Fatigue Crack Paths 2003

This differs from the original formulation of Seweryn and Mroz [1] where the form

(0'c — G0) was used. Introduce the ratio 0': / 6: = 17 and assume that

77:6: : 60 : Klth :Kltih.

(31)

>1<

6 0 6 c K 1 0 K 1 0

In view of Eqs (14), (28) and (30), the damageevolution rule takes the form

d 5 A [

K1

)dKI

(32)

n :

* W L W_ T I * '

( l _ n ) n + 1K l c ( l _ a ) n ) p K I C

In this stage the stress value 6,, increases but the values of GO and (7c decrease, accord

ing to Eqs (28) and (30). W h e n5,, reaches the critical value 6*” = 66 and K1=K16, the

crack growth process occurs, so that the condition

F c : G n_ G 0: 6 _n G c ( 1 _ 6:n 0) p

i

*

,

dl > 0

(33)

or

c=r

is satisfied.

The consistency condition for the growth crack is

dFc = d6, —doc = 0,

<11? =c dKI -<1K,,(a,)= 0.

(34)

W ehave therefore

2 K * LI-G,(1-a>,)P=0 or L

2dK

* L _ L I +poc(1—c0n)p1dc0n=0.

.

(35)

N121td0

Nl2itdo

Let us note that K1 = K1(G, I), so we have

K K dKI = a i l d d + a i l d b

(36)

8o

8!

In most cases the first term dominates as the crack growth value dl/dN is small. Then

(1K, E Mk \t'nTlda

(3 7)

where M kdepends on the geometry of the plate.

The damagegrowth during the propagation stage is decomposedinto two terms

(16, = do”, +da,,,

d6", > 0,

do", < 0

(38)

where the first term is associated with loading increment and the second is associated

with damagezone propagation so: