Fatigue Crack Paths 2003

TheK6 factor is knownas tenacity of the material.

To avoid such a sequential and irregular criterion, one could adapt the Paris’ law, letting

the exponent go to infinity :

6am) : a w e )( “ S W 0 ” ,TL —> +50

(2)

llKllOo (T

So that 6a(s; T) tends to 0 with n if K(s; T) is smaller than a value linked to Kc (here

||K||O0 (T)) or could be non zero ifK(s; T) is equal to this value.

Bueckner-Rice Weight Function Theory

Let us suppose n o wthat K (s; T) is k n o w nat step T. The advance is then given by (1) or

(2). Rice[3] has shownthat the SIF at step T + 1 changes by the amount 6 K(so) given, to

the first order in the perturbation, by the formula :

6K(s0) : %PV/ % K o m a_6IoI.(S)] ) d5

(3)

where D denotes the Cartesian distance, W a function of two points so and s (which also

dependsuponthe entire geometryofthe bodyand the crack) linked to the weight function

of the crack.

A similar formula for the amount6W(s1;52) can be stated :

D 2 6W(s1, $2) I % PWV [6a(s) /— 6a**(s)] ds

(4)

J:

Formulae and (4) are legitimate for special normal advances 6a,..(s) and 6a,...(s)

that preserve the shape of the front and such that 6a,.(s0) I 6a(s0), 6a**(s1) I 6a(s1)

and 6a**(s2) I 5a(s2) so as to ensure the existence of the integrals as Cauchy principal

value (PV). Here, these advances are built from a combination of translations, rotation

and scaling (see [1] for example).

Formulae (1) or (2), (3) and (4) lead now to an iterative scheme that can be used to

deal with manykinds of propagation problems : the following part study one of these.

A P P L I C A T TI OTN H EP E R T U R BT EU DN N E L - C R A C K

Leblond [4] has shownthat a sinusoidal slightly perturbed tunnel-crack front tends to re

cover the straight configuration if the wavelength is smaller than a critical value We and

tends to develop if it is bigger than )Ic.

The idea here is to extand these results to propagation path using the procedure depict

ed above. For numerical reasons, it was difficult to study sinusoidal perturbations. Instead

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