Crack Paths 2012

Afterwards he determines by using the KV,I,II and KIII a spatial comparative stress

intensity factor K

V,I,II,III

(11).

4 ) 2 1 ( K K ˜ ˜ Q Q ) 2 1 ( K

K

K

5,1

IIIII,I,V,

III,V,

I2II,V,

IC 2 I I I 2

In order to be able to make conclusions about the occurence of unstable crack growth

the KV,I,II,III

can be compared with the fracture toughness KIC. The crack kinking angle

M0 can be obtained by:

) 1 c o s 3 ( sin 0 I I 0 I M M K K

(12)

by:

and the crack twisting angle

0

2K

III ) 2 1 ( Q

(13).

\

2tan

III,V, K

0

The crack deflection angles (see Figure 1b) results in a range of [-70.5°,+70.5°] for

M0 and [-45°,+45°] for

0.

Criterion by Schöllmann et al.

The 1 V c-criterion by Schöllmann et al. [12, 13] is based on the assumption that crack

growth develops perpendicularly to the direction of 1Vc

(Figure 3). For the

determination of this special maximum principal stress the near-field equations

(Eq. 3a-3f) are used.

Figure 3. Cylindrical coordinate system and stress components at a 3D-crack front

224