Section 11.4.1. Effect of Stress Concentration
The effect of stress concentration is fairly easy to estimate
for small cracks because the stress-intensity factor for an elementary crack
problem can be multiplied by the elastic stress concentration factor (kt). Example 11.4.1
illustrates this point. For longer
cracks initiating at stress concentrations, the crack will be propagating
through the stress field created by the stress concentration and the influence
of stress gradient should be taken into account. Example 11.4.2 discusses an
approximate method for estimating the stress intensity factor for a crack
moving through a stress field generated by a stress concentration.
A geometrical description of the physical problem is provided
in the figure, where a small edge crack is shown growing from the edge of a
wing cutout. The stress-intensity
factor for an edge crack (small with respect to the element width) is found in
Table 11.3.8, and is given by
A Small
Edge Crack Located at Stress Concentration
The stress term (s) in the general equation typically represents the
remote stress in the uniformly loaded edge cracked plate. This stress is also the stress that would
exist along the line of crack propagation if no crack were present. As indicated by the figure, the stress along
the line of crack propagation (assuming no crack for a moment) for the given
structural configuration is the product of the remote stress and the stress
concentration factor (kt) associated with the cutout, i.e.,
the local stress is:
For the given structural configuration, the stresses along the
line of crack propagation more closely represent the type of loading that the
small edge crack would experience if it were in a
In general, as long as one is dealing with small edge cracks in
which the width or other geometrical effects are not important, the final
equation provides a reasonable approximation to the stress-intensity factor for
an edge crack in the vicinity of a stress concentration. See Example 11.4.2
for a discussion of stress gradient effects.
EXAMPLE
11.4.2 An Edge Crack Growing
from a Stress Concentration Site
One difficulty in
utilizing the Example 11.4.1 final equation for
cracks that emanate from a stress concentration site is that the stress
concentration normally generates its own stress field. The stress concentration stress field
typically exhibits the highest stresses in the vicinity of the concentration
and these high stresses decay as a function of distance from the stress
concentration site. The question that
needs to be answered is: If the
stresses along the crack propagation path are not constant, as in the case of a
uniformly loaded edge cracked plate, what stresses should be used to estimate
the stress-intensity factor:
Distribution
of Stresses Normal to the Crack Path for a Radial Crack Growing from an
Uniaxially Loaded Hole in a Wide Plate
The stress distribution
associated with an uncracked hole in a wide plate is shown in the figure. As can be seen, the (normal) stress drops
off rapidly as a function of distance from the edge of the hole. An evaluation of the normal stress right at
the edge of the hole, i.e., the local stress, leads one to the fact that
(which is obtained by
letting R/X = 1 in the equation given in the figure). Thus kt for the uniaxially
loaded hole problem is three, i.e., kt = 3 and the stress-int ensity factor for a very small crack of length
a at the edge of the hole is
One estimate of the
stress-intensity factor for a longer crack would be given by the equation
above; but, this estimate would be high since the stresses along the crack
propagation path are noted to be dropping.