Fatigue Crack Paths 2003

where multiplier it can be specified from the consistency condition of (9), F = 0, and

5 is a scalar measure of displacement discontinuity. Assumingthe critical stress value to

decrease with 5, a full decohesion, G6 = 0, occurs at 5 = 5c. The cohesive crack model

predicts the generation and growth of the damage zone governed by the cohesive law

(76 = (76(0) and also growth of crack occurring at 5= 5c. The application of the cohesive

crack modelto study growth of fatigue crack was presented by de Andre's et al. [14].

The concept of non-local description of crack initiation and propagation is natural

whena heterogeneous material structure is considered with randomly varying stress and

strain. The non-local values on any physical plane can be specified as follows

G.ds,.

i.

<12)

1'

r

where Sr represents the averaging area and ar(r), r = ]x — y , is the weighting function

which decreases with the distance r from the point x. The simplest case is when on, = 1

within the specified domain of size 06r and vanishes outside. Then Eq. (14) provide the

meanvalues of stresses within specified plane domains.

The formulation of Seweryn and Mroz [1, 2] followed the idea of non-local stress or

strain measures on the critical plane area of size do >< d0. Denoting the resulting shear

stress in the plane by 13, so that

r..=]1]=(1ni2+1.22f

(13>

T h elocal failure functiontakes the f o r m

6 n I n

Rf‘, = R6[

(l4)

7

6 C T C

where (7c and to are the failure stresses in tension and shear. Analogously to the analysis

of the strength of cracked body considering the microcrack opening and contact with

accompanying slip and friction cf. Mroz and Seweryn [15], the elliptic condition for

on 2 ]t'n]tang0d

and the Coulomb condition for on < ]t'n]tangod

was assumed (Fig. 1),

thus

0,5

2

2

a t n + ”

,

on 2 ]tn]tang0d

TBA

(15)

L

6 C

R 0 ‘=

[irni + G n t a ' n ( q+) fg o d)1:

6 n< ‘Tnita'ngod

T C

where (0d and (of denotes the dilatancy angle and the friction angle respectively.