Week 4
MECHANICAL PROPERTIES
AND TESTS
MATERIALS SCIENCE
Stress
 Stress is a measure of the intensity of the internal
forces acting within a deformable body.
 Mathematically, it is a measure of the average
force per unit area of a surface within a the body
on which internal forces act
 The SI unit for stress is Pascal (symbol Pa), which is
equivalent to one Newton (force) per square meter
(unit area).
 Three types of stresses -> Tensile; Compressive;
Shear
Mechanism of Stress (Tensile)
Strain
 Strain is deformation of a physical body under the action
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of applied forces
It is the geometrical measure of deformation
representing the relative displacement between particles
in the material body
Strain is a dimensionless quantity
Strain accounts for elongation, shortening, or volume
changes, or angular distortion
Normal stress causes normal strain (tensile or
compressive)
Shear strain is defined as the change in angle between
two originally orthogonal material lines
Types of Strains
tensile load
produces
an elongation and
positive linear
strain.
compressive load
produces contraction
and a negative linear
strain.
torsional
deformation
TENSILE TEST AND STRESS STRAIN RELATIONSHIP
Tensile Test
 Used for determining UTS,
yield strength, %age
elongation, and Young’s
Modulus of Elasticity
 The ends of a test piece are
fixed into grips. The specimen
is elongated by the moving
crosshead; load cell and
extensometer measure,
respectively, the magnitude of
the applied load and the
elongation
Stress-Strain Relationship
Important Terms (Stress-Strain Rel.)
 Elastic Limit -> Maximum
amount of stress up to which
the deformation is absolutely
temporary
 Proportionality Limit ->
Maximum stress up to which
the relationship between
stress & strain is linear.
 Hooke’s Law -> Within elastic
limit, the strain produced in a
body is directly proportional
to the stress applied.
σ=Eε
Important Terms (Stress-Strain Rel.)
 Young’s Modulus of elasticity
-> the ratio of the uniaxial
stress over the uniaxial strain
in the range of stress in which
Hooke's Law holds
 Elasticity -> the tendency of a
body to return to its original
shape after it has been
stretched or compressed
 Yield Point -> the stress at
which a material begins to
deform plastically
Important Terms (Stress-Strain Rel.)
 Plasticity -> the deformation
of a material undergoing nonreversible changes of shape in
response to applied forces
 Ultimate Strength -> It is the
maxima of the stress-strain
curve. It is the point at which
necking will start.
 Necking -> A mode of tensile
deformation where relatively
large amounts of strain
localize disproportionately in
a small region of the material
Important Terms (Stress-Strain Rel.)
 Fracture Point -> The stress
calculated immediately before
the fracture.
 Ductility -> The amount of
strain a material can endure
before failure.
 Ductility is measured by
percentage elongation or area
reduction
Important Terms (Stress-Strain Rel.)
 A knowledge of ductility is
important for two reasons:
1. It indicates to a designer the
degree to which a structure
will deform plastically
before fracture.
2. It specifies the degree of
allowable deformation
during fabrication
Engineering stress– strain behavior for Iron
at three temperatures
Resilience
 Resilience is the capacity of a material
to absorb energy when it is deformed
elastically and then, upon unloading, to
have this energy recovered
 Modulus of Resilience (Ur) is the
strain energy per unit volume required
to stress a material from an unloaded
state up to the point of yielding.
Resilience
 Assuming a linear elastic region
 For SI units, this is joules per cubic meter (J/m3,
equivalent to Pa)
 Thus, resilient materials are those having high yield
strengths and low moduli of elasticity; such alloys
would be used in spring applications
Shear and Torsional Tests
Shear Stress:
 The shear strain γ is defined as the tangent of
the strain angle θ
 Torsion is a variation of pure shear, wherein a
structural member is twisted in the manner of
the figure
 Torsional stress -> The shear stress on a
transverse cross section resulting from a
twisting action
 Torsional forces produce a rotational motion
about the longitudinal axis of one end of the
member relative to the other end
ANELASTICITY
 In most engineering materials, there also exists a
time-dependent elastic strain component.
 This time-dependent elastic behavior is known as
anelasticity
 For metals the anelastic component is normally
small and is often neglected
 For some polymeric materials its magnitude is
significant; in this case it is termed viscoelastic
behavior
EXAMPLE PROBLEM 6.1
 A piece of copper originally 305mm (12 in.) long is
pulled in tension with a stress of 276MPa
(40,000psi). If the deformation is entirely elastic,
what will be the resultant elongation?
 Magnitude of E for copper from Table 6.1 is 110GPa
Poisson’s Ratio
 Poisson’s ratio is defined as the
ratio of the lateral and axial strains
 Theoretically, Poisson’s ratio for
isotropic materials should be 1/4;
furthermore, the maximum value
for ν is 0.50
EXAMPLE PROBLEM 6.2
 A tensile stress is to be applied along the long axis of a
cylindrical brass rod that has a diameter of 10mm.
Determine the magnitude of the load required to produce a
0.0025mm change in diameter if the deformation is
entirely elastic.
For the strain in the x direction:
EXAMPLE PROBLEM 6.2
True Stress and Strain
 The decline in the stress necessary to
continue deformation past the point
M, indicates that the metal is
becoming weaker.
 Material is increasing in strength.
 True stress σT is defined as the load
F divided by the instantaneous crosssectional area Ai over which
deformation is occurring
 True strain ЄT is defined as:
True Stress and Strain
 If no volume change occurs during deformation—
that is, if
Aili = A0l0
 Then true and engineering stress and strain are
related according to
 The equations are valid only to the onset of necking;
beyond this point true stress and strain should be
computed from actual load, cross-sectional area, and
gauge length measurements
Assignment
 (a) Completely describe “Compression Test”. (b)
How is it different from Tensile test? (c) What are
the effects of Friction and Workpiece’s height-todiameter ratio on the test? (d) Derive relationship
between true stress/strain and engineering
stress/strain for compression test (also show by
stress-strain curve)
 Submission on or before 18-Oct-2012
EXAMPLE PROBLEM 6.4
 A cylindrical specimen of steel having an original diameter
of 12.8mm is tensile tested to fracture and found to have
an engineering fracture strength σf of 460MPa. If its
cross-sectional diameter at fracture is 10.7mm, determine:
(a) The ductility in terms of percent reduction in area
(b) The true stress at fracture
Ductility is computed as
EXAMPLE PROBLEM 6.4
True stress is defined by Equation
where the area is taken as the fracture area Af
However, the load at fracture must first be computed
from the fracture strength as
And the true stress is calculated as
Elastic Recovery after Plastic Deformation
 Upon release of the load during the
course of a stress–strain test, some
fraction of the total deformation is
recovered as elastic strain
 During the unloading cycle, the
curve traces a near straight-line path
from the point of unloading (point
D), and its slope is virtually parallel
to the initial elastic portion of the
curve
 The magnitude of this elastic strain,
which is regained during unloading,
corresponds to the strain recovery
Hardness
 Hardness is the property of material by virtue of
which it resists against surface indentation and
scratches.
 Macroscopic hardness is generally characterized by
strong intermolecular bonds
 Hardness is dependent upon strength and ductility
 Common examples of hard matter are diamond,
ceramics, concrete, certain metals, and superhard
materials (PcBN, PcD, etc)
Hardness Tests (BRINELL HARDNESS
TEST)
 Used for testing metals and nonmetals of low to
medium hardness
 The Brinell scale characterizes the indentation
hardness of materials through the scale of
penetration of an indenter, loaded on a material testpiece
 A hardened steel (or cemented carbide) ball of
10mm diameter is pressed into the surface of a
specimen using load of 500, 1500, or 3000 kg.
BRINELL HARDNESS TEST
where:
P = applied force (kgf)
D = diameter of indenter (mm)
d = diameter of indentation
(mm)
 The resulting BHN has
units of kg/mm2, but the
units are usually omitted in
expressing the numbers
Rockwell Hardness Test
 Rockwell test determines the hardness by measuring
the depth of penetration of an indenter under a large
load compared to the penetration made by a preload
 A cone shaped indenter or small diameter ball (D =
1.6 or 3.2mm) is pressed into a specimen using a
minor load of 10kg
 Then, a major load of 150kg is applied
 The additional penetration distance d is converted to
a Rockwell hardness reading by the testing machine.
Rockwell Hardness Test
Vickers Hardness Test
 Uses a pyramid shaped indenter made of diamond.
 It is based on the principle that impressions made by
this indenter are geometrically similar regardless of
load.
 The basic principle, as with all common measures of
hardness, is to observe the questioned material's
ability to resist plastic deformation from a standard
source.
 Accordingly, loads of various sizes are applied,
depending on the hardness of the material to be
measured
Vickers Hardness Test
Where:
F = applied load (kg)
D = Diagonal of the impression
made the indenter (mm)
The hardness number is
determined by the load over
the surface area of the
indentation and not the area
normal to the force
Knoop Hardness Test
 It is a microhardness test - a test for mechanical
hardness used particularly for very brittle materials or
thin sheets
 A pyramidal diamond point is pressed into the polished
surface of the test material with a known force, for a
specified dwell time, and the resulting indentation is
measured using a microscope
 Length-to-width ratio of the pyramid is 7:1
Knoop Hardness Test (contd…)
 The indenter shape facilitates reading the
impressions at lighter loads
 HK = Knoop hardness value; F = load (kg); D = long
diagonal of the impression (mm)
Hardness of Metals and Ceramics
Hardness of Polymers
TOUGHNESS
 It is a property of material by virtue of which it
resists against impact loads.
 Toughness is the resistance to fracture of a material
when stressed
 Mathematically, it is defined as the amount of energy
per volume that a material can absorb before
rupturing
 Toughness can be determined by measuring the area
(i.e., by taking the integral) underneath the stressstrain curve
Toughness (contd…)
 Toughness =
Where
 ε is strain
 εf is the strain upon failure
 σ is stress
The Area covered under stress
strain curve is called
toughness
Toughness (contd…)
 Toughness is measured in units of joules per cubic
meter (J/m3) in the SI system
 Toughness and Strength -> A material may be
strong and tough if it ruptures under high forces,
exhibiting high strains
 Brittle materials may be strong but with limited
strain values, so that they are not tough
 Generally, strength indicates how much force the
material can support, while toughness indicates how
much energy a material can absorb before rupture
Effect of Temperature on Properties
 Generally speaking, materials are lower in strength
and higher in ductility, at elevated temperatures
Hot Hardness
 A property used to characterize strength and
hardness at elevated temperatures is Hot Hardness
 It is the ability of a material to retain its hardness at
elevated temperatures
Numerical Problems
 Problems 6.3 to 6.9;
 6.14 to 6.23;
 6.25 to 6.33;
 6.46 to 6.48