Crack Paths 2012

K

M

(3e),

W

cos

˜

III

S ˜

M

2

r

2

2

M

z

M Q V V Q V ˜ ˜

˜ ˜ ˜ sin cos K K ¨©§

¸ ¹ ·

(3f).

S

(

)

2

r

2

z

r

M

I

II

2

2D-Mixed-Modecriteria

For plane-mixed-mode problems in the literature there are many hypotheses [2]. Here in

this paper only a few of them are presented.

Criterion by Erdogan and Sih

The crack growth predictions of the maximumtangential stress criterion by Erdogan

and Sih [3] are based on the tangential stress , Eq. 3b. According to this criterion, the

perpendicular to the maximumtangential

crack growth follows the direction of = 0

stress

,max . The crack growth starts radial from the crack tip and becomes unstable as

soon as

exceeds the material limit value

–or–if the comparative stress

,max

,C

intensity factor KV, resulting from crack deflecti n angle

0 can be btained by: ,max

, exceeds the fracture toughness KIC [2]. The

2

and

ww

M M VM

0

w

V

2

M

0

w

M

M

M M

Finally the following equation for the crack deflection angle

0 results:

3 K K K K

ª

2I 2 I I 8

2I

«

(4).

arccos

M

K

K

« ¬

9

0

2I

2I

»¼º

The fracture limit surface is given by the maximumcomparative stress intensity

fractor:

II

(5).

cos

K

V

2

S

r

¸¸¹·¨¨©§ 2 c o s 0 M

K

M

K

M

˜

¨ ¨ © §

¸ ¸ ¹ ·

maxV,

max,

I

2 0

0

˜

2

23

»¼º )sin(

«¬ª

M

2D-criterion by Richard

This criterion was empirically developed by Richard [2, 4]. Here the comparative stress

intensity factor KV is defined by

IC 2 I I 2 I I V 3 6 6 , 5 2 1 2 K K K K K ˜ (6)

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