Fatigue Crack Paths 2003

d6 = 0,

dro = 0,

dl = 0.

(48)

n

W h e nthe stress value 5,, reaches the threshold value 60, the damagegrowth process

occurs, but the zone length and crack length remain unchanged(stage II of cycle), thus

am > 0,

dro = 0,

dl = 0.

(49)

I’!

This stage is the same as the stage II in the approach presented earlier, so 6,, < Go. The

damagegrowth rule is defined by Eq. (29), the values (70 and (7c decrease according to

Eq. (30).

W h e nthe stress value 5,, reaches the critical value (7c damagezone growth process

occurs (stage III of cycle), so

a, =o:(l—@)p,

(1r, >0,

(11:0.

(50)

Except for the stress equality condition, the stable damage zone growth condition

(47) must be satisfied. The damage growth d5" depends on stress variation in zone 9

and zone length growth with the terms (dfinl) and (dfinz) according to Eq. (38). The

condition (35b) takes the form

dvnll’upA )(l-wnfj=wn(l—w..)rlpoi

di

(51)

r0

—17

The increment of the mean value 6*” depends on load increase (stress intensity factor

increase) and damagezone growth, thus

d6 = Z;dK —K "i

(52)

n

( —I

I

CombiningEqs (51) and (52) we obtain

2dK 1+ 1’

_ (1_wn)”1]=1<

O[1+

_1 (l—atn)p ]+

A

dl’

Ii (1—17)

lro

(1—17)

(53)

+a7n(1—con)”_1po:\/%d;.

v’ro

W h e nthe size r0 reaches the critical value do, the crack propagation process occurs

(stage IV of cycle). The crack propagation criterion takes the form

r0 = d0,

d6, > 0

(54)