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Materials 41
The true strain corresponding to 15 percent cold work is obtained from Eq. (2–17). Thus

A 0
ε i = ln = ln 1.176 = 0.1625
A i
Since ε i <ε u , Eqs. (2–18) and (2–19) apply. Therefore,
Answer S = σ 0 ε = 90(0.1625) 0.25 = 57.1 kpsi
m

y
i
Answer S = S u = 49.5 = 58.2 kpsi

u
1 − W 1 − 0.15

2–4 Hardness
The resistance of a material to penetration by a pointed tool is called hardness. Though
there are many hardness-measuring systems, we shall consider here only the two in
greatest use.
Rockwell hardness tests are described by ASTM standard hardness method E–18
and measurements are quickly and easily made, they have good reproducibility, and
the test machine for them is easy to use. In fact, the hardness number is read directly
from a dial. Rockwell hardness scales are designated as A, B, C,..., etc. The inden-
1
ters are described as a diamond, a -in-diameter ball, and a diamond for scales A, B,
16
and C, respectively, where the load applied is either 60, 100, or 150 kg. Thus the
Rockwell B scale, designated R B , uses a 100-kg load and a No. 2 indenter, which is
a 1 -in-diameter ball. The Rockwell C scale R C uses a diamond cone, which is the
16
No. 1 indenter, and a load of 150 kg. Hardness numbers so obtained are relative.
Therefore a hardness R C = 50 has meaning only in relation to another hardness num-
ber using the same scale.
The Brinell hardness is another test in very general use. In testing, the indenting
tool through which force is applied is a ball and the hardness number H B is found as
a number equal to the applied load divided by the spherical surface area of the inden-
tation. Thus the units of H B are the same as those of stress, though they are seldom
used. Brinell hardness testing takes more time, since H B must be computed from the
test data. The primary advantage of both methods is that they are nondestructive in
most cases. Both are empirically and directly related to the ultimate strength of the
material tested. This means that the strength of parts could, if desired, be tested part
by part during manufacture.
Hardness testing provides a convenient and nondestructive means of estimating the
strength properties of materials. The Brinell hardness test is particularly well known for
this estimation, since for many materials the relationship between the minimum
ultimate strength and the Brinell hardness number is roughly linear. The constant of
proportionality varies between classes of materials, and is also dependent on the load
used to determine the hardness. There is a wide scatter in the data, but for rough approx-
imations for steels, the relationship is generally accepted as

0.5H B kpsi
S u = (2–21)
3.4H B MPa