Crack Paths 2006

M

0

ModeI

ModeII

a)

b)

c)

\

ModeI+II+III

M o d eIII

d)

Figure 7. Development of fracture surface for ModeI-, ModeII-, ModeIII- and Mixed–

Mode-loading of cracks

a) Development for a crack subjected to ModeI

b) Kinking of the crack under ModeII

c) Crack front twisting under ModeIII

d) Deflected crack for superimposed Modes I, II and III

The kinking angle M0 and the twisting angle \0 can be determined by different

criteria [5-7]. Simple approximation functions for those angles are given by [7]

II

ª

º

¸¹· ¨ ¨ © § q III 2 II I I I 0 K K K K 7 0 K K K K 1 4 0 B (1) q III II I

M

«

»

« ¬

» ¼

III I I I I I I I I 33 K K K K

ª

º

¨ §

B 78

K K K K ,

(2)

0

¸¹·

«

»

q

\

q

2

« ¬

» ¼

©

I

I I I I I

whereby M0<0° for KII>0 and M0>0°for KII<0 and \0<0° for KIII>0 and \0>0° for KIII<0.

In a spatial Mixed-Mode-loading situation the fatigue crack growth depends on all

fracture Modes. Therefore an equivalent cyclic stress intensity factor

K 4 K 1 5 5 . 1 4 K 2 1 2 2III II 2 2I ' ' ' (3)

I ' K

'K

eq

might be defined in order to reasonably describe fatigue crack growth.

Fatigue crack growth starts, if 'Keq exceeds the threshold value of fatigue crack

growth 'Kth. This material parameter 'Kth needs to be determined for the given