Chapter 3: Solid Materials
Iron is taken from the earth and copper is smelted from ore.
Man puts an end to the darkness;
he searches the farthest recesses for ore in the darkness.
The Bible (Job 28:2-3)
Image: Iron flows from a blast furnace. Source:
American Iron and Steel Institute.
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
Ductile Tension Test Specimens
Figure 3.1 Ductile material from a standard
tensile test apparatus. (a) Necking; (b) failure.
©1998 McGraw-Hill
text reference: Figure 3.1, page 90
Hamrock, Jacobson and Schmid
Brittle Tension Test Specimen
Figure 3.2 Failure of a brittle material from a standard
tesile test apparatus.
©1998 McGraw-Hill
text reference: Figure 3.2, page 91
Hamrock, Jacobson and Schmid
Strength/Density Comparison
Figure 3.3 Strength/density for various materials.
©1998 McGraw-Hill
text reference: Figure 3.3, page 94
Hamrock, Jacobson and Schmid
Fiber Reinforced Composite
Figure 3.4 Cross section of
fiber reinforced composite
material.
©1998 McGraw-Hill
text reference: Figure 3.4, page 95
Hamrock, Jacobson and Schmid
Ductile - diagram
Figure 3.5 Stress-strain diagram for a ductile material.
©1998 McGraw-Hill
text reference: Figure 3.5, , page 96
Hamrock, Jacobson and Schmid
Yield Strength Definition
Figure 3.6 Typical stress-strain behavior
for ductile metal showing elastic and
plastic deformations and yield strength Sy.
©1998 McGraw-Hill
text reference: Figure 3.6, page 97
Hamrock, Jacobson and Schmid
Brittle and Ductile Metal Comparison
Figure 3.7 Typical tensile
stress-strain diagrams for brittle
and ductile metals loaded to
fracture.
©1998 McGraw-Hill
text reference: Figure 3.7, page 98
Hamrock, Jacobson and Schmid
Stress-Strain Diagram for a Ceramic
Figure 3.8 Stress-strain diagram for a ceramic in tension and in compression.
©1998 McGraw-Hill
text reference: Figure 3.8, page 99
Hamrock, Jacobson and Schmid
Composite Bar
Figure 3.9 Bending strength of bar used in Example 3.6.
©1998 McGraw-Hill
text reference: Figure 3.9, page 100
Hamrock, Jacobson and Schmid
Stress-Strain Diagram for Polymers
Figure 3.10 Stress-strain diagram for polymer below, at, and above its glass transition
temperature Tg.
©1998 McGraw-Hill
text reference: Figure 3.10, page 101
Hamrock, Jacobson and Schmid
Density of Various Materials
Figure 3.11 Density for various
metals, polymers and ceramics at
room temperature (20°C, 68°F)
[From ESDU (1984)].
©1998 McGraw-Hill
text reference: Figure 3.11, page 102
Hamrock, Jacobson and Schmid
Material
kg/m3
Dens ity, 
Metals
Aluminum and its alloysa
2.7 x 103
Aluminum tin
3.1 x 103
Babbitt, lead-based white metal
10.1 x 103
Babbitt, tin-based white metal
7.4 x 103
Brasses
8.6 x 103
Bronze, aluminum
7.5 x 103
Bronze, leaded
8.9 x 103
b
Bronze, phosphor (cast)
8.7 x 103
Bronze, porous
6.4 x 103
Copper
8.9 x 103
Copper lead
9.5 x 103
Iron, cast
7.4 x 103
Iron, porous
6.1 x 103
Iron, wrought
7.8 x 103
Magnesium alloys
1.8 x 103
c
Steels
7.8 x 103
Zinc Alloys
6.7 x 103
Polymers
Acetal (polyformaldehyde)
1.4 x 103
Nylons (polyamides)
1.14 x 103
Polyethylene, high density
0.95 x 103
Phenol formaldehyde
1.3 x 103
d
Rubber, natural
1.0 x 103
Rubber, silicone
1.8 x 103
Ceramics
Alumina (Al2 O3 )
3.9 x 103
Graphite, high strength
1.7 x 103
Silicon carbide (SiC)
2.9 x 103
Silicon nitride (Si3 N4 )
3.2 x 103
a
Structural alloys
b
Bar stock typically 8.8 x 103 kg/m3 (0.03lbm/in3.)
c
Excluding “refractory” steels
d
“Mechanical” rubber
©1998 McGraw-Hill
lbm/in3
0.097
0.11
0.36
0.27
0.31
0.27
0.32
0.31
0.23
0.32
0.34
0.27
0.22
0.28
0.065
0.28
0.24
0.051
0.041
0.034
0.047
0.036
0.065
Density for
Various
Materials
Table 3.1 Density for
various metals,
polymers, and ceramics
at room temperature
(20°C; 68°F). [From
ESDU (1984)]
0.14
0.061
0.10
0.12
text reference: Table 3.1, page 103
Hamrock, Jacobson and Schmid
Elastic Modulus for
Various Materials
Figure 3.12 Modulus of elasticity for
various metals, polymers, and
ceramics at room temperature (20°C,
68°F) [From ESDU (1984)].
©1998 McGraw-Hill
text reference: Figure 3.12, page 105
Hamrock, Jacobson and Schmid
Material
Modulus of Elas ticity, E
GPa
Mps i
Metals
Aluminum
62
Aluminum alloysa
70
Aluminum tin
63
Babbitt, lead-based white metal
29
Babbitt, tin-based white metal
52
Brasses
100
Bronze, aluminum
117
Bronze, leaded
97
Bronze, phosphor
110
Bronze, porous
60
Copper
124
Iron, grey cast
109
Iron, malleable cast
170
Iron, spheroidal graphiteb
159
Iron, porous
80
Iron, wrought
170
Magnesium alloys
41
Steel, low alloys
196
Steel, medium and high alloys
200
Steel, stainlessc
193
Steel, high speed
212
Zinc alloysd
50
Polymers
Acetal (polyformaldehyde)
2.7
Nylons (polyamides)
1.9
Polyethylene, high density
0.9
Phenol formaldehydee
7.0
Rubber, naturalf
0.004
Ceramics
Alumina (Al2 O3 )
390
Graphite
27
Cemented carbides
450
Silicon carbide (SiC)
450
Silicon nitride (Si3 N4 )
314
a
Structural alloys
b
For bearings
c
Precipitation-hardened alloys up to 211 Gpa (30 Mpsi).
d
Some alloys up to 96 Gpa (14 Mpsi).
e
Filled
f
2.5%-carbon-black “mechanical” rubber.
©1998 McGraw-Hill
9.0
10.2
9.1
4.2
7.5
14.5
17.0
14.1
16.0
8.7
18.0
15.8
24.7
23.1
11.6
24.7
5.9
28.4
29.0
28.0
30.7
7.3
0.39
0.28
0.13
1.02
0.0006
Elastic Modulus for
Various Materials
Figure 3.12 Modulus of
elasticity for various metals,
polymers, and ceramics at
room temperature (20°C;
68°F). [From ESDU (1984)]
56.6
3.9
65.3
65.3
45.5
text reference: Table 3.2, page 106
Hamrock, Jacobson and Schmid
Material
Metals
Aluminum and its alloysa
Aluminum tin
Babbitt, lead-based white metal
Babbitt, tin-based white metal
Brasses
Bronze
Bronze, porous
Copper
Copper lead
Iron, cast
Iron, porous
Iron, wrought
Magnesium alloys
Steels
Zinc alloys
Polymers
Acetal (polyformaldehyde)
Nylons (polyamides)
Polyethylene, high density
Phenol formaldehydee
Rubber
Ceramics
Alumina (Al2 O3 )
Graphite, high strength
Cemented carbides
Silicon carbide (SiC)
Silicon nitride (Si3 N4 )
a
Structural alloys
©1998 McGraw-Hill
Pois s on’s ratio, 
0.33
------0.33
0.33
0.22
0.33
--0.26
0.20
0.30
0.33
0.30
0.27
--0.40
0.35
--0.50
Poisson’s Ratio for
Various Materials
Table 3.3 Poisson’s ratio for
various metals, polymers, and
ceramics at room temperature
(20°C; 68°F). [From ESDU
(1984)]
0.28
--0.19
0.19
0.26
text reference: Table 3.3, page 107
Hamrock, Jacobson and Schmid
Thermal Condictivity
for Various Materials
Figure 3.13 Thermal conductivity for
various metals, polymers, and
ceramics at room temperature (20°C,
68°F). [From ESDU (1984)].
©1998 McGraw-Hill
text reference: Figure 3.13, page 113
Hamrock, Jacobson and Schmid
Material
Metals
Aluminum
Aluminum alloys, casta
Aluminum alloys, siliconb
Aluminum alloys, wroughtc
Aluminum tin
Babbitt, lead-based white metal
Babbitt, tin-based white metal
Brassesa
Bronze, aluminuma
Bronze, leaded
Bronze, phosphor (cast)d
Bronze, porous
Coppera
Copper lead
Iron, grey cast
Iron, spheroidal graphite
Iron, porous
Iron, wrought
Magnesium alloys
Steel, low alloyse
Steel, medium
Steel, stainlessf
Zinc alloys
Polymers
Acetal (polyformaldehyde)
Nylons (polyamides)
Polyethylene, high density
Phenol formaldehydee
Rubber, naturalf
Ceramics
Alumina (Al2 O3 )g
Graphite, high strength
Silicon carbide (SiC)
Silicon nitride (Si3 N4 )
a
At 100°C
b
At 100°C (~150 W/m-°C at 25°C)
c
20 to 100°C
d
Bar stock typically 69 W/m-°C
e
20 to 200°C
f
Typically 22W/m-°C at 200°C
g
Typically 12W/m-°C at 400°C
©1998 McGraw-Hill
Thermal Conductivity, K t
W/m-°C
Btu/ft-hr°F
209
146
170
151
180
24
56
120
50
47
50
30
170
30
50
30
28
70
110
35
30
15
110
120
84
98
87
100
14
32
69
29
27
29
17
98
17
29
17
16
40
64
20
17
8.7
64
0.24
0.25
0.5
--1.6
0.14
0.14
0.29
--0.92
25
125
15
---
14
72
8.6
---
Thermal Conductivity
for Various Materials
Table 3.4 Thermal conductivity
for various metals, polymers,
and ceramics at room
temperature (20°C; 68°F). [From
ESDU(1984)]
text reference: Table 3.4, page 114
Hamrock, Jacobson and Schmid
Thermal Expansion
Coefficient for
Various Materials
Figure 3.14 Linear thermal
expansion coefficient for various
metals, polymers, and ceramics
applied over temperature range 20 to
200°C (68 to 392°F) [From ESDU
(1984)].
©1998 McGraw-Hill
text reference: Figure 3.14, page 115
Hamrock, Jacobson and Schmid
Material
Metals
Aluminum
Aluminum alloysa
Aluminum tin
Babbitt, lead-based white metal
Babbitt, tin-based white metal
Brasses
Bronzes
Copper
Copper lead
Iron, cast
Iron, porous
Iron, wrought
Magnesium alloys
Steel, alloyb
Steel, stainless
Steel, high speed
Zinc alloys
Polymers
Thermoplasticsc
Thermosetsd
Acetal (polyformaldehyde)
Nylons (polyamides)
Polyethylene, high density
Phenol formaldehydee
Rubber, naturalf
Rubber, nitrileg
Rubber, silicone
Ceramics
Alumina (Al2 O3 )h
Graphite, high strength
Silicon carbide (SiC)
Silicon nitride (Si3 N4 )
a
Structural alloys
b
Cast alloys can be up to 15 x 10-6 /(°C)
c
Typical bearing materials
d
25 x 10-6 (°C)-1 to 80 x 10-6 (°C)-1 when reinforced
e
Mineral filled
f
Fillers can reduce coefficients
g
Varies with composition
h
0 to 200°C
©1998 McGraw-Hill
Linear Thermal Expans ion
Coefficient, a
(°C) -1
(°F) -1
23 x 10-6
24 x 10-6
24 x 10-6
20 x 10-6
23 x 10-6
19 x 10-6
18 x 10-6
18 x 10-6
18 x 10-6
11 x 10-6
12 x 10-6
12 x 10-6
27 x 10-6
11 x 10-6
17 x 10-6
11 x 10-6
27 x 10-6
12.8 x 10-6
13.3 x 10-6
13.3 x 10-6
11 x 10-6
13 x 10-6
10.6 x 10-6
10.0 x 10-6
10.0 x 10-6
10.0 x 10-6
6.1 x 10-6
6.7 x 10-6
6.7 x 10-6
15 x 10-6
6.1 x 10-6
9.5 x 10-6
6.1 x 10-6
15 x 10-6
(60-100) x 10-6
(10-80) x 10-6
90 x 10-6
100 x 10-6
126 x 10-6
(25-40) x 10-6
(80-120) x 10-6
34 x 10-6
57 x 10-6
(33-56) x 10-6
(6-44) x 10-6
50 x 10-6
56 x 10-6
70 x 10-6
(14-22) x 10-6
(44-67) x 10-6
62 x 10-6
103 x 10-6
5.0 x 10-6
1.4-4.0 x 10-6
4.3 x 10-6
3.2 x 10-6
2.8 x 10-6
0.8-2.2 x 10-6
2.4 x 10-6
1.8 x 10-6
Linear Thermal
Expansion Coefficient
for Various Materials
Table 3.5 Linear thermal
expansion coefficient for various
metals, polymers and ceramics at
room temperature (20°C; 68°F).
[From ESDU (1984)]
text reference: Table 3.5, page 116
Hamrock, Jacobson and Schmid
Specfic Heat
Capacity for
Various Materials
Figure 3.15 Specific heat capacity
for various metals, polymers, and
ceramics at room temperature
(20°C; 68°F) [From ESDU
(1984)].
©1998 McGraw-Hill
text reference: Figure 3.15, page 117
Hamrock, Jacobson and Schmid
Specific Heat Capacity for Various Materials
Material
S pecific Heat Capacity, C p
kJ/kg-°C
Btu/lb°F
Metals
Aluminum and its alloys
0.9
Aluminum tin
0.96
Babbitt, lead-based white metal
0.15
Babbitt, tin-based white metal
0.21
Brasses
0.39
Bronzes
0.38
Coppera
0.38
Copper lead
0.32
Iron, cast
0.42
Iron, porous
0.46
Iron, wrought
0.46
Magnesium alloys
1.0
Steelsb
0.45
Zinc alloys
0.4
Polymers
Thermoplastics
1.4
Thermosets
--Rubber, natural
2.0
Ceramics
Alumina (Al2 O3 )h
--Graphite
0.8
Cemented Carbides
0.7
Silicon carbide (SiC)
--Silicon nitride (Si3 N4 )
--a
Aluminum bronze up to 0.48 kJ/kg-°C (0.12 Btu/lbm-°F)
b
Rising to 0.55 kJ/kg-°C (0.13 Btu/lbm-°F) at 200°C (392 °F)
0.22
0.23
0.036
0.05
0.093
0.091
0.091
0.076
0.10
0.11
0.11
0.24
0.11
0.096
0.33
--0.48
--0.2
0.17
-----
Table 3.6 Specific heat capacity for various metals, polymer, and ceramics at
room temperature (20°C; 68°F). [From ESDU (1984)]
©1998 McGraw-Hill
text reference: Table 3.6, page 118
Hamrock, Jacobson and Schmid
Rigid Beam Assembly
Figure 3.16 Rigid beam assembly used in Example 3.12.
©1998 McGraw-Hill
text reference: Figure 3.16, page 120
Hamrock, Jacobson and Schmid
Elastic
Modulus vs.
Density
Figure 3.17 Modulus of
Elasticity plotted against
density. The heavy
envelopes enclose data for
a given class of material.
The diagonal contours show
the longitudinal wave
velocity. The guidelines of
constant E/, E1/2/ , and
E1/3/ allow selection of
materials for minimum
weight, deflection-limited
design. [From Ashby
(1992)].
©1998 McGraw-Hill
text reference: Figure 3.17, page 122
Hamrock, Jacobson and Schmid
Material Classes
Clas s
Enginering alloys
(the metals and alloys of
engineering)
Engineering polymers
(the thermoplastics and
thermosets of engineering)
Engineering ceramics
(fine ceramics capable of
load-bearing application)
©1998 McGraw-Hill
Members
Aluminum alloys
Copper alloys
Lead alloys
Magnesium alloys
Molybdenum alloys
Nickel alloys
Steels
Tin alloys
Titanium alloys
Tungsten alloys
Zinc alloys
Epoxies
Melamines
Polycarbonate
Polyester
Polyethylene, high density
Polyethylene, low density
Polyformaldehyde
Polymethylmethacrylate
Polypropylene
Polytetrafluoroethylene
Polyvinyl chloride
Alumina
Diamond
Sialons
Silicon carbide
Silicon nitride
Zirconia
S hort name
Al alloys
Cu alloys
Lead alloys
Mg alloys
Mo alloys
Ni alloys
Steels
Tin alloys
Ti alloys
W alloys
Zn alloys
EP
MEL
PC
PEST
HDPE
LDPE
PF
PMMA
PP
PTFE
PVC
Al2 O3
C
Sialons
SiC
Si3 N4
ZrO2
text reference: Table 3.7, page 123
Table 3.7 Material classes
and members and short
names of each member.
[From Ashby (1992)].
Hamrock, Jacobson and Schmid
Material Classes (cont.)
Clas s
Engineering compos ites
(the composites of
engineering practice) A
distinction is drawn
between the properties of a
ply (uniply) and a laminate
(laminates)
Porous ceramics
(traditional ceramics,
cements, rocks, and
minerals
Glas s es
(ordinary silicate glass)
Woods
Separate clusters describe
properties parallel to the
grain and normal to it and
wood products
Elastomers
(natural and artificial
rubbers)
Polymer foams
(foamed polymers of
engineering)
©1998 McGraw-Hill
Members
Carbon-fiber reinforced
polymer
Glass-fiber reinforced
polymer
Kevlar-fiber reinforced
polymer
S hort name
CFRP
Brick
Cement
Common rocks
Concrete
Porcelain
Pottery
Borosilicate glass
Soda glass
Silica
Ash
Balsa
Fir
Oak
Pine
Wood products (ply, etc.)
Natural rubber
Hard butyl rubber
Polyurethanes
Silicone rubber
Soft butyl rubber
Cork
Polyester
Polystyrene
Polyurethane
Brick
Cement
Rocks
Concrete
Pcln
Pot
B-glass
Na-glass
SiO2
Ash
Balsa
Fir
Oak
Pine
Wood products
Rubber
Hard butyl
PU
Silicone
Soft butyl
Cork
PEST
PS
PU
GFRP
KFRP
text reference: Table 3.7, page 123
Table 3.7 Material classes
and members and short
names of each member.
[From Ashby (1992)].
Hamrock, Jacobson and Schmid
Strength vs.
Density
Figure 3.18 Strength
plotted against density
(yield strength for
metals and polymers,
compressive strength
for ceramics, tear
strength for
elastomers, and tensile
strength for
composites). The
guidelines of S/,
S2/3/, and S1/2/ allow
selection of materials
for minimum-weight,
yield-limited design.
[From Ashby (1992)].
©1998 McGraw-Hill
text reference: Figure 3.18, page 125
Hamrock, Jacobson and Schmid
Elastic
Modulus vs.
Strength
Figure 3.19 Modulus
of elasticity plotted
against strength. The
design guidelines
help with the
selection of materials
for such machine
elements as springs,
knife-edges,
diaphragms, and
hinges. [From Ashby
(1992)].
©1998 McGraw-Hill
text reference: Figure 3.19, page 127
Hamrock, Jacobson and Schmid
Wear
Constant
vs. Limiting
Pressure
Figure 3.20 Archard
wear constant
plotted against
limiting pressure.
[From Ashby
(1992)].
©1998 McGraw-Hill
text reference: Figure 3.20, page 129
Hamrock, Jacobson and Schmid
Elastic
Modulus vs.
Cost x
Density
Figure 3.21 Modulus
of elasticity plotted
against cost times
density. The reference
lines help with
selection of materials
for machine elements.
[From Ashby (1992)].
©1998 McGraw-Hill
text reference: Figure 3.21, page 131
Hamrock, Jacobson and Schmid