Page 416 - Mechanical Behavior of Materials

Section 9.1 Introduction 417

Even at stresses well below a given material’s ultimate strength, this microscopic damage can
accumulate with continued cycling until it develops into a crack or other macroscopic damage
that leads to failure of the component. This process of damage and failure due to cyclic loading
is called fatigue. Use of this term arose because it appeared to early investigators that cyclic
stresses caused a gradual, but not readily observable, change in the ability of the material to resist
stress.
Mechanical failures due to fatigue have been the subject of engineering efforts for more
than 150 years. One early study was that of W. A. J. Albert, who tested mine hoist chains
under cyclic loading in Germany around 1828. The term fatigue was used quite early, as
in an 1839 book on mechanics by J. V. Poncelet of France. Fatigue was further discussed
and studied in the mid-1800s by a number of individuals in several countries in response to
failures of components such as stagecoach and railway axles, shafts, gears, beams, and bridge
girders.
The work in Germany of August W¨ ohler, starting in the 1850s and motivated by railway axle
failures, is especially noteworthy. He began the development of design strategies for avoiding fatigue
failure, and he tested irons, steels, and other metals under bending, torsion, and axial loads. W¨ ohler
also demonstrated that fatigue was affected not only by cyclic stresses, but also by the accompanying
steady (mean) stresses. More detailed studies following W¨ ohler’s lead included those of Gerber and
Goodman on predicting mean stress effects. The early work on fatigue and subsequent efforts up to
the 1950s are reviewed in a paper by Mann (1958).
Fatigue failures continue to be a major concern in engineering design. Recall from Chapter 1
that the economic costs of fracture and its prevention are quite large, and note that an estimated 80%
of these costs involve situations where cyclic loading and fatigue are at least a contributing factor.
As a result, the annual cost of fatigue of materials to the U.S. economy is about 3% of the gross
national product (GNP), and a similar percentage is expected for other industrial nations. These
costs arise from the occurrence or prevention of fatigue failure for ground vehicles, rail vehicles,
aircraft of all types, bridges, cranes, power plant equipment, offshore oil well structures, and a wide
variety of miscellaneous machinery and equipment, including everyday household items, toys, and
sports equipment. For example, wind turbines used in power generation, Fig. 9.1, are subjected to
cyclic loads due to rotation and wind turbulence, making fatigue a critical aspect of the design of
the blade and other moving parts.
At present, there are three major approaches to analyzing and designing against fatigue
failures. The traditional stress-based approach was developed to essentially its present form by
1955. Here, analysis is based on the nominal (average) stresses in the affected region of the
engineering component. The nominal stress that can be resisted under cyclic loading is determined
by considering mean stresses and by adjusting for the effects of stress raisers, such as grooves, holes,
fillets, and keyways. Another approach is the strain-based approach, which involves more detailed
analysis of the localized yielding that may occur at stress raisers during cyclic loading. Finally,
there is the fracture mechanics approach, which specifically treats growing cracks by the methods
of fracture mechanics.
The stress-based approach is introduced in this chapter and further considered in Chapter 10,
and the fracture mechanics approach is treated in Chapter 11. Discussion of the strain-based
approach is postponed until Chapter 14, as it is necessary to first consider plastic deformation in
materials and components in Chapters 12 and 13.