Chapter 2: MECHANICAL PROPERTIES OF
MATERIALS
1. MECHANICAL PROPERTIES
 Physical and mechanical properties
2. STATIC STRESS
 Tension, Compression and Shear
 Stress-Strain Relationships
3. HARDNESS AND TESTING
4. DYNAMIC STRESS
 Fatigue, Creep, etc
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Mechanical Properties in
Design and Manufacturing
 Physical properties: A general method to differentiate
materials
 e.g: Density, melting point, optical property
(transparency or opaque), electrical conductivity
 Mechanical properties: Determine a material’s behavior
when subjected to mechanical stresses/ load or forces
 Properties include elastic modulus, ductility,
hardness, and various measures of strength
 Dilemma: mechanical properties desirable to the designer,
such as high strength, usually make manufacturing more
difficult
 The manufacturing engineer should appreciate the
design viewpoint
 And the designer should be aware of the manufacturing
viewpoint
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Stress-Strain Relationships




Two types of stress/ load: static and dynamics
Static stress is when forces that are applied to
material are constant.
Static stresses to which materials can be
subjected:
1. Tensile - tend to stretch the material
2. Compressive - tend to squeeze material
3. Shear – tend to slide material
Stress-strain curve - basic relationship that
describes mechanical properties for materials
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Tensile Test
Most common test for
studying stress-strain
relationship, especially
metals
In the test, a force pulls the
material, elongating it and
reducing its diameter
Figure 2.1 Tensile test: (a) tensile
force applied in (1) and (2)
resulting elongation of material
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Tensile Test Specimen
ASTM (American
Society for Testing and
Materials) specifies
preparation of test
specimen
Figure 2.2 Tensile test:
(b) typical test specimen
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Tensile Test Setup
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Tensile Test Sequence
Figure 2.3 Typical progress of a tensile test: (1) beginning of
test, no load; (2) uniform elongation and reduction of
cross-sectional area; (3) continued elongation, maximum
load reached; (4) necking begins, load begins to decrease;
and (5) fracture. If pieces are put back together as in (6),
final length can be measured.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Engineering Stress
Defined as force divided by original area:
F
e 
Ao
where e = engineering stress (tegasan kejuruteraan)
(MPa @ N/mm2),
F = applied force (N), and
Ao = original area of test specimen (mm2)
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Engineering Strain
Defined at any point in the test as
L  Lo
e
Lo
where e = engineering strain (terikan kejuruteraan) (dimensionless);
L = length at any point during elongation (mm);
Lo = original gage length (mm)
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Typical Engineering Stress-Strain Plot
Figure 2.4 Typical engineering stress-strain plot in a
tensile test of a metal.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Tensile-test Specimen and Machine
Figure 2.5 (a) A standard tensile-test specimen before and after pulling, showing
original and final gage lengths. (b) A tensile-test sequence showing different stages
in the elongation of the specimen.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Yield Point in Stress-Strain Curve
 As stress increases, a point in the linear
relationship is finally reached when the
material begins to yield
 Yield point Y can be identified by the
change in slope at the upper end of the
linear region
 Y = a strength property
 Other names for yield point = yield
strength, yield stress, and elastic limit
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Two Regions of Stress-Strain Curve
The two regions indicate two distinct forms of
behavior:
1. Elastic region
2. Plastic region
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Elastic Region in Stress-Strain Curve
 Relationship between stress and strain is
linear
 Material returns to its original length when
stress is removed
Hooke's Law:
e = E e
where E = modulus of elasticity
 E is a measure of the inherent stiffness of
a material
 Its value differs for different materials
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Plastic Region in Stress-Strain Curve
 Yield point marks the beginning of plastic
deformation
 The stress-strain relationship is no longer
guided by Hooke's Law
 As load is increased beyond Y, elongation
proceeds at a much faster rate than before,
causing the slope of the curve to change
dramatically
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Tensile Strength in Stress-Strain Curve
 Elongation is accompanied by a uniform
reduction in cross-sectional area, consistent
with maintaining constant volume
 Finally, the applied load F reaches a maximum
value, and engineering stress at this point is
called the tensile strength TS (a.k.a. ultimate
tensile strength)
Fmax
TS (UTS) =
Ao
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Ductility in Tensile Test
Ability of a material to plastically deform without
fracture
 Ductility measure = elongation EL
Lf  Lo
EL 
Lo
where EL = elongation; Lf = specimen length
at fracture; and Lo = original specimen length
Lf is measured as the distance between gage
marks after two pieces of specimen are put
back together
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
EXAMPLE
A tensile test uses a test specimen that has a
gauge length of 50 mm and an area = 200mm2.
During the test, the specimen yields under a load
of 98 kN. The corresponding gage length = 50.23
mm. This is the 0.2 % yield point. The maximum
load = 168,000 N is reached at a gauge length =
64.2 mm. Determine: (a) yield strength Y, (b)
percentage elongation (c) modulus of elasticity E,
and (d) tensile strength TS.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
True Stress
Stress value obtained by dividing the
instantaneous area into applied load
F

A
where  = true stress; F = force; and A =
actual (instantaneous) area resisting the
load
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
True Strain
Provides a more realistic assessment of
"instantaneous" elongation per unit length
L
dL
L
 
 ln
Lo
L L
o
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
True Stress-Strain Curve
Figure 2.6 - True stress-strain curve for the previous
engineering stress-strain plot in Figure 3.3.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Compression Test
Applies a load that squeezes the
ends of a cylindrical specimen
between two platens
As the specimen is compressed, its
height is reduced and its crosssectional area is increased.
Figure 2.7 Compression test:
(a) compression force applied to test
piece in (1) and (2) resulting change
in height.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Compression Test Setup
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Engineering Stress in Compression
As the specimen is compressed, its height is
reduced and cross-sectional area is
increased
e = - F
Ao
where Ao = original area of the specimen
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Engineering Strain in Compression
Engineering strain is defined
h  ho
e
ho
Since height is reduced during compression, value
of e is negative (the negative sign is usually
ignored when expressing compression strain)
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Shear Properties
Application of stresses in opposite directions on
either side of a thin element
Figure 2.8 Shear (a) stress and (b) strain.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Shear Stress and Strain
F
Shear stress defined as  
A
where F = applied force; and A = area over
which deflection occurs.
Shear strain defined as  

b
where  = deflection element; and b =
distance over which deflection occurs
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Torsion Stress-Strain Curve
Figure 2.9 Typical shear stress-strain curve from a
torsion test.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Shear Elastic Stress-Strain Relationship
In the elastic region, the relationship is defined as
  G
where G = shear modulus, or shear modulus of
elasticity
For most materials, G  0.4E, where E = elastic
modulus
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Testing of Brittle Materials
 Hard brittle materials (e.g., ceramics) possess
elasticity but little or no plasticity
 Often tested by a bending test (also called
flexure test)
 Specimen of rectangular cross-section is
positioned between two supports, and a
load is applied at its center
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Bending Test
Figure 2.10 Bending of a rectangular cross-section
results in both tensile and compressive stresses in the
material: (1) initial loading; (2) highly stressed and
strained specimen; and (3) bent part.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Bend-test Methods
Figure 2.11 Two bend-test methods for brittle materials: (a) three-point
bending; (b) four-point bending. The areas on the beams represent the
bending-movement diagrams, described in texts on mechanics of solids. Note
the region of constant maximum bending movement in (b); by contrast, the
maximum bending moment occurs only at the center of the specimen in (a).
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Hardness
 It is defined as resistance to permanent
indentation
 Good hardness generally means material is
resistant to scratching and wear
 Most tooling used in manufacturing must be
hard for scratch and wear resistance
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Hardness Tests
 Commonly used for assessing material
properties because they are quick and
convenient
 Variety of testing methods are appropriate due
to differences in hardness among different
materials
 Most well-known hardness tests are Brinell
and Rockwell
 Other test methods are also available, such as
Vickers, Knoop, Scleroscope, and durometer
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Brinell Hardness Test
Widely used for
testing metals and
nonmetals of low to
medium hardness
A hard ball is pressed
into specimen
surface with a load
of 500, 1500, or
3000 kg
Figure 2.12 Hardness testing methods: (a) Brinell
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Brinell Hardness Number
Brinell Hardness Number (BHN)
= Load divided into indentation surface area
HB 
2F
Db (Db  Db2  Di2 )
where HB = Brinell Hardness Number (BHN),
F = indentation load, kg;
Db = diameter of ball, mm, and
Di = diameter of indentation, mm
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
EXAMPLE
In a Brinell hardness test, a 1500 kg load is
pressed into a specimen using a 10 mm
diameter hardened steel ball. The resulting
indentation has a diameter of 3.2 mm.
Determine the Brinell hardness number for
the metal
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Rockwell Hardness Test
 Another widely used test
 A cone shaped indenter is pressed into
specimen using a minor load of 10 kg, thus
seating indenter in material
 Then, a major load of 150 kg is applied,
causing indenter to penetrate beyond its
initial position
 Additional penetration distance d is converted
into a Rockwell hardness reading by the
testing machine
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Rockwell Hardness Test
Figure 2.13 Hardness testing methods: (b) Rockwell:
(1) initial minor load and (2) major load.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Table 2.1: Common Rockwell Hardness Scales
Rockwell
Scale
Hardness
Symbol
Indenter
Load
(kg)
Typical Material
Tested
A
HRA
Cone
60
Carbides, ceramic
B
HRB
1.6 mm ball
100
Nonferrous metals
C
HRC
Cone
150
Ferrous metals, tool
steels
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
2.53 VICKERS HARDNESS TEST
This test, also developed in the early 1920s, uses a pyramidshaped indenter made of diamond.
It is based on the principle that impressions made by this
indenter are geometrically similar regardless of load.
1.854 F
HV 
D2
where
F = applied load (kg)
D = diagonal of the impression made
by the indenter (mm)
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
2.54 KNOOP HARDNESS TEST



Developed by F. Knoop in 1939 uses a
diamond indenter in the shape of an elongated
pyramid, with applied loads ranging generally
from 25 g to 5 kg.
Because of the light loads that are applied, it is
a microhardness test.
Therefore, it is suitable for very small or very
thin specimens and for brittle materials such
as carbides, ceramics, and glass.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Knoop Hardness Test
F
HK  14.2 2
D
where F = load (kg)
D = long diagonal of the indenter
(mm)
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Hardness-testing Methods and Formulas
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Dynamic Properties
Dynamic loadings:
 Sudden impact or loads
 Repeated cycles of loading and unloading
 Changes in the mode of loading, such as
tension to compression
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
FATIGUE
 In many engineering applications, products or
components are subjected to various
dynamic stress/ load.
 Cyclic stresses may be caused by fluctuating
mechanical load, such as on gear teeth, or by
thermal stresses, such as on a cool die
coming into repeated contact with hot
workpiece.
 Under these conditions, the part fails at a
stress level below than at which failure would
occur under static loading.
 This phenomenon is known as fatigue failure.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
CREEP
Creep is the permanent elongation of a
component under a static load maintained for
a period of time.
It is a phenomenon of metals and of certain
nonmetallic materials, such as thermoplastics
and rubber, and it can occur at any
temperature.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Creep Tests




The creep test typically consists of subjecting a
specimen to a constant tensile load at a certain
temperature and of measuring the changes in
length at various time increments.
A typical creep curve usually consists of primary,
secondary, and tertiary stages.
The specimen eventually fails by necking and
fracture, called rupture or creep rupture.
The creep rate increases with temperature and the
applied load.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Figure 2.14: Typical creep curve
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
IMPACT




A typical impact test consists of placing a
notched specimen in an impact tester and
breaking it with a swinging pendulum.
In the Charpy test, the specimen is supported at
both ends.
In the Izod test, it is supported at one end like a
cantilever beam.
Materials that have high impact resistance are
generally those that have high strength and high
ductility, and hence high toughness.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Impact Test Specimens
Figure 2.15 Impact test specimens: (a) Charpy; (b) Izod.
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
Material Failures
Figure 2.16 Schematic illustrations of types of failures in materials:
(a) necking and fracture of ductile materials; (b) buckling of ductile
materials under a compressive load; (c) fracture of brittle materials
in compression; (d) cracking on the barreled surface of ductile
materials in compression
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e
©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e