Fatigue Crack Paths 2003

O n the other hand, in the case of a slim parabolic notch (i.e. a blunt crack, with 20t=0

and q=2, see Figures 1-2) Eqs 3 coincide with Creager-Paris’ formulation [9]. Only in

this case the distance between the notch tip and the origin of the co-ordinate system is

r0=p/2. Otherwise, the distance r0 varies as a function of q, according to the expression

reported in Figure 2.

For Mode1 problems, the parameter a1 can be correlated to the peak stress value

according to the following expression [21]:

(5

m a x

(4)

3 . 1 :

%1r3‘“1{1+%.+xb,(1—M)+I(1+i1)xd,+x.,l

‘1 I 40-0

P R I N C I P ASLT R E SDSI S T R I B U T IDOUNET OM O DIEL O A CDO N D I T I O N S

IN FINITESIZEC O M P O N E N T S

Equations 3 are valid in the close neighbourhood of the notch tip, where the influence of

the remotely applied stress does not appear. Obviously the crack length can overcome

this region and therefore a correction of such formulas, capable to prolong their range of

validity, is clearly desirable. That would allow us a rapid calculation of the SIF on the

basis of the principal stress distribution of the uncracked body. Following these

guidelines, an analytical approach useful for finite size components under tensile loads

was presented in Ref [28], with reference to the tensile stress 69 I 6:0 :Gy along the notch

bisector (Figure 2). It was given as follows:

6 = — 6 m a4(q_x1) 1+—atan[(r_r°)m]

F +qo)I i W (5)

y 4 ( q — l ) + q 0 ) I

r o m

r0

_ xd,(l+iu)+x.l

where

I

_

6

1 + > H + X(1_b7\I'1)

( )

The coefficient 031 is given in Table 1. Eq. 5 represents an extension of the local stress

distribution given in Ref. [21]:

G m a x

_ i 7cI—l

i III-l

6y —4(q_I)+q0)lI4(q 0L0) +q®1Ir0J I

(7)

Due to its nature, Eq. 5 coincides with Eq. 7 in highly stressed regions but it is also

capable to describe the transition between notch stress zone and the nominal stress zone.

It is worth noting that the parameter m in Eq. 5 can be evaluated on the basis of

equilibrium conditions, without any best fitting of numerical data. A number of