Fatigue Crack Paths 2003

X2

virtual extended

crack tip

(K| i K|| )

(k| i

k|| )

’

initial crack tip

I

X1: h X1

Figure l. A kinked and curved crack.

Figure 2. Virtually extended crack.

As a consequence of the crack propagation criterion of local symmetry the SIF Kn

vanishes along the smooth crack path and the shape parameters of the natural crack ge

ometry are obtained as

ct I -21

I

2

— — b 1 T Y : { k l l+kkn1 k 2 1 + 2 H ) € + { | : k I ( 2 k 2 2 _ k 1 1 ) + — — b 1

} a

(4)

where the quantities kwkwk22 represent the effects of the far field boundary conditions

on the crack growth. If we consider a crack under local symmetryat the initial crack tip,

i.e. k11= 0, we find or I [3 I 0. Therefore the parabolic crack profile

b — 1 I(X)=1X2.i=]l+k k

(5)

l

l

2 l

21 k l

holds. In this case, the crack will propagate without kinking with a continuous deflec

tion. But in the case of a self-similar virtual crack extension of the postulated straight

crack the SIFs

— _ KI = k I +? + k l k 1 h1, KII = ? + k , k 2 1 bl _ — bll

(6)

are obtained. Finally for a selected increment Ah one obtains the following geometrical

information of the real crack path

_ 2

_ 4

A A K A K A(p=—2 ,A1=— KHAh, AaIAh 1+g H I3 H .

(7)

k,

k,

3 1r,

5 k,

It can be seen that under the local symmetry criterion Kn = 0 the change of the slope