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

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

2nd Revised Pages

9.11 Fatigue in Polymeric Materials • 319

70

60

Cycles to failure, N

(logarithmic scale)

40

50

30

20

10

400

300

200

100

Stress (10

3

psi)

Stress,

S

(MPa)

P = 0.99

P = 0.90

P = 0.50

P = 0.01

P = 0.10

104 105 106 107 108 109

Figure 9.26 Fatigue

S–Nprobability of

failure curves for a

7075-T6 aluminum

alloy;Pdenotes the

probability of failure.

(From G. M. Sinclair

and T. J. Dolan,

Trans. ASME, 75 ,

1953, p. 867.

Reprinted with

permission of the

American Society of

Mechanical

Engineers.)

Several statistical techniques have been developed to specify fatigue life and

fatigue limit in terms of probabilities. One convenient way of representing data

treated in this manner is with a series of constant probability curves, several of which

are plotted in Figure 9.26. ThePvalue associated with each curve represents the

probability of failure. For example, at a stress of 200 MPa (30,000 psi), we would

expect 1% of the specimens to fail at about 10^6 cycles and 50% to fail at about 2×

107 cycles, and so on. Remember thatS–Ncurves represented in the literature are

normally average values, unless noted otherwise.

The fatigue behaviors represented in Figures 9.25aand 9.25bmay be classified

into two domains. One is associated with relatively high loads that produce not only

elastic strain but also some plastic strain during each cycle. Consequently, fatigue

lives are relatively short; this domain is termedlow-cycle fatigueand occurs at less

than about 10^4 to 10^5 cycles. For lower stress levels wherein deformations are totally

elastic, longer lives result. This is calledhigh-cycle fatigueinasmuch as relatively

large numbers of cycles are required to produce fatigue failure. High-cycle fatigue is

associated with fatigue lives greater than about 10^4 to 10^5 cycles.

9.11 FATIGUE IN POLYMERIC MATERIALS

Polymers may experience fatigue failure under conditions of cyclic loading. As with

metals, fatigue occurs at stress levels that are low relative to the yield strength.

Fatigue testing in polymers has not been nearly as extensive as with metals; however,

fatigue data are plotted in the same manner for both types of material, and the

resulting curves have the same general shape. Fatigue curves for several common

polymers are shown in Figure 9.27, as stress versus the number of cycles to failure

(on a logarithmic scale). Some polymers have a fatigue limit. As would be expected,

fatigue strengths and fatigue limits for polymeric materials are much lower than for

metals.

The fatigue behavior of polymers is much more sensitive to loading frequency

than for metals. Cycling polymers at high frequencies and/or relatively large stresses

can cause localized heating; consequently, failure may be due to a softening of the

material rather than to typical fatigue processes.