Lecture Presentation (2).ppt

V SIVAHAR / LEVEL 1 / MT 101 1
PHASE DIAGRAMS
Alloy:
An alloy is a metallic material consisting of
two or more elements. The principal
element is generally a metal the other
elements can be metallic or non-metallic
elements.
e.g. Steel (Fe + C)

PHASE DIAGRAMS
Alloys can be formed in three different
ways.
1. Interstitial Solid Solution (ISS)
2. Substitutional Solid Solution (SSS)
3. Intermediate Compounds

PHASE DIAGRAMS
Interstitial Solid Solution e.g. C in Fe
Solvent atoms
(Fe)
Solute atoms
(C)

PHASE DIAGRAMS
Substitutional Solid Solution e.g. Zn in Cu
Solvent atoms
(Cu)
Solute atoms
(Zn)

PHASE DIAGRAMS
Intermediate Compound e.g. Fe3C
•Intermediate compounds have fixed compositions.
•Find the weight percentage of carbon in Fe3C. (Ans : 6.67%)
•If both the elements are metals it is known as an Intermetallic
Compound. E.g. CuAl2

PHASE DIAGRAMS
Phase
A state in which a material can exist. E.g.
water can exist in solid (ice), liquid (water)
and gaseous (steam) phases.
• Existence of particular phase depends on
temperature and pressure.
• The factors temperature and pressure are
known as the variables.

PHASE DIAGRAMS
• In an alloy, composition becomes the third
variable.
PHASE DIAGRAM
Phase diagram is a graphical representation
of the phases present in a material system
under different conditions.

PHASE DIAGRAM – PURE WATER

PHASE DIAGRAM – PURE IRON
1539 0C
1394 0C
910 0C
P atm
T0C
α – IRON (BCC)
γ – IRON (FCC)
δ – IRON (BCC)
LIQUID
VAPOR

BINARY ALLOY PHASE
DIAGRAMS
• Alloys containing two elements are known
as binary alloys. E.g.: Steel (Fe + C)
• Binary alloy phase diagrams are obtained
for Temperature and Composition while
maintaining the pressure constant –
usually 1 atm

BINARY ALLOY PHASE
DIAGRAMS
• Binary alloy phase diagrams are
considered under 3 different categories:
1. Complete solubility in solid state
2. Complete insolubility in solid state
3. Partial solubility in solid state

Complete solubility
Line 1
T 0C
TB
LIQUID liquidus
L + α solidus
TA
α
100A 50A 0A
0B 50B 100B

Complete solubility
• Microstructural changes along line 1
LIQUID α

Complete insolubility
1 2 3
T 0C
TB
LIQUID
TA
L + A L + B
TE
E
A + B
100A 50A 0A
0B 50B 100B

• At point E along line 2
LIQUID A + B
Such a transformation is known as eutectic
transformation. E is known as the eutectic point
and TE is known as eutectic temperature.

LINE 2
LIQUID B
A

LINE 1
B
A
LIQUID

LINE 3
B
A
LIQUID

Partial solubility
1 2 3 4 5 6 7
T 0C
TB
LIQUID
TA
L + α L + β
TE
α β
E α + β
100A 50A 0A
0B 50B 100B

Partial solubility
LINE 4
LIQUID β
α

Partial solubility
LINE 3
β
α
LIQUID

Partial solubility
LINE 5
β
α
LIQUID

Partial solubility
LIQUID α
LINE 1

Partial solubility
LIQUID β
LINE 7

Partial solubility
LINE 2
LIQUID α α β

Partial solubility
LIQUID β
LINE 6
β α

Lever rule
• Lever rule is used to find the proportions of
the phases present in a two-phase region
30B 45B 65B
Liquid
L+α
α
70A 55A 35A
X Y
T

Lever rule
• Find the relative proportions of liquid and α phases
at the temperature T for an alloy of 55%A + 45%B
 
1
Y
%
X
L% 


 
%
43
%
35
15
100
%
%
57
%
35
20
100
L%







 
35
%
100
15
α%
20
L%
Y
X
%
100
X
α%
Y
L%
1
equation
From





 
2
100%
%
L% 



Lever rule
• What are the compositions of the liquid and α
phases at this temperature?
Answer:
• Liquid phase – 70A+30B
• α phase – 35A+65B

MECHANICAL PROPERTIES
• Reaction of materials to the action of external
stresses is indicated as mechanical properties
A
F
]
[
2
Pa
m
N
A
F
Stress 


• Application of a stress causes a material to
deform. A stress as shown below elongates
the material. Elongation (or contraction), when
expressed per unit length is known as strain.
l0 e 0
l
e
Strain 


(Uniaxial) Tensile Stress
(Uniaxial) Compressive Stress

• Mechanical properties of a material is studied by
performing tensile test. Tensile test employs a
specimen as shown below.
l0
do
lo – Gauge length do – Initial diameter
Ao – Initial area 4
2
d
Ao 


• The specimen will be subjected to a
progressively increasing tensile force until it
fractures.

• From the test, Force-Extension curve is
obtained.
e
F

• Force-Extension curve is then converted
to a Stress-Strain [σ-ε] diagram.
ε
σ

• Form of Stress-Strain [σ-ε] diagram of Cu, Al etc.
ε
σ
UTS
YS
FS
UTS – Ultimate Tensile Strength
YS – Yield Stress
FS – Fracture Stress

• Form of Stress-Strain [σ-ε] diagram of steel
ε
σ
UTS
UYS
LYS
FS
UTS – Ultimate Tensile Strength
UYS – Upper Yield Stress
LYS – Lower Yield Stress

Stress-Strain Diagram Steel

• Form of Stress-Strain [σ-ε] diagram for glass,
diamond, cast iron, ceramics etc.
ε
σ
FS

• Form of Stress-Strain [σ-ε] diagram for a plastic
ε
σ

• Form of Stress-Strain [σ-ε] diagram for rubber
ε
σ

ELASTICITY
• All materials show temporary deformation
to a certain extent
• Such a deformation is known as elastic
deformation
• Property of possessing elastic deformation
is known as elasticity
• Elasticity of most of the materials gives a
straight line in the σ-ε diagram – known as
linear elastic materials

ELASTICITY
• For linear elastic materials
• E is known as Elastic modulus or Young’s
modulus
• E of steel is 2 x 1011Pa
Eε
σ
;
ε
σ 

ε
σ

ELASTICITY
• Elasticity of some other materials does not
give a straight line in the σ-ε diagram –
known as non-linear elastic materials -
rubber
• Elasticity in materials is due to the
stretching of atomic bonds.
ε
σ

PLASTICITY
• The deformation becomes permanent
beyond a certain stress level in metals
• It known as plastic deformation and the
property is known as plasticity
• Plastic deformation begins at the yield
stress.
• Plastic deformation facilitates solid-state
fabrication in metals
ε
σ

PLASTICITY
• Plastic deformation in metals occurs due to
a phenomenon known as slip [relative
displacement of atomic planes]
ε
σ

PLASTICITY
• Slip is favored by the movement of
dislocations
ε
σ

PLASTICITY
ε
σ

PLASTICITY
• Movement of dislocations and slip occurs
on close packed planes in close packed
directions
• In FCC metals slip takes place on (111)
plane in [110] direction
• In BCC metals slip takes place on (110)
plane in [111] direction
ε
σ

PLASTICITY
ε
σ
Atoms are packed more closer in (111) of FCC
Slip occurs more favorably in FCC structures
(110) BCC (111) FCC

ε
σ
DUCTILE &BRITTLE MATERIALS
• Ductile materials – materials that exhibit
plastic deformation – most metals are
ductile
• Brittle materials – materials that do not
have plasticity – glass, cast iron
ε
σ

DUCTILITY
• Ability of a metal to undergo plastic
deformation is defined as ductility
• Plastic strain at fracture εpf is a
measure of ductility
ε
σ
εpf

DUCTILITY
• Ductility of copper is greater than that of
steel
ε
σ

DUCTILITY
• Ductility can also be measured by
I. Percentage elongation
II. Percentage reduction in area
%
100


o
o
f
l
l
l
%
100


o
f
o
A
A
A

DUCTILITY
• Example
• Why ductility of copper is greater than that
of steel at room temperature?
Note:
• Brittleness is the property that is opposite
to ductility

STRENGTH
• Ability of a material to withstand the
applied stresses without failure is defined
as strength
[Maximum stress that can be applied on a
material]
• Strength of a brittle material is given by
it’s fracture stress
ε
σ
FS

STRENGTH
• Yield stress is considered as the strength
for a ductile material
• UTS is not considered, since significant
plastic deformation takes place before
UTS is reached

STRENGTH
ε
σ
UTS
YS
FS
Strength of steel 227MPa

PROOF STRESS
• Proof stress is defined as the stress
required to cause a certain amount of
plastic strain.
• E.g. : 0.1% Proof stress is the stress at a
plastic strain of 0.1% or 0.001
• Following diagram demonstrates the
method to find 0.1% Proof Stress

PROOF STRESS
ε
σ
0.001
0.1% PROOF STRESS

WORK HARDENING
• Stress required for plastic deformation
increase continuously up to the UTS. This
phenomenon is known as work hardening.
• Work hardening increases the strength
and hardness while decreasing the
ductility and toughness.
• Effect of work hardening on strength is
demonstrated by a tensile test as follows

WORK HARDENING
ε
σ
SPECIMEN UNLOADED
B
P
P
F
O
YS2
YS1
Test stopped at B
and the specimen
is unloaded
It is then reloaded
The new σ-ε
diagram is PBF
This shows that
the strength has
increased from
YS1 to YS2

WORK HARDENING
Mechanism:
• During plastic deformation dislocations not
only move but also multiply.
• Increased number of dislocations
increases dislocation interactions within
themselves as well as with external factors
such as grain boundaries

WORK HARDENING
Mechanism [contd…]:
• This increases the resistance for the
movement of dislocations in the
metal.
• As a result stress required for plastic
deformation continue to increase

NECKING
• At the UTS a localized deformation begins
in the specimen
• This localized deformation is called
necking

NECKING
• The area of cross-section continue to
decrease at the neck as the test continues
• Fracture occurs at the neck
• Fracture surfaces give cup & cone
appearance

TOUGHNESS
• Work done during the deformation of a
material is stored in the form of strain
energy
• Strain energy absorbed by a material up
to fracture is defined as toughness
• Toughness can also be defined as the
work done at fracture

TOUGHNESS
• Area under the σ-ε diagram is a measure
of toughness [cross hatched area]
ε
σ
σ
ε

TOUGHNESS
• The above σ-ε diagrams show that
ductile materials have greater
toughness than brittle materials
• Toughness can also be measured by
performing Impact Test

IMPACT TEST
• Impact test employs a notched specimen
as shown
IMPACT LOAD
[applied by a swinging pendulum]

IMPACT TEST
M 1
2
SPECIMEN
PIVOT
PENDULUM
h
H

IMPACT TEST
• Energy of pendulum
– At position ‘1’ = MgH + 0
– At position ‘2’ = Mgh + 0
• Energy change = Mg(H-h)
• This is the toughness of the material used

DUCTILE-BRITTLE TRANSITION
• Whether a material is ductile or brittle
depends on the temperature
• Ductile materials show brittle behavior as
the temperature is lowered
• This is known as ductile-brittle transition
• Ductile-brittle transition behavior of
materials is studied by performing impact
test over a range of temperatures

TEMPERATURE 0C
STEEL [BCC] ENERGY
DBTT
0
DUCTILE
BRITTLE

TEMPERATURE 0C
COPPER [FCC] ENERGY
0
DUCTILE
BRITTLE

• In BCC metals like steel, a sudden change
in behavior is observed over a narrow
range of temperature.
• Ductile-Brittle Transition Temperature
(DBTT) is the middle value of this
temperature range
• In FCC metals like copper the change is
gradual

HARDNESS
• Hardness of metals [and some other
materials] is defined as the resistance
for indentation
• Hardness of metals is measured by
indentation test
• Hardness of brittle materials is defined as
resistance to scratching
• Brittle material hardness is measured
using Moh’s scale

HARDNESS OF METALS
• In the indentation test the metal is subject
to indentation with a hard indenter as
shown. Depth of indentation is the
measure of hardness
F
INDENTER
HARD SOFT

HARDNESS OF METALS
• Hardness units differ depending on the
type of indenter used and the load
applied
1. Brinell (HB)
 10mm diameter steel / WC ball indenter
 Any load ‘P’ can be applied
 Diameter ‘d’ of the indentation is measured
in place of the depth

HARDNESS OF METALS
 
2
2
2
d
D
D
D
P
HB




P
INDENTER
d
D = 10mm

2. Vickers (HV)
 Pyramid shaped indenter made of diamond
is used
 Any load ‘P’ can be applied
 Diagonal lengths d1 and d2 of the diamond-
shape indentation are measured
 Average d = (d1+d2)/2 is used in the
calculation
HARDNESS OF METALS

HARDNESS OF METALS
2
2
854
.
1
2
136
sin
2
d
P
d
P
HV


d2
P
INDENTER
d1
θ = 1360

HARDNESS OF METALS
3. Rockwell
1. Rockwell A, C & D – these 3 units use cone
shaped indenter made of diamond
 HRA – 60 kg
 HRD – 100 kg
 HRC – 150 kg

HARDNESS OF METALS
2. Rockwell B, F & G – these 3 units use 1/16”
diameter (1.5mm approx.) ball made of steel
/ WC
 HRF – 60 kg
 HRB – 100 kg
 HRG – 150 kg
3. Rockwell E – uses 1/8” diameter (3mm
approximately) ball
 100 kg - HRE

HARDNESS OF OTHER
MATERIALS
Hardness of brittle materials like
ceramics is measured using Moh’s
scale. In this scale 10 hardness
numbers are given to ten standard
materials. Hardness of the given
material is given relative to the hardness
numbers of these materials.

MOH’S SCALE
1. Talc
2. Gypsum
3. Calcite
4. Fluorite
5. Apatite
6. Orthoclase
7. Quartz
8. Topaz
9. Corundum
10.Diamond

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