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CHAPTER 34
ENGINEERING PROPERTIES
OF METALS
James E. Stallmeyer
INTRODUCTION
The design of equipment to withstand shock and vibration requires (1) a determina-
tion of the loads and resultant stresses acting on the equipment, and (2) the selection
of a suitable material. The loads and stresses may be determined from an appropri-
ate model of the equipment as described in Chap. 41. This chapter describes some of
the considerations required to adapt the results from the model analysis to the selec-
tion of suitable materials, including such engineering properties as the stress-strain
properties of metals and metal fatigue.
The selection of an appropriate material often involves an evaluation of the types
of stress condition to which the equipment will be subjected. If a small number of
severe stresses constitute the most critical situation, the most important considera-
tion is to design the equipment for adequate strength. For equipment that will be
subjected to sustained vibration or a large number of repeated applications of a
load, fatigue strength is likely to be the critical design parameter. The relative impor-
tance of these types of loading must be determined for each application.
When strength is the primary design factor, an appropriate balance between
stress and ductility is the most important consideration. Analytical models gener-
ally indicate the maximum stress based on linear properties of the material. If non-
ductile materials are used or if permanent deformation cannot be tolerated, the
equipment must be designed in such a way that the stress does not exceed the elas-
tic limit of the material. In some cases, permanent deformation may not be accept-
able because it would cause misalignment of parts whose proper operation depends
on accurate alignment. In other cases, permanent deformation of some structural
members may be acceptable. Several empirical procedures have been developed
for these cases.
One procedure, for members subjected to bending, is to permit some predeter-
mined percentage of the cross section to yield. Ductility of the material is required
for this procedure. The permanent deformation of the member, after the load has
been removed, will be less than the maximum deflection because the core of an elas-
tic material tends to restore the member to its original shape. This procedure is not
34.1
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34.2
CHAPTER THIRTY-FOUR
easily adapted to members subjected to loading other than bending. Another proce-
dure establishes a maximum allowable stress equal to the yield point plus some
incremental percentage of the difference between the yield point and the ultimate
strength of the material. As the incremental percentage increases, the magnitude of
permanent deformation increases. Consequently, the magnitude of the incremental
percentage will depend upon the function of the particular member and the ability
to make adjustments or repairs. For bolts which are inaccessible for retightening, the
increment is generally zero. In cases where dimensional stability is important, but
some yielding can be tolerated, only a small percentage increment may be permissi-
ble. When significant yielding can be tolerated, the increment may be as much as 50
percent. For bearing surfaces or where permanent deformation is permissible, the
ultimate strength of the material may be used for design.
Design of equipment subject to vibration or repeated load applications requires a
more detailed evaluation of the stress versus time response for the life of the structure.
Three fatigue analysis procedures are available: the stress-life method, the strain-life
method, and the fracture-mechanics method. Which of the three procedures is applica-
ble will depend on the stress-time history. Knowledge of all three methods allows the
engineer to choose the most appropriate method for the specific application.
STRESS-STRAIN PROPERTIES
STATIC PROPERTIES
The important static properties are yield strength, ultimate tensile strength, elonga-
tion at failure, and reduction of area. A standard tensile test specimen, defined by
ASTM Specification A370, 1 is used to evaluate these properties. The rate of loading
and the procedure for evaluation of properties are defined in the specification.
Under dynamic loading the yield strength and the ultimate strength depend upon
the strain rate, which in turn depends upon the geometry of the structure and the
type of loading. Dynamic properties are not standardized easily. There is little infor-
mation about these properties for the wide range of available metals.
The standard tensile test provides a plot of stress versus strain from which many
of the mechanical properties may be
obtained. A typical stress-strain curve is
presented in Fig. 34.1. For materials
which are linearly elastic, the elongation
e is directly proportional to the length of
the test bar l and the stress
. The pro-
portionality constant is called the modu-
lus of elasticity E. The plot of stress
versus strain usually deviates from lin-
ear behavior at the proportional limit,
which depends on the sensitivity of the
instrumentation. Most metals can be
stressed slightly higher than the propor-
tional limit without showing permanent
deformation upon removal of the load.
This point is referred to as the elastic
limit. Mild steels exhibit a distinct yield
point, at which permanent deformation
σ
FIGURE 34.1 Typical stress-strain diagram
for a metal with a yield point.
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34.3
ENGINEERING PROPERTIES OF METALS
begins suddenly and continues with no increase in stress. For materials which exhibit
a nonlinear stress-strain relationship, the term yield strength is generally used. The
yield strength of a material is that stress which produces, on unloading, a permanent
strain of 0.002 in./in. (0.2 percent).
Beyond the yield strength, large permanent deformations occur at a reduced
modulus, the strain-hardening modulus. The strain-hardening modulus decreases at
increasing loads until the cross-sectional area of the test bar begins to decrease,
necking, at the ultimate load. Beyond this point further extension takes place with
decreasing force. This ability of the material to flow without immediate rupture is
called ductility, which is defined as the percent reduction of cross-sectional area
measured at the section of fracture. Another measure of ductility is the percent elon-
gation of the gage length. This value depends on the shape and size of the specimen
and the gage length.
Other static properties of materials find application in the design of equipment to
withstand shock and vibration. The modulus of rigidity G is the ratio of shear stress
to shear strain; it may be determined from the torsional stiffness of a thin-walled
tube of the material. The value of G for steel is 12
is the
ratio of the lateral unit strain to the normal unit strain in the elastic range of the
material. This ratio evaluates the deformation of a material that occurs perpendicu-
lar to the direction of application of load. The value of
×
10 6 lb/in. 2 . Poisson’s ratio
ν
for steel is 0.3. More com-
plete data on materials and their properties as used in machine and equipment
design are compiled in available references. 2–4 Values of the static properties of typ-
ical engineering materials are given in Tables 34.1 to 34.3. (All values of
ν
σ
, G, and E
in these and later tables may be converted to SI units by MPa
=
145 lb/in. 2 .)
TABLE 34.1
Mechanical Properties of Typical Cast Irons ( A. Vallance and V. Doughtie. 2 )
Endur-
ance
Ultimate strength
Modulus of elasticity
limit in
Elon-
Ten-
Com-
reversed
Brinell
Tension
gation
sion,
pression,
bending
hard-
and
Shear
in
lb/in. 2 ,
lb/in. 2 ,
lb/in. 2 ,
ness
compression,
lb/in. 2 ,
2 in.,
Material
σ u †
σ u
σ e
number
lb/in. 2 , E
G
%
Gray, ordinary
18,000
80,000
9,000
100–150
10–12,000,000
4,000,000
0–1
Gray, good*
24,000
100,000
12,000
100–150
12,000,000
4,800,000
0–1
16,000
Gray, high grade
30,000
120,000
15,000
100–150
14,000,000
5,600,000
0–1
Malleable, S.A.E. 32510
50,000
120,000
25,000
100–145
23,000,000
9,200,000
10
Nickel alloys:
Ni-0.75, C-3.40, Si-1.75,
32,000
120,000
16,000
200
15,000,000
6,000,000
1–2
Mn-0.55*
24,000
175
Ni-2.00, C-3.00, Si-1.10,
40,000
155,000
20,000
220
20,000,000
8,000,000
1–2
Mn-0.80*
31,000
200
Nickel-chromium alloys:
Ni-0.75, Cr-0.30, C-3.40,
32,000
125,000
16,000
200
15,000,000
6,000,000
1–2
Si-1.90, Mn-0.65
Ni-2.75, Cr-0.80, C-3.00,
45,000
160,000
22,000
300
20,000,000
8,000,000
1–2
Si-1.25, Mn -0.60
* Upper figures refer to arbitration test bars. Lower figures refer to the center of 4-in. round specimens.
† Flexure: For cast irons in bending, the modulus of rupture may be taken as 1.75
σ u (tension) for circular sec-
tions, 1.50
σ u for rectangular sections and 1.25
σ u for I and T sections.
 
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34.4
CHAPTER THIRTY-FOUR
TABLE 34.2
Mechanical Properties of Typical Carbon Steels ( A. Vallance and V. Doughtie. 2 )
Yield strength
Ten-
Endur-
sion
ance
Modulus of elasticity
and
limit
Ultimate strength
com-
in re-
Tension
Elon-
Ten-
pres-
versed
Brinell
and com-
ga-
sion,
Shear,
sion,
Shear,
bending
hard-
pression,
Shear,
tion
lb/in. 2 ,
lb/in. 2 ,
lb/in. 2 ,
lb/in. 2 ,
lb/in. 2 ,
ness
lb/in. 2 ,
lb/in. 2 ,
2 in.,
Material
σ u
σ u
σ y
σ y
σ e
number
E
G
%
Wrought iron
48,000
50,000
27,000
30,000
25,000
100
28,000,000
11,200,000 30–40
Cast steel:
Soft
60,000
42,000
27,000
16,000
26,000
110
30,000,000
12,000,000
22
Medium
70,000
49,000
31,500
19,000
30,000
120
30,000,000
12,000,000
18
Hard
80,000
56,000
36,000
21,000
34,000
130
30,000,000
12,000,000
15
SAE 1025:
Annealed
67,000
41,000
34,000
20,000
29,000
120
30,000,000
12,000,000
26
Water-quenched*
78,000
55,000
41,000
24,000
43,000
159
30,000,000
12,000,000
35
90,000
63,000
58,000
34,000
50,000
183
27
SAE 1045:
Annealed
85,000
60,000
45,000
26,000
42,000
140
30,000,000
12,000,000
20
Water-quenched*
95,000
67,000
60,000
35,000
53,000
197
30,000,000
12,000,000
28
120,000
84,000
90,000
52,000
67,000
248
15
Oil-quenched*
96,000
67,000
62,000
35,000
53,000
192
30,000,000
12,000,000
22
115,000
80,000
80,000
45,000
65,000
235
16
SAE 1095:
Annealed
110,000
75,000
55,000
33,000
52,000
200
30,000,000
12,000,000
20
Oil-quenched*
130,000
85,000
66,000
39,000
68,000
300
30,000,000
11,500,000
16
188,000
120,000
130,000
75,000
100,000
380
10
* Upper figures: steel quenched and drawn to 1300
°
F. Lower figures: steel quenched and drawn to 800
°
F.
Values for intermediate drawing temperatures may be approximated by direct interpolation.
TEMPERATURE AND STRAIN-RATE EFFECTS
The static properties of most engineering materials depend upon the testing tem-
perature. As the testing temperature is increased above room temperature, the yield
point, ultimate strength, and modulus of elasticity decrease. For example, the yield
point of structural carbon steel is about 90 percent of the room-temperature value at
400°F (204°C), 60 percent at 800°F (427°C), 50 percent at 1000°F (538°C), 20 percent
at 1300°F (704°C), and 10 percent at 1600°F (871°C). The corresponding changes for
ultimate strength are 100 percent of the room-temperature value at 400°F, 85 per-
cent at 800°F, 50 percent at 1000°F, 15 percent at 1300°F, and 10 percent at 1600°F.
Changes in the modulus of elasticity are 95 percent of the room-temperature value
at 400°F, 85 percent at 800°F, 80 percent at 1000°F, 70 percent at 1300°F, and 50 per-
cent at 1600°F. As a result of these changes in properties, the ductility is increased
significantly.
When materials are tested in temperature ranges where creep of the material
occurs, the creep strains will contribute to the inelastic deformation. The magnitude
of the creep strain increases as the speed of the test decreases. Consequently, tests at
elevated temperatures should be conducted at a constant strain rate, and the value
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34.5
ENGINEERING PROPERTIES OF METALS
TABLE 34.3 Mechanical Properties of Copper-Zinc Alloys (Brass)
( A. Vallance and V. Doughtie 2 )
Modulus of
elasticity
Elon-
Ultimate
Yield
Brinell
Tension
gation
strength
strength
Endurance
hard-
and com-
in
Tension,
Tension,
limit,
ness
pression,
2 in.,
Type of material
lb/in. 2 , σ u
lb/in. 2 , σ e
lb/in. 2 , σ e
number
lb/in. 2 , E
%
Commercial bronze
(90 Cu, 10 Zn):
Rolled, hard
65,000
63,000
18,000
107
15,000,000
18
Rolled, soft
35,000
11,000
12,000
52
15,000,000
56
Forged, cold
40,000–65,000
25,000–61,000
12,000–16,000
62–102
15,000,000
55–20
Red brass
(85 Cu, 15 Zn):
Rolled, hard
75,000
72,000
20,000
126
15,000,000
18
Rolled, soft
37,000
14,000
14,000
54
15,000,000
55
Forged, cold
42,000–62,000
22,000–54,000 14,000–18,000
63–120
15,000,000
47–20
Low brass
(80 Cu, 20 Zn):
Rolled, hard
75,000
59,000
22,000
130
15,000,000
18
Rolled, soft
44,000
12,000
15,000
56
15,000,000
65
Forged, cold
47,000–80,000
20,000–65,000
63–133
15,000,000
30–15
Spring brass
(75 Cu, 25 Zn):
Hard
84,000
64,000
21,000
107*
14,000,000
5
Soft
45,000
17,000
17,000
57*
18,000,000
58
Cartridge brass
(70 Cu, 30 Zn):
Rolled, hard
100,000
75,000
22,000
154
15,000,000
14
Rolled, soft
48,000
30,000
17,000
70
15,000,000
55
Deep-drawing brass
(68 Cu, 32 Zn):
Strip, hard
85,000
79,000
21,000
106*
15,000,000
3
Strip, soft
45,000
11,000
17,000
13*
15,000,000
55
Muntz metal
(60 Cu, 40 Zn):
Rolled, hard
80,000
66,000
25,000
151
15,000,000
20
Rolled, soft
52,000
22,000
21,000
82
15,000,000
48
Tobin bronze
(60 Cu, 39.25 Zn, 0.75 Sn):
Hard
63,000
35,000
21,000
165
15,000,000
35
Soft
56,000
22,000
90
15,000,000
45
Manganese bronze
(58 Cu, 40 Zn):
Hard
75,000
45,000
20,000
110
15,000,000
20
Soft
60,000
30,000
16,000
90
15,000,000
30
* Rockwell hardness F.
 
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