The linear elastic fracture mechanics approach to the analysis
of cracked structures depends on the calculation of stress-intensity factors (K)
for the typical crack geometries of interest.
The opening mode
stress-intensity factor can always be expressed as
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(11.2.1)
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where s is the nominal stress remote from the crack and a
is the crack size. The factor b
is a function of crack geometry and of structural geometry. Since the dimension of K is ksiÖin.
or equivalent, b
must be dimensionless. For a central
crack of length, 2a, in an infinite sheet, the stress-intensity factor
may be written
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(11.2.2)
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Comparison with Equation 11.2.1 shows that for an infinite
sheet b
is unity. Thus, b
may be considered as a correction factor relating the actual stress-intensity
factor to the central crack in an infinite sheet. The correction factors for various geometrical conditions under a
given load condition may be combined in the form of a product to account for
the increase or decrease in the stress-intensity factor.
As the linear elastic fracture mechanics approach to
engineering problems became a typical design approach, a widespread need for
stress-intensity factor solutions for typical geometries arose. This need was met by a series of handbooks
which presented available solutions in a compact format. Some of these handbooks include
·
Handbook of Stress Intensity Factor (Sih, 1973),
·
The Stress Analysis of Cracks Handbook (Tada, et al.,
1973),
·
Compendium of Stress Intensity Factors (Rooke &
Cartwright, 1976),
·
Stress Intensity Factors Handbook (Murakami, 1987)
The handbook solutions, which are typically fundamental, may be
extended to more complex cases through the principle of superposition or by
compound analysis. The handbook
solutions are also quite useful for bounding exact solutions as discussed in
Section 11.4. When the structural
geometry and loading system is fairly complicated, engineers normally resort to
numerical analysis procedures (e.g., finite element analysis) which have been
proven for their accuracy in establishing stress-intensity factors.