Page 54 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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2.3 Fatigue Strength
Previous discussion is mainly about strength analysis of elements under static loads.
More often than not, machine elements are subjected to fluctuating loads and the
behaviour of an element under variable loads is entirely different from that under static
loads. The failure mode under fluctuating loads is fatigue. The stress-life, strain-life
and elastic fracture mechanics methods are currently used to analyse fatigue strength.
These methods aim to predict the life in a number of cycles to failure at a specific level
of loads. This section will only introduce the stress-life method. The latter two methods
will not be covered in this book. Interested readers can read the relevant references
[2,3,8,9].

2.3.1 The Nature of Fatigue
Most machines operate under fluctuating loads rather than static loads. Fluctuating
loads produce variable stresses, causing fatigue fracture failure after a period of ser-
vice. Contrary to static fracture failures that happen at high loads and large distortions,
fatigue fracture failures are sudden phenomena, usually at relatively low loads, giving no
warning in advance and hence are much more dangerous.
Fatigue is a progressive and localized structural damage that occurs when material is
subjected to cyclic loading. It starts with a microscopic crack at critical area with high
local stresses. The high local stresses at critical area are most likely due to geometrical
discontinuities, like keyways, holes and threads; or minute material flaws, like voids and
hard precipitated particles or fabrication faults, like tool marks, surface scratches and so
on. The microcracks under high cyclic stress may initiate and propagate to a size when
the remaining uncracked material is sufficiently weakened and can no longer support
the applied load, resulting in a sudden, rapid fracture without warning.
Figure 2.3a shows schematic fracture surface diagram due to fatigue fracture. Fatigue
fracture failure usually starts at microcrack A on the surface, propagates across most
of thecross sectionshown by thebeach marksatzone B, and finally fracture at zone
C. Although a fracture surface feature depends on loading conditions and geometri-
cal discontinuities, it typically consists of a smooth surface fatigue zone B and a rough
final fracture zone C. The smooth surface fatigue zone is the bench-marked area, devel-
oped by repeated contacting and separating of the mating crack surfaces. The rough

(a) (b)
Figure 2.3 Fracture surface diagram.