Material Properties 3
sectional area. This leads to the ‘‘corrected’’ curve in Figure 7
For some metals and alloys the region of the true stre
the onset of plastic deformation to the point at which nec
approximated by
Real Stress and Strain
!T " K # Tn
True
Stress
M%
Corrected
M
Engineering
Strain
FIGURE 7.16 A c
tensile engineerin
true stress–strain
begins at point M
curve, which corre
true curve. The ‘‘
stress–strain curv
the complex stres
neck region.
7.7 True Stress and Strain
●
169
Table 7.3 Tabulation of n and K Values (Equation 7.19) for
Several Alloys
K
Material
Low-carbon steel
(annealed)
Alloy steel
(Type 4340, annealed)
Stainless steel
(Type 304, annealed)
Aluminum (annealed)
Aluminum alloy
(Type 2024, heat treated)
Copper (annealed)
Brass
(70Cu–30Zn, annealed)
n
MPa
psi
0.26
530
77,000
0.15
640
93,000
0.45
1275
185,000
0.20
0.16
180
690
26,000
100,000
0.54
0.49
315
895
46,000
130,000
Source: From Manufacturing Processes for Engineering Materials by
Seope Kalpakjian,  1997. Reprinted by permission of Prentice-Hall,
Inc., Upper Saddle River, NJ.
In this expression, K and n are constants, which values will vary from alloy to alloy,
and will also depend on the condition of the material (i.e., whether it has been
plastically deformed, heat treated, etc.). The parameter n is often termed the strainhardening exponent and has a value less than unity. Values of n and K for several
alloys are contained in Table 7.3.
Problem
•
A steel cylinder with an original diameter of 12.8
mm is tested under tension until fracture. The
engineering fracture strength 𝝈f is found to be 460
MPa. If the cross sectional area at fracture is 10.7
mm calculate;
•
The ductility in terms of area
•
The true stress at fracture.
•
The ductility in terms of area
Ceramics
•
Previously only really looked at metal cases
Mans first materials were ceramics
in the form of stone
Non metal solid
inorganic
Mechanical Properties of
Ceramics
Chapter 7 / Mechanical Properties
Possible cross sections
F
b
d
Rectangular
Circular
Support
L
2
L
2
FIGURE 7.18 A three-point
loading scheme for measuring the
stress–strain behavior and flexural
strength of brittle ceramics,
including expressions for
computing stress for rectangular
and circular cross sections.
Flexural strength
R
! = stress = Mc
I
where M = maximum bending moment
c = distance from center of specimen
to outer fibers
I = moment of inertia of cross section
F = applied load
M
c
I
!
Rectangular
FL
4
d
2
bd 3
12
3 FL
2 bd 2
Circular
FL
4
R
#R 4
4
FL
#R 3
the moment of inertia of the cross section; these parameters are noted in Figure
7.18 for rectangular and circular cross sections. The maximum tensile stress (as
7.13 Stress–Strain Beh
FIGURE 7.19 Typical
behavior to fracture f
oxide and glass.
40
250
Stress (MPa)
Aluminum oxide
150
20
100
Stress (1 0 3 psi)
30
200
10
50
Glass
0
0
0.0 0 0 4
0.0 0 0 8
0
0.0 0 1 2
Strain
7.11 ELASTIC BEHAVIOR
The elastic stress–strain behavior for ceramic materials using these
Why So Brittle
Bonds: Ceramics are held to gather by Ionic and covalent bonds
(stronger than metallic bonds)
The measured fracture strengths for most brittle materials are
significantly lower than those predicted by theoretical calculations
based on atomic bonding energies.
Limited Slip system
Stress raisers: The effect of a stress raiser is more significant in brittle
than in ductile materials.
from the right surface of the crystal, forming an edge that is one atomic distance
wide; this is shown in Figure 8.1 c.
The process by which plastic deformation is produced by dislocation motion
is termed slip; the crystallographic plane along which the dislocation line traverses
is the slip plane, as indicated in Figure 8.1. Macroscopic plastic deformation
simply corresponds to permanent deformation that results from the movement
of dislocations, or slip, in response to an applied shear stress, as represented
in Figure 8.2 a.
Dislocation motion is analogous to the mode of locomotion employed by a
caterpillar (Figure 8.3). The caterpillar forms a hump near its posterior end by
pulling in its last pair of legs a unit leg distance. The hump is propelled forward
by repeated lifting and shifting of leg pairs. When the hump reaches the anterior
FIGURE 8.3
Representation of the analogy between caterpillar and dislocation motion.
Hardness testing
•
Measure of a materials resilience to plastic
deformation.
•
Mohs scale measures the ability to scratch a
surface with one material on another (1- talc, 10diamond).
•
•
Simple and inexpensive test, which can be
performed on any sample.
•
Non-destructive
•
Can be used to infer other properties of the
materials (i.e. other than hardness).
Rockwell Hardness test
•
The system uses spherical tungsten carbide balls as
indent ors
•
sizes are (diameter)
•
1.588 mm
•
3.175 mm
•
6.350 mm
•
12.70 mm
•
Also used is the Brale, a conical diamond indenter
Scale Symbol
A
B
C
D
E
F
G
H
K
7.16 Hardness
The Scales
Table 7.5a
Rockwell Hardness Scales
●
179
Table 7.5b
Indenter
Major Load (kg)
Diamond
!"# in. ball
Diamond
Diamond
$% in. ball
!"# in. ball
!"# in. ball
$% in. ball
$% in. ball
60
100
150
100
100
60
150
60
150
Superficial Rockwell Hardness Scales
Scale Symbol
Indenter
Major Load (kg)
Scale Symbol
Indenter
Major Load (kg)
A
B
C
D
E
F
G
H
K
Diamond
!"# in. ball
Diamond
Diamond
$% in. ball
!"# in. ball
!"# in. ball
$% in. ball
$% in. ball
60
100
150
100
100
60
150
60
150
15N
30N
45N
15T
30T
45T
15W
30W
45W
Diamond
Diamond
Diamond
!"# in. ball
!"# in. ball
!"# in. ball
$% in. ball
$% in. ball
$% in. ball
15
30
45
15
30
45
15
30
45
Table 7.5b
Superficial Rockwell Hardness Scales
Scale Symbol
Indenter
Major Load (kg)
15N
30N
45N
15T
30T
45T
15W
30W
45W
Diamond
Diamond
Diamond
!"# in. ball
!"# in. ball
!"# in. ball
$% in. ball
$% in. ball
$% in. ball
15
30
45
15
30
45
15
30
45
The modern apparatus for making Rockwell hardness m
chapter-opening photograph for this chapter) is automated a
hardness is read directly, and each measurement requires o
The modern testing apparatus also permits a variatio
application. This variable must also be considered in interp
BRINELL HARDNESS TESTS15
In Brinell tests, as in Rockwell measurements, a hard, spher
into the surface of the metal to be tested. The diameter of
tungsten carbide) indenter is 10.00 mm (0.394 in.). Standard
500 and 3000 kg in 500-kg increments; during a test, the load
●
Hardness Testing Techniques
Shape of Indentation
Test
Brinell
Indenter
Side View
10-mm sphere
of steel or
tungsten carbide
D
Vickers
microhardness
Diamond
pyramid
Knoop
microhardness
Diamond
pyramid
a
#
Diamond
cone
!"#, $%, $&, $' in.
diameter
steel spheres
Load
P
d
HB !
2P
! D [D " ! D 2 " d 2 ]
d
1 3 6#
d1
t
l/b = 7.1 1
b/t = 4.0 0
Rockwell and
Superficial
Rockwell
Top View
Formula for
Hardness Number a
1 2 0#
d1
P
HV ! 1.854P / d 21
b
P
HK ! 14.2P / l 2
l
"
"
60 kg
100 kg Rockwell
150 kg
15 kg
30 kg Superficial Rockwell
45 kg
For the hardness formulas given, P (the applied load) is in kg, while D, d, d1 , and l are all in mm.
Source: Adapted from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior. Copyright  1965 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.
Chapter 7 / Mechanical Properties
Table 7.4
178
Other tests
7.18 Tear Strength and Hardness of Polymers
FIGURE 7.30
Comparison of several
hardness scales.
(Adapted from G. F.
Kinney, Engineering
Properties and
Applications of Plastics,
p. 202. Copyright
 1957 by John
Wiley & Sons, New
York. Reprinted by
permission of John
Wiley & Sons, Inc.)
1 0,0 0 0
10
Diamond
5,0 0 0
2,0 0 0
1,0 0 0
80
1000
800
600
60
500
300
200
100
100
20
200
100
80
0
60
Rockwell
C
40
20
0
Knoop
hardness
50
Cutting tools
Rockwell
B
20
9
8
Topaz
7
Quartz
6
Orthoclase
5
Apatite
4
3
Fluorite
Calcite
2
Gypsum
1
Talc
File hard
40
110
400
Nitrided steels
Corundum
or
sapphire
Easily
machined
steels
Brasses
and
aluminum
alloys
Most
plastics
10
5
Brinell
hardness
7.17 HARDNESS
OF
CERAMIC MATERIALS
Mohs
hardness
●
181
Questions on Material Properties
Material
Yield
Strength!
(MPa)
Tensile
Strength
(MPa)
Strain at
Facture
Fracture
Strength!
(MPa)
Elastic
Modulus
(MPa)
A
310
340
0.23
265
210
B
100
120
0.4
105
150
C
415
550
0.15
500
310
D
700
850
0.14
720
210
E
Fractures
Before
Yielding
650
350
Which is hardest ?