Fatigue Crack Paths 2003

[:/2[’°+“(d/2)_X2cyx

dYdx=ll D3

(21)

2 68 I1 Ol'l'lgI‘OSS

Iii/2 Irv (a/zf-x2

omax

1_ Y-r0 4 (q_1) 1+ atan[(Y—r0)m] Mil + q mY W1

0

i.

4 (q—l)+q0)1

d/2

rom

1 r0

[Jo/2v —X2 +1, —Y]dYdX=%on0mgmSSD3

(22)

In Eq. 22 6 represents obviously the peak stress value at Y=0. Eqs 21-22 take

m a x

advantage of the double symmetry of the geometry, so that calculations involve only a

quarter of the transverse section.

A C O M P A R I BS OE NT W E TEHNE O R E T IAC NA LDN U M E R I CRAE SL U L T S

Due to the approximate nature of Eq. 8, an accurate check of the theoretical stress

distributions was made along the notch bisector. In particular, 69 plane models were

analysed (see Table 2), where the ratio between the ligament width and the notch tip

radius ranged from 2 to 80 and K net from 1.62 to 11.85. In parallel, 23 axi-symmetric

modelswere considered, with d/p ranging from 4 to 80 and K net from 1.50 to 5.07. All

FE analyses were performed by using isoparametric parabolic elements and taking

advantage of symmetryconditions to create very fine meshes.

6y/(smax

G y / G m a x

l

0.8

O F E MGnom gross — E q .8 (Prof/‘A A +

0.8

n o F E M Gnom gross — E q .8

"

A +

0-6

2'5,

‘135°

-

“1

Win45‘)

\#

0 4 0.2

t t 40 > J_2.5 " “ \ L h v ;

0 I

I

I

I

' )

O

4

6

8

0

10

2O

3O

4O

distance from the tip/p

distance from the tip/ p

Figure 5. Stress distributions under pure

Figure 6. Stress distributions under pure

bending (Model No.23, PDEN).

bending (ModelNo.1 1, BCN).