Crack Paths 2012

Cgdrara/octdwkNet,h

@ _ C" (AKm - Kit”) l dn T (1-R)K/c-AK i

l

l

l

l

iiiiiil

l

l

ilii

K t h

K f c

SIF range, A K

Fig. I . Qualitative trend ofthe crack growth rate against the SIF range A Kfor metallic

material: the Paris law holds for intermediate A K values (the Klesnil andLucas

relationship [I 7] is reported).

According to such a definition, the damage model presented above and the fatigue

assessment based on the crack propagation law can be related to each other, that is, the

crack size aD related to the damage D can be determined as is described in the

following. Note that ath is the initial crack size below which the propagation does not

take place for stress amplitude lower than or equal to 06,.

After n loading cycles, the corresponding crack size a < aC can be easily obtained

from the integration of the Donahuelaw ([16], see Eq. (82)) for the Griffith problem, i.e.

for the simple case characterised by the geometric factor Y(a) I 1, Va :

2 — m 2 — m

1

2

n I —

With (DI1/C'(o'a-\/;)" for m ¢ 2 (10)

> l < 2 _ > l < 2 a 0 a

(D m - 2

where a"‘0 I a0 —a,h and a* I a —a,h (for long cracks: a* z a). The above relationship

can be rewritten as follows:

1

2

2 l 2 l 1 2 (1.3%

2 l

: _ >l< (I) m - 2 a 0

2 _ >l<

2

+ _ '

1:

. 1 _ D2

=

a c

(I)

m - 2 P

N

v

(11)

>l<

2

"1*

I a i m * * = N — — C i-DZ =N- _ { _—ah -1-D;’J = l i m * ( (I) m * 7t 0}, t ( ) 1 1 K f c

\

—

\

Q

. IN—Q-(1—D,’,")IN—

- N a L ,,-(1_D,',"): *’"*

0 f D I D or P P0

.

1—(DP0-a*C+a,h)m

N for DPIl

299