Page 321 - Materials Science and Engineering An Introduction

Questions and Problems • 293

(c) Determine a ductile-to-brittle transition tem- load cycling along its axis. Compute the maximum
perature as the temperature at which the impact and minimum loads that will be applied to yield a
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energy is 20 J. fatigue life of 1.0 10 cycles. Assume that data
8.15 What is the maximum carbon content possible in Figure 8.20 were taken for repeated axial ten-
for a plain carbon steel that must have an impact sion–compression tests, that stress plotted on the
energy of at least 200 J at 50 C? vertical axis is stress amplitude, and data were
taken for a mean stress of 50 MPa.
8.22 The fatigue data for a brass alloy are given as follows:
Cyclic Stresses
The S–N Curve Stress Amplitude (MPa) Cycles to Failure
8.16 A fatigue test was conducted in which the mean 170 3.7 10 4
stress was 70 MPa (10,000 psi), and the stress am- 5
plitude was 210 MPa (30,000 psi). 148 1.0 10 5
(a) Compute the maximum and minimum stress 130 3.0 10
levels. 114 1.0 10 6
(b) Compute the stress ratio. 92 1.0 10 7
(c) Compute the magnitude of the stress range. 80 1.0 10 8
8.17 A cylindrical bar of ductile cast iron is subjected 74 1.0 10 9
to reversed and rotating–bending tests; test results (a) Make an S–N plot (stress amplitude versus
(i.e., S–N behavior) are shown in Figure 8.20. If logarithm of cycles to failure) using these data.
the bar diameter is 9.5 mm, determine the maxi-
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mum cyclic load that may be applied to ensure (b) Determine the fatigue strength at 4 10
that fatigue failure will not occur. Assume a factor cycles.
of safety of 2.25 and that the distance between (c) Determine the fatigue life for 120 MPa.
loadbearing points is 55.5 mm.
8.23 Suppose that the fatigue data for the brass alloy
8.18 A cylindrical 4340 steel bar is subjected to in Problem 8.22 were taken from bending–rotat-
reversed rotating–bending stress cycling, which ing tests and that a rod of this alloy is to be used
yielded the test results presented in Figure 8.20. for an automobile axle that rotates at an average
If the maximum applied load is 5,000 N, compute rotational velocity of 1800 revolutions per minute.
the minimum allowable bar diameter to ensure Give the maximum bending stress amplitude pos-
that fatigue failure will not occur. Assume a factor sible for each of the following lifetimes of the rod:
of safety of 2.25 and that the distance between 1 year
loadbearing points is 55.0 mm. (a)
(b) 1 month
8.19 A cylindrical 2014-T6 aluminum alloy bar is
subjected to compression–tension stress cycling (c) 1 day
along its axis; results of these tests are shown in (d) 1 hour
Figure 8.20. If the bar diameter is 12.0 mm, cal-
culate the maximum allowable load amplitude (in 8.24 The fatigue data for a steel alloy are given as follows:
N) to ensure that fatigue failure will not occur at
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10 cycles. Assume a factor of safety of 3.0, data in Stress Amplitude [MPa (ksi)] Cycles to Failure
Figure 8.20 were taken for reversed axial tension– 470 (68.0) 10 4
compression tests, and that S is stress amplitude. 440 (63.4) 3 10 4
8.20 A cylindrical rod of diameter 6.7 mm fabricated 390 (56.2) 10 5
from a 70Cu-30Zn brass alloy is subjected to 350 (51.0) 3 10 5
rotating–bending load cycling; test results (as S–N 6
behavior) are shown in Figure 8.20. If the maximum 310 (45.3) 10
and minimum loads are +120 N and –120 N, respec- 290 (42.2) 3 10 6
tively, determine its fatigue life. Assume that the 290 (42.2) 10 7
separation between loadbearing points is 67.5 mm. 290 (42.2) 10 8
8.21 A cylindrical rod of diameter 14.7 mm fabricated
from a Ti-5Al-2.5Sn titanium alloy (Figure 8.20) (a) Make an S–N plot (stress amplitude versus
is subjected to a repeated tension–compression logarithm of cycles to failure) using these data.