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276 Mechanical Engineering Design
Because of this necessity for testing, it would really be unnecessary for us to proceed
any further in the study of fatigue failure except for one important reason: the desire to
know why fatigue failures occur so that the most effective method or methods can be
used to improve fatigue strength. Thus our primary purpose in studying fatigue is to
understand why failures occur so that we can guard against them in an optimum man-
ner. For this reason, the analytical design approaches presented in this book, or in any
other book, for that matter, do not yield absolutely precise results. The results should be
taken as a guide, as something that indicates what is important and what is not impor-
tant in designing against fatigue failure.
As stated earlier, the stress-life method is the least accurate approach especially
for low-cycle applications. However, it is the most traditional method, with much
published data available. It is the easiest to implement for a wide range of design
applications and represents high-cycle applications adequately. For these reasons the
stress-life method will be emphasized in subsequent sections of this chapter.
However, care should be exercised when applying the method for low-cycle applications,
as the method does not account for the true stress-strain behavior when localized
yielding occurs.

6–5 The Strain-Life Method

The best approach yet advanced to explain the nature of fatigue failure is called by some
the strain-life method. The approach can be used to estimate fatigue strengths, but when
it is so used it is necessary to compound several idealizations, and so some uncertain-
ties will exist in the results. For this reason, the method is presented here only because
of its value in explaining the nature of fatigue.
A fatigue failure almost always begins at a local discontinuity such as a notch,
crack, or other area of stress concentration. When the stress at the discontinuity exceeds
the elastic limit, plastic strain occurs. If a fatigue fracture is to occur, there must exist
cyclic plastic strains. Thus we shall need to investigate the behavior of materials sub-
ject to cyclic deformation.
In 1910, Bairstow verified by experiment Bauschinger’s theory that the elastic lim-
its of iron and steel can be changed, either up or down, by the cyclic variations of stress. 2
In general, the elastic limits of annealed steels are likely to increase when subjected to
cycles of stress reversals, while cold-drawn steels exhibit a decreasing elastic limit.
R. W. Landgraf has investigated the low-cycle fatigue behavior of a large number
of very high-strength steels, and during his research he made many cyclic stress-strain
3
plots. Figure 6–12 has been constructed to show the general appearance of these plots
for the first few cycles of controlled cyclic strain. In this case the strength decreases
with stress repetitions, as evidenced by the fact that the reversals occur at ever-smaller
stress levels. As previously noted, other materials may be strengthened, instead, by
cyclic stress reversals.
The SAE Fatigue Design and Evaluation Steering Committee released a report in
1975 in which the life in reversals to failure is related to the strain amplitude ε/2. 4

2 L. Bairstow, “The Elastic Limits of Iron and Steel under Cyclic Variations of Stress,” Philosophical
Transactions, Series A, vol. 210, Royal Society of London, 1910, pp. 35–55.
3 R. W. Landgraf, Cyclic Deformation and Fatigue Behavior of Hardened Steels, Report no. 320, Department
of Theoretical and Applied Mechanics, University of Illinois, Urbana, 1968, pp. 84–90.
4 Technical Report on Fatigue Properties, SAE J1099, 1975.