Fatigue Crack Paths 2003

and the locus of the crack tip can be interpreted as the consequence of AKH i 0 for a vir

tual tangential crack extension Ah (Fig. 3). Therefore, in the case of proportional load

ing conditions the analysis of a smooth crack path can be carried out by a small virtual

tangential crack extension as the predictor-step in combination with a finite change of

the crack path as the corrector-step. O n account of the predictor-step the calculation of

KI : KI and AKH is necessary in conjunction with the related tangential crack extension

Ah. From Eqs 7 the need for an efficient numerical modeseparation technique in con

junction with the step-by-step analysis can be seen.

Figure 3. Step of a curved crack propagation.

I M P R O VMEVDC CMIE T H O D

With respect to this requirement the M V C C mIethodhas proved to be highly advanta

geous, because it delivers the separated strain energy release rates of the two modes

simultaneously without any additional effort (Buchholz [8]).

For 8-noded quadrilaterals at the crack tip, which are necessary to model the parbolic

x2‘?

XZ‘T

“

M

F2.i

F2,i+1

> 2 ‘ '

‘*1

ii+1 i+2 __

Fi

F m

X,‘

A U Z P Z

AUzi-1

'.

v

"

x1

> — 1 : : :

A U L F Z

A U L F ' I

X2}

11

M

M

F2,i

F2,i+1 F2,i+2 F2,i+3

‘

.1 i

F i+1

i+2 F1 i+3

A u 2 , i * 4Al"'2,i-3 A U Z J - ZA u Z iy -

4 > _

v

v

1'

x1

~

>

->

= :

=

=

Au1,i*4 Autieii A U L P ZA U L F ' I

Figure 4. First and second order evaluation of the M V C CmIethod.