Unit I

Mechanical Behaviour of metals

Arrangement of Atoms

Arrangement of atoms in
(a) face-centred cubic structure,
(b) close-packed hexagonal structure, and
(c) body-centred cubic structure

When Does it take place?

• Deformation in metals or alloys takes place when stress
is applied.
• Deformation is the change in the dimension or the form of
the material under the action of applied force

Elastic Deformation:
• Deformation in metals can occur either by elastic
movement or by plastic flow. In elastic deformation a
limited distortion of the crystal lattice is produced, but the
atoms do not move permanently from their ordered
positions, and as soon as the stress is removed the
distortion disappears.
Elastic Deformation:
• Characteristics of Elastic Deformation:
(1) it is reversible,
(2) stress and strain are linearly proportional to
each other according to Hooke’s Law and
(3) strain is usually small (i.e. <1% elastic strain).

Plastic Deformation
• When a metal is stressed beyond the elastic limit plastic deformation
takes place
• Movement of the atoms into new positions, since considerable
permanent distortion is produced. Plastic deformation is permanent

A: Before straining B: After straining

Plastic Deformation
• Permanent or plastic deformation may be carried out intentionally
many times as in working or shaping processes like bending,
stamping, drawing, spinning, rolling, forging extruding etc.
• Plastic deformation may also be carried out in order to improve some
mechanical properties of metals and alloys.

Mechanism of Plastic Deformation Structure

Structure Insensitive sensitive

Lattice Defects: Electrical

Elastic constants conductivity
• Lattice defects help explain mechanical Semiconductor
properties of materials such as: Melting point properties
• Yield strength Density Yield stress
Fracture
• Fracture strength
Specific Heat strength
• Creep strength Coefficient of
thermal expansion Creep Strength

Point Defects

Schematic representation of different point

defects in a crystal.
(1) vacancy;
(2) self interstitial;
(3) interstitial impurity;
(4), (5) substitutional impurities.
The arrows show the local stresses
introduced by the point
What are dislocations?
• Dislocations are line defects that exist in metals
• There are two types of dislocations: edge and screw
• The symbol for a dislocation is
• The dislocation density in annealed metals is normally r = 106/cm2

How does a dislocation move?

Deformation by slip

Types of dislocations

Screw

Edge
Dislocation motion Û plastic deformation

Note: Dislocations normally move under a shear stress

Stress field of
a dislocation

Analog to
an electric
charge
 Dislocation –TEM picture of dislocation network in
cold worked aluminium

TEM is Transmission Electron Microscopy .

In this technique a thin foil of 100nm is

prepared from the sample.
This thin foil becomes transparent to
electrons in electron microscope and
therefore it becomes possible to view the
dislocation network, stacking faults etc.

Dislocation interaction
Positive Positive

^ ^ Repulsion

Positive Negative
Attraction
^
&
Annihilation

Note: More positive-positive interactions in reality

 Positive-positive dislocation interaction
• Results in more stress to move dislocations (or cause plastic
deformation)
• Due to the process of work hardening
• This type of interaction also leads to dislocation multiplication
which leads to more interactions and more work hardening

Modes of deformation

• Slip

• Twinning

Slip
• Dislocations move on a certain crystallographic plane: slip plane
• Dislocations move in a certain crystallographic direction: slip direction
• The combination of slip direction and slip plane is called a slip system
• Slip planes are normally close-packed planes
• Atoms move easily on a packed planes
• Slip directions are normally close-packed

Recall for fcc close-packed planes are {111}

Close-packed directions are <110>
Slip systems
Crystal Slip plane Slip Total Active
system direction number of slip
slip systems
systems
fcc {111} <110> 4X3 12

hcp {0001} <1120> 1X3 3

bcc {110} <111> 6X2 12

{211} <111> 12X1 12
{321} <111> 24X1 24

Classical slip

Under the action of Shear Load

Twinning
• Common in hcp and fcc structures
• Limited deformation but helps in plastic deformation in hcp and
bcc crystals
• Occurs on specific twinning planes and twinning directions

Typical Slip planes and directions for Twinning

Metal Structure Slip System

Slip Slip
Plane Direction

Zn, Mg, Cd HCP {1012} <1011>

Cu, Ag, Au FCC {111} <112>
Fe, Cr, V, Mo,
W BCC {112} <111>
 Mechanical Twins and Annealing twins

(a) Neumann’s bands in Fe,

(b) Mechanical twins produced in Zn on polishing and
(c) Annealing twins generated after annealing in gold-silver alloy

Difference between slip and Twinning

 Difference between slip and twinning:

Slip Twinning
1. All the atoms in one 1. Atoms in successive plane
block move the same within a block move
distance different distance
2. Under microscope the 2. Twins appears as broad
slip appears as a thin lines or bands
line 3. There is a markedly
3. There is very little different lattice orientation
change in the lattice in the twinned region
orientation 4. Whenever the possible slip
4. Twining usually requires systems are considerably
higher shear stress than limited, as in the case of
slip initially HCP metals, twinning
becomes the mode of
deformation

Deformation by Slip:
Earlier it was thought that slip occurs by simultaneous gliding of
complete block of atoms over another. But this requires that the
shearing force must have the same value over all points of the slip
plane. The vibration of atoms and the difficulty in applying a
uniformly distributed force makes this condition unattainable.

Wrinkled sheet of paper example

Dislocations are imperfections or distorted region in the otherwise

prefect crystal and the step by step movement of dislocations
explains why the force required to produce slip is of the order of
1000 times less than the theoretical assuming simultaneous slip
over a whole system.
 Deformation by Slip:
The Burgers vector b is the vector which defines the magnitude and
direction of slip.
It has already been shown that for a pure edge dislocation the
Burger’s vector is perpendicular to the dislocation line, while for a pure
screw dislocation the Burger’s vector is parallel to the dislocation line.
Actually, dislocations in real crystals are rarely straight lines and rarely lie
in a single plane.
A dislocation will be partly edge and partly screw in character

Slip occurs at a definite point where dislocation exists and proceeds by

movement of the dislocation in a given plane of the crystal due to shear
stresses.
A dislocation results in the slip band

Deformation by Stacking Faults

Faulted structures,
(a) Face-centered cubic packing;
(b) deformation fault in fcc
(c) twin fault in fcc
(d) hcp packing.
 Deformation by Stacking Faults
FCC HCP

slip or C

or C

• All defects cost energy (J/m2 or erg/cm2).

• Stress, dislocation motion can create Stacking Faults.

Deformation by Kinking:
Consideration of the equation for critical resolved shear stress
shows that it will be difficult to deform a hexagonal crystal when the
basal plane is nearly parallel to the crystal axis.

Orowan found that if a cadmium crystal of this orientation were

loaded in compression it would deform by a localized region of the
crystal suddenly snapping into a tilted position with a sudden
shortening of the crystal.
Deformation in polycrystalline Materials
Until now we considered the deformation in single crystals in terms of
the movement of dislocations and the basic deformation mechanisms
of slip and twinning.

Commercially available materials are made of polycrystalline aggregates

made of a large number of small grains.

Grains are not free to move

as they are-
Surrounded by other grains,
grain boundaries and have
different crystallographic
orientation

Microstructure of Fe-C alloy

Deformation in polycrystalline Materials

• Each of the light areas is called a

grain, or crystal, which is the
region of space occupied by a
continuous crystal lattice
• The dark lines surrounding the
grains are grain boundaries.
• (B) represents four grains of
different orientation and the grain
(A) Microscopic (B) Atomic boundaries that arise at the
interfaces between the grains.

• (A) Random grain Orientation –

isotropic properties
• (B) Directional properties

(A) Random Cold (B) Preferred grain-

Rolled Non Oriented oriented structure

https://engineeringlibrary.org/reference/structure-of-metals-doe-handbook
 Yield Point and grain diameter correlation

Deformation in polycrystalline Materials

Restricted movement :
A large amount of stress is required to move the dislocations across the
grains due to difference in the orientation of the grains.
Grain boundaries restrict the movement of the dislocations resulting in
the pile up of dislocations at the grain boundary
Grain Size also plays an important role in the movement of dislocations
in the early stages of deformation

Stages in the deformation process of

polycrystalline materials
1. Elastic Deformation
2. Plastic deformation sets in- Elastic after effect where stresses develop and the
elastically deformed crystals force the plastically deformed crystals into their
original positions.
3. Majority of crystals deform plastically
4. Yielding of the polycrystalline material
 Yield point phenomenon Luders Bands

Tensile test specimen the

Two distinct yield points called as upper yield point fillet act as stress raisers
and lower yield point and at these points the
Stress value rises higher with strain and fluctuates at luders bands are formed.
a lower value before the load is again increased They are generally at
The elongation that takes place at constant stress is approximately at an angle
called as Yield point elongation and the 0f 45 to 50 degree to
phenomenon is called as Yield Point phenomenon. tensile axis.

Strain Hardening of Single Crystals:

shear stress required to produce slip continuously increases with

increasing shear strain. The increase in the stress required to cause slip
because of previous plastic deformation is known as strain hardening, or
work hardening.

An increase in flow stress of over 100 per cent from strain

hardening is not unusual in single crystals of ductile metals.

Strain hardening is caused by dislocations interacting with each

other and with barriers which impede their motion through the
crystal lattice.
 Strain Hardening of Single Crystals:

•As deformation proceeds the metal becomes progressively

harder and stronger and, whether by slip or by twinning, a point is
reached when no more deformation can be produced. Any further
increase in the applied force will lead only to fracture.

•In this condition, when tensile strength and hardness have

reached a maximum and ductility a minimum, the material is said
to be work hardened. As deformation proceeds the capacity for
further deformation decreases and the force necessary to produce it
increases.

•This increase in the stress required to cause slip because of the

previous plastic deformation or the increase in strength of material
due to mechanical working is known as strain hardening or
work hardening

Strain Hardening of Single Crystals:

•Strain hardening is very commonly applied to pure
metals or alloys as a means to improve the
mechanical properties such as hardness and
strength.

Cold working
Strain hardening is expressed in
terms of % cold work
%CW = ((Ao-Ad)/Ao)*100
Ao = Original Area
Ad = Deformed area
Bauschinger effect of complete reversal of slip
Effect- direction on stress- strain curve.
 Data of cold work with TS and Ductility

Example
Compute the tensile strength and ductility (%EL) of a cylindrical copper rod if
the diameter is reduced from 15.2 mm to 12.2 mm

Data is available to compute strength and ductility from the value of % CW

 Hot Working and cold working

• Hot working – metal working processes carried out above the

recrystallization temperature are called as hot working
processes.
• Cold working processes: metal working processes carried out
below the recrystallization temperature are called as hot
working processes.
• Under the action of heat and force the atoms reach a certain
higher energy level and new crystals start to form.
• Recrystallization destroys the older grain structure deformed by
mechanical working and new crystals that are strain free are
formed.

53

Hot Working and cold working

A B C D

A B : Recrystallization
B, C & D : Grain Growth
• Grain begin start to nucleate at the sites of severest deformation due to a
very high stored energy.
• Recrystallization Temperature: is defined as “approximate minimum
temperature at which complete recrystallization of a cold worked metal
occurs within a specified time”
American Society of Materials

54
 Hot Working and cold working

• Three EBSD (Electron Back Scatter

Diffraction) maps of the stored energy
in an Al-Mg-Mn alloy after exposure
to increasing recrystallization
temperature. The volume fraction of
recrystallized grains (light) increases
with temperature for a given time
• The recrystallization
temperature generally varies
between 1/3rd of to half the
melting point of most metals.

39

Hot Working and cold working

Typical values of Recrystallization Temperatures

Ref: Manufacturing technology by P.N. Rao Volume –I 3rd edition

Melting points:
Lead : 327 oC Zinc: 419 oC Copper: 1083 oC
Tin: 232 oC Magnesium: 670 oC Iron:1539 oC
Cadmium: 321 oC Aliminium: 660 oC Tungsten: 3000 oC
Nickel: 1452 oC Titanium: 1795 oC Beryllium: 1287 oC
40
 Hot Working and cold working
Effect of amount of plastic deformation on the
recrystallization temperature

Recrystallization temperature
also depends upon the amount
of cold work the materials has
already received.
Higher the cold work lower is
the recrystallization

temperature

Ref: Manufacturing technology by P.N. Rao Volume –I 3rd edition 57

Hot Working and cold working

Effect of other parameters on the recrystallization
temperature

Ref: Manufacturing technology by P.N. Rao Volume –I 3rd edition

42
 Hot Working and cold working

• Recrystallization kinetics are

commonly observed to follow
the profile shown. There is an
initial 'nucleation
period' t0 where the nuclei
form, and then begin to grow
at a constant rate consuming
the deformed matrix.

Variation of recrystallized volume fraction

with time
43

Hot Working and cold working

Schematic showing the variation of grain size in hot rolling

process (Grain Reformation)
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 Hot Working and cold working
• This process is generally performed on a metal held at such a
temperature that the metal does not work-harden. A few metals
e.g., Pb and Sn (since they possess low crystallization
temperature) can be hot worked at room temperature.
• Raising the metal temperature lowers the stresses required to
produce deformations and increases the possible amount of
deformation before excessive work hardening takes place.
• Hot working is preferred where large deformations have to be
performed that do not have the primary purpose of causing work
hardening.
• Hot working produces the same net results on a metal as cold
working and annealing. It does not strain harden the metal.

45

Hot Working and cold working

• In hot working processes, compositional irregularities are ironed
out and nonmetallic impurities are broken up into small,
relatively harmless fragments, which are uniformly dispersed
throughout the metal instead of being concentrated in large
stress-raising metal working masses.
• Hot working such as rolling process refines grain structure.
• The coarse columnar dendrites of cast metal are refined to
smaller equi-axed grains with corresponding improvement in
mechanical properties of the component.
• Surface finish of hot worked metal is not nearly as good as with
cold working, because of oxidation and scaling.

46
 Hot Working and cold working
• One has to be very careful with the temperatures at which to
start hot work and at which to stop because this affects the
properties to be introduced in the hot worked metal.
• Too high a temperature may cause phase change and overheat
the steel whereas too low temperature may result in excessive
work hardening.
• Defects in the metal such as blowholes, internal porosity and
cracks get removed or welded up during hot working.
• During hot working, self-annealing occurs and recrystallization
takes place immediately following plastic deformation. This
self-annealing action prevents hardening and loss of ductility.

47

Advantages of hot rolling

• As the material is above the recrystallization temperature, any
amount of working can be imparted since there is no strain
hardening taking place.
• At a high temperature, the material would have higher amount
of ductility and therefore there is no limit on the amount of
hot working that can be done on a material.
• Even brittle materials can be hot worked.
• In hot working process, the grain structure of the metal is
refined and thus mechanical properties improved.
• Porosity of the metal is considerably minimized.
• If process is properly carried out, hot work does not affect
tensile strength, hardness, corrosion resistance, etc.
• No residual stresses are present in hot worked metals
48
 Disadvantages of Hot Working
• Due to high temperature in hot working, rapid oxidation or
scale formation and surface de-carburization take place on
the metal surface leading to poor surface finish and loss of
metal.
• On account of the loss of carbon from the surface of the steel
piece being worked the surface layer loses its strength. This is
a major disadvantage when the part is put to service.
• The weakening of the surface layer may give rise to a fatigue
crack which may ultimately result in fatigue failure of the
component.

49

cold working
• Cold working of a metal is carried out below its recrystallization
temperature. Although normal room temperatures are ordinarily
used for cold working of various types of steel, temperatures up
to the recrystallization range are sometimes used.

PURPOSE OF COLD WORKING

• The common purposes of cold working are given as under
• Cold working is employed to obtain better surface finish on parts.
• It is commonly applied to obtain increased mechanical properties.
• It is widely applied as a forming process of making steel products
using pressing and spinning.
• It is used to reduce thickness of materials like from slabs to
sheets.

66
 CHARACTERISTICS OF COLD WORKING

• Cold working involves plastic deformation of a metal, which

results in strain hardening.
• It usually involves working at ordinary (room) temperatures but
for high melting point metals, e.g., tungsten, the cold working
may be carried out at a red heat.
• The stress required for deformation increases rapidly with the
amount of deformation.
• The amount of deformation, which can be performed without
introducing other treatment, is limited.
• Cold rolling process generally distorts grain structure.

51

CHARACTERISTICS OF COLD WORKING

• Good surface finish is obtained in cold rolling.

• The upper temperature limit for cold working is the maximum
temperature at which strain hardening is retained. Since cold
working takes place below the recrystallization temperature, it
produces strain hardening.
• Excessive cold working gives rise to the formation and
propagation of cracks in the metal.
• The loss of ductility during cold working has a useful side effect
in machining.
• With less ductility, the chips break more readily and facilitate
the cutting operation.
• Directional properties can be easily imparted.

52
 CHARACTERISTICS OF COLD WORKING

• For relatively ductile metals, cold working is often

more economical than hot working.
• Cold working process increases:
– Ultimate tensile strength & Yield strength
– Hardness
– Fatigue strength
– Residual stresses
• Cold working processes decreases:
– Percentage elongation
– Reduction of area
– Impact strength
– Resistance to corrosion
– Ductility
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ADVANTAGES OF COLD WORKING

• In cold working processes, smooth surface finish can be
easily produced.
• Accurate dimensions of parts can be maintained.
• Since the working is done in cold state, no oxide would
form on the surface and consequently good surface
finish is obtained.
• Cold working increases the strength and hardness of
the material due to the strain hardening which would
be beneficial in some situations.
• There is no possibility of decarburization of the surface
• It is far easier to handle cold parts and it is also
economical for smaller sizes.
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 DISADVANTAGES OF COLD WORKING
• Brittle materials cannot be cold worked easily.
• Since the material has higher yield strength at lower
temperatures, the amount of deformation that can be given to is
limited by the capability of the presses or hammers used.
• A distortion of the grain structure is created.
• Since the material gets strain hardened, the maximum amount of
deformation that can be given is limited. Any further deformation
can be given after annealing.
• Internal stresses are set up which remain in the metal unless they
are removed by proper heat-treatment.

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COMPARISIN OF HOT WORKING & COLD WORKING

Sr. No. Hot working Cold Working
HW is carried out above the recrystallization CW is carried out below the recrystallization
1 temperature temperature

2Strain hardening does not take place Strain hardening of metals takes place

No internal or residual stresses are generated in the In this process internal stresses are generated in the
3 metal due to HW metal

It helps in reducing segregation of alloying elements in It results in loss of uniformity of composition and
4 the metals by breaking down the structure affects the metal properties

5Close dimensional tolerances cannot be maintained Better dimensional tolerances are obtained

6Inferior surface finish Smooth surface finish is obtained

It results in improvements in the mechanical properties
like impact strength and elongation (ductility) It results in improvement of properties like impact
7 strength and hardness

Hot working refines the grain structure resulting in Most of the common CW processes result in
8 better mechanical properties distortion of grains

The defects like blow holes and cracks are removed In CW processes the existing cracks are propagated
9 during HW process and new cracks are formed.

If properly performed HW does not affect UTS, YS,It improves UTS, YS, harness but reduces the corrosion
hardness, corrosion resistance and fatigue strength ofresistance and impact strength of the metals 72
10the metals
 Strain Hardening of Single Crystals:
One of the earliest dislocation concepts to explain
strain hardening was the idea that dislocations pile
up on slip planes at barriers in the crystal.
The pile-ups produce a back stress which opposes
the applied stress on the slip plane.
The existence of a back stress was demonstrated
experimentally by shear tests on zinc single crystals.
Zinc crystals are ideal for Shear strain crystal-
plasticity experiments because they slip only on the
basal plane, and hence complications due to duplex
slip are easily avoided.
The crystal is strained to point 0, unloaded, and then
reloaded in the direction opposite to the original slip
direction. Note that on reloading the crystal the stress
is reduced

Strain Hardening of Single Crystals:

Furthermore, when the slip direction is reversed,

dislocations of opposite sign could be created at the
same sources that produced the dislocations
responsible for strain in the first slip direction.
opposite sign attract and annihilate since dislocations
of each other, the net effect would be a further softening
of the lattice.
This explains the fact that the flow curve in the reverse
direction lies below the curve for continued flow in the
original direction.
The lowering of the yield stress when deformation in one
direction is followed by deformation in the opposite
direction is called the Bauschinger effect.
 Stages of work Hardening:

Stage I: This is known as the

region of easy glide.
This immediately follows the
yield point and is characterized
by little strain hardening
undergone by the crystal.
During easy glide the dislocations
are able to move over relatively
large distances without
encountering barriers.
During easy glide the slip occurs
Stages of work hardening only on one slip system.
in FCC crystal

Stages of work Hardening:

Stage II: This region is

marked by a rapid increase
in work hardening the slope
of which is approximately
independent of applied
stress, temperature or alloy
content.
In this region slip occurs on
more than one set of planes
i.e. both the primary and
Stages of work secondary slip systems.
hardening in FCC crystal
 Stages of work Hardening:

Stage II: . As a result of this a

lot of irregularities are likely to
be formed that include
• Forest dislocations
• Lomer Cottrell barriers
• Jogs produced either by
moving dislocations cutting
through forest dislocations
or forest dislocations cutting
through the primary
dislocations.
Stages of work
hardening in FCC crystal

Stages of work Hardening:

The pile up theory:
According to this theory some of the dislocations given out
by the Frank Read sources are eventually stopped at barriers
like grain boundaries resulting in increase of stress on the
leading dislocations
The breakdown of a barrier occur
by
1) Slip on a new plane.
2)Climb of dislocation around the
barrier.
3)Generation of high enough
tensile stress to produce a crack

As the deformation proceeds the number of barriers increases until

each source becomes completely surrounded by barriers.
 Stages of work Hardening:
Stage III:
It is a region of decreasing strain
hardening.
• At sufficiently high stress value or
temperature in region III, the
dislocations held up in stage II are
able to move by a process that had
been suppressed at lower stress
and temperature.
Stages of work •In stage III cross slip takes place
hardening in FCC
crystal
and the slip lines are broad, deep
and consist of segments joined by
cross slip traces.
•The screw dislocations held in stage II, cross slip and return
to the primary slip plane by double cross slip.

Effect of Heating After %CW (Annealing)

The influence of
annealing
temperature
(1 hour) on the
tensile strength
and ductility of a
brass alloy.
Grain size is shown
as a function of
annealing
temperature.
 Anisotropy - Polycrystals

rolling
direction
-
Grains are
elongated

before rolling after rolling

Isotropic Anisotropic (directional)
grains are approx. spherical, since rolling affects grain
equiaxed & randomly oriented. orientation and shape.
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Annealing • Annealing includes three stages:

– Recovery
– Recrystallization
– Grain Growth
Recovery
• During recovery, some of the stored internal strain energy is relieved through
dislocation motion due to enhanced atomic diffusion at the elevated temperatures.
• There is some reduction in the number of dislocations.
• Physical properties (electrical and thermal conductivity) are recovered to their
• pre-cold worked states.
Annihilation reduces dislocation density.

Mechanical
properties are
largely unchaged

84
 Recrystallization

• Even after recovery is complete, the grains are still in a

relatively high strain energy state.
• Recrystallization is the formation of a new set of
strain-free and equiaxed grains that have low
dislocation densities (pre-cold work state).
• The driving force to produce the new grain structure is
the internal energy difference between strained and
unstrained material.
• The new grains form as very small nuclei and grow
until they consume the parent material.
• Recrystallization temperature is 1/3 <Tm <1/2.

85

Recrystallization
• Brass: shows several stages of recrystallization and grain
growth.

33% CW grains Initial recrystallization; Partial replacement Complete recryst.

After 3 seconds, 580˚C of CW grains; after 8 seconds
After 4 seconds

86
Recrystallization with temperature vs %CW for iron. For
deformations less than 5% CW, recrystallization will not occur.

69

GRAIN GROWTH

• After recrystallization is
complete, the strain-free
grains will continue to grow
if the metal specimen is left
at elevated temperatures.
• As grains increase in size, the
total boundary area
decreases, as does the total
energy.
• Large grains grow at the
expense of smaller grains.

70
• Grain diameter versus time for grain growth at specific
temperatures (log scale). Brass Alloy example 89

Assignment I

1. Draw a neat labelled diagram of stress strain curve for mild steel
and explain the following.
a. Young’s modulus
b. Ductility
c. Yield point
d. ultimate tensile strength
e. Fracture point
2. Explain the motion of the edge type dislocation with a neat
diagram.
3. What is the difference between engineering and true stress strain curve?
4. What is yield point Phenomenon?
5. Differentiate between cold working and hot working.