Callister - An introduction - 8th edition

166 • Chapter 6 / Mechanical Properties of Metals
rise over the run, or the change in stress divided by the corresponding change
in strain; in mathematical terms,
E slope ¢s
¢ s 2 s 1
2 1
(6.10)
Inasmuch as the line segment passes through the origin, it is convenient to
take both 1 and 1 as zero. If 2 is arbitrarily taken as 150 MPa, then 2 will
have a value of 0.0016. Therefore,
1150 02 MPa
E 93.8 GPa 113.6 10 6 psi2
0.0016 0
which is very close to the value of 97 GPa (14 10 6 psi) given for brass in
Table 6.1.
(b) The 0.002 strain offset line is constructed as shown in the inset; its intersection
with the stress–strain curve is at approximately 250 MPa (36,000 psi),
which is the yield strength of the brass.
(c) The maximum load that can be sustained by the specimen is calculated
by using Equation 6.1, in which s is taken to be the tensile strength, from
Figure 6.12, 450 MPa (65,000 psi). Solving for F, the maximum load, yields
F sA 0 s a d 2
0
2 b p
1450 10 6 N/m 2 2 a 12.8 103 2
m
b p 57,900 N 113,000 lb
2
f 2
(d) To compute the change in length, l, in Equation 6.2, it is first necessary
to determine the strain that is produced by a stress of 345 MPa. This is
accomplished by locating the stress point on the stress–strain curve, point A,
and reading the corresponding strain from the strain axis, which is approximately
0.06. Inasmuch as l 0 250 mm, we have
¢l l 0 10.0621250 mm2 15 mm 10.6 in.2
ductility
Ductility
Ductility is another important mechanical property. It is a measure of the degree
of plastic deformation that has been sustained at fracture. A metal that experiences
very little or no plastic deformation upon fracture is termed brittle. The tensile
stress–strain behaviors for both ductile and brittle metals are schematically illustrated
in Figure 6.13.
Ductility may be expressed quantitatively as either percent elongation or percent
reduction in area. The percent elongation %EL is the percentage of plastic
strain at fracture, or
Ductility, as percent
elongation
%EL a l f l 0
l 0
b 100
(6.11)