Section 5.5.4. Crack Shape
The most common crack shape in crack growth analysis is the
quarter-circular corner flaw at the edge of a hole. Stress-intensity factor solutions for this case are presented in
Section 11. For use in crack growth
analysis, these solutions present some additional problems. The stress-intensity factor varies along the
periphery of the crack. Since crack
growth is a function of the stress-intensity factor, crack extension also will
vary along the crack front. If this is
accounted for in a calculation, the flaw shape at a hole changes from
quarter-circular to quarter-elliptical.
For the calculation, it would be sufficient to include two
points of the crack front, e.g., the crack tip at the surface and the crack tip
at the edge of the hole. The
stress-intensity factor is calculated at these points, and the amount of crack
growth determined. There will be a
different amount of growth along the surface than along the edge of the
hole. For an initially quarter-circular
crack of size ai, the new
crack will have a size ai+Das along the surface, and a size ai+Dah
along the hole. For the next crack
growth increment the crack may be considered a quarter-elliptical flaw with
semi-axes ai+Das, and ai+Dah.
There are three reasons why the above procedure may not give
the accuracy expected for crack growth life estimating:
The variation of stress-intensity factor along a corner
flaw front at the edge of a hole is not accurately known.
The differences in stress-intensity factor cause
differences in growth and flaw shape development. If this is so, the difference in crack growth properties in the
two directions (anisotropy) should be accounted for too.
The differences in growth rates and stress-intensity
factor levels also give different retardation effects.
When the flaw size becomes equal to the plate thickness, the
flaw will become a through-thickness-crack with a curved front for which
stress-intensity solutions are readily available. Cracks usually have a tendency to quickly become
normal-through-thickness cracks once they reach the free surface (Figure 5.5.11).
Therefore, it is recommended to conservatively assume the crack to
become a normal-through-thickness-crack of a size equal to the thickness
immediately after it reaches the free surface (a = B, Figure 5.5.11).
Figure 5.5.11. Development of Flaws