Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-09 GTBL042-Callister-v3 October 4, 2007 11:53

2nd Revised Pages

336 • Chapter 9 / Failure

70

80

60

40

50

30

20

10

0 0

103 104 105 106 107 108 109 1010

Stress amplitude,

S (MPa)

Stress amplitude

500

400

300

200

100

1045 steel

2014–T6 aluminum alloy

Red brass

Cycles to failure, N

(10

3 psi)

Figure 9.41 Stress magnitudeSversus the

logarithm of the numberNof cycles to

fatigue failure for red brass, an aluminum

alloy, and a plain carbon steel. (Adapted

from H. W. Hayden, W. G. Moffatt, and

J. Wulff,The Structure and Properties of

Materials,Vol. III,Mechanical Behavior,

p. 15. Copyright©c1965 by John Wiley &

Sons, New York. Reprinted by permission

of John Wiley & Sons, Inc. Also adapted

fromASM Handbook, Vol. 2,Properties

and Selection: Nonferrous Alloys and

Special-Purpose Materials,1990. Reprinted

by permission of ASM International.)

Temperature(◦C) Impact Energy(J)

0 105

− 25 104

− 50 103

− 75 97

− 100 63

− 113 40

− 125 34

− 150 28

− 175 25

− 200 24

(a)Plot the data as impact energy versus tem-

perature.

(b)Determine a ductile-to-brittle transition

temperature as that temperature corre-

sponding to the average of the maximum

and minimum impact energies.

(c)Determine a ductile-to-brittle transition

temperature as that temperature at which

the impact energy is 50 J.

Cyclic Stresses (Fatigue)

The S–N Curve

Fatigue in Polymeric Materials

9.10A fatigue test was conducted in which the

mean stress was 70 MPa (10,000 psi), and the

stress amplitude was 210 MPa (30,000 psi).

(a)Compute the maximum and minimum

stress levels.

(b)Compute the stress ratio.

(c)Compute the magnitude of the stress

range.

9.11A 6.4 mm (0.25 in.) diameter cylindrical rod

fabricated from a 2014-T6 aluminum alloy

(Figure 9.41) is subjected to reversed tension-

compression load cycling along its axis. If the

maximum tensile and compressive loads are

+5340 N (+1200 lbf) and−5340 N (−1200 lbf),

respectively, determine its fatigue life. Assume

that the stress plotted in Figure 9.41 is stress

amplitude.

9.12The fatigue data for a steel alloy are given as

follows:

Stress Amplitude Cycles to

[MPa(ksi)] Failure

470 (68.0) 104

440 (63.4) 3 × 104

390 (56.2) 105

350 (51.0) 3 × 105

310 (45.3) 106

290 (42.2) 3 × 106

290 (42.2) 107

290 (42.2) 108

(a)Make anS–Nplot (stress amplitude ver-

sus logarithm cycles to failure) using these

data.

(b)What is the fatigue limit for this alloy?

(c)Determine fatigue lifetimes at stress am-

plitudes of 415 MPa (60,000 psi) and 275

MPa (40,000 psi).