Page 237 - Materials Science and Engineering An Introduction

Questions and Problems • 209

Elastic Properties of Materials 6.21 A cylindrical metal specimen 15.0 mm (0.59 in.)
6.15 A cylindrical specimen of steel having a di- in diameter and 150 mm (5.9 in.) long is to be
ameter of 15.2 mm (0.60 in.) and length of 250 subjected to a tensile stress of 50 MPa (7250 psi);
mm (10.0 in.) is deformed elastically in tension at this stress level, the resulting deformation will
with a force of 48,900 N (11,000 lb f ). Using be totally elastic.
the data contained in Table 6.1, determine the (a) If the elongation must be less than 0.072 mm
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following: (2.83 * 10 in.), which of the metals in Table 6.1
are suitable candidates? Why?
(a) The amount by which this specimen will elon-
gate in the direction of the applied stress. (b) If, in addition, the maximum permissible di-
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ameter decrease is 2.3 * 10 mm (9.1 * 10 in.)
(b) The change in diameter of the specimen. Will when the tensile stress of 50 MPa is applied, which
the diameter increase or decrease? of the metals that satisfy the criterion in part (a)
6.16 A cylindrical bar of aluminum 19 mm (0.75 in.) in are suitable candidates? Why?
diameter is to be deformed elastically by applica- 6.22 A cylindrical metal specimen 10.7000 mm
tion of a force along the bar axis. Using the data in diameter and 95.000 mm long is to be sub-
in Table 6.1, determine the force that produces an jected to a tensile force of 6300 N; at this force
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elastic reduction of 2.5 * 10 mm (1.0 * 10 in.) level, the resulting deformation will be totally
in the diameter. elastic.
6.17 A cylindrical specimen of a metal alloy 10 mm (a) If the final length must be less than 95.040
(0.4 in.) in diameter is stressed elastically in ten- mm, which of the metals in Table 6.1 are suitable
sion. A force of 15,000 N (3370 lb f ) produces a candidates? Why?
reduction in specimen diameter of 7 * 10 -3 mm (b) If, in addition, the diameter must be no
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(2.8 * 10 in.). Compute Poisson’s ratio for this greater than 10.698 mm while the tensile force of
material if its elastic modulus is 100 GPa (14.5 * 6300 N is applied, which of the metals that satisfy
6
10 psi). the criterion in part (a) are suitable candidates?
6.18 A cylindrical specimen of a hypothetical Why?
metal alloy is stressed in compression. If its 6.23 Consider the brass alloy for which the stress–
original and final diameters are 30.00 and strain behavior is shown in Figure 6.12. A cylin-
30.04 mm, respectively, and its final length is drical specimen of this material 10.0 mm (0.39
105.20 mm, compute its original length if the in.) in diameter and 101.6 mm (4.0 in.) long is
deformation is totally elastic. The elastic and pulled in tension with a force of 10,000 N (2250
shear moduli for this alloy are 65.5 and 25.4 lb f ). If it is known that this alloy has a value for
GPa, respectively. Poisson’s ratio of 0.35, compute (a) the specimen
6.19 Consider a cylindrical specimen of some hypo- elongation and (b) the reduction in specimen
thetical metal alloy that has a diameter of 10.0 diameter.
mm (0.39 in.). A tensile force of 1500 N (340 lb f ) 6.24 A cylindrical rod 120 mm long and having a
produces an elastic reduction in diameter of diameter of 15.0 mm is to be deformed using a
6.7 * 10 -4 mm (2.64 * 10 -5 in.). Compute the tensile load of 35,000 N. It must not experience
elastic modulus of this alloy, given that Poisson’s either plastic deformation or a diameter reduc-
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ratio is 0.35. tion of more than 1.2 * 10 mm. Of the following
materials listed, which are possible candidates?
6.20 A brass alloy is known to have a yield strength Justify your choice(s).
of 240 MPa (35,000 psi), a tensile strength of
310 MPa (45,000 psi), and an elastic modulus of
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110 GPa (16.0 * 10 psi). A cylindrical specimen Modulus of Yield
of this alloy 15.2 mm (0.60 in.) in diameter and Elasticity Strength Poisson’s
380 mm (15.0 in.) long is stressed in tension and Material (GPa) (MPa) Ratio
found to elongate 1.9 mm (0.075 in.). On the basis Aluminum alloy 70 250 0.33
of the information given, is it possible to compute Titanium alloy 105 850 0.36
the magnitude of the load necessary to produce Steel alloy 205 550 0.27
this change in length? If so, calculate the load; if
not, explain why. Magnesium alloy 45 170 0.35