1. 1
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
CHAPTER OBJECTIVES
• Show relationship of stress
and strain using experimental
methods to determine stress-
strain diagram of a specific
material
• Discuss the behavior
described in the diagram for
commonly used engineering
materials
• Discuss the mechanical properties and other test
related to the development of mechanics of
materials
2. 2
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
CHAPTER OUTLINE
1. Tension and Compression Test
2. Stress-Strain Diagram
3. Stress-Strain Behavior of Ductile and Brittle
Materials
4. Hooke’s Law
5. Strain Energy
6. Poission’s Ratio
7. Shear Stress-Strain Diagram
8. *Failure of Materials Due to Creep and Fatigue
3. 3
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
• Strength of a material can only be determined by
experiment
• One test used by engineers is the tension or
compression test
• This test is used primarily to determine the
relationship between the average normal stress
and average normal strain in common
engineering materials, such as metals, ceramics,
polymers and composites
3.1 TENSION & COMPRESSION TEST
4. 4
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Performing the tension or compression test
• Specimen of material is made into “standard”
shape and size
• Before testing, 2 small punch marks identified
along specimen’s length
• Measurements are taken of both specimen’s initial
x-sectional area A0 and gauge-length distance L0;
between the two marks
• Seat the specimen into a testing machine shown
below
3.1 TENSION & COMPRESSION TEST
5. 5
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Performing the tension or compression test
• Seat the specimen into a testing machine shown
below
3.1 TENSION & COMPRESSION TEST
• The machine will stretch
specimen at slow constant
rate until breaking point
• At frequent intervals during
test, data is recorded of the
applied load P.
6. 6
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Performing the tension or compression test
• Elongation δ = L − L0 is measured using either a
caliper or an extensometer
• δ is used to calculate the normal strain in the
specimen
• Sometimes, strain can also be read directly using
an electrical-resistance strain gauge
3.1 TENSION & COMPRESSION TEST
7. 7
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
• A stress-strain diagram is obtained by plotting the
various values of the stress and corresponding
strain in the specimen
Conventional stress-strain diagram
• Using recorded data, we can determine nominal
or engineering stress by
3.2 STRESS-STRAIN DIAGRAM
P
A0
σ =
Assumption: Stress is constant over the x-section
and throughout region between gauge points
8. 8
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional Stress-Strain Diagram
• Likewise, nominal or engineering strain is found
directly from strain gauge reading, or by
3.2 STRESS-STRAIN DIAGRAM
δ
L0
=
Assumption: Strain is constant throughout region
between gauge points
By plotting σ (ordinate) against (abscissa), we
get a conventional stress-strain diagram
9. 9
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
• Figure shows the characteristic stress-strain
diagram for steel, a commonly used material for
structural members and mechanical elements
3.2 STRESS-STRAIN DIAGRAM
10. 10
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
Elastic behavior.
• A straight line
• Stress is proportional to
strain, i.e., linearly elastic
• Upper stress limit, or
proportional limit; σpl
• If load is removed upon
reaching elastic limit,
specimen will return to its
original shape
11. 11
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
Figure 3-4
Yielding.
• Material deforms
permanently; yielding;
plastic deformation
• Yield stress, σY
• Once yield point reached, specimen continues to
elongate (strain) without any increase in load
• Note figure not drawn to scale, otherwise induced
strains is 10-40 times larger than in elastic limit
• Material is referred to as being perfectly plastic
12. 12
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
Figure 3-4
Strain hardening.
• Ultimate stress, σu
• While specimen is
elongating, its x-
sectional area will
decrease
• Decrease in area is fairly
uniform over entire gauge
length
13. 13
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
Figure 3-4
Necking.
• At ultimate stress, x-
sectional area begins to
decrease in a localized
region
• As a result, a constriction
or “neck” tends to form in
this region as specimen
elongates further
• Specimen finally breaks at fracture stress, σf
14. 14
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Conventional stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
Figure 3-4
Necking.
• Specimen finally breaks
at fracture stress, σf
15. 15
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
True stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
• Instead of using original cross-sectional area and
length, we can use the actual cross-sectional area
and length at the instant the load is measured
• Values of stress and strain thus calculated are
called true stress and true strain, and a plot of their
values is the true stress-strain diagram
16. 16
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
True stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
• In strain-hardening range, conventional σ-
diagram shows specimen supporting decreasing
load
• While true σ- diagram shows material to be
sustaining increasing stress
17. 17
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
True stress-strain diagram
3.2 STRESS-STRAIN DIAGRAM
• Although both diagrams are different, most
engineering design is done within elastic range
provided
1.Material is “stiff,” like most metals
2.Strain to elastic limit remains small
3.Error in using engineering values of σ and is
very small (0.1 %) compared to true values
18. 18
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Ductile materials
• Defined as any material that can be subjected to
large strains before it ruptures, e.g., mild steel
• Such materials are used because it is capable of
absorbing shock or energy, and if before
becoming overloaded, will exhibit large
deformation before failing
• Ductility of material is to report its percent
elongation or percent reduction in area at time of
fracture
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
19. 19
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Ductile materials
• Percent elongation is the specimen’s fracture
strain expressed as a percent
• Percent reduction in area is defined within
necking region as
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
Percent elongation =
Lf − L0
L0
(100%)
Percent reduction in area =
A0 − Af
A0
(100%)
20. 20
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Ductile materials
• Most metals do not exhibit constant yielding
behavior beyond the elastic range, e.g. aluminum
• It does not have well-defined yield point, thus it is
standard practice to define its yield strength using
a graphical procedure called the offset method
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
21. 21
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Ductile materials
Offset method to determine yield strength
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
1. Normally, a 0.2 % strain is
chosen.
2. From this point on the
axis, a line parallel to
initial straight-line portion
of stress-strain diagram is
drawn.
3. The point where this line
intersects the curve
defines the yield strength.
22. 22
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Brittle Materials
• Material that exhibit little or no yielding before
failure are referred to as brittle materials, e.g.,
gray cast iron
• Brittle materials do not have a well-defined
tensile fracture stress, since appearance of
initial cracks in a specimen is quite random
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
23. 23
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Brittle Materials
• Instead, the average fracture stress from a set of
observed tests is generally reported
3.3 STRESS-STRAIN BEHAVIOR OF DUCTILE & BRITTLE MATERIALS
24. 24
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
• E represents the constant of proportionality, also
called the modulus of elasticity or Young’s
modulus
• E has units of stress, i.e., pascals, MPa or GPa.
3.4 HOOKE’S LAW
• Most engineering materials exhibit a linear
relationship between stress and strain with the
elastic region
• Discovered by Robert Hooke in 1676 using
springs, known as Hooke’s law
σ = E
25. 25
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
• As shown above, most grades
of steel have same modulus of
elasticity, Est = 200 GPa
• Modulus of elasticity is a
mechanical property that
indicates the stiffness of a
material
• Materials that are still have
large E values, while spongy
materials (vulcanized rubber)
have low values
3.4 HOOKE’S LAW
26. 26
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
IMPORTANT
• Modulus of elasticity E, can be used only if a
material has linear-elastic behavior.
• Also, if stress in material is greater than the
proportional limit, the stress-strain diagram ceases
to be a straight line and the equation is not valid
3.4 HOOKE’S LAW
27. 27
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Strain hardening
• If a specimen of ductile material (steel) is loaded
into the plastic region and then unloaded, elastic
strain is recovered as material returns to its
equilibrium state
• However, plastic strain remains, thus material is
subjected to a permanent set
3.4 HOOKE’S LAW
28. 28
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Strain hardening
• Specimen loaded beyond yield point A to A’
• Inter-atomic forces have to be overcome to
elongate specimen elastically, these same
forces pull atoms back together when load is
removed
3.4 HOOKE’S LAW
• Since E is the same,
slope of line O’A’ is the
same as line OA
29. 29
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Strain hardening
• Load reapplied, atoms will be displaced until
yielding occurs at or near A’, and stress-strain
diagram continues along same path as before
3.4 HOOKE’S LAW
• New stress-strain
diagram has higher
yield point (A’), a result
of strain-hardening
• Specimen has a greater
elastic region and less
ductility
30. 30
2005 Pearson Education South Asia Pte Ltd
3. Mechanical Properties of Materials
Strain hardening
• As specimen is unloaded and loaded, heat or
energy may be lost
• Colored area between the curves represents lost
energy and is called mechanical hysteresis
3.4 HOOKE’S LAW
• It’s an important
consideration when
selecting materials to
serve as dampers for
vibrating structures and
equipment
