Fatigue Crack Paths 2003

do

L 1 2K 0,, = i Gndr = ‘ M 1 ,

(27)

d0

N/21td0

0

where K1 is the stress intensity factor for modeI. Let us note that 5,, is twice as large as

the stress value at the end of damagezone.

The cycle of fatigue loading we divide into four stages (Fig. 3).

5.1m.)

stage III

stage IV

o'0

da—),,=0

stage 11

til I 0

(Klth< KI< Klc)

stage I

w

1

Figure 3. Consecutive stages in one loading cycle.

W h e nthe stress in a cycle increases from zero, in the stage I there is no damage

growth as 5,, < GO and K 1

values. Let us note that both 60 and Km1 depend on the damagestate, thus

* i (7 = 6 (1_C0 )p:

Klth :Kl‘ll'i(l_6n)p

(28)

O

O

n

where G: and K[1h are the respective values for the undamagedmaterial.

In the second stage 60 < 5” < Go, the damagegrowth occurs in the zone 9, accord

ing to the following rule

L i _ ” (1*

i

i

C ' s - 0 ' O 0'C — U 0

d o ):” wA %

7 d 6 >"0 7 o-Vl > 6 0 ’

and w ehave

66 = G : ( l — 5 n ) p , K1c :KI*c(l_6n)p

(30)

where G: and KI: are the critical values for the undamaged material.

Let us note that in Eq. (29) the stress difference ((7: — 6 in the denominator occurs.