Crack Paths 2006

3.2 Crack growth direction

According to the results showed in the previous section, the attention of the authors has been

focused on the crack which is located just under the worst loading condition (i.e. x = y = 0 m m

and z = 0.25 mm). In particular, points A and B, where the maximumKII fluctuations have been

detected, are considered; as previously shown, in these locations KIII is nearly null.

Referring to that crack in the plane x-z (Figure 9), the stress in the tips vicinity under mixed

modeI and II can be described as [12]:

º T T ¸ ¹· 2 tan 2 s i n 2 3

V

S T 21 cos 2 r

ª

¨ © § T 2 s i n 1 2

I I I I K K (1)

K

r

I

« ¬

» ¼

cos 2 23

(2)

T T S 2 c o s 2 1 2 I r K

VT

K

sin

II

«¬ª

T

»¼º

T

(3)

@ 1

2 12 S

WT r

r

cos 2

K

sin

T

K

cos3

T

I

II

>

Figure 9. Crack in plane x-z and definition of the

coordinate system for the computation of the stress at the

crack tip.

The tensile and shear SIF (K and K) can be defined as follows:

T

)(

S V

(4)

cos 2 23 2

sin

K

T

2

r

T 2cos

«¬ª

K

K

T

»¼º

V

T

I

II

(5)

T S W T W r r K

T

K

K

I

II

)(

>

@)1

2

2cos21

sin

T

cos3(

T

It is evident that, for a given value of (i.e.

T T ), K and K are functions of the KI and KII

and consequently they fluctuate according to the load position. In order to find the direction

propagation of the crack, it is useful to compute the tensile and shear range for T T :

(6)

'

K K

K

_

_

_

T T V

min, max, T T V T T V