Page 238 - Materials Science and Engineering An Introduction

210 • Chapter 6 / Mechanical Properties of Metals

6.25 A cylindrical rod 500 mm (20.0 in.) long and (a) Compute the magnitude of the load necessary
having a diameter of 12.7 mm (0.50 in.) is to to produce an elongation of 2.25 mm (0.088 in.).
be subjected to a tensile load. If the rod is to What will be the deformation after the load
experience neither plastic deformation nor an (b)
has been released?
elongation of more than 1.3 mm (0.05 in.) when
the applied load is 29,000 N (6500 lb f ), which 6.30 A cylindrical specimen of stainless steel having a
of the four metals or alloys listed in the follow- diameter of 12.8 mm (0.505 in.) and a gauge length
ing table are possible candidates? Justify your of 50.800 mm (2.000 in.) is pulled in tension. Use
choice(s). the load–elongation characteristics shown in the
following table to complete parts (a) through (f).

Modulus of Yield Tensile
Elasticity Strength Strength Load Length
Material (GPa) (MPa) (MPa) N lb f mm in.
Aluminum alloy 70 255 420 0 0 50.800 2.000
Brass alloy 100 345 420 12,700 2,850 50.825 2.001
Copper 110 210 275 25,400 5,710 50.851 2.002
Steel alloy 207 450 550 38,100 8,560 50.876 2.003
50,800 11,400 50.902 2.004
76,200 17,100 50.952 2.006
Tensile Properties
6.26 Figure 6.22 shows the tensile engineering stress– 89,100 20,000 51.003 2.008
strain behavior for a steel alloy. 92,700 20,800 51.054 2.010
(a) What is the modulus of elasticity? 102,500 23,000 51.181 2.015
107,800 24,200 51.308 2.020
(b) What is the proportional limit?
119,400 26,800 51.562 2.030
(c) What is the yield strength at a strain offset of
0.002? 128,300 28,800 51.816 2.040
149,700 33,650 52.832 2.080
(d) What is the tensile strength?
159,000 35,750 53.848 2.120
6.27 A cylindrical specimen of a brass alloy having a 160,400 36,000 54.356 2.140
length of 100 mm (4 in.) must elongate only 5 mm
(0.2 in.) when a tensile load of 100,000 N (22,500 159,500 35,850 54.864 2.160
lb f ) is applied. Under these circumstances, what 151,500 34,050 55.880 2.200
must be the radius of the specimen? Consider 124,700 28,000 56.642 2.230
this brass alloy to have the stress–strain behavior Fracture
shown in Figure 6.12.
6.28 A load of 140,000 N (31,500 lb f ) is applied to a (a) Plot the data as engineering stress versus en-
cylindrical specimen of a steel alloy (displaying gineering strain.
the stress–strain behavior shown in Figure 6.22)
that has a cross-sectional diameter of 10 mm (b) Compute the modulus of elasticity.
(0.40 in.). (c) Determine the yield strength at a strain offset
of 0.002.
(a) Will the specimen experience elastic and/or
plastic deformation? Why? (d) Determine the tensile strength of this alloy.
(b) If the original specimen length is 500 mm (e) What is the approximate ductility, in percent
(20 in.), how much will it increase in length when elongation?
this load is applied? (f) Compute the modulus of resilience.

6.29 A bar of a steel alloy that exhibits the stress– 6.31 A specimen of magnesium having a rectangular
strain behavior shown in Figure 6.22 is subjected cross section of dimensions 3.2 mm * 19.1 mm
3
1
to a tensile load; the specimen is 375 mm (14.8 in.) ( in. * in.) is deformed in tension. Using the
4
8
long and has a square cross section 5.5 mm (0.22 in.) load–elongation data shown in the following ta-
on a side. ble, complete parts (a) through (f).