STRENGTH OF MATERIALS FOR MECHANICAL ENGINEERS

1. BIBIN CHIDAMBARANATHAN
STRENGTH
OF
MATERIALS
FOR MECHANICAL ENGINEERS

2. Mechanical Properties of Engineering Materials
The characteristics of the materials which describe their
behaviour under external loads are known as Mechanical
Properties.

3. Mechanical Properties of Engineering Materials
Strength:
❖ When an external load is applied on a material, then the capacity of the material to
withstand that load without destruction is called strength of a material.
❖ The stronger the material the greater the load it can handle. Therefore it determines the
ability of a material to withstand stress without failure.
❖ The strength of materials varies according to the types of load.
❖ The maximum stress that a material can withstand before destruction is called the
ultimate strength.
❖ The tenacity of a material is the value of its ultimate strength in tension.

4. Mechanical Properties of Engineering Materials
Elasticity:
❖ The ability of a material to return to its original position after
deformation when the external load acting on it is removed is called
elasticity.
❖ Elasticity is the tensile property of the material.

5. Mechanical Properties of Engineering Materials
Stiffness:
❖ The resistance of a material to elastic deformation or deflection is called stiffness or
rigidity.
❖ A material that suffers less deformation under the action of load possesses a high
degree of stiffness or rigidity.
❖ For example a steel and aluminium beam is suspended. Both are enough strong to
carry the required load but there is a greater deflection in the aluminium beam. This
indicates that the steel beam has a greater stiffness than the aluminium beam.
❖ If the material is following Hooke’s law, in that case the stiffness of material is
measured by young’s modulus E. The higher the value of the young’s modulus the more
will be the stiffness.

6. Mechanical Properties of Engineering Materials
Flexibility:
❖ It is defined as the ability of the material to bend easily.
❖ This mechanical properties of materials allow it to form in any
shape.

7. Mechanical Properties of Engineering Materials
Plasticity:
❖ Plasticity is defined as the ability of a material to undergo some degree
of permanent deformation without rupture or failure.
❖ The plastic deformation appears when the material is stressed beyond
the elastic range.
❖ Plasticity is important in shaping, forming, extruding and many other hot
or cold working process.
❖ Generally plasticity increases with the increase in temperature.

8. Mechanical Properties of Engineering Materials
Ductility:
❖ Ductility is a property of a solid material which indicates that how easily a
material gets deformed under tensile stress.
❖ Ductility is often categorized by the ability of material to get stretched into a
wire by pulling or drawing.
❖ This mechanical property is also an aspect of plasticity of material and is
temperature dependent.
❖ With rise in temperature, the ductility of material increases.
❖ For example: gold, copper, iron, mild steel etc.

9. Mechanical Properties of Engineering Materials
Malleability:
❖ Malleability is a property of solid materials which indicates that how easily a
material gets deformed under compressive stress.
❖ Malleability is the ability of a material to be hammered or rolled into thin
sheets. This mechanical property is an aspect of plasticity of material.
Malleability of material is temperature dependent.
❖ With rise in temperature, the malleability of material increases.
❖ Aluminium, copper, silver, tin, steel etc. are malleable metals.

10. Mechanical Properties of Engineering Materials
Toughness:
❖ It is the ability of a material to absorb the energy and gets plastically
deformed without fracturing.
❖ Its numerical value is determined by the amount of energy per unit volume.
Its unit is 𝐽𝑜𝑢𝑙𝑒/𝑚3.
❖ Value of toughness of a material can be determined by stress-strain
characteristics of a material.
❖ For good toughness, materials should have good strength as well as ductility.

11. Mechanical Properties of Engineering Materials
Resilience:
❖ Resilience is the ability of material to absorb the energy when it is deformed
elastically by applying stress and release the energy when stress is removed.
❖ Proof resilience is defined as the maximum energy that can be absorbed
without permanent deformation.
❖ The modulus of resilience is defined as the maximum energy that can be
absorbed per unit volume without permanent deformation.
❖ It can be determined by integrating the stress-strain cure from zero to elastic
limit. Its unit is 𝑗𝑜𝑢𝑙𝑒/𝑚3.

12. Mechanical Properties of Engineering Materials
Hardness:
❖ The ability of a material by which it is able to resist scratching, cutting,
abrasion, indentation or penetration. It is closely related to strength.
❖ There are various measure of hardness are
❖ Scratch Hardness,
❖ Indentation Hardness and
❖ Rebound Hardness.

13. Mechanical Properties of Engineering Materials
Scratch Hardness:
❖ Scratch Hardness is the ability of materials to the oppose the scratches to
outer surface layer due to external force.
Indentation Hardness:
❖ It is the ability of materials to oppose the dent due to punch of external hard
and sharp objects.
Rebound Hardness or dynamic hardness:
❖ It is determined by the height of “bounce” of a diamond tipped hammer
dropped from a fixed height on the material.

14. Mechanical Properties of Engineering Materials
Hardenability:
❖It is the ability of a material to attain the hardness by heat treatment
processing.
❖It is determined by the depth up to which the material becomes
hard.
❖The SI unit of hardenability is meter (similar to length).
❖Hardenability of material is inversely proportional to the
weldability of material.

15. Mechanical Properties of Engineering Materials
Brittleness:
❖ Brittleness of a material indicates that how easily it gets fractured when it is subjected to a
force or load.
❖ When a brittle material is subjected to a stress it observes very less energy and gets
fractures without significant strain.
❖ Brittleness is converse to ductility of material. Brittleness of material is temperature
dependent.
❖ Some metals which are ductile at normal temperature become brittle at low temperature.
❖ Example: glass, cast iron.

16. Mechanical Properties of Engineering Materials
Machinability:
❖ It is the ability of the material to be cut easily by a sharp tool.
❖ The machinability of a metal is indicated by percentages which is called
machinability index. All machinable metals are compared to a basic standard.
The standard metal used for the 100 percent machinability is free cutting
steel.
❖ The machinability index of carbon steels generally ranged from 40 to 60 per
cent and that of cast iron from 50 to 80 percent. The metals with higher
range of machinability index can be machined or cut easily.

17. Mechanical Properties of Engineering Materials
Creep:
❖ Creep is the property of a material which indicates the tendency of material to move slowly and deform
permanently under the influence of external mechanical stress. Viscous flow is the simplest type of creep
deformation.
❖ The creep deformation occurs in a material which is exposed for a long time to high level of stresses that are
below yield strength.
❖ Creep is more severe in material that are subjected to heat for long time. There are three stages of creep.
❖ In the first stage the material elongates rapidly but at a decreasing rate.
❖ In the second stage, the rate of elongation is constant.
❖ In the third stage, the rate of elongation increases rapidly until the material fails.

18. Mechanical Properties of Engineering Materials
Fatigue:
❖ Fatigue is the weakening of material caused by the repeated loading of the material.
❖ When a material is subjected to cyclic loading, and loading greater than certain threshold value
but much below the strength of material (ultimate tensile strength limit or yield stress limit),
microscopic cracks begin to form at grain boundaries and interfaces.
❖ Eventually the crack reaches to a critical size.
❖ This crack propagates suddenly and the structure gets fractured.
❖ The shape of structure affects the fatigue very much.
❖ Square holes and sharp corners lead to elevated stresses where the fatigue crack initiates.

19. Mechanical Properties of Engineering Materials
S.no Mechanical Property Definition of the Mechanical Property
1. Strength The capacity of a material to withstand load without destruction.
2. Elasticity
The ability of the material to return to its original condition after deformation on the removal of
external load.
3. Stiffness Resistance to elastic deformation or deflection
4. Flexibility The ability of the material to be bend.
5. Plasticity
The ability of a material to undergo some degree of permanent
deformation without rupture or failure.
6. Ductility The ability of the material to be drawn into thin wires.
7. Malleability The ability of the material to be hammered into thin sheets.
8. Toughness The ability of a material to withstand both the elastic and plastic deformation.
9. Resilience The capacity or ability of a material to absorb energy elastically.
10. Hardness The ability of a material to resist scratching, cutting, abrasion, indentation or penetration.
11. Brittleness The property of breaking of materials without much permanent distortion.
12. Machinability It is the ability of the material to be cut easily
13. Creep
The slow and progressive deformation of a material with the passage of time when it is subjected
to constant stress.
14. Fatigue The phenomena of weakening of material when it is subjected to repeated or fluctuating stress.

20. Elastic constant
❖When an elastic body is subjected to stress, a proportionate
amount of strain is produced.
❖The ratio of the applied stresses to the strains generated will
always be constant and is known as elastic constant.
❖Elastic constant represents the elastic behaviour of objects.

21. Elastic constants
Different elastic constants are as follows :
❖Young’s modulus
❖Bulk modulus
❖Rigidity modulus
❖Poisson’s ratio

22. Young’s Modulus
❖ It is defined as the ratio of tensile stress or compressive stress to the corresponding strain within
elastic limit.
❖ It is denoted by symbol E.
❖ It is also known as modulus of elasticity or elastic modulus.
❖ The unit of modulus of elasticity is the same as the unit of stress which is Mega Pascal (MPa).
❖ 1 MPa is equal to 1 𝑁/𝑚𝑚2
.
𝑌𝑜𝑢𝑛𝑔’𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝐸 =
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑜𝑟 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑜𝑟 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑎𝑖𝑛
=
𝜎
𝑒

23. Rigidity Modulus
❖ When a body is subjected to shear stress the shape of the body gets changed,
the ratio of shear stress to the corresponding shear strain is called rigidity
modulus or modulus of rigidity.
❖ It is denoted by the letters “G” or “C” or “N”. Unit of rigidity modulus is MPa.
𝑅𝑖𝑔𝑖𝑑𝑖𝑡𝑦 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝐺 =
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛
=
𝜏
𝜑

24. Bulk Modulus
❖ When a body is subjected to mutually perpendicular direct stresses which
are alike and equal, within its elastic limits, the ratio of direct stress to the
corresponding volumetric strain is found to be constant.
❖ This ratio is called bulk modulus and is represented by letter “K”. Unit of Bulk
modulus is MPa.
𝐵𝑢𝑙𝑘 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝐾 =
𝐷𝑖𝑟𝑒𝑐𝑡 𝑠𝑡𝑟𝑒𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑠𝑡𝑟𝑎𝑖𝑛
=
𝜎
(
𝑑𝑉
𝑉
)

25. Poisson’s Ratio
❖ When a body is subjected to simple tensile stress within its elastic limits then there is a change in the
dimensions of the body in the direction of the load as well as in the opposite direction.
❖ When these changed dimensions are divided with their original dimensions, longitudinal strain and
lateral strain are obtained.
❖ The ratio of the lateral strain to the longitudinal strain is called Poisson’s ratio.
❖ It is represented by the symbol “µ”. Poisson’s ratio is maximum for an ideal elastic incompressible
material and its value is 0.5.
❖ For most of the engineering materials, Poisson’s ratio lies between 0.25 and 0.33.
❖ It has no units.
𝑃𝑜𝑖𝑠𝑠𝑖𝑜𝑛′𝑠 𝑟𝑎𝑡𝑖𝑜 𝜇 =
𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑎𝑖𝑛
=
𝑒𝑡
𝑒𝑙

26. Relationship between Elastic Constants
❖ The relationship between Young’s modulus (E), rigidity modulus (G) and
Poisson’s ratio (µ) is expressed as 𝑬 = 𝟐𝑮(𝟏 + 𝝁)
❖ The relationship between Young’s modulus (E), bulk modulus (K) and
Poisson’s ratio (µ) is expressed as
❖ Young’s modulus can be expressed in terms of bulk modulus (K) and
rigidity modulus (G) as
❖ Poisson’s ratio can be expressed in terms of bulk modulus (K) and rigidity
modulus (G) as
𝑬 = 𝟑𝑲(𝟏 − 𝟐𝝁)
𝑬 =
𝟗𝑲𝑮
𝟑𝑲 + 𝑮
𝝁 =
𝟑𝑲 − 𝟐𝑮
𝟔𝑲 + 𝟐𝑮

27. Stress-Strain Curve
❖ Stress strain curve is the plot of stress and strain of a material on the
graph.
❖ In this, the stress is plotted on the y-axis and its corresponding strain
on the x-axis.
❖ After plotting the stress and its corresponding strain on the graph,
we get a curve, and this curve is called stress strain curve or stress
strain diagram.
❖ The stress-strain diagram for different material is different.
❖ It may vary due to the temperature and loading condition of the
material.

28. Stress strain curve for brittle materials
Brittle materials
❖ The materials that are easily snapped or broken are
known as brittle materials.
❖ These materials cannot withstand with continuous
external loading.
❖ They instantly break as stress is applied, without any
plastic deformation after producing a sound.
❖ For most brittle materials the permanent elongation
(i.e. increase in length) is less than 10%.

29. Stress strain curve for ductile materials
Proportional Limit (A):
❖ Up to this limit, the stress and the strain
induced in the specimen are directly
proportional to each other, i.e. the specimen
obeys Hooke’s law.
❖ Beyond this point, the stress is not
proportional to the strain.

30. Stress strain curve for ductile materials
Elastic Limit (B):
❖ The elastic limit is the limit beyond which
the material will no longer go back to its
original shape when the load is removed.
❖ It is the maximum stress that may be
developed such that there is no
permanent or residual deformation when
the load is entirely removed.

31. Stress strain curve for ductile materials
Upper Yield Point (C):
❖ It is the point where material starts yielding or
elongation.
❖ After this point the curve is no longer a straight
line.
❖ After this point, the material undergoes more rapid
deformation.
❖ This point gives the yields strength of the material.
❖ Yield stress is defined as the stress after which
material extension takes place more quickly with
no or little increase in load.

32. Stress strain curve for ductile materials
Lower Yield Point (D):
❖ Point D represents the lower yield point of the material.
❖ It is point after which material try to regain its strength.
❖ lower yield point stress is the minimum stress required to
maintain the deformation in the material.
❖ At the lower yield point for the low carbon steels ( mild
steels) the stress strain curve is in some wave nature, this
is because to break bonds with impurities while
dislocations are moving out of the material, hence
resistance increases and decreases periodically after that
strain hardening takes place which increases resistance
slowly by increasing of dislocations in the material.

33. Stress strain curve for ductile materials
Ultimate strength (E):
❖It is the maximum stress value that
material can withstand.
❖It is the point of interest for design
engineers.
❖This ultimate strength is referred as the
tensile strength of material.

34. Stress strain curve for ductile materials
Breaking Point (F):
❖ This is the point at which the specimen fails.
❖ After the ultimate stress point, necking of the
specimen takes place, which causes a loss in the
load carrying capacity of the specimen and
ultimately causes it to fail.
❖ The stress associates with this point known as
breaking strength or rupture strength.

35. Materials on the basis of elastic properties
❖ Homogeneous Material
❖ Isotropic Material
❖ Anisotropic Material
❖ Orthotropic Material

36. Homogeneous Material
❖ A material of uniform composition throughout that
cannot be mechanically separated into different
materials.
❖Examples of homogeneous materials are certain types of
plastics, ceramics, glass, metals, alloys, paper, board and
resins.

37. Isotropic Material
❖Isotropic material means a material having identical
values of a property in all directions. Glass and metals are
examples of isotropic materials.

38. Anisotropic Material
❖It is a term used in various scientific disciplines to indicate that
certain properties of matter (such as a material or radiation) vary
with the direction from which they are measured.
❖For instance, if the refractive index or density of a material is
different when measured along different axes, that property is
said to be anisotropic.
❖Anisotropy is the opposite of isotropic, a term used when
properties are the same when measured from any direction.

39. Orthotropic Material
❖In materials science and solid mechanics, orthotropic
materials have material properties that differ along three
mutually orthogonal twofold axes of rotational symmetry.
❖ They are a subset of anisotropic materials, because their
properties change when measured from different
directions.

40. Thank You