C
Percent 
transformed
•
Austenite (stable)
Te
700
Pearlite
600
50 % completion
500
100 % completion
0 % completion
400
1
10
102
time (s)
103
104
Chapter 9 - 15
105
Fig. 10.14 in Callister
Chapter 9 - 16
Completing the Plots
•
•
Other than eutectoid
compositions have proeutectoid
phases
– Cementite (%C > 0.76)
– , Ferrite (%C < 0.76)
– At low enough temperatures,
this phase is suppressed
Bainite
– Forms below “knee” of curve
– Not really a new phase
– Ferrite and cementite phases
– No longer lamellar structure
Martensite
– Quench fast enough to avoid
other transformations
– Forms at very low
temperatures
– Nonequilibrium and
diffusionless
800

600
+C (Hypereutectoid)
(Hypoeutectoid)
+
 +P
Pearlite, P
500
 +B
Te
700

Temperature °C
•
400
Bainite, B

300
200
10-1
M (start)
M (50%)
M (90%)
1
0%
50% 100%
Martensite, M
10
102
103
104
time (s)
Chapter 9 - 17
105
Pearlite, Bainite, Martensite
•


FCC Structure
Above 725 C
Transforms to other phases
Ferrite




–
–
–
–
Austenite






•
Compound, Fe3C
Hard and Brittle
Contains 6.7% C
•
Formed by diffusion
Ferrite and cementite
Lamellar structure
Stronger than ferrite
Bainite
–
–
–
–
Iron + C in solid solution
Max. C is 0.022%
Ductile
Cementite
Pearlite
Not as much diffusion
Ferrite and cementite
Not lamellar structure
Harder that pearlite
Martensite
–
–
–
–
Diffusionless
transformation
Speed of sound
BCT Structure (bodycentered tetragon) with
carbon interstitials
Chapter 9 - 18
Strong and brittle
Bainite & Martensite
•
Upper
bainite
•
Lower
bainite
•
Martensite
From: Callister
Chapter 9 - 19
Pearlite Formation
•
•
Back to eutectoid
composition
Above knee form pearlite as
described in last lecture
Thickness of lamellae
depends on isotherm
– Course pearlite
•
•
•
Higher temperatures
Diffusion rate high
Carbon travels larger
distances
– Fine pearlite
•
•
Close to 540 °C
Diffusion suppressed
800

Te
700
(Coarse pearlite)
Pearlite, P
(Fine pearlite)

Temperature °C
•
 +P
600
500

 +B
Bainite, B
400
300
200
10-1
M (start)
M (50%)
M (90%)
1
Martensite, M
10
102
103
104
time (s)
Chapter 9 - 20
105
Bainite Formation
Below knee form bainite
Upper bainite
– ~300 - 540 °C
– Ferrite grows first, then
Fe3C drops out
– Needles of ferrite
separated by elongated
cementite particles
•
Lower bainite
– ~200 - 300 °C
– Thin plates of ferrite
containing fine blades of
cementite
•
•
Cannot transform pearlite to
bainite
Can coexist with each other
800

Te
700

Temperature °C
•
•
 +P
600
500

Pearlite, P
(upper Bainite)
 +B
Bainite, B
400
300
200
10-1
M (start)
M (50%)
M (90%)
1
(lower
Bainite)
Martensite, M
10
102
103
104
time (s)
Chapter 9 - 21
105
Martensite Formation
•
Nonequilibrium (metastable)
phase
Due to FCC/BCT transition
– Happens quickly (velocity
of sound)
– Little atomic motion
– Diffusionless
transformation
– Time independent
– –46 °C for complete
transformation
•
•
•
800

Te
700

Temperature °C
•
600
500

 +P
Pearlite, P
 +B
Bainite, B
400
300
M (start)
Lath: long thin plates (%C < 0.6)
Lenticular: needlelike
Characteristically brittle, strong,
hard
200
M (50%)
M (90%)
10-1
1
10
Martensite, M
102
103
104
time (s)
Chapter 9 - 22
105
Representative TTT Diagrams
Presence of other alloying elements
1021 Steel
1045 Steel
1095 Steel
4140 Steel
Mn 0.77
Cr 0.98
Mo 0.21
4340 Steel
Mn 0.78
Cr 0.80
Mo 0.33
Ni 1.79
Chapter 9 - 23
Alloying Effects
•
Higher carbon content
– Shifts curve to right (slightly!)
– Change proeutectoid phase from ferrite to
cementite
– If %C < 0.4, steel is not “hardenable”
• Necessary cooling rate would be far too quick to
form martensite
• Book says 0.25%, but realistically very difficult
below 0.4%
•
•
Alloying other than carbon
– Shift austenite nose to longer times
– Formation of separate bainite nose
What does this mean?
– To form equilibrium products, cooling rate must
be much slower
– Easier to form martensite
Chapter 9 – Thicker parts will have more uniform hardness
24
Continuous Cooling Transformation (CCT)
•
•
•
Isothermal heat treatment not
common
– Practically, want to cool
steadily to room
temperature
Isothermal curves shifted to
longer times and lower
temperatures
Bainite will not form for plain
carbon steel
Alloying agents shifts the
pearlite transformation curve
to the right
– Now possible to obtain
bainite
– 2 “knees” appear on
curve
800

Te
 +P
700

Temperature °C
•
Pearlite, P
600
500

Bainite, B
400
 +B
300
M (start)
200
M (50%)
M (90%)
10-1
1
10
Martensite, M
102
103
104
time (s)
Chapter 9 - 25
105
Example: 4340 Steel
1. Martensite
Pearlite
2. Martensite
Banite
3. Martensite
Ferrite
Banite
Bainite
1
2 3
4
4. Ferrite
Pearlite
5
5. Pearlite
Chapter 9 - 26
Linking Important Concepts
•
•
•
The composition of an alloy determines
the phase change kinetics
The cooling rate determines the
microstructure of an alloy
The microstructure determines the
mechanical properties
Chapter 9 - 27
Mechanical Properties
(Pearlite & Bainite)
•
•
Brinell Hardness
600
Bainite
Pearlite
80
280
60
240
200
40
160
20
120
500
400
80
300
0
200
0.2
0.4
0.6
0.8
1.0
wt% C
100
500
300
400
600 700
Transformation temperature (°C)
Spheroidite
Coarse Pearlite
Fine Pearlite
Chapter 9 - 28
%RA
•
Cementite harder & more brittle than
ferrite
Spheroidite: spherical Fe3C particles in 
matrix, very soft & ductile
Pearlite: Fine is harder & more brittle than
coarse
Bainite: Stronger & harder than pearlite,
good ductility
Brinell Hardness
•
Mechanical Properties
(Martensite)
Very strong and hard
Brittle
– C interstitials
– Few slip systems
•
•
Large internal stresses due
to volume change from
austenite phase
To recover ductility, need to
do special heat treatment
called tempering…
700
Brinell Hardness
•
•
 ultimate  3.5 BHN MPa
Martensite
600
500
400
Tempered martensite
300
200
Pearlite
100
0.0
0.2
0.4 0.6
Carbon, %
0.8
1.0
Chapter 9 - 29
Mechanical Properties
(Tempered Martensite)
Tempering: Reheating
martensite up to a
sub-eutectoid
temperature for long
time
•
Trade strength for
ductility
1800
Tensile
1600
Yield
1400
1200
60
50
1000
40
800
200
30
300
400
500
600
Tempering temperature, °C
Chapter 9 - 30
% RA
martensite(BCT single phase) 
tempered martensite(   Fe3C )
4340 steel
Strength, MPa
•
Austenitic Transformations
Chapter 9 - 31
Objectives for Chapter 11
•
•
•
•
•
•
•
•
Have basic understanding of types of steels, relative C content,
strength, and applications.
Know fundamental differences between the types of cast iron.
Describe the purpose of and procedures for process annealing, stress
relief annealing, normalizing, full annealing, and spheroidizing.
Define hardenability and list the class steels that have low
hardenability.
Know how to use the Jominy End Quench Test - see lab on
hardenability.
Explain the procedure to precipitation harden an alloy and what
characteristics on the phase diagram allow the alloy to be hardened by
this mechanism.
Explain the shape of the strength vs time curve for precipitation
hardened alloys in terms of the mechanism of hardening in each stage.
Distinguish between the four types of forming operations.
Distinguish between the four types of casting techniques.
Chapter 9 - 32
Ferrous Alloys
Chapter 9 - 33
Metal Fabrication
Chapter 9 - 34
Heat Treating Steel
Temperature °C
1000

800


600
 + Fe3C
0
•
 + Fe3C
% Carbon
1%
Full Annealing
– Heat to 15-40 °C above phase transition line, hold for
diffusion, and slow cool (usually in a furnace, often
takes number of hours).
– Returns microstructure to coarse pearlite.
– Often performed on steels to be machined or formed to
increase ductility
Chapter 9 - 35
Heat Treating Steel
Temperature °C
1000

800


600
 + Fe3C
0
•
 + Fe3C
% Carbon
1%
Normalizing
– Heat to the fully austenite region and air cool.
– Fine pearlite microstructure
– Refine grain size and distribution (often done
after a rolling operation)
Chapter 9 - 36
Heat Treating Steel
Temperature °C
1000

800


600
 + Fe3C
0
•
 + Fe3C
% Carbon
1%
Spheroidizing
– Heat a medium-high carbon steel below the eutectoid
line and hold for several hours
– Forms small Fe3C spherical particles in  matrix.
– For higher carbon steels, even pearlite is often brittle
and difficult to deform
– Spheroidizing minimizes hardness and is highly
Chapter 9 machinable
37
Heat Treating Steel
Temperature °C
1000

800


600
 + Fe3C
0
•
 + Fe3C
% Carbon
1%
Quenching
– Heat to fully austenitize steel
– Rapidly cool (quench in water, oil, etc)
– No time for carbon to diffuse
– Produces a non-equilibrium microstructure called
martensite
• Very hard, strong, brittle with large internal stresses
Chapter 9 - 38
Heat Treating Steel
Temperature °C
1000

800


600
 + Fe3C
0
•
 + Fe3C
% Carbon
1%
Tempering
– After quenching to form martensite
– Reheat below eutectoid temperature
– Hold for several hours to precipitate carbides and
relieve residual stresses
– Forms tempered martensite
• Relatively hard, strong, much more ductile
• Often ideal microstructure ...
Chapter 9 - 39
Hardenability
•
Hardness vs. Hardenability
– Hardness – resistance to deformation
– Hardenability – ability to be form martensite
(to be hardened)
•
Formal definition:
– Hardenability – ability of an alloy to be
hardened by formation of martensite due to
given heat treatment
•
High hardenability  martensite forms (i.e.
hardens) far into specimen, not just at surface
Chapter 9 - 40
Jominy End Quench Test
Standard test for measuring hardness of any material
Hardness, HRC
Sample of fixed geometry suspended over water jet
Geometric factors all constant
Only effect on hardness is alloying content
Hardness measured as function of distance from quenched
end
Distance
–
–
–
–
Cooling rate
•
Distance from quenched end
Chapter 9 - 41
Hardness Profiles
Cooling rate at 700 °C (°C/s )
•
170 70
Cooling rate
18
9
5.6
3.9
2.8
2
•
Microstructure
–
–
–
–
Slower
Martensite
Cooling
Bainite
Fine Pearlite
Course Pearlite
Hardness, HRC
– Highest at quenched end
60
– Smoothly decreases with distance
8660
50
40
8640
30
8630
8620
•
Often plot cooling rate and distance
10
•
Increasing carbon content
20
30
40
Distance from quenched end, mm
– Maximum possible hardness increases
– Higher overall hardness (more hardenable)
Chapter 9 - 42
50
Severity of Quench
•
•
Rate of cooling!
Depends on
– Medium- Fluid in which an austenetized part is plunged
• Most common: air, oil, water
– Agitation - Relative motion of quenching medium during
cooling
• Agitation rate influences cooling rate
– Surface area to volume ratio • All heat removed at surface
• More surface area provides more opportunity to
remove heat
• Irregular shapes with edges have large quenching
surfaces
•
For highly stressed part, want 80% martensite throughout part
– Usually from a “guideline” for specific company
Chapter 9 - 43
Using Cooling Curves
•
•
Normal quenching takes place on radial surface
Can predict hardness across radius of a bar from
Jominy tests.
Chapter 9 - 44
Review: Heat Treatment of Steel
•
•
•
•
•
Annealing- Heat, holding at temperature, gradual
cool
– General term, but also used for specific
processes
Tempering -Heat martensite to get diffusional
transformation:
– martensite (BCT single phase)  tempered martensite (  Fe3C )
– Still have ultra-fine microstructure, but more
ductile
Process annealing -Reverse effects of cold work;
recovery, recrystallization, but little grain growth
Stress relief - Lower temperature anneal to undo
thermal stress or transformation mismatch
stress
Spheroidizing - Heat pearlite just below eutectoid
temp to produce spheroidal structure; makes
Chapter 9 - 45
steel easier to machine
Surface Hardening Techniques
•
•
Many applications, especially wear
– Strong, hard, wear-resistant surface
– Tough, fracture resistant inner core
– Two different heat treatments - through, then
surface
Methods
– Chose material with steep cooling curve
– Case Hardening - Change chemical composition
of surface
•
•
•
Carburizing
Nitriding
Carbonitriding
– Decremental Hardening – Very localized heat
treatment
•
•
Flame Hardening
Induction Hardening
Chapter 9 - 46
Alloys for Surface Hardness
Cooling rate at 700 °C (°C/s )
170 70
18
9
5.6
3.9
2.8
2
100
4340
80
A
B
Hardness, HRC
50
50
4140
40
8640
30
A
5140
B
1040
10
Prescribe:
Percent Martensite
60
20
30
40
50
Distance from quenched end, mm
Minimum hardness at A
Maximum hardness at B
Must know the cooling rates at each point!
Chapter 9 - 47
Carburizing
•
Hardens steel by causing carbon
to diffuse into the surface.
– Furnace heat to a temperature
at which carbon will diffuse
– Hold until diffusion creates the
proper case depth.
•
Must be a carbon rich
environment
•
For steels with low carbon content
(%C < 0.2)
•
Used extensively on gears and
shafts to harden them yet
maintain the core toughness.
•
Decarburization is opposite
process for high carbon steels softer case
From: Callister p. 92, 224
Chapter 9 - 48
Flame Hardening
•
For steels of hardenable carbon
content (%C  0.4)
•
A high intensity oxy-acetylene flame
is applied to the bring the region of
interest to an austenite
transformation.
•
The interior never reaches high
temperature.
•
The heated region is quenched to
achieve the desired hardness.
•
The depth of hardening can be
increased by increasing the heating
time.
•
In addition, large parts, which will
not normally fit in a furnace, can be
heat-treated
From: Scheer p. 43
Chapter 9 - 49
Precipitation Hardening
•
Form extremely small, dispersed particles of a
second phase
•
Small second phase particles called precipitates
•
Age hardening - strength develops as the alloy
ages
– Time dependent
– There is a maximum attainable effect
•
Different than tempering martensite
– Similar heat treatment procedure
– Different strengthening mechanism
Chapter 9 - 50
Precipitation Hardening
•
•
Primary strengthening mechanism
for
– Aluminum
– Nickel based superalloys
– Titanium
Examples
 Ti in b Ti matrix
– Al/Cu
– Cu/Sn
– Mg/Al
Ni3Al in Ni matrix
From: Socie
Chapter 9 - 51
Phase Diagrams & Treatment

Temperature
L
L+
L+b
b

b
Precipitation hardenable alloys have:
 Appreciable maximum solubility
 Decreasing solubility with
temperature
 Composition less than maximum
solubility
Solution Treating:
Heat into the single phase region and
rapidly quench to room temperature to
produce a supersaturated solid solution
Aging:
Composition
Heat to a temperature below the phase
transition to allow time for precipitates
to form
Chapter 9 - 52
Why Precipitation Harden?
•
Look at Aluminum rich side of Al/Cu system


–
Coarse q phase weakens the alloy
Temperature
•
°C
 is a substitutional solid solution of copper in aluminum
q is an intermetallic compound CuAl2
One slow cool in is NOT helpful in strengthening
700
600

500
400
100% 
(95.5% Al, 4.5% Cu)
Coarse q precipitates
At  grain boundaries
q
300
200
100
Al
5
10
wt % Cu
time
Chapter 9 - 53
How to Precipitation Harden
•
Two reheating treatments are needed:
–
–
•
Solution treatment
Age hardening
Fine precipitates strengthen & harden material
100%  solid solution
Temperature
°C
700
600
500

Equilibrium
Microstructure
400
q
300
Fine precipitates in grains
(retained after cooling)
200
100
Al
5
10
wt % Cu
time
Chapter 9 - 54
Overaging
If precipitates get too big, strengthening/hardening is lost
Process sped up by temperature
Some alloys age at room temperature
Why is strength lost?
100%  solid solution
Temperature
•
•
•
•
Fine precipitates in grains
Coarse precipitates
in grains
taging
time
Chapter 9 - 55
Strength Development
•
•
•
•
Fine precipitates (Guinier-Preston zones  q’’ phase) are
coherent with lattice
Deformation of crystal impedes dislocation motion
At optimal aging time, precipitates are dispersed, small, and
coherent.
After optimal aging time, precipitates get too big, incoherent with
matrix.
From: Callister
Chapter 9 - 56
Age vs. Material Properties
•
Must age carefully to avoid
overaging
– Too high temperature
– Too long age time
•
Precipitation rate maximized at
intermediate temperatures
– Near solvus  no driving
force for nucleation
– Low temperatures 
diffusion is slow
Nucleation
T
Diffusion
t
Gm   G * 
N ~ N o exp  
 exp  

kT
k

T




From: Callister
Chapter 9 - 57
Strengthening Mechanisms
• Dislocation Looping
• Dislocation cutting
From: Hertzberg
Chapter 9 - 58
What is Attractive About
Aluminum?
•
•
Upside
•
– Lightweight (  Al  0.3*  Steel)
– Ductile
– Heat treatable
– Castable
– Corrosion resistant
•
– Good conductor
Downside
– Formability is lower
• Simpler shapes
E Al  31 E Steel
–
– For same stiffness, need
larger section
Longitudinal stiffness(~EA/L)
E St ASt  E Al AAl
AAl 
ESt
E Al
ASt  3* ASt
 Al AAl L   St ASt L
Bending stiffness (~EI)
– Rect. section, constant
b
I  bh3
b
3
3
E St bhSt
 E Al bhAl
h Al  3
ESt
h
E Al St
h
 1.44 * hSt
W Al  Al AAl L  Al h Al b


 0.43
WSt  St ASt L  St hSt b
Chapter 9 - 59
Aluminum Designations
•
•
–
–
–
–
Alloying Composition
–
–
Aluminum
1xxx
Aluminum
• Copper
• Manganese
• Silicon
• Magnesium
• Mg and Si
• Zinc
Common alloys:
Tempering Designations
2xxx
3xxx
4xxx
5xxx
6xxx
7xxx
2024-T4 ,
6061-T6,
7075-T6
-O: Annealed
-F: As fabricated
-H1: Strain Hardened
-H2: Strain Hardened/ Partial
Annealed
– -T: Thermally Processed
• -T2: Annealed (cast products)
• -T3: Solution treated, CW,
naturally aged
• -T4: Solution treated, naturally
aged
• -T5: Artificially aged, no
solution treatment
• -T6: Solution treated, artificially
aged
• -T7: Solution treated, over-aged
• -T8: Solution treated, CW,
artificially aged
• -T9: Solution treated, artificially
aged , CW
Chapter 9 - 60
New Concepts & Terms
• Applications of hardness profiles
(Jominy curves)
• Precipitation hardening
– Heat treatment process
– Effect of overaging
– Microstructures
– Effect on strength
• Applications of aluminum
– Know tradeoffs, especially with
steels
– Which alloys are precipitation
hardenable?
Chapter 9 - 61