Fatigue Crack Paths 2003

The actual value r0 can be evaluated from the equation

r0

Ill-[max 6 M 0 ) r = max6” (t) —1

r0 S d0,

(45)

6.0)

6.0) _ ’

0

where t denotes time. The critical value of (7c depends on the damage state in view of

Eq. (30). In Eq. (45) we have to place the maximalvalue of ratio 6,, / 60 during a fa

tigue loading process. Considering asymptotic solution for stress fields (first, singular

term only), we can rewrite Eq. (45) in the form as follows

_ 2 Kb 2 r0 - i m a x | : W : | . (46)

—6,,(r

Let us consider uniaxial cyclic loading. N o wwe divide the cycle of fatigue loading

into five stages (Fig. 8).

5,. (Kl)

stage IV

stage III

stage 11

stage I

Figure 8. Five stages of loading in one cycle.

In the first stage, the mean value 6 n

is lower than the damage initiation threshold

value 60, thus

'0

6,, =1J-o0,,(19=0)dr< a0,

(47)

"0

0

where 60 depends on the damagestate, see Eq. (40).

In stage I (Fig. 8) there is no damagegrowth, damage zone growth and crack propaga

tion, so w ehave