This document discusses various concepts related to stress and strain. It begins by explaining the three main types of loads - tension, compression, and shear. It then provides diagrams demonstrating these different types of loads. The document goes on to define engineering stress and strain and discuss their units. Several mechanical properties are also defined, including yield strength, ultimate tensile strength, and elongation. Finally, the document discusses various tests used to determine mechanical properties, including tensile, compression, hardness, and impact tests.

1. Katkar A.A.

2. CONCEPTS OF STRESS AND STRAIN
 There are three principal ways in which a load may be
applied:
 tension,
 compression,
 shear.
 In engineering practice many loads are torsional rather than
pure shear.

3. CONCEPTS OF STRESS AND STRAIN
Tension Compression
before
after

4. CONCEPTS OF STRESS AND STRAIN
Shear Torsion
before
after

5. CONCEPTS OF STRESS AND STRAIN
 Engineering stress σ is defined by the relationship
 Engineering strain is defined according to

6. CONCEPTS OF STRESS AND STRAIN
 The units of engineering stress (or stress) are
 megapascals, MPa (SI) (1 MPa = 106 N/m2),
 pounds force per square inch, psi (U.S.).

7. CONCEPTS OF STRESS AND STRAIN
 Engineering strain (or strain) is unitless,
 but meters per meter or inches per inch are often used;
 the value of strain is independent of the unit system.
 Sometimes strain is expressed in %.

8. Mechanical properties indicates the response of a
metal or alloy to elastic and plastic deformations under
the applied forces.
Many finished products are accepted or rejected on
the basis of their mechanical properties .
Evaluation of these properties is essential for proper
selection of materials for the given service
requirements.

9. There are many tests to determine mechanical
properties .
These tests are classified as
A)Destructive Testing
B)Non – Destructive Testing

10. Destructive Testing
Tensile test
Compression test
Hardness test
Impact test
Fatigue test
Creep test

11. TENSILE TEST
This test is widely used to determine strength,
ductility , resilience , toughness and several other
material properties.
A test specimen of circular, square or rectangular
cross-section of a suitable size is prepared from the
material to be tested .
During preparation of the specimen, care should be
taken to avoid sharp changes in section to reduce
stress concentration.
This is care to avoid the failure of specimen at low
stress values .

12. The specimen is held by suitable means between
the two heads of a testing machine and subjected to
a progressively increasing tensile load until it
fractures .
A record of load acting on the specimen with
progressive extension of the specimen is obtained .
The common machines used for tensile test are
Universal testing machine ,Hounsfield tensometer,
Instron and MTS ( Material testing System)

13. Tensile test

14. Tension test
Schematic representation of the apparatus used to conduct tensile stress–
strain tests.

16. Important Mechanical Properties
from a Tensile Test
 Young's Modulus: This is the slope of the linear
portion of the stress-strain curve, it is usually specific
to each material; a constant, known value.
 Yield Strength: This is the value of stress at the yield
point, calculated by plotting young's modulus at a
specified percent of offset (usually offset = 0.2%).
 Ultimate Tensile Strength: This is the highest value
of stress on the stress-strain curve.
 Percent Elongation: This is the change in gauge
length divided by the original gauge length.

17. 17

18. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
• Localized deformation of a ductile material during a
tensile test produces a necked region.
• The image shows necked region in a fractured sample

19. Compression test
 Conducted in a manner similar to the tensile test,
 except that the force is compressive and the specimen
contracts along the direction of the stress.
 By convention, a compressive force is taken to be
negative, which yields a negative stress.
 Computed compressive strains are also negative.

20. Compression test
 Tensile tests are more common because they are easier to
perform;
 Very little additional information is obtained from
compressive tests.
 Compressive tests are used when
 a material’s behavior under large and permanent (i.e.,
plastic) strains is desired, or
 the material is brittle in tension.

21. Shear and Torsional Tests
 For tests performed using a pure shear force,
the shear stress is computed according to
 The
 shear strain γ is defined as the tangent of the
strain angle θ

22. Shear and Torsional Tests
 Torsion is a variation of pure shear,
wherein a structural member is
twisted
 Torsional forces produce a rotational
motion about the longitudinal axis.
 Examples: machine axles, drive
shafts.

23. Shear and Torsional Tests
 Torsional tests are normally performed on cylindrical
solid shafts or tubes.
 A shear stress is a function of the applied torque ,
whereas shear strain γ is related to the angle of twist .

24. Strength is the ability of a material to resist applied
forces without yielding or fracturing.
Strength of a material may change considerably with
respect to the way it is deformed.
Mode of stress, type of stress & rate of stress
application may affect the strength of a material.
Strength data are usually obtained from lab. Tests
which are performed under strictly standardized
specimens under controlled conditions. These tests
also serve for obtaining σ-ε relationships.

25. σ-ε curves can be grouped into three as:
• Ductile Materials → exhibit both elastic &
plastic behavior
• Brittle Materials → exhibit essentially elastic
behavior
• Viscoelastic Materials → exhibit large elastic
deformation

29. SPECIAL FEATURES OF STRESS-STRAIN DIAGRAMS
σPL
σE
σY
σF
σU
A B
C
D
E

30. Point A (Proportional Limit): The greatest stress (σPL) that
can be developed in the material without causing a
deviation from the law of proportionality of stress to
strain. In other words it is the stress upto which the
material responds following Hooke’s Law.
Point B (Elastic Limit): Maximum stress (σE) that can be
developed in a material without causing permanent
deformation. In other words it is the stress upto which
the deformations are recoverable upon unloading.

31. Point C (Yield Point): The stress at which the material
deforms appreciably without an increase in stress.
Sometimes it can be represented by an upper and lower
yield points. σY,U represents the elastic strength of the
material and σY,L is the stress beyond which the material
behaves plastically.
Point D (Ultimate Strength): It is the maximum stress that
can be developed in a material as determined from the
original X-section of the specimen.

32. Point E (Fracture Strength): The stress at which the
material breaks, fails.

35. In an engineering σ-ε plot the original area (A0) &
length (l0) are used when determining stress from
the load and strain from deformations.
In the true σ-ε plot instantaneous area & length are
used.
The true values of stress & strain for instantaneous
area & length of the specimen under tension will
differ markedly, particularly close to the breaking
point where reduction in cross-section & elongation
of the specimen are observed.

36. 0
A
P
E 
 &
0
l
E


 Engineering
i
T
A
P

 &
i
T
l


 True

37. DUCTILITY & BRITTLENESS
 Ductility can be defined as strain at fracture.
 Ductility is commonly expressed as:
a) Elongation
b) % reduction in cross-sectional area
 A ductile material is the one which deforms appreciably
before it breaks, whereas a brittle material is the one
which does not.
 Ductility in metals is described by:
100
%
0
0



A
A
A
R
f
A
 If %RA > 50 % →
Ductile metal

40. TOUGHNESS & RESILIENCE
Toughness is the energy absorption capacity during
plastic deformation.
In a static strength test, the area under the σ-ε curve
gives the amount of work done to fracture the specimen.
This amount is specifically called as Modulus of
Toughness.
It is the amount of energy that can be absorbed by the
unit volume of material without fracturing it.

41. σ
ε
T (Joule/m3)
σu
σf
σPL
εu
εf
εPL
The area under the σ-ε diagram can be determined
by integration.
If the σ-ε relationship is described by a parabole.
f
u
T 

3
2


42. Resilience is the energy absorption capacity during
elastic deformation.
R
εPL ε
σPL
σ 
 PL
R
2
1

E
PL

 
Since
 
E
R PL
2
2
1 

If you assume σPL = σy
E
R
y
2
2



43. YIELD STRENGTH
It is defined as the maximum stress that can be
developed without causing more than a specified
permissible strain.
It is commonly used in the design of any structure.
If a material does not have a definite yield point to
measure the allowable strains, “Proof Strength” is used.
Proof strength is determined by approximate methods
such as the 0.2% OFF-SET METHOD.
At 0.2% strain, the initial tangent of the σ-ε diagram is
drawn & the intersection is located.

44. DETERMINATION OF E FROM σ-ε DIAGRAMS
 For materials like concrete, cast iron & most non-
ferrous metals, which do not have a linear
portion in their σ-ε diagrams, E is determined by
approximate methods.
1. Initial Tangent Method: Tangent is drawn to the
curve at the origin
2. Tangent Method: Tangent is drawn to the curve
at a point corresponding to a given stress
3. Secant Method: A line is drawn between the
origin & a point corresponding to a given stress

45. HARDNESS
Hardness can be defined as the resistance of a
material to indentation.
It is a quick & practical way of estimating the quality of
a material.
Early hardness tests were based on natural minerals
with a scale constructed solely on the ability of one
material to scratch another that was softer.
A qualitative & somewhat arbitrary hardness indexing
scheme was devised, temed as Mohs Scale, which
ranged from 1 on the soft end for talc to 10 for
diamond.

46. 1. Talc
2. Gypsum
3. Calcite
4. Fluorite
5. Apatite
6. Orthoclase
7. Quartz
8. Topaz
9. Corundum
10. Diamond
HARDER
An unknown material will
scratch a softer one & will
be scratched by harder
one.
EX:
•Fingernail-(2.5)
•Gold, Silver-(2.5-3)
•Iron-(4-5)
•Glass-(6-7)
•Steel-(6-7)

47. The hardness of a metal is determined by pressing an
indenter onto the surface of the material and measuring
the size of an indentation.
The bigger the indentation the softer is the material.
Common hardness test methods are:
 Brinell Hardness
 Vicker’s Hardness
 Rockwell Hardness

49. 49
Hardness Testers

50. 1. Brinell Hardness
• Load P is pressed for 30 sec.
and the indentation diameter is
measured as d.
P
d
 
2
2
2
d
D
D
D
P



Brinell Hardness =
(kgf/mm2)

52. How to calculate hardness #?
  
2
2
d
D
D
2
/
D
P
BNH




P – load in kg
D – diameter of the ball in mm
d – diameter of indentation in mm

53. P/D2 ratio for Brinell test
Material P/D2 ~BHN
Steels and
cast iron
30 Over 100
Copper and Al
alloys
10 30-200
Pure Al 5 15-100
Tin, lead and
their alloys
1 3-20

54. Limitations of the Brinell Hardness Test
a) Sample must be ten times thicker than the indentation
depth (sample usually should be at least 3/8" thick).
b) Test is most accurate if the indentation depth is 2.5 - 5.0
mm. Adjust load to achieve this.
c) Test is no good if BHN > 650
d) Sensitivity problem

55. Advantages of the Brinell Test
 Widely used and well accepted
 Large ball gives good average reading with a single test
 Accurate
 Easy to learn and use

56. Disadvantages of the Brinell Test
 Destructive
 Non-portable
 High initial cost ($5,000)
 Error due to operator reading Brinell Microscope
(10%max)

57. Hardness and Tensile Strength
Tensile Strength = BHN x 500 [psi]

58. 2. Rockwell Hardness
• Instead of the indentation diameter,
indentation depth is measured.
• However, the surface roughness may
affect the results.
• So, an initial penetration is measured
upto some load, and the penetration
depth is measured with respect to this
depth.
ΔH = H2 – H1
P1
Initial
load
H1
P2
Final
load
H2

59. Limitations of the Rockwell Test
1) Sample must be ten times thicker than the
indentation depth (sample usually
should be at least 1/8" thick).
2) Need 3 tests (minimum) to avoid
inaccuracies due to impurities, hard spots
3) The indenter travel is limited to 100 Rockwell
points or 0.2mm.

60. Advantages of the Rockwell Test
 Widely used and well accepted
 Little operator subjectivity – direct reading
 Accurate
 Fast
 Large range of scales (plastics to steels)
 Regular surface preparation (polishing not needed)

61. Disadvantages of the Rockwell Test
 Destructive
 Non-Portable
 Initial cost ($5,000)
 Compared to Brinell the device is not as rugged and
need adjustments
 Small impressions not so representative as Brinell

62. 3. Vickers Hardness
• Instead of a sphere a conical
shaped indenter is used.
P
Top
View Indentation
d2
d1
(kgf/mm2)
2
2
1 d
d
d


Vicker’s Hardness = 2
854
.
1
d
P

63. Impact testing.

64. lzod impact test:
 A standard notched test piece is clamped in a vice at one
end.
 A heavy pendulum is allowed to strike and fracture the
testpiece after being released from a fixed height.
 The striking energy is 163 Joules .

65. lzod impact test:
 Having fractured the test piece, the pendulum
continues to swing, carrying with it a drag pointer,
which it leaves at its highest point of swing.
 The position of this indicates the amount of energy
used to fracture the test piece.

66. lzod impact test:

67. Charpy test:
 The Charpy impact test operates on the same principle as the
Izod test: There are three significant differences however:
 In the Charpy test, the test piece is held at both ends.
 The pendulum is held higher and has a striking energy of
300joules
 The pendulum strikes on the opposite side to the notch.

68. Charpy test:

69. Impact Test Specimens
Impact test specimens: (a) Charpy; (b) Izod.

70. Creep
Creep is the slow deformation of materials over time.
The amount of deformation is dependant on the load and
the time the load is applied.
High temperatures will increase the rate of creep
Very important for turbine blades.

71. Creep
When a weight is hung from a piece of lead and left for
a number of days the lead will stretch. This is said to be
creep. Problems with creep increase when the
materials are subject to high temperature or the
materials themselves have low melting points such as
lead. Creep can cause materials to fail at a stress well
below there tensile strength.

72. Fatigue
Fatigue is the failure of a material due to on/off cyclic
loading.
Example: piston in a car engine.

73. Fatigue
 Fatigue is due to the repeated loading and unloading.
 When a material is subjected to a force acting in different
directions at different times it can cause cracking. In time this
causes the material to fail at a load that is much less than its
tensile strength, this is fatigue failure. Vibration for example
is a serious cause of fatigue failure.
 Fatigue can be prevented with good design practice.
1. A smooth surface finish reduces the chance of surface
cracking.
2. Sharp corners should be avoided.
3. Corrosion should be avoided as this can cause fatigue cracks.

74. Fatigue

75. • Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches y.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.
Summary

76. Questions?