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272 Mechanical Engineering Design
6–2 Approach to Fatigue Failure in Analysis and Design

As noted in the previous section, there are a great many factors to be considered, even
for very simple load cases. The methods of fatigue failure analysis represent a combi-
nation of engineering and science. Often science fails to provide the complete answers
that are needed. But the airplane must still be made to fly—safely. And the automobile
must be manufactured with a reliability that will ensure a long and troublefree life and
at the same time produce profits for the stockholders of the industry. Thus, while sci-
ence has not yet completely explained the complete mechanism of fatigue, the engineer
must still design things that will not fail. In a sense this is a classic example of the true
meaning of engineering as contrasted with science. Engineers use science to solve their
problems if the science is available. But available or not, the problem must be solved,
and whatever form the solution takes under these conditions is called engineering.
In this chapter, we will take a structured approach in the design against fatigue
failure. As with static failure, we will attempt to relate to test results performed on sim-
ply loaded specimens. However, because of the complex nature of fatigue, there is
much more to account for. From this point, we will proceed methodically, and in stages.
In an attempt to provide some insight as to what follows in this chapter, a brief descrip-
tion of the remaining sections will be given here.

Fatigue-Life Methods (Secs. 6–3 to 6–6)
Three major approaches used in design and analysis to predict when, if ever, a cyclically
loaded machine component will fail in fatigue over a period of time are presented. The
premises of each approach are quite different but each adds to our understanding of the
mechanisms associated with fatigue. The application, advantages, and disadvantages of
each method are indicated. Beyond Sec. 6–6, only one of the methods, the stress-life
method, will be pursued for further design applications.

Fatigue Strength and the Endurance Limit (Secs. 6–7 and 6–8)
The strength-life (S-N) diagram provides the fatigue strength S f versus cycle life N of a
material. The results are generated from tests using a simple loading of standard laboratory-
controlled specimens. The loading often is that of sinusoidally reversing pure bending.
The laboratory-controlled specimens are polished without geometric stress concentra-
tion at the region of minimum area.
For steel and iron, the S-N diagram becomes horizontal at some point. The strength
6
at this point is called the endurance limit S and occurs somewhere between 10 and 10 7

e

cycles. The prime mark on S refers to the endurance limit of the controlled laboratory
e
specimen. For nonferrous materials that do not exhibit an endurance limit, a fatigue
strength at a specific number of cycles, S , may be given, where again, the prime denotes

f
the fatigue strength of the laboratory-controlled specimen.
The strength data are based on many controlled conditions that will not be the same
as that for an actual machine part. What follows are practices used to account for the
differences between the loading and physical conditions of the specimen and the actual
machine part.
Endurance Limit Modifying Factors (Sec. 6–9)
Modifying factors are defined and used to account for differences between the speci-
men and the actual machine part with regard to surface conditions, size, loading, tem-
perature, reliability, and miscellaneous factors. Loading is still considered to be simple
and reversing.