Free Download Link (Copy URL): https://sites.google.com/view/varunpratapsingh/teaching-engagements Unit I : Materials : Classification of engineering material, Composition of Cast iron and Carbon steels, Iron Carbon diagram. Alloy steels their applications. Mechanical properties like strength, hardness, toughness, ductility, brittleness, malleability etc. of materials, Tensile test- Stress-strain diagram of ductile and brittle materials, Hooks law and modulus of elasticity, Hardness and Impact testing of materials, BHN, etc.

1. Basic Mechanical Engineering
BMET 102/BMEP 102
Unit 1st
Materials
NOTES
By
Mr. Varun Pratap Singh
Assistant Professor
Department of Mechanical Engineering
College of Engineering Roorkee

2. Unit I:
Materials: Classification of engineering material, Composition of Cast iron and Carbon steels,
Iron Carbon diagram. Alloy steels their applications. Mechanical properties like strength,
hardness, toughness, ductility, brittleness, malleability etc. of materials, Tensile test- Stress-
strain diagram of ductile and brittle materials, Hooks law and modulus of elasticity, Hardness
and Impact testing of materials, BHN etc.

3. Classification of Engineering Materials
Introduction
Materials are an important aspect of engineering design and analysis. The importance of
materials science and engineering can be noted from the fact that historical ages have
been named after materials. In the customer driven competitive business environment, the
product quality is of paramount importance. The product quality has been found to be
influenced by the engineering design, type of materials selected and the processing technology
employed. Therefore, the importance of materials and their processing techniques cannot be
undervalued in today’s world. Materials form the stuff of any engineering application or
product. It has been found that the engineers do not give adequate attention to this important
subject. Moreover, it has not been adequately represented in the course curriculum of various
universities. Therefore, it becomes imperative to highlight the importance of engineering
materials for all engineers related to the various aspects of engineering applications. There is a
wide variety of materials available which have shown their potential in various engineering
fields ranging from aerospace to house hold applications. The materials are usually selected
after considering their characteristics, specific application areas, advantages and limitations.
The challenge for designers is to select an optimal material suitable for the specific design
requirements. The stringent design requirements generally lead to development of new
materials to meet the specific operating conditions and environments. The new materials are
developed from the conventional materials by either by the intrinsic or the extrinsic
modification. In intrinsic modification, minor alloying or heat treatment is carried out. In
extrinsic modification, external reinforcements are added to the parent material to alter its
properties in order to meet the specific design requirements. The composite materials represent
an example of the extrinsic modification. The modification is usually done to improve the
properties of the existing materials. As the new materials are conceptualized and realized in the
laboratories, the hunt for their commercialization begins. The engineers are then entrusted with
the task of finding suitable techniques which would lead to high quality cost-effective
processing of these materials. In order to achieve this objective, it is imperative for all engineers
to have a fundamental understanding of the existing materials and their processing techniques.
It has been found that there are adequate of courses in the curriculum of various universities
where the processing techniques for metals are dealt in detail. The processing of non-metals is
usually not covered as a core subject at the under-graduate level and therefore the engineers do
not have a fundamental understanding about the processing of important non-metals such as
plastics and ceramics. The course has been designed to study the basic nature of different non-
metals and the manufacturing processes associated thereof. The various non-metals covered in
the course include glasses, ceramics, plastics and different types of composite materials.

4. Figure: Periodic Table
Basic Classification of Engineering Materials
Basically Engineering Materials can be classified into two categories-
1. Metals
2. Non-Metals
Metals
Metals are polycrystalline bodies which are having number of differentially oriented fine
crystals. Normally major metals are in solid states at normal temperature. However, some
metals such as mercury are also in liquid state at normal temperature. All metals are having
high thermal and electrical conductivity. All metals are having positive temperature coefficient
of resistance. Means resistance of metals increases with increase in temperature.
Examples of metals – Silver, Copper, Gold, Aluminium, Iron, Zinc, Lead, Tin etc.
Metals can be further divided into two groups- (Ferrous Metals and Non-Ferrous Metals)
1. Ferrous Metals
– All ferrous metals are having iron as common element. All ferrous materials are having very
high permeability which makes these materials suitable for construction of core of electrical
machines. Ferrous metals have a high carbon content which generally makes them vulnerable

5. to rust when exposed to moisture. There are two exceptions to this rule: wrought iron resists
rust due to its purity and stainless steel is protected from rust by the presence of chromium.
Most ferrous metals are magnetic which makes them very useful for motor and electrical
applications. The use of ferrous metals in your refrigerator door allows you to pin your
shopping list on it with a magnet.
Examples: Cast Iron, Wrought Iron, Steel, Silicon Steel, High Speed Steel, Spring Steel etc.
Steel
Steel is made by adding iron to carbon which hardens the iron. Alloy steel becomes even
tougher as other elements like chromium and nickel are introduced. Steel is made by heating
and melting iron ore in furnaces. The steel can is tapped from the furnaces and poured into
molds to form steel bars. Steel is widely used in the construction and manufacturing industries.
Carbon Steel
Carbon steel has a higher carbon content in comparison to other types of steel making it
exceptionally hard. It is commonly used in the manufacturing of machine tools, drills, blades,
taps, and springs. It can keep a sharp cutting edge.
Alloy Steel
Alloy steels incorporate elements such as chromium, nickel and titanium to impart greater
strength and durability without increasing weight. Stainless steel is an important alloy steel
made using chromium. Alloy steels are used in construction, machine tools, and electrical
components.
Cast Iron
Cast iron is an alloy made from iron, carbon, and silicon. Cast iron is brittle and hard and
resistant to wear. It’s used in water pipes, machine tools, automobile engines and stoves.
Wrought Iron
Wrought iron is an alloy with so little carbon content it’s almost pure iron. During the
manufacturing process, some slag is added which gives wrought iron excellent resistance to
corrosion and oxidation, however, it is low in hardness and fatigue strength. Wrought iron is
used for fencing and railings, agricultural implements, nails, barbed wire, chains, and various
ornaments.
2. Non-Ferrous Metals - All non-ferrous metals are having very low permeability. Their main
advantage over ferrous materials is their malleability. They also have no iron content, giving
them a higher resistance to rust and corrosion, and making them ideal for gutters, liquid pipes,
roofing and outdoor signs. Lastly they are non-magnetic, which is important for many
electronic and wiring applications.
Example: aluminium, copper, lead, zinc and tin, as well as precious metals like gold and silver.
Aluminum

6. Aluminum is lightweight, soft and low strength. Aluminum is easily cast, forged, machined
and welded. It’s not suitable for high-temperature environments. Because aluminum is
lightweight, it is a good choice for the manufacturing of aircraft and food cans. Aluminum is
also used in castings, pistons, railways, cars, and kitchen utensils.
Copper
Copper is red in color, highly ductile, malleable and has high conductivity for electricity and
heat. Copper is principally used in the electrical industry in the form of wire and other
conductors. It’s also used in sheet roofing, cartridge cases, statutes, and bearings. Copper is
also used to make brass, an alloy of copper and zinc.
Lead
Lead is a soft, heavy, malleable metal with a low melting point and low tensile strength. It can
withstand corrosion from moisture and many acids. Lead is widely used in electrical power
cables, batteries, building construction and soldering.
Zinc
Zinc is a medium to low strength metal with a very low melting point. It can be machined
easily, but heating may be required to avoid cleavage of crystals. Zinc is most widely used in
galvanizing, the process of applying a protective zinc coating to iron or steel to prevent rust.
Tin
Tin is very soft and malleable, ductile with low tensile strength. It’s often used to coat steel to
prevent corrosion. Tinplate steel is used to make tin cans to hold food. In the late 19th century,
tin foil was commonly used to wrap food products, but has since largely been replaced by
aluminium foil. Tin can also be alloyed with copper to produce tin brass and bronze.

7. Figure: Ferrous and Non Ferrous
Non-Metals
Non-Metal materials are non-crystalline in nature. These exists in amorphic or mesomorphic
forms. These are available in both solid and gaseous forms at normal temperature. Normally
all non-metals are bad conductor of heat and electricity. Examples: Plastics, Rubber, Leathers,
Asbestos etc. As these non-metals are having very high resistivity which makes them suitable
for insulation purpose in electrical machines.
Non-metals are a special bunch. Only 25 of us exist and we are broken up into two main
groups.
An element that lacks metallic attributes by having the following properties:
 low electronegatity
 good conductivity of electricity and heat
 low ionization energies
 positive and negative oxidation number

8. Metalloids:
This small group of elements has both the properties of non-metals and metals
Figure: Metalloids

9. Difference between Metals and Non Metals
Other classification of engineering materials:
Engineering materials can also be classified as below-
 Metals and Alloys
 Ceramic Materials
 Organic Materials
Metals and Alloys
Metals are polycrystalline bodies which are have number of differentially oriented fine crystals.
Normally major metals are in solid states at normal temperature. However, some metals such
as mercury are also in liquid state at normal temperature. Pure metals are having very a low
mechanical strength, which sometimes does not match with the mechanical strength required
for certain applications. To overcome this draw back alloys are used. Alloys are the

10. composition of two or more metals or metal and non-metals together. Alloys are having good
mechanical strength, low temperature coefficient of resistance. Example: Steels, Brass, Bronze,
Gunmetal, Invar. Super Alloys etc.
Ceramic Materials
Ceramic materials are non-metallic solids. These are made of inorganic compounds such as
Oxides, Nitrides, Silicates and Carbides. Ceramic materials possess exceptional Structural,
Electrical, Magnetic, Chemical and Thermal properties. These ceramic materials are now
extensively used in different engineering fields. Examples: Silica, glass, cement, concrete,
garnet, Mgo, Cds, Zno, SiC etc.
Organic Materials
All organic materials are having carbon as a common element. In organic materials carbon is
chemically combined with oxygen, hydrogen and other non-metallic substances. Generally
organic materials are having complex chemical bonding. Example: Plastics, PVC, Synthetic
Rubbers etc.

11. Cast Iron
Cast iron is a group of iron-carbon alloys with a carbon content greater than 2%. Its usefulness
derives from its relatively low melting temperature. The alloy constituents affect its colour
when fractured: white cast iron has carbide impurities which allow cracks to pass straight
through, grey cast iron has graphite flakes which deflect a passing crack and initiate countless
new cracks as the material breaks, and ductile cast iron has spherical graphite "nodules" which
stop the crack from further progressing.
Carbon (C) ranging from 1.8 to 4 wt%, and silicon (Si) 1–3 wt%, are the main alloying elements
of cast iron. Iron alloys with lower carbon content are known as steel.
Cast iron tends to be brittle, except for malleable cast irons. With its relatively low melting
point, good fluidity, castability, excellent machinability, resistance to deformation and wear
resistance, cast irons have become an engineering material with a wide range of applications
and are used in pipes, machines and automotive industry parts, such as cylinder heads, cylinder
blocks and gearbox cases. It is resistant to damage by oxidation.
Composition of Cast Iron
Cast iron is a group of ALLOYS with a carbon content greater than 2%. It is
combination of Free carbon (Graphite) and combined carbon or cementite. Its major
composition is Carbon 2-3.5% , Silicon 1-4%
Proportion of percentage of Free Carbon and combined carbon depends on the rate of
cooling from molten state. Slow cooling means more free carbon.
Major Properties of Cast Iron
a) Low melting temperature.
b) Brittle
c) Good fluidity and Castability
d) Excellent Machinability,
e) Resistance to deformation Wear resistance
f) Resistant to damage by Oxidation.
g) Low cost
h) High Compressive Strength with High damping capacity

12. i) Weak points of Cast Iron
j) Low Tensile Strength
k) Brittle
l) Low Fatigue & shock strength
Applications of Cast Iron: wide range of applications as follows
a) Casting of casing, covers
b) Brake shoe of IC Engine
c) Cast iron pipe & Fittings
d) Valve Casing
e) Pulleys
f) AUTO parts (such as Cylinder head, Engine housing,
Types of Cast Iron
A. white cast iron: It displays white fractured surfaces due to the presence of an iron carbide
precipitate called cementite (carbide impurity).
Composition: Carbon (1.75-3.5%), Silicon (0.5 – 1.8%), Manganese (0.25 to 0.8%),
Sulphur (0.1 to 0.3%), Phosphorus <0.2%
Characteristics:
1. High wear resistance
2. Highly abrasive
3. High tensile strength
4. Low compressive strength
5. Hard and brittle
6. Non-machinability (Only grinding)
7. White iron is too brittle for use in many structural components, but have good
hardness and abrasion resistance and relatively low cost,
Applications:
1. Wear surfaces
2. Shell liners and lifter
3. Autogenous grinding mill
4. Balls and rings in coal pulveriser
5. Teeth of digging bucket
6. Car Wheels
7. Rollers
Grey cast iron: It is characterised by its graphitic microstructure, which causes fractures
of the material to have a grey appearance. Its mechanical properties are controlled by the size
and shape of the graphite flakes
Composition: Carbon (2.5-3.75%), Silicon (1 – 2.75%), Manganese (0.4 to 1%),
Sulphur (0.02 to 0.15%), Phosphorus (1.5 to 1%)
Characteristics:
1. Low melting point
2. No ductility
3. Low tensile strength
4. High compressive strength
5. More shock resistant
6. Hard and brittle
7. Easily machinable

13. Applications:
1. Used in foundry
2. Piston Rings
3. Covers, Casing, Pipes, Tools
Malleable Cast Iron with controlled heat treatment
Composition: Carbon (2.2 -3.6%), Silicon (0.4 – 1.1%), Manganese (0.1 to 0.4%),
Sulphur (0.03 to 0.3%), Phosphorus (0.1 - 0.2%)
Characteristics:
1. High yield strength
2. Wear resistant
3. Good weldability
4. Good machinability
5. High damping capacity
Applications:
1. Gear Wheels
2. Crank Shaft
3. Axle
Graphite in the form of Spherical Nodules (thicker piece) which stop the crack from
further progressing.
Composition: Carbon (3 -4%), Silicon (1 – 3%), Manganese (0.3 to 1%), Phosphorus (0.15 -
1%)
Characteristics:
1. High Cast ability
2. High Wear resistant
3. High weldability & machinability
4. Medium damping capacity
5. Ductile
Applications:
1. Pipes
2. Valves & Valve fitting
3. Pumps
4. Compressor
5. IC Engine
Composition of (Carbon) Steel
Crystalline Alloy (No free graphite) with carbon less than 2%. High carbon content results
high tensile strength, High Yield Strength and low ductility.
Alloying elements increases strength, resistance to abrasion, corrosion & high temperature
properties.
Low Carbon Steel (Mild Steel) MS Carbon content 0.05 to 0.3 %
Characteristics
1. Bright fibrous structure
2. Soft, Ductile and Machin able
3. Easily forged and welded

14. 4. Rust prone
Applications
1. Wires, wire
2. Rivets
3. Nuts
4. Screws
5. Nails
Medium Carbon Steel Carbon composition (0.3 – 0.7%)
Applications
1. Tubes, Wires, Wire Rope, Spring,
2. Axle
3. Forgings
4. Hammers
5. Forged dies
6. Machine components
High Carbon Steel Carbon composition (0.7 – 2%)
Characteristics
1. Fine granular structure
2. Easy to temper and Harden
3. Magnetized
4. Easily forged and welded
5. Rust prone
Applications
1. Wrenches & Clutch disc
2. Chisels, knives, razors, drills, Rock drill, Punches
3. Springs, keys, pins
4. Machine tools
High Speed Steel: It is used for making tools for manufacturing machines at high
speed with heavy cuts.
A. Tungsten HSS: Tungsten 18%, Chromium 4%, Vanadium 1-2%, Cobalt 5-8%
B. Molybdenum Steel: Molybdenum 5-8%, Tungsten 1.5 - 6%, Chromium 4%, Vanadium
1-2%, Cobalt 8-12%
Characteristics
1. Hard and difficult to machine
2. Wear and Abrasion resistance
3. High Hardness at high temperature
Applications
1. Machine tools
2. Dies for forgings
3. Chisels, punches, drills, milling cutters & Hammers
Alloy Steels: Carbon steel alloyed with other elements to improve its mechanical
properties
A. Low Alloy Steel (Alloying elements less than 8%)
B. High Alloy Steel (Alloying elements more than 8%)
Composition: Carbon (0.9 -1.1%), Silicon (0.3 – 0.6%), Manganese (0.3 to 1.1%),
Chromium (0.9 to 1.6%), Tungsten (1.2 – 1.6%)
Characteristics

15. 1. Increased resistant to wear
2. Improved machinability & ductility
3. Stable at high temperature
4. High elastic limit
5. Ability to get hardened
Applications
1. Taps, Reamers
2. Master Gauges
3. Tools, cutters & Dies

16. Mechanical Properties of Material
Introduction:
Mechanical properties of material are related to the behaviour under load or stress in tension,
compression or shear.
Properties are determined by engineering tests under appropriate conditions, commonly
determined mechanical properties are the tensile strength, elastic limit, creep strength, stress
rupture, fatigue, elongation (ductility), impact strength (toughness and brittleness), hardness,
and modulus of elasticity (ratio of stress to elastic strain-rigidity). Usually, the strain may be
elastic (present only during stressing) or plastic (permanent) deformation.
Mechanical properties are helpful in determining whether or not a material can be produced in
the desired shape and also resist the mechanical forces anticipated.
The words mechanical and physical are often erroneously used interchangeably. The above are
mechanical properties. Sometimes modulus of elasticity is considered to be a physical property
of a material because it is an inherent property that cannot be changed substantially by practical
means such as heat treatment or cold working. The mechanical properties of materials are
explained as follows
Strength
It is the ability of a material to resist the externally applied forces without breaking or yielding.
The internal resistance offered by a part to an externally applied force is called stress.
Stiffness
Stiffness is the ability of a material to resist deformation under stress. The modulus of elasticity
is the measure of stiffness.
Elasticity
Elasticity is the tendency of solid materials to return to their original shape after being
deformed.

17. It is the property of a material to regain its original shape after deformation when the external
forces are removed. This property is desirable for materials used in tools and machines.
It may be noted that steel is more elastic than rubber.
Plasticity
Plasticity is the property by which a metal retains its deformation permanently, when the
external force applied on it is released.
Plasticity is a property of a material which retains the deformation produced under load
permanently. This property of the material is necessary for forgings, in stamping images on
coins and in ornamental work.
Ductility
Ductility is the property by which a metal can be drawn into thin wires. It is determined
by percentage elongation and percentage reduction in the area of metal.
Ductility is the property of a material enabling it to be drawn into a wire with the application
of a tensile force. A ductile material must be both strong and plastic. The ductility is usually
measured by the terms, percentage elongation and percentage reduction in area. The ductile
material commonly used in engineering practice are mild steel, copper, aluminium, nickel, zinc,
tin and lead.
Brittleness
The tendency of material to fracture or fail upon the application of a relatively small
amount of force, impact or shock.
It is the property of breaking of a material with little permanent distortion. Brittleness of a
material is opposite to ductility property.
Brittle materials are withstanding compression load. When subjected to tensile loads snap off
without giving any sensible elongation. Cast iron is a brittle material.
Malleability
Malleability is the property by which a metal can be rolled into thin sheets.
It is a special case of ductility which permits materials to be rolled or hammered into thin
sheets, making wire. A malleable material should be plastic but it is not essential to be so
strong. The malleable materials commonly used in engineering practice are lead, soft steel,
wrought iron, copper, and aluminium.
Toughness
Toughness is the property of a material to resist fracture due to high impact. It is measured by
the amount of energy that a unit volume of the material has absorbed after being stressed up to
the point of fracture.
This property is desirable in parts subjected to shock and impact loads. Normally the toughness
of the material decreases when it is subjected heat. This property is essential for designing the
hammer and Press machine.
Machinability
It is the property of a material which refers to a relative ease with which a material can be cut.
The machinability of a material can be measured in a number of ways such as comparing the
tool life for cutting different materials or thrust required to remove the material at some given
rate or the energy required to remove a unit volume of the material. For example, that brass
can be easily machined than steel. That means the machinability property of brass is high when
compare to steel.

18. Resilience
It is the property of a material to absorb energy and to resist shock and impact loads. It is
measured by the amount of energy absorbed per unit volume within elastic limit. This property
is essential for designing the spring materials.
Creep
When a metal is subjected to a constant force at a high temperature below its yield point,
for a prolonged period of time, it undergoes a permanent deformation.
When a material is subjected to a constant stress at high temperature for a long period of time,
it will undergo a slow and permanent deformation called creep. This property is considered in
designing internal combustion engines, boilers, and turbines.
Fatigue
Fatigue is the of material weakening or breakdown of equipment subjected to stress,
especially a repeated series of stresses.
Fatigue is the repeated loading and unloading of metal due to direct load variation, eccentricity
in a rotating shaft and differential thermal expansion of a structure. Even substantially below
the yield point (elastic limit) of a metal or alloy this repeated loading can lead to failure, usually
measured in terms of the number of cycles (repeated load applications) to failure.
Some studies have suggested that well over 80% of all mechanical failures of metal are
attributable to fatigue.
This property is considered in designing shafts, connecting rods, springs, gears, etc.
Hardness
Hardness is the ability of material to resist permanent change of shape caused by an
external force.
Hardness is a very important property of the metals and has a wide variety of meanings. It also
embraces many different properties such as resistance to wear, scratching, deformation and
machinability etc.
Also, it is the property of a metal, which gives it the ability to resist being permanent, deformed
(bent, broken, or have its shape changed) when a load is applied. The greater the hardness of
the metal, the greater resistance it has to deformation.
It also means that the ability of a metal to cut another metal. The hardness is usually expressed
in numbers which are dependent on the method of making the test.
They are four types of tests are used to determine the hardness of metals, they are
 Brinell hardness test,
 Rockwell hardness test,
 Vickers hardness test,
 Shore scleroscope.
Conclusion
By understanding these basic Mechanical Properties of Material one can able to select a
correct material for the specific application.

19. Types of Loads
Different types of loads in engineering mechanics are compression, tension, torsion and
bending.
Compression:
Compression loading is an effect in which the component reduces it size. During compression
load there is reduction in volume and increase in density of a component.
Tension:
Tension is the act of stretching rod, bar, spring, wire, cable etc. that is being pulled from the
either ends.
Torsion:
Torsion is the act of twisting of a rod, wire, spring etc. about an axis due to applied Couple.
Bending:
Bending is act of changing component from straight form into a curved or angular form.

20. Types of Mechanical Forces
A force exerted on a body can cause a change in either the shape or the motion of the body.
The unit of force in SI system is the newton (N) and CGS system is dyne. No solid body is
perfectly rigid and when forces are applied to it, changes in dimensions occur. Such changes
are not always perceptible to the human eye since they are negligible. For example, the span
of a bridge will sag under the weight of a vehicle and a spanner will bend slightly when
tightening a nut.
There are three main types of mechanical forces that can act on a body. They are:
1. Tensile force
2. Compressive force and
3. Shear force
1. Tensile force
Tensile force that tends to stretch a material, as shown in the figure 1 below.
Figure: Tensile force
For example,
1. Rubber bands, when stretched, are in tension.
2. The rope or cable of a crane carrying a load is in tension.
3. When a nut is tightened, a bolt is under tension.
A tensile force will increase the length of the material on which it acts.
2. Compressive force
Compressive force that tends to squeeze or crush a material, as shown in the figure 2 below.
Figure: Compressive force
For example,
1. A pillar supporting a bridge is in compression.
2. The sole of a shoe is in compression.
3. The jib of a crane is in compression.
A compressive force will decrease the length of the material on which it acts.
3. Shear force
Shear force that tends to slide one face of the material over an adjacent face.
Figure: Shear force
For example,
1. A rivet holding two plates together is in shear if a tensile force is applied
between the plates as shown in Figure 3.
2. A guillotine cutting sheet metal, or garden shears, each provide a shear force.
3. A horizontal beam is subject to shear force.
4. Transmission joints on cars are subject to shear forces.
A shear force can cause a material to bend, slide or twist.

21. Mechanics of rigid bodies:
The mechanics of rigid bodies is primarily concerned with the static and dynamic behaviour
under external forces of engineering components and systems which are treated as infinitely
strong and undeformable Primarily we deal here with the forces and motions associated with
particles and rigid bodies.
Mechanics of deformable solids:
Mechanics of solids:
The mechanics of deformable solids is more concerned with the internal forces and associated
changes in the geometry of the components involved. Of particular importance are the
properties of the materials used, the strength of which will determine whether the components
fail by breaking in service, and the stiffness of which will determine whether the amount of
deformation they suffer is acceptable. Therefore, the subject of mechanics of materials or
strength of materials is central to the whole activity of engineering design. Usually the
objectives in analysis here will be the determination of the stresses, strains, and deflections
produced by loads. Theoretical analyses and experimental results have an equal role in this
field.
Analysis of stress and strain:
Concept of stress: Let us introduce the concept of stress as we know that the main problem
of engineering mechanics of material is the investigation of the internal resistance of the
body, i.e. the nature of forces set up within a body to balance the effect of the externally
applied forces.
The externally applied forces are termed as loads. These externally applied forces may be due
to any one of the reason.
(i) due to service conditions
(ii) due to environment in which the component works
(iii) through contact with other members
(iv) due to fluid pressures
(v) due to gravity or inertia forces.
As we know that in mechanics of deformable solids, externally applied forces acts on a body
and body suffers a deformation. From equilibrium point of view, this action should be
opposed or reacted by internal forces which are set up within the particles of material due to
cohesion.
These internal forces give rise to a concept of stress. Therefore, let us define a stress
Therefore, let us define a term stress
Stress:
Let us consider a rectangular bar of some cross – sectional area and subjected to some load or
force (in Newtons )

22. Let us imagine that the same rectangular bar is assumed to be cut into two halves at section
XX. The each portion of this rectangular bar is in equilibrium under the action of load P and
the internal forces acting at the section XX has been shown
Now stress is defined as the force intensity or force per unit area. Here we use a symbol s to
represent the stress.
Where A is the area of the X – section
Here we are using an assumption that the total force or total load carried by the rectangular
bar is uniformly distributed over its cross – section.
But the stress distributions may be for from uniform, with local regions of high stress known
as stress concentrations.
If the force carried by a component is not uniformly distributed over its cross – sectional area,
A, we must consider a small area, ‘dA' which carries a small load dP, of the total force ‘P',
Then definition of stress is
As a particular stress generally holds true only at a point, therefore it is defined
mathematically as
Units:
The basic units of stress in S.I units i.e. (International system) are N / m2
(or Pa)
MPa = 106
Pa
GPa = 109
Pa
KPa = 103
Pa
Sometimes N / mm2
units are also used, because this is an equivalent to MPa. While US
customary unit is pound per square inch psi.
TYPES OF STRESSES:
only two basic stresses exist: (1) normal stress and (2) shear stress. Other stresses either are
similar to these basic stresses or are a combination of these e.g. bending stress is a
combination tensile, compressive and shear stresses. Torsional stress, as encountered in
twisting of a shaft is a shearing stress.
Let us define the normal stresses and shear stresses in the following sections.

23. Normal stresses: We have defined stress as force per unit area. If the stresses are normal to
the areas concerned, then these are termed as normal stresses. The normal stresses are
generally denoted by a Greek letter (σ )
This is also known as uniaxial state of stress, because the stresses acts only in one direction
however, such a state rarely exists, therefore we have biaxial and triaxle state of stresses
where either the two mutually perpendicular normal stresses acts or three mutually
perpendicular normal stresses acts as shown in the figures below:
Tensile or compressive stresses:
The normal stresses can be either tensile or compressive whether the stresses act out of the
area or into the area
Bearing Stress: When one object presses against another, it is referred to a bearing stress (
They are in fact the compressive stresses ).

24. Shear stresses:
Let us consider now the situation, where the cross – sectional area of a block of material is
subject to a distribution of forces which are parallel, rather than normal, to the area
concerned. Such forces are associated with a shearing of the material, and are referred to as
shear forces. The resulting force interests are known as shear stresses.
The resulting force intensities are known as shear stresses, the mean shear stress being equal
to
Where P is the total force and A the area over which it acts.
As we know that the particular stress generally holds good only at a point therefore we can
define shear stress at a point as
The Greek symbol τ (tau) (suggesting tangential) is used to denote shear stress.
However, it must be borne in mind that the stress (resultant stress) at any point in a body is
basically resolved into two components s and t one acts perpendicular and other parallel to
the area concerned, as it is clearly defined in the following figure.

25. The single shear takes place on the single plane and the shear area is the cross - sectional of
the Rivett, whereas the double shear takes place in the case of Butt joints of rivets and the
shear area is the twice of the X - sectional area of the Rivett.
ANALYSIS OF STRAINS
CONCEPT OF STRAIN
Concept of strain: if a bar is subjected to a direct load, and hence a stress the bar will change
in length. If the bar has an original length L and changes by an amount dL, the strain produce
is defined as follows:
Strain is thus, a measure of the deformation of the material and is a non-dimensional Quantity
i.e. it has no units. It is simply a ratio of two quantities with the same unit.

26. Since in practice, the extensions of materials under load are very very small, it is often
convenient to measure the strain in the form of strain x 10-6
i.e. micro strain, when the symbol
used becomes .
Sign convention for strain:
Tensile strains are positive whereas compressive strains are negative. The strain defined earlier
was known as linear strain or normal strain or the longitudinal strain now let us define the shear
strain.
Definition: An element which is subjected to a shear stress experiences a deformation as
shown in the figure below. The tangent of the angle through which two adjacent sides rotate
relative to their initial position is termed shear strain. In many cases the angle is very small and
the angle itself is used, (in radians), instead of tangent, so that g = Angle AOB - Angle A'OB'
= 
Shear strain: As we know that the shear stresses acts along the surface. The action of the
stresses is to produce or being about the deformation in the body consider the distortion
produced b shear sheer stress on an element or rectangular block
This shear strain or slide is f and can be defined as the change in right angle. or The angle of
deformation g is then termed as the shear strain. Shear strain is measured in radians & hence is
non – dimensional i.e. it has no unit. So we have two types of strain i.e. normal stress & shear
stresses.

27. Hook's Law:
A material is said to be elastic if it returns to its original, unloaded dimensions when load is
removed.
Hook's law therefore states that
Stress ()  strain ()
Depending upon the nature of force applied on the body, the modulus of the elasticity is
classified in the following three types:
1. Young’s Modulus of Elasticity (Y)
When a wire is acted upon by two equal and opposite forces in the direction of its length, the
length of the body is changed. The change in length per unit length (Δl/l) is called the
longitudinal strain and the restoring force (which is equal to the applied force in equilibrium)
per unit area of cross-section of wire is called the longitudinal stress.
For small change in the length of the wire, the ratio of the longitudinal stress to the
corresponding strain is called the Young’s modulus of elasticity (Y) of the wire. Thus,
Let there be a wire of length ‘l’ and radius ‘r’. Its one end is clamped to a rigid support and a
mass M is attached at the other end. Then
F = Mg and A = πr2
Substituting in above equation, we have

28. 2. Bulk Modulus of Elasticity (B)
When a uniform pressure (normal force) is applied all over the surface of a body, the volume
of the body changes. The change in volume per unit volume of the body is called the ‘volume
strain’ and the normal force acting per unit area of the surface (pressure) is called the normal
stress or volume stress. For small strains, the ratio of the volume stress to the volume strain is
called the ‘Bulk modulus’ of the material of the body. It is denoted by B. Then
Here, the negative sign in formula implies that when the pressure increases volume decreases
and vice-versa.
Compressibility
The reciprocal of the Bulk modulus of the material of a body is called the
“compressibility’ of that material. Thus,
Compressibility = 1/B
3. Modulus of Rigidity (η)
When a body is acted upon by an external force tangential to a surface of the body, the opposite
surfaces being kept fixed, it suffers a change in shape of the body, its volume remains
unchanged. Then the body is said to be sheared.

29. The ratio of the displacement of a layer in the direction of the tangential force and the distance
of the layer from the fixed surface is called the shearing strain and the tangential force acting
per unit area of the surface is called the ‘shearing stress’.
For small strain in the ratio of the shearing stress to the shearing strain is called the ‘modulus
of rigidity ‘of the material of the body. It is denoted by ‘η’.
Poisson's ratio: If a bar is subjected to a longitudinal stress there will be a strain in this
direction equal to σ / E. There will also be a strain in all directions at right angles to σ. The
final shape being shown by the dotted lines.
It has been observed that for an elastic material, the lateral strain is proportional to the
longitudinal strain. The ratio of the lateral strain to longitudinal strain is known as the poison's
ratio.
Poison's ratio () = - lateral strain / longitudinal strain
For most engineering materials the value of m his between 0.25 and 0.33.

30. STRESS - STRAIN RELATIONS
Stress – Strain Relations: The Hook's law, states that within the elastic limits the stress is
proportional to the strain since for most materials it is impossible to describe the entire stress
– strain curve with simple mathematical expression, in any given problem the behaviour of the
materials is represented by an idealized stress – strain curve, which emphasizes those aspects
of the behaviours which are most important is that particular problem.
(i) Linear elastic material:
A linear elastic material is one in which the strain is proportional to stress as shown
below:
There are also other types of idealized models of material behaviour.
(ii) Rigid Materials:
It is the one which donot experience any strain regardless of the applied stress.
(iii) Perfectly plastic (non-strain hardening):
A perfectly plastic i.e non-strain hardening material is shown below:
(iv) Rigid Plastic material (strain hardening):
A rigid plastic material i.e strain hardening is depicted in the figure below:

31. (v) Elastic Perfectly Plastic material:
The elastic perfectly plastic material is having the characteristics as shown below:
(vi) Elastic – Plastic material:
The elastic plastic material exhibits a stress Vs strain diagram as depicted in the figure below:

32. Stress-Strain diagram for Ductile material
Considering low Carbon Steel having Carbon content less 0.15% and its example is Mild Steel.
Uniaxial Tension Test: This test is of static type i.e. the load is increased comparatively slowly
from zero to a certain value.
Standard specimens are used for the tension test.
There are two types of standard specimen's which are generally used for this purpose, which
have been shown below:
Specimen I:
This specimen utilizes a circular X-section.
Specimen II:
This specimen utilizes a rectangular X-section.
Lg = gauge length i.e. length of the specimen on which we want to determine the mechanical
properties. The uniaxial tension test is carried out on tensile testing machine and the following
steps are performed to conduct this test.
(i) The ends of the specimens are secured in the grips of the testing machine.
(ii) There is a unit for applying a load to the specimen with a hydraulic or mechanical drive.
(iii) There must be some recording device by which you should be able to measure the final
output in the form of Load or stress. So the testing machines are often equipped with the
pendulum type lever, pressure gauge and hydraulic capsule and the stress Vs strain diagram is
plotted which has the following shape.
A typical tensile test curve for the mild steel has been shown below

33. Nominal stress – Strain OR Conventional Stress – Strain diagrams:
Stresses are usually computed on the basis of the original area of the specimen; such stresses
are often referred to as conventional or nominal stresses.
True stress – Strain Diagram:
Since when a material is subjected to a uniaxial load, some contraction or expansion always
takes place. Thus, dividing the applied force by the corresponding actual area of the specimen
at the same instant gives the so called true stress.
SALIENT POINTS OF THE GRAPH:
(A) So it is evident form the graph that the strain is proportional to strain or elongation is
proportional to the load giving a σt.line relationship. This law of proportionality is valid up to
a point A.
or we can say that point A is some ultimate point when the linear nature of the graph ceases or
there is a deviation from the linear nature. This point is known as the limit of proportionality
or the proportionality limit.
(B) For a short period beyond the point A, the material may still be elastic in the sense that the
deformations are completely recovered when the load is removed. The limiting point B is
termed as Elastic Limit.
(C) and (D) - Beyond the elastic limit plastic deformation occurs and strains are not totally
recoverable. There will be thus permanent deformation or permanent set when load is removed.

34. These two points are termed as upper and lower yield points respectively. The stress at the
yield point is called the yield strength.
A study a stress – strain diagrams shows that the yield point is so near the proportional limit
that for most purpose the two may be taken as one. However, it is much easier to locate the
former. For material which do not possess a well define yield points, In order to find the yield
point or yield strength, an offset method is applied.
In this method a line is drawn parallel to the straight line portion of initial stress diagram by
offsetting this by an amount equal to 0.2% of the strain as shown as below and this happens
especially for the low carbon steel.
(E) A further increase in the load will cause marked deformation in the whole volume of the
metal. The maximum load which the specimen can with stand without failure is called the load
at the ultimate strength.
The highest point ‘E' of the diagram corresponds to the ultimate strength of a material.
σu = Stress which the specimen can with stand without failure & is known as Ultimate Strength
or Tensile Strength.
σu is equal to load at E divided by the original cross-sectional area of the bar.
(F) Beyond point E, the bar begins to forms neck. The load falling from the maximum until
fracture occurs at F.
[ Beyond point E, the cross-sectional area of the specimen begins to reduce rapidly over a
relatively small length of bar and the bar is said to form a neck. This necking takes place whilst
the load reduces, and fracture of the bar finally occurs at point F]
Note: Owing to large reduction in area produced by the necking process the actual stress at
fracture is often greater than the above value. Since the designers are interested in maximum
loads which can be carried by the complete cross section, hence the stress at fracture is seldom
of any practical value.

35. Stress-Strain diagram for Brittle material
Ductile and Brittle Materials:
Based on this behaviour, the materials may be classified as ductile or brittle materials
Ductile Materials:
It we just examine the earlier tension curve one can notice that the extension of the materials
over the plastic range is considerably in excess of that associated with elastic loading. The
Capacity of materials to allow these large deformations or large extensions without failure is
termed as ductility. The materials with high ductility are termed as ductile materials.
Brittle Materials:
A brittle material is one which exhibits a relatively small extensions or deformations to fracture,
so that the partially plastic region of the tensile test graph is much reduced.
This type of graph is shown by the cast iron or steels with high carbon contents or concrete.

36. Classification of Materials on the basis of Mechanical Properties
Mechanical properties help us to measure how materials behave under a load. Mechanical
properties of materials can classify materials are mentioned below.
Elastic Material:
A material which regains its original size and shape on removal stress is said to be elastic stress.
Plastic material:
A material which can undergo permanent deformation without rupture aid to be plastic
material. This property of the material is known as plasticity. Plasticity is important when a
material is to be mechanically formed by causing the material to flow.
Ductile Material:
A material which an undergo considerable deformation without rupture is said to be ductile
material. The major portion of deformation is plastic.
Brittle Material:
A material which ruptures with little or no plastic deformation is said to brittle materials.
The deformation or strain remaining in a body after removal of stress is known as permanent
set. This is due to elastic property of material.
Elastic limit:
The greatest stress that a material can take without permanent set on the removal of stress is
known as elastic limit.
Proportionality limit:
The greatest stress that a material can take without deviation from straight line between stress
and strain is known as proportionality limit.
Endurance limit or Fatigue limit:
The greatest stress, applied infinite number of times, that a material can take without causing
failure is known as endurance limit or fatigue limit.
Ultimate Strength:
The maximum stress material can take is known as ultimate strength. Ultimate strength is equal
to maximum load divided by original area of cross section.
Modulus of Resilience:
The energy stored per unit volume at the elastic limit is known as modulus of resilience.
Modulus of Toughness:
The amount of work required per unit volume to cause failure, under static loading, is called
modulus of toughness.

37. Modulus of Rupture:
The ultimate strength in flexure or torsion is known as modulus of rupture.
Strain hardening:
The increase in strength after plastic zone due to rearrangement of molecules in the material.
Proof stress:
The stress which is just sufficient to cause a permanent set(elongation) equal to a specified
percentage of the original gauge length.
Elastic Strain:
Elastic strain is a dimensional change that occur in a material due to the application of loads
and disappears completely on the removal of the loads.
Plastic Strain:
It is a dimensional change that occurs in a material due to application of the loads and does not
disappear after the removal of the loads.
Ductility and malleability:
The plastic response of material to tensile force is known as ductility and plastic response to
compression force is known as malleability. The elongation and reduction of area of test piece
tested to failure in tension are generally taken as measures of ductility of material.
Creep:
The long term deflection due to sustained (constant) loads.
Factor of Safety
Factor of safety (F.O.S) also known as Safety Factor (SF), is a term describing structural
capacity of system beyond the expected load or actual load.
 Ductile:
 Brittle:
 Margin of Safety: M.O.S= F.O.S-1

38. Hardness Testing Basics
Hardness is a characteristic of a material, not a fundamental physical property. It is defined as
the resistance to indentation, and it is determined by measuring the permanent depth of the
indentation.
More simply put, when using a fixed force (load)* and a given indenter, the smaller the
indentation, the harder the material. Indentation hardness value is obtained by measuring the
depth or the area of the indentation using one of over 12 different test methods.
Hardness testing is used for two general characterizations
1.Material Characteristics
• Test to check material
• Test hardenability
• Test to confirm process
• Can be used to predict Tensile strength
2. Functionality
• Test to confirm ability to function as designed.
• Wear Resistance
• Toughness
• Resistance to impact

39. Compression Test:
Machines used for compression testing are basically similar to those used for tensile testing
often the same machine can be used to perform both tests.
Shape of the specimen: The shape of the machine to be used for the different materials are as
follows:
(i) For metals and certain plastics: The specimen may be in the form of a cylinder
(ii) For building materials: Such as concrete or stone the shape of the specimen may be in
the form of a cube.
Shape of stress stain diagram
(a) Ductile materials: For ductile material such as mild steel, the load Vs compression
diagram would be as follows
(1) The ductile materials such as steel, Aluminum, and copper have stress – strain diagrams
similar to ones which we have for tensile test, there would be an elastic range which is then
followed by a plastic region.
(2) The ductile materials (steel, Aluminum, copper) proportional limits in compression test are
very much close to those in tension.
(3) In tension test, a specimen is being stretched, necking may occur, and ultimately fracture
fakes place. On the other hand, when a small specimen of the ductile material is compressed,
it begins to bulge on sides and becomes barrel shaped as shown in the figure above. With
increasing load, the specimen is flattened out, thus offering increased resistance to further
shortening (which means that the stress – strains curve goes upward) this effect is indicated in
the diagram.
Brittle materials in compression test)
Brittle materials in compression typically have an initial linear region followed by a region in
which the shortening increases at a higher rate than does the load. Thus, the compression stress
– strain diagram has a shape that is similar to the shape of the tensile diagram.
However, brittle materials usually reach much higher ultimate stresses in compression than in
tension.
For cast iron, the shape may be like this

40. Brittle materials in compression behave elastically up to certain load, and then fail suddenly by
splitting or by cracking in the way as shown in figure. The brittle fracture is performed by
separation and is not accompanied by noticeable plastic deformation.
Hardness Testing:
The term ‘hardness' is one having a variety of meanings; a hard material is thought of as one
whose surface resists indentation or scratching, and which has the ability to indent or cut other
materials.
Hardness test: The hardness test is a comparative test and has been evolved mainly from the
need to have some convenient method of measuring the resistance of materials to scratching,
wear or in dentation this is also used to give a guide to overall strength of a materials, after as
an inspection procedure, and has the advantage of being a non – destructive test, in that only
small indentations are lift permanently on the surface of the specimen.
Four hardness tests are customarily used in industry namely
(i) Brinell
(ii) Vickers
(iii) Rockwell
(vi) Shore Scleroscopy
The most widely used are the first two.
In the Brinell test the indenter is a hardened steel ball which is pressed into the surface using a
known standard load. The diameter of resulting indentation is than measured using a
microscope & scale.
Units:
The units of Brinell Hardness number in S.I Unit would have been N/mm2
or Mpa
To avoid the confusion which would have been caused of her wise Hardness numbers are
quotes as kgf / mm2

41. Brinell Hardness test:
In the Brinell hardness test, a hardened steel ball is pressed into the flat surface of a
test piece using a specified force. The ball is then removed and the diameter of the resulting
indentation is measured using a microscope.
The Brinell Hardness no. ( BHN ) is defined as
BHN = P / A
Where P = Force applied to the ball.
A = curved area of the indentation
It may be shown that
D = diameter of the ball,
d = the diameter of the indentation.
In the Brinell Test, the ball diameter and applied load are constant and are selected to suit the
composition of the metal, its hardness, and selected to suit the composition of the metal, its
hardness, the thickness etc. Further, the hardness of the ball should be at least 1.7 times than
the test specimen to prevent permanent set in the ball.
Disadvantage of Brinell Hardness Test: The main disadvantage of the Brinell Hardness test
is that the Brinell hardness number is not independent of the applied load. This can be realized
from. Considering the geometry of indentations for increasing loads. As the ball is pressed into
the surface under increasing load the geometry of the indentation charges.
Here what we mean is that the geometry of the impression should not change w.r.t. load,
however the size it impression may change.

42. Vickers Hardness test:
The Vicker's Hardness test follows a procedure exactly a identical with that of Brinell
test, but uses a different indenter. The steel ball is replaced by a diamond, having the from of a
square – based pyramid with an angle of 1360
between opposite faces. This is pressed into the
flat surface of the test piece using a specified force, and the diagonals of the resulting
indentation measured is using a microscope. The Hardness, expressed as a Vicker's pyramid
number is defined as the ratio F/A, where F is the force applied to the diamond and A is the
surface area of the indentation.
It may be shown that
In the Vicker Test the indenters of pyramidal or conical shape are used & this overcomes the
disadvantage which is faced in Brinell test i.e. as the load increases, the geometry of the
indentation's does not change

43. The Variation of Hardness number with load is given below.
Advantage: Apart from the convenience the vicker's test has certain advantages over the
Brinell test.
(i) Harder material can be tested and indentation can be smaller & therefore less obtrusive or
damaging.
Upto a 300 kgf /mm2
both tests give the same hardness number but above too the Brinell test
is unreliable.

44. Rockwell Hardness Test:
The Rockwell Hardness test also uses an indenter when is pressed into the flat surface
of the test piece, but differs from the Brinell and Vickers’s test in that the measurement of
hardness is based on the depth of penetration, not on the surface area of indentation. The
indenter may be a conical diamond of 1200
included angle, with a rounded apex. It is brought
into contact with the test piece, and a force F is applied.
A = Depth reached by indenter after application of preload (minor load)
B = Position of indenter during Total load, Minor plus Major loads
C = Final position reached by indenter after elastic recovery of sample material
D = Distance measurement taken representing difference between preload and major load position. This
distance is used to calculate the Rockwell Hardness Number.
Advantages:
Rockwell tests are widely applied in industry due to rapidity and simplicity with which they
may be performed, high accuracy, and due to the small size of the impressions produced on the
surface.
Impact testing:
In an ‘impact test' a notched bar of material, arranged either as a cantilever or as a simply
supported beam, is broken by a single blow in such a way that the total energy required to
fracture it may be determined.
The energy required to fracture a material is of importance in cases of “shock loading' when a
component or structure may be required to absorb the K.E of a moving object.
Often a structure must be capable of receiving an accidental ‘shock load' without failing
completely, and whether it can do this will be determined not by its strength but by its ability
to absorb energy. A combination of strength and ductility will be required, since large amounts
of energy can only be absorbed by large amounts of plastic deformation. The ability of a
material to absorb a large amount of energy before breaking is often referred as toughness, and
the energy absorbed in an impact test is an obvious indication of this property.

45. Impact tests are carried out on notched specimens, and the notches must not be regarded simply
as a local reduction in the cross – sectional area of the specimen, Notches – and, in fact, surface
irregularities of many kind – give rise to high local stresses, and are in practice, a potential
source of cracks.
The specimen may be of circular or square cross – section arranged either as a cantilever or a
simply supported beam.
Toughness: It is defined as the ability of the material to withstand crack i.e to prevent the
transfer or propagation of cracks across its section hence causing failures. Cracks are
propagated due to stress concentration.
Creep: Creep is the gradual increase of plastic strain in a material with time at constant load.
Particularly at elevated temperatures some materials are susceptible to this phenomenon and
even under the constant load, mentioned strains can increase continually until fractures. This
form of facture is particularly relevant to the turbines blades, nuclear reactors, furnaces rocket
motors etc.
The general from of strain versus time graph or creep curve is shown below.

46. The general form of Î Vs t graph or creep curve is shown below for two typical operation
conditions, In each case the curve can be considered to exhibit four principal features
(a) An initial strain, due to the initial application of load. In most cases this would be an elastic
strain.
(b) A primary creep region, during which he creep rate (slope of the graph ) dimensions.
(c) A secondary creep region, when the creep rate is sensibly constant.
(d) A tertiary creep region, during which the creep rate accelerate to final fracture.
It is obvious that a material which is susceptible to creep effects should only be subjected to
stresses which keep it in secondary (st.line) region throughout its service life. This enables the
amount of creep extension to be estimated and allowed for in design.
Practice Problems:
PROB 1: A standard mild steel tensile test specimen has a diameter of 16 mm and a gauge
length of 80 mm such a specimen was tested to destruction, and the following results obtained.
Load at yield point = 87 kN
Extension at yield point = 173 x 16-6
m
Ultimate load = 124 kN
Total extension at fracture = 24 mm
Diameter of specimen at fracture = 9.8 mm
Cross - sectional area at fracture = 75.4 mm2
Cross - sectional Area ‘A' = 200 mm2
Compute the followings:
(i) Modulus of elasticity of steel
(ii) The ultimate tensile stream
(iii) The yield stress
(iv) The percentage elongation
(v) The Percentage reduction in Area.
PROB 2:
A light alloy specimen has a diameter of 16mm and a gauge Length of 80 mm. When tested in
tension, the load extension graph proved linear up to a load of 6kN, at which point the extension
was 0.034 mm. Determine the limits of proportionality stress and the modulus of elasticity of
material.
Note: For a 16mm diameter specimen, the Cross – sectional area A = 200 mm2
This is according to tables Determine the limit of proportion try stream & the modulus of
elasticity for the material.
Ans: 30 MN /m2
, 70.5 GN /m2
solution: