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where a and c are as defined in figure 3.10. If a = c eq (3.42) reduces to

Figure 3.10. Elliptical crack

Figure 3.10. Elliptical crack eq (3.41), as should be the case. Values for <P can be found in mathematical tables or in a graph as in figure 3.11. It is possible to develop a series expansion for <f>:

Even for a ratio a/c approaching zero the third term contributes only about 5 per cent and therefore it can be neglected in most cases, yielding

3 The elastic crack-tip stress field 0.5 0.4

2c a

Figure 3.11. Surface flaw parameter

and also:

With only slight modifications eqs (3.42) and -(3-46) can be applied to semi-elliptical surface flaws and to quarter-elliptical corncr cracks (figure 3.12). Therefore the equations arc of great practical interest. It turns out that X] varies along the crack front. At the end of the minor axis (<p = n,2) the stress intensity is the largest. At the end of the major axis ((/? = ()) it is the lowest. Therefore:

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