Crack Paths 2012

a1’ depends on the near-field-stresses oq), oz and r(PZ as follows:

’ 2 g l z+5,l(o-i(p—o'Zz) +41‘pZ o"(p+o-Z 1

(14)~

According to this criterion the crack kinking angle (p0 occurs as soon as 0'1’ reaches

its maximu vmalue. Therefor Eq. 14 has to fulfil the following conditions:

620

I

60‘;

1

< 0

2 M 0 and ‘M

6o

(PIQ’O

After substituting the near-field equations (Eq. 3a-3f) into Eq. 14, considering 02 is

zero and differentiating partially with respect to $0, the following equation can be found

for $0:

_ 6 K 1 t a n [ &K H] [_6_ 12 t a n 2 [ & ]+]{[412_l2K11t a n [ & ]~ ]

2

2

2

¢

¢

¢

‘ [ —6 K t1 a n [_?K 0H]_[ t6 a n 2 [ ? 0 ] ] ] — t a n [ ? 0 ) .

2

2

2 —l/2

.[l+tanz{%n}~{[4KI—12KHtan[%]] +64Klzn[l+tanz[%n} = 0

In order to understand the complete crack growth behaviour for spatial-mixed-mode

case a specification of the twisting angle y/O is necessary. The twisting angle is defined

by the direction of 0'1’ and can be formulated as follows:

2T,” ($0)

1 ,

I].

[

(16).

= — a r c t a n

O-q)

_ O-Z

A comparative stress intensity factor KVInalX can be established out of Eq. 14 by

using:

: 0" 2n - r

(17)

V, m a x

1, m a x

with (0 = (00 the K Vmax results from:

225