Page 291 - Marks Calculation for Machine Design

P1: Shashi
15:4
January 4, 2005
Brown.cls
Brown˙C07
CHAPTER 7
FATIGUE AND DYNAMIC
DESIGN

7.1 INTRODUCTION

A machine element may have been designed to be safe under static conditions, only to
fail under repeated dynamic loading, called a fatigue failure. This repeated loading could
be a complete reversal of the load, be a fluctuating load, or be due to a combination of
loadings. The loading may produce either normal stresses or shear stresses, or the loading
can produce a combination of both normal and shear stresses so that either by Mohr’s circle
or by the appropriate equations the principal stresses are found. All of these types of loading
conditions will be discussed in this section.
If the design of a machine element becomes unsafe under dynamic conditions, it usually
fails suddenly and below the static strengths of the material, either the yield strength (S y ) for
ductile materials or the ultimate tensile strength (S ut ) for brittle materials. It is interesting,
although not unexpected, that a brittle material would fail suddenly under either static or
dynamic conditions. Ductile materials fail as if they were brittle from excessive repeated
loading at a stress level below the yield strength (S y ). The most accepted method of deter-
mining this critical stress level will be presented shortly.
The mode of failure under dynamic conditions appears to be a result of a very small
crack, too small to see with the naked eye, developing at a point where the geometry of
the machine element changes, usually on the surface. A crack can even develop at a part
identification stamp, or at a surface scratch accidentally put on the part during assembly or
repair. Under repeated loading, this crack grows due to stress concentrations until the area
over which the load must be carried is reduced rapidly, causing the stress to increase just as
rapidly. Sudden failure, without any warning, occurs when the stress level exceeds a critical
value for a specified number of cycles. Therefore, a fatigue failure can be differentiated
visually from a static failure by the appearance of two regions on the failed part. The first
region is due to the propagation of the crack, and the second region is due to the sudden
fracture, not unlike what would be seen in the static failure of a brittle material, such as
cast iron. This is in contrast to what would be seen in the static failure of a ductile material,
where considerable yielding would be visible.
Some materials, like steel, have a critical stress value, which if never exceeded, ensure
the machine element has an infinite life. For other materials, like aluminum, there is no such
value at any number of cycles so the machine element will fail at some point no matter how
low the stress level is kept.
Thestudyoffatigueisrelativelyrecentandcommencedonlypost-WorldWarII.However,
some machines designed even in the middle-to-late nineteenth century have been operating

273

Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use.