Page 322 - Materials Science and Engineering An Introduction

294 • Chapter 8 / Failure

(b) What is the fatigue limit for this alloy? stress of 2.75 MPa (400 psi). Plot the data as strain
(c) Determine fatigue lifetimes at stress amplitudes versus time, then determine the steady-state or
of 415 MPa (60,000 psi) and 275 MPa (40,000 psi). minimum creep rate. Note: The initial and instan-
taneous strain is not included.
4
(d) Estimate fatigue strengths at 2 10 and 6
5
10 cycles.
Time (min) Strain Time (min) Strain
8.25 Suppose that the fatigue data for the steel alloy 0 0.00 18 0.82
in Problem 8.24 were taken for bending–rotating
tests and that a rod of this alloy is to be used for 2 0.22 20 0.88
an automobile axle that rotates at an average 4 0.34 22 0.95
rotational velocity of 600 revolutions per minute. 6 0.41 24 1.03
Give the maximum lifetimes of continuous driving 8 0.48 26 1.12
that are allowable for the following stress levels:
10 0.55 28 1.22
(a) 450 MPa (65,000 psi)
12 0.62 30 1.36
(b) 380 MPa (55,000 psi)
14 0.68 32 1.53
(c) 310 MPa (45,000 psi) 16 0.75 34 1.77
(d) 275 MPa (40,000 psi)
8.26 Three identical fatigue specimens (denoted A, Stress and Temperature Effects
B, and C) are fabricated from a nonferrous alloy.
Each is subjected to one of the maximum–mini- 8.32 A specimen 975 mm (38.4 in.) long of an S-590
mum stress cycles listed in the following table; the alloy (Figure 8.32) is to be exposed to a tensile
frequency is the same for all three tests. stress of 300 MPa (43,500 psi) at 730 C (1350 F).
Determine its elongation after 4.0 h. Assume that
the total of both instantaneous and primary creep
Specimen S max (MPa) S min (MPa)
elongations is 2.5 mm (0.10 in.).
A 450 150 8.33 For a cylindrical S-590 alloy specimen (Figure
B 300 300 8.32) originally 14.5 mm (0.57 in.) in diameter and
C 500 200 400 mm (15.7 in.) long, what tensile load is nec-
essary to produce a total elongation of 52.7 mm
(a) Rank the fatigue lifetimes of these three (2.07 in.) after 1150 h at 650 C (1200 F)? Assume
specimens from the longest to the shortest. that the sum of instantaneous and primary creep
(b) Now, justify this ranking using a schematic elongations is 4.3 mm (0.17 in.).
S–N plot. 8.34 A cylindrical component 50 mm long con-
8.27 Cite five factors that may lead to scatter in fa- structed from an S-590 alloy (Figure 8.32) is to be
tigue life data. exposed to a tensile load of 70,000 N. What mini-
mum diameter is required for it to experience
Crack Initiation and Propagation an elongation of no more than 8.2 mm after an
exposure for 1,500 h at 650 C? Assume that the
Factors That Affect Fatigue Life sum of instantaneous and primary creep elonga-
8.28 Briefly explain the difference between fatigue tions is 0.6 mm.
striations and beachmarks in terms of (a) size and
(b) origin. 8.35 A cylindrical specimen 13.2 mm in diameter of
an S-590 alloy is to be exposed to a tensile load of
8.29 List four measures that may be taken to increase 27,000 N. At approximately what temperature will
the resistance to fatigue of a metal alloy. the steady-state creep be 10 h ?
1
3
8.36 If a component fabricated from an S-590 alloy
Generalized Creep Behavior (Figure 8.31) is to be exposed to a tensile stress of
8.30 Give the approximate temperature at which 100 MPa (14,500 psi) at 815 C (1500 F), estimate
creep deformation becomes an important con- its rupture lifetime.
sideration for each of the following metals: tin, 8.37 A cylindrical component constructed from an
molybdenum, iron, gold, zinc, and chromium.
S-590 alloy (Figure 8.31) has a diameter of 14.5 mm
8.31 The following creep data were taken on an (0.57 in.). Determine the maximum load that may
aluminum alloy at 480 C (900 F) and a constant be applied for it to survive 10 h at 925 C (1700 F).