Crack Paths 2012

a)

b)

V

K

min

min

R

V

K

max

max

Figure 2. a) KI-KII-KIII-diagram with the range of fatigue crack growth

b) Definition of the cyclic stress intensity factor ¨ Kand R-ratio

There are numerous hypotheses and concepts for plane- and spatial-mixed-mode

problems, which will be described in the following.

EXISTIN2GD- A N D3 D - M I X E D - M OCDREITERIA

For the prediction of the growth of mixed-mode-loaded cracks the determination of

comparative stress intensity factors is essential. The transformation of ModeI-,

ModeII- and ModeIII-stress intensity factor, e. g. by using Eq. 2, into only one cyclic

comparative stress intensity factor ¨KVmakes it possible to compare this value with the

cyclic fracture toughness value ¨KIC = (1-R)KIC.

Consequently, conclusions could be drawn on crack growth. Furthermore the crack

growth direction is required for a complete description of crack growth behaviour. For

this purpose some existing hypotheses are mentioned below. All of these hypotheses are

based on the near-field-solutions for the stress distribution at the crack front:

(3a),

¸¹·¨©§˜ ˜˜˜˜ ¸¹·¨©§ ˜˜˜˜23sin32sin52423cos2cos524IIIrMMSMMSVrKrK

(3b),

¹· ¸ ˜ ¨©§ ˜ ˜ ˜ ˜ cos32 cos 32 4 2 4 II I S M M S K r r K

¸¹· ¨©§ ˜ ˜ ˜ sin3 2 23 sin3 M M

V

M

(3c),

W

2 4 S K r

M M

S K r

M

M

sin 2 sin 3

¨©§ ˜ ¸ ˜ ˜ ¹· cos 2 2 4 2 II ˜

¨ © §

r

I

˜ ˜ ˜

23 cos3

¸¹·

M

K

M 2sin

III

(3d),

W

2

˜ r ˜

S

rz

221