Fatigue Crack Paths 2003

thickness, so to build a structure which is w =  7  m mby d = 5 0 m mdeep and

h = 7.9mmhigh. It is subject to a cycle bending momentwhich range is from o to

477kN× m m .Thebending load is generated by the application of linear distributed

in-plane forces (q = 56N/mm)of compression and tension at the tips of the lower

and upper skin, respectively (see Fig.4). For the numerical simulation symmetry in

the xy plane has been considered.

Figure 4: X-core: bending load

A central crack of various size has been placed in the middle plate of the top

skin which is found to sustain the most severe normal stress.

Although the model is fully mixed-mode, the relevance on modeIIIhas not been

proven yet to be signi cant, so it is ignored. The jyy contour for a crack of size

a = 5 m mis shown, the stress concentration near crack tips is clear (Fig.5). The normalized { K M a x / K o , where K o = qs Za/t are plotted for the individual deforma

tion modes against crack size in Fig. 6 (note that {KMaxII/Ko has been magni ed

of a factor of 25).

Although the skins are the elements under the most severe conditions, the concen

tration of shear stress in the webs makesworthwhile a closer investigation. Therefore

a crack ( a = 2 m m) as been placed into the upper central web, inside the stress concentration area. The resulting KMaxare normalized by Ko = M h e sZa/Ie,

where he and Ie are the thickness and the inertia momentumof an equivalent struc

ture. These results are then found, again for the individual deformation modes: {KMaxI/Ko= 0.35 and {KMaxII/Ko = 0.237.

C O N C L U S I O N

The numerical prediction of the SIF is essential to provide an e!cient analysis of

crack behaviour in modern structures such as aircraft components. The boundary

element methodhas already given good results whenapplied to simpler geometries.

Thenewchallenge is to show its exibility to adapt to more complex geometries. As