Crack Paths 2006

Along the deflected segments, an effective driving force can be determined by

applying the coplanar strain energy release rate theory. Accordingly, the effective SIF

is given by:

effk

k k

(3a)

eff k

2 I2I I

and, by using Eq. 1, we obtain:

-cos

k

K

(3b)

eff

I

N o wlet us apply the Paris-Erdogan law to the periodically-kinked crack:

Im dsN K' C

(4)

where dNds = crack growth rate for the kinked crack (s = linear-piecewise coordinate

along the kinked-crack path);

I K ' = mean value of the Stress Intensity (SI) range for the

kinked crack.

The value of

I K ' is represented by the weighted average of the ModeI SI range

I K '

along the straight segments and of the effective SI range

(see Eq. 3b in terms of SI

effk'

ranges) along the deflected segments [3], that is

b a k b K a eff I ' '

-cos

'

K

K b a I '

I

(5a)

b a

and, since b a, we obtain:

cos - Considering the fact that, when the kinked crack spans a distance b a, the projected 1

' ' I I K K

(5b)

2

straight crack spans a distance

-cosba , the following relationship between the crack

growth rate for the kinked crack (dNds) and that for the projected straight crack

(dNdl)holds :

(6a)

dsN b a - cos

dl

dN

b a

and, since b a, we obtain:

dsN

dl

-cos1 2

(6b)

dN

By substituting Eqs 5b and 6b in Eq. 4, the following fatigue crack growth law in

terms of the nominal quantities dNdl and

I K ' is determined:

dNdl

m '»¼º«¬ª --cos1cos121 I

(7)

The modified expression of the Paris-Erdogan law proposed in Eq. 7 takes into account

the influence of the degree of kinking on the fatigue crack growth rate. In particular, it is

I K ' values, the crack growth rate dNdl decreases as the value of

shown that, at equal

the kinking angle increases.