Crack Paths 2009

1

2

1

h

E — D ( l 1 )1 _ / l/2 D 0 1 1) _ / 3/2

8

ll,slant

7: a

‘1'

1

(

x a ) ‘1'

2 (

x a )

( )

h22,slant 5.‘

_ . x a

D 1 0 2 )( 1 _X / d ) 1 /‘1'2 D 5 2 2 ) — x / a ) 3 / 2 ]

with the coefficients D which can be represented for (p < 7t/4 by

of“) I 0.568 +1.48o2 + 1.05 a“,

D5“) I

<10)

of”) I 0.568 + 0.587 a2 + 0.34440“,

D?” I 0284 + (1096M2 — 086M‘ (11>

with (p in radian. The mixed weight functions for (p < 7t/6 are given in [4]. They read for

small angles of rp§30°

11mm, 5 I ll(0.942,/1 I x/a I0.411(1 I x/a)3/2)¢)

(12)

7Z'Cl

2 ( 3 / 2 71mm, 5 I l— 0.689\/1— x/a +1.2501(1I x/a) )o

(13)

7Z'Cl

Stress intensity factors for the kink crack

Since the tangent to the real crack and the auxiliary straight crack include a finite angle

,6, a kink stress intensity factor has to be added, i.e.

K L k i n k: K L s l a n t g l+l K l L s l a n t g l 2

KlLkink : KLslant 321 + Kll,slantg22

(15)

using the functions gij according to [2]

8n I ¢Os3(fl/2)

(16a)

812 I —3sin(fl/2)¢0s2(fl/2)

(16b)

821 I Sin(fl/2)COS2(fl/2)

(16c)

g22 Icos(,B/2)(1—3sin2(,B/2))

(16d)

618