Crack Paths 2009

xIa/R,v is the Poisson ratio,

Y(x,v):1.015[A(v)+ B(v)[1x]+ C(WKIXJZ + 0 0 % ” 4)(v)?: 1.683 +

,

—l-X

—l-X

—l-X

12'3 , C(v)I—l.089+ 14'5 , D(v)I1.068—5'568 -

B(v)I—l.025 —

7 — 5 v

7 — 5 v

7 — 5 v

It was assumed that the propagation of the fatigue crack is divided in three stages: (1)

a short crack propagation during Nainwo cycles, from initiation am, to the crack size a0,

then (ii) a small crack propagation period of Naom- cycles, from a0 to the crack size a,~,

and (iii) a long crack propagation N,,-_,

cycles, from a,- to the final crack size a. With

these three different regimes (illustrated in Figure 8b) the very quick propagation of

short crack and the quick propagation of small crack compared to long crack were

considered. From[6] the three durations of the three previous stages are :

2

(a/2-1)

2

J ?

E

(“0] _1 ,

NM, _ i 2 E[17,043]

and

N .

_a I

_

—

° Y02o'Z7t(a/2—l)

am,

r0265”

1‘ a,

2E2Y0

3 l a 3 l ;

=— I‘ 1 — x* ‘ i f Y(a,/R)3o':n' l) a, l. a :|

Y 0 : Y ( a 0a/ nR d)NTotalzNalm-ao‘l'Nao-ai‘l'Nai-a

ai-a

The previous equations were applied to our data assuming that the initial crack has a

AK,,,

length, d(), corresponding to the corner: 3;; I b;

I 1. Two cases were considered

E0 %

in Table 2, a pit of R I 4 8p m on a pre-corroded specimen with New,e,,-,,,,,,,,,,1I5.5><108

cycles and a pit with RI300p m for a specimen under sea water fl o w with a life of

1.83><108 cycles. In the first case 99.1% of the fatigue life is due to initiation. For the

second case, 9 4 % of the fatigue life was consumedby the initiation phase. One can

notice that with a high 01 and large aim/a0 one obtains similar NToml results than with a

low or and small aim/a0, that is because with a higher or the crack does not grow as far

due to the slope of the da/dNcurve in the threshold region, then aim/a0 must be larger,

and with a lower or, aim/a0 mustbe smaller. Furthermoreone can notice that an equally

appropriate approximation of the crack growth period according to [6]: NpInE2/[2(A6)2]

gives results in the sameorder comparedto NToml (Table 2 right).

Table 2.a. Hemispherical surface crack growth vs. experimental fatigue life for a first

case, for a0I9.32 um,xI3, 0:25, 100 and 200, and different aim/a0 ratios.

Case 1; 6,=360 MPa, RI48 1.1m, a= 2.4 mm, 1\I.,,,.,,,,,,,,,,,=5.5><108

cycles

1

a

aim/a0

Naint-aO

NaO-ai

Nai-a

NTotal (Cycles)

Nplcycles)

0.9

6,704

4,557,935

25

0.94

2,947

44,151

4,507,080

4,554,178

0.97

1,192

4,552,423

0.9

115,801

4,667,032

100

0.94

13,163

44,151

4,507,080

4,564,394

539,600

0.97

2,300

4,553,531

0.9

11,184,860

15,736,091

200

0.94

150,676

44,151

4,507,080

4,701,907

0.97

6404

4,557,635

629