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 a_i, the new crack will have a size a_i+Da_s along the surface, and a size a_i+Da_h along the hole.  For the next crack growth increment the crack may be considered a quarter-elliptical flaw with semi-axes a_i+Da_s, and a_i+Da_h.

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