Crack Paths 2012

W e assume that G, remains approximately constant along the crack path (it is not a

strong assumption since the crack extension lengths are very small especially in fatigue,

which is easy to check a posteriori). For simplicity we note Gf = G, = G, and Gm is the

toughness of a material having the same elastic moduli but a failure corresponding to

km (the GSIF at the peak of a fatigue cycle) and we set or I klm / k1]...

To be consistent with the fatigue model derived from the Dugdale C Z M ,it is assumed

that the toughness is degraded at each cycle of a quantity A G proportional to Gm ( ,B is

an adjustable parameter), then for n cycles during the nucleation phase

Gm:Gf—nAG, if doze/*6," then Gm(1+na/3):of

(11)

According to (9), it comes

1-2,

221 -1

1 f _ *

— *

Af

Sf

with

G l-d,

22,-1

1..: —l"

Li?

A..

S..

(12)

* 1”] Au : A1 +maA12+ m j A 2; Sa :((s1+mas2)"rf+lt1+matq2of) *

k 2 k _ maziljzf1 :llf‘1 a:f,m

k l

k l

a

Where If and lm are the extension lengths derived from the coupled criterion, they are

solution to (10) where Gf and Gm successively replace G,

G s"2

I : a

“, a = ,m

13

a 6212 A,

f

( )

C C

It is important to note that the intensity of the cyclic loading occurs only through Gm.

From(12), we deduce

Hi i H. i 24.-1 A S

a = —G’”

(14)

G.

Am

Sm

Inserting in (11) leads to

453