Short Notes: Stress-Strain Diagrams for Engineering Materials | Short Notes for Mechanical Engineering PDF Download

 Page 1


Stress-Strain Diagrams for Engineering Materials  
Stress-Strain Diagrams and their relationships are the primary requirements in the 
selection of Engineering material for all purposes. We cannot utilise any material in 
manufacturing process without having proper knowledge of its behaviour on the 
application of force or stress.
The relationship between the stress and strain that a material displays is known as 
a Stress-Strain curve. It is unique for each material and is found by recording the 
amount of deformation (strain) at distinct intervals of tensile or compressive 
loading. These curves reveal many of the properties of a material (including data to 
establish the Modulus of Elasticity, E).
Stress-Strain diagrams are obtained by drawing a graph or curve from the data 
obtained in a tensile test. There are resulting changes in length which can be 
observed and recorded by strain measuring devices.
Stress-Strain diagram for Steel:
Stress-Strain diagram for Cemented tungsten carbide:
Page 2


Stress-Strain Diagrams for Engineering Materials  
Stress-Strain Diagrams and their relationships are the primary requirements in the 
selection of Engineering material for all purposes. We cannot utilise any material in 
manufacturing process without having proper knowledge of its behaviour on the 
application of force or stress.
The relationship between the stress and strain that a material displays is known as 
a Stress-Strain curve. It is unique for each material and is found by recording the 
amount of deformation (strain) at distinct intervals of tensile or compressive 
loading. These curves reveal many of the properties of a material (including data to 
establish the Modulus of Elasticity, E).
Stress-Strain diagrams are obtained by drawing a graph or curve from the data 
obtained in a tensile test. There are resulting changes in length which can be 
observed and recorded by strain measuring devices.
Stress-Strain diagram for Steel:
Stress-Strain diagram for Cemented tungsten carbide:
Stress (N/mm2 )
Stress-Strain diagram for Plaster of Paris:
Stress-Strain diagram for Soft rubber:
• In the case of ductile materials, at the beginning of the test, the material 
extends elastically. The strain (both longitudinal and lateral) at first increases 
proportionally to the stress and the sample or specimen returns to its original 
length on the removal of the stress. The limit of proportionality (stress a 
strain) is the stage up to which the specimen, i.e., material obeys Hooke’s law 
perfectly.
• On further increasing the applied stress, i.e., beyond the elastic limit, it 
produces plastic deformation so that a permanent extension remains even 
after the removal of the applied load, i.e. stress. The resultant strain, in this 
stage, begins to increase more quickly than the corresponding stress and 
continues to increase till the yield point is reached. We must note that at the 
yield point the material suddenly stretches.
• The ratio of applied load to the original cross-sectional area is called the 
normal stress and this continues to increase with elongation, due to work 
hardening or strain hardening, until the tensile stress is maximum. This is the 
value of stress at maximum load and one can calculate it by dividing the
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Stress-Strain Diagrams for Engineering Materials  
Stress-Strain Diagrams and their relationships are the primary requirements in the 
selection of Engineering material for all purposes. We cannot utilise any material in 
manufacturing process without having proper knowledge of its behaviour on the 
application of force or stress.
The relationship between the stress and strain that a material displays is known as 
a Stress-Strain curve. It is unique for each material and is found by recording the 
amount of deformation (strain) at distinct intervals of tensile or compressive 
loading. These curves reveal many of the properties of a material (including data to 
establish the Modulus of Elasticity, E).
Stress-Strain diagrams are obtained by drawing a graph or curve from the data 
obtained in a tensile test. There are resulting changes in length which can be 
observed and recorded by strain measuring devices.
Stress-Strain diagram for Steel:
Stress-Strain diagram for Cemented tungsten carbide:
Stress (N/mm2 )
Stress-Strain diagram for Plaster of Paris:
Stress-Strain diagram for Soft rubber:
• In the case of ductile materials, at the beginning of the test, the material 
extends elastically. The strain (both longitudinal and lateral) at first increases 
proportionally to the stress and the sample or specimen returns to its original 
length on the removal of the stress. The limit of proportionality (stress a 
strain) is the stage up to which the specimen, i.e., material obeys Hooke’s law 
perfectly.
• On further increasing the applied stress, i.e., beyond the elastic limit, it 
produces plastic deformation so that a permanent extension remains even 
after the removal of the applied load, i.e. stress. The resultant strain, in this 
stage, begins to increase more quickly than the corresponding stress and 
continues to increase till the yield point is reached. We must note that at the 
yield point the material suddenly stretches.
• The ratio of applied load to the original cross-sectional area is called the 
normal stress and this continues to increase with elongation, due to work 
hardening or strain hardening, until the tensile stress is maximum. This is the 
value of stress at maximum load and one can calculate it by dividing the
maximum load by the original cross-sectional area. This stress is called 
ultimate tensile stress.
• At a certain value of load the strain continues at slow rate without any further 
stress or loading. This phenomenon of slow extension increasing with time, at 
constant stress, is termed creep. A neck begins to develop at this point, along 
the length of the specimen and further plastic deformation is localized within 
the neck. The cross-sectional area decreases in proportion to the increasing 
length during elastic elongation. We must note that the volume of the test bar, 
i.e. specimen remains constant.
Stree-strain diagram for a brittle material:
• Stress-strain diagram for mild steel clearly shows the limit of proportionality, 
elastic limit, yield point, ultimate tensile stress and fracture stress at the 
breaking points. We note that this diagram shows a well-defined yield point. 
Poorly defined yield point as in the case of brittle materials is shown in the 
following figure.
Stress vs. strain curve fo r a brittle m aterial
• For the determination of the yield strength in such materials, following the 
general practice, one has to draw a straight line parallel to the elastic portion 
of the stress-strain curve at a predetermined strain ordinate value (say 0.1%). 
The point at which this line intersects the stress vs. strain curve is the yield 
point at off-set and called the yield strength at 0.1 % or 0.2% of set strain.
• Stress vs. strain curves also helps to explain the properties of ductile 
materials.
We find that:
• Greater the angle of inclination of the line of stress vs. strain proportionality 
to the ordinates, the more elastic is that metal.
• A higher yield point reveals greater hardness of the metal.
• A higher value of the maximum stress point shows that the metal is a 
stronger one.
• The toughness and brittleness of metal are indicated by the distance from the 
ordinates of the breaking stress or load point.
• The metal is more brittle when the distance is shorter.
Engineering and True Stress-Strain Diagrams:
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Stress-Strain Diagrams for Engineering Materials  
Stress-Strain Diagrams and their relationships are the primary requirements in the 
selection of Engineering material for all purposes. We cannot utilise any material in 
manufacturing process without having proper knowledge of its behaviour on the 
application of force or stress.
The relationship between the stress and strain that a material displays is known as 
a Stress-Strain curve. It is unique for each material and is found by recording the 
amount of deformation (strain) at distinct intervals of tensile or compressive 
loading. These curves reveal many of the properties of a material (including data to 
establish the Modulus of Elasticity, E).
Stress-Strain diagrams are obtained by drawing a graph or curve from the data 
obtained in a tensile test. There are resulting changes in length which can be 
observed and recorded by strain measuring devices.
Stress-Strain diagram for Steel:
Stress-Strain diagram for Cemented tungsten carbide:
Stress (N/mm2 )
Stress-Strain diagram for Plaster of Paris:
Stress-Strain diagram for Soft rubber:
• In the case of ductile materials, at the beginning of the test, the material 
extends elastically. The strain (both longitudinal and lateral) at first increases 
proportionally to the stress and the sample or specimen returns to its original 
length on the removal of the stress. The limit of proportionality (stress a 
strain) is the stage up to which the specimen, i.e., material obeys Hooke’s law 
perfectly.
• On further increasing the applied stress, i.e., beyond the elastic limit, it 
produces plastic deformation so that a permanent extension remains even 
after the removal of the applied load, i.e. stress. The resultant strain, in this 
stage, begins to increase more quickly than the corresponding stress and 
continues to increase till the yield point is reached. We must note that at the 
yield point the material suddenly stretches.
• The ratio of applied load to the original cross-sectional area is called the 
normal stress and this continues to increase with elongation, due to work 
hardening or strain hardening, until the tensile stress is maximum. This is the 
value of stress at maximum load and one can calculate it by dividing the
maximum load by the original cross-sectional area. This stress is called 
ultimate tensile stress.
• At a certain value of load the strain continues at slow rate without any further 
stress or loading. This phenomenon of slow extension increasing with time, at 
constant stress, is termed creep. A neck begins to develop at this point, along 
the length of the specimen and further plastic deformation is localized within 
the neck. The cross-sectional area decreases in proportion to the increasing 
length during elastic elongation. We must note that the volume of the test bar, 
i.e. specimen remains constant.
Stree-strain diagram for a brittle material:
• Stress-strain diagram for mild steel clearly shows the limit of proportionality, 
elastic limit, yield point, ultimate tensile stress and fracture stress at the 
breaking points. We note that this diagram shows a well-defined yield point. 
Poorly defined yield point as in the case of brittle materials is shown in the 
following figure.
Stress vs. strain curve fo r a brittle m aterial
• For the determination of the yield strength in such materials, following the 
general practice, one has to draw a straight line parallel to the elastic portion 
of the stress-strain curve at a predetermined strain ordinate value (say 0.1%). 
The point at which this line intersects the stress vs. strain curve is the yield 
point at off-set and called the yield strength at 0.1 % or 0.2% of set strain.
• Stress vs. strain curves also helps to explain the properties of ductile 
materials.
We find that:
• Greater the angle of inclination of the line of stress vs. strain proportionality 
to the ordinates, the more elastic is that metal.
• A higher yield point reveals greater hardness of the metal.
• A higher value of the maximum stress point shows that the metal is a 
stronger one.
• The toughness and brittleness of metal are indicated by the distance from the 
ordinates of the breaking stress or load point.
• The metal is more brittle when the distance is shorter.
Engineering and True Stress-Strain Diagrams:
• When we calculate the stress on the basis of the original area, it is called the 
engineering or nominal stress.
• If we calculate the stress based upon the instantaneous area at any instant of 
load it is then termed as true stress.
• If we use the original length to calculate the strain, then It is called the 
engineering strain.
E n g in e e rin g a n d tr u e s tr e s s - s tr a in diagram s for c o p p e r
Brittleness
• It may be defined as the property of a metal by virtue of which it will fracture 
without any appreciable deformation.
• This property is just opposite to the ductility of a metal.
• Example: cast iron, glass and concrete.
• This property of metals finds its importance for the design of machine tools, 
which are subjected to sudden loads.
• Metals with less than 5% elongation are known to be brittle ones.
Toughness
• It may be defined as the property of a metal by virtue of which it can absorb 
maximum energy before fracture takes place.
• Toughness is also calculated in terms of area under the stress-strain curve.
• Toughness is the property of materials which enables a material to be twisted, 
bent or stretched under a high stress before rupture.
• The value of toughness falls with the rise in temperature.
• Toughness is the highly desirable property for structural and mechanical parts 
which have to withstand shock and vibration.
Page 5


Stress-Strain Diagrams for Engineering Materials  
Stress-Strain Diagrams and their relationships are the primary requirements in the 
selection of Engineering material for all purposes. We cannot utilise any material in 
manufacturing process without having proper knowledge of its behaviour on the 
application of force or stress.
The relationship between the stress and strain that a material displays is known as 
a Stress-Strain curve. It is unique for each material and is found by recording the 
amount of deformation (strain) at distinct intervals of tensile or compressive 
loading. These curves reveal many of the properties of a material (including data to 
establish the Modulus of Elasticity, E).
Stress-Strain diagrams are obtained by drawing a graph or curve from the data 
obtained in a tensile test. There are resulting changes in length which can be 
observed and recorded by strain measuring devices.
Stress-Strain diagram for Steel:
Stress-Strain diagram for Cemented tungsten carbide:
Stress (N/mm2 )
Stress-Strain diagram for Plaster of Paris:
Stress-Strain diagram for Soft rubber:
• In the case of ductile materials, at the beginning of the test, the material 
extends elastically. The strain (both longitudinal and lateral) at first increases 
proportionally to the stress and the sample or specimen returns to its original 
length on the removal of the stress. The limit of proportionality (stress a 
strain) is the stage up to which the specimen, i.e., material obeys Hooke’s law 
perfectly.
• On further increasing the applied stress, i.e., beyond the elastic limit, it 
produces plastic deformation so that a permanent extension remains even 
after the removal of the applied load, i.e. stress. The resultant strain, in this 
stage, begins to increase more quickly than the corresponding stress and 
continues to increase till the yield point is reached. We must note that at the 
yield point the material suddenly stretches.
• The ratio of applied load to the original cross-sectional area is called the 
normal stress and this continues to increase with elongation, due to work 
hardening or strain hardening, until the tensile stress is maximum. This is the 
value of stress at maximum load and one can calculate it by dividing the
maximum load by the original cross-sectional area. This stress is called 
ultimate tensile stress.
• At a certain value of load the strain continues at slow rate without any further 
stress or loading. This phenomenon of slow extension increasing with time, at 
constant stress, is termed creep. A neck begins to develop at this point, along 
the length of the specimen and further plastic deformation is localized within 
the neck. The cross-sectional area decreases in proportion to the increasing 
length during elastic elongation. We must note that the volume of the test bar, 
i.e. specimen remains constant.
Stree-strain diagram for a brittle material:
• Stress-strain diagram for mild steel clearly shows the limit of proportionality, 
elastic limit, yield point, ultimate tensile stress and fracture stress at the 
breaking points. We note that this diagram shows a well-defined yield point. 
Poorly defined yield point as in the case of brittle materials is shown in the 
following figure.
Stress vs. strain curve fo r a brittle m aterial
• For the determination of the yield strength in such materials, following the 
general practice, one has to draw a straight line parallel to the elastic portion 
of the stress-strain curve at a predetermined strain ordinate value (say 0.1%). 
The point at which this line intersects the stress vs. strain curve is the yield 
point at off-set and called the yield strength at 0.1 % or 0.2% of set strain.
• Stress vs. strain curves also helps to explain the properties of ductile 
materials.
We find that:
• Greater the angle of inclination of the line of stress vs. strain proportionality 
to the ordinates, the more elastic is that metal.
• A higher yield point reveals greater hardness of the metal.
• A higher value of the maximum stress point shows that the metal is a 
stronger one.
• The toughness and brittleness of metal are indicated by the distance from the 
ordinates of the breaking stress or load point.
• The metal is more brittle when the distance is shorter.
Engineering and True Stress-Strain Diagrams:
• When we calculate the stress on the basis of the original area, it is called the 
engineering or nominal stress.
• If we calculate the stress based upon the instantaneous area at any instant of 
load it is then termed as true stress.
• If we use the original length to calculate the strain, then It is called the 
engineering strain.
E n g in e e rin g a n d tr u e s tr e s s - s tr a in diagram s for c o p p e r
Brittleness
• It may be defined as the property of a metal by virtue of which it will fracture 
without any appreciable deformation.
• This property is just opposite to the ductility of a metal.
• Example: cast iron, glass and concrete.
• This property of metals finds its importance for the design of machine tools, 
which are subjected to sudden loads.
• Metals with less than 5% elongation are known to be brittle ones.
Toughness
• It may be defined as the property of a metal by virtue of which it can absorb 
maximum energy before fracture takes place.
• Toughness is also calculated in terms of area under the stress-strain curve.
• Toughness is the property of materials which enables a material to be twisted, 
bent or stretched under a high stress before rupture.
• The value of toughness falls with the rise in temperature.
• Toughness is the highly desirable property for structural and mechanical parts 
which have to withstand shock and vibration.
Stress-strain curves
Stiffness
• This may be defined as the property of a metal by virtue of which it resists 
deformation.
• Modulus of rigidity is the measure of stiffness.
• The term flexibility is quite opposite of stiffness.
• The materials which suffer less deformation under load have high degree of 
stiffness.
Resilience
• This may be defined as the property of a metal by virtue of which it stores 
energy and resists shocks or impacts.
• It is measured by the amount of energy absorbed per unit volume, in stressing 
a material up to elastic limit.
• This property is of great importance in the selection of a material used for 
various types of springs.
Endurance:
• This is defined as the property of a metal by virtue of which it can withstand 
varying stresses (same or opposite nature).
• The maximum value of stress, which can be applied for indefinite times 
without causing its failure, is termed as its endurance limit.
• For ordinary steel, the endurance limit is about half the tensile strength.
• This property of a metal is of great importance in the design and production 
of parts in reciprocating machines and components subjected to vibrations.
Anelastic Behaviour:
• Recoverable deformation that takes place as a function of time is termed an­
elastic deformation.
• Due to some relaxation process within the material, the elastic deformation of 
the material continues even after the application of the load.
• On removal of the load, some part of the elastic deformation is recovered only 
as a function of time, with the reversal of the relaxation process.
Viscoelastic Behavior:
• This is found in those materials which respond to an applied stress by both 
recoverable and permanent deformations, which are time-dependent.
• Non-crystalline organic polymers exhibit this behaviour.
• Time dependent permanent deformation is termed as viscous flow.