Crack Paths 2006

rate at each discrete point of a crack front has to be provided. Those information

necessarily needs to be of local character, since the local loading situations may

substantially change along a 3D-crack front.

Crack growth direction

The direction of crack growth in A D A P C R A C Kis3deDtermined by the V1’-criterion

[3]. This criterion assumes that crack growth will occur radial from the existing crack

front in a direction, that is perpendicular to a maximumprinciple stress V1’. Thereby

this stress V1’ is evaluated on a curved cylinder with centre line along the crack front.

This criterion yields two angles M0 and \0, whereby M0 describes a local kinking of the

crack front and \0 a local twisting (Figure 2). Despite both angles are functions of all

three fracture modes, there is a close correlation between on the one side ModeII and

the kinking angle M0 and on the other side ModeIII and the twisting angle \0.

M

M

70.5°

\

45°

\

n

K

II

Mode-III

Mode-III

Mode-II

Mode-II

n

n

K

K

n

III

n

K

III

K

I

I

Mode-I

Mode-I

Figure 2. The crack deflection angles M0 and \0 according to the V1’-criterion

Equivalent stress intensity factor

For an arbitrary Mixed-Mode-situation it is necessary to calculate an equivalent

stress intensity factor from the single Mode components KI, KII and KIII. By the V1’-

criterion this equivalent stress intensity factor Keq is defined as

° ¯ ° ® ­

° ¿ ° ¾ ½

» K4 s i n K 2 3 2 c o s K s i n K 2 3 2 c o s . º « ¬ ª M ¸ ¹ · ¨ © § M M ¸ ¹ · ¨ © § M 2II 2 0 I I 0 (1)

¸¹·¨©§M

K

0 2cos21

eq

¼

This definition enables to compare a Mixed-Mode-loading situation to the (Mode I-)

fracture toughness KIc. Moreover this relation can be applied in fatigue crack growth