Crack Paths 2006

(8)

N1 I K a 5 3 . 0 'a˜ Y K ˜ ˜ S ' (T = 0°) 326.0

302.0 I K a 2 6 9 . 0 K a 4 7 9 . 0 a Y K '˜ ˜ ' ˜ ˜ ˜ S ' N1 326.0

(9)

(T = 22.5°)

N2

Equation (9) can be used to evaluate the residual life of welded joints by integration

of Paris’ law. In particular, referring to the data already shown in Figure 2, we assume

here an initial crack length ai=0.3 m m(Atzori et al., 1999a) whereas the coefficients in

Paris’ law are: m = 3.0 and C = 0.183x10-12 or, alternatively, m = 4.0 and C =

0.2046x10-15, both couples of values chosen according to Gurney (1991). In the y-axis it

will appear the stress parameter 'Vg,i, i.e. the initial value of the nominal stress range

defined on the gross transverse section of the welded joints:

N 2 3 0 2 . 0 i N1 3 2 6 . 0 i i , g K a 2 6 9 . 0 K a479.0 ' ˜ ˜ ' ˜ ˜ ' V (T=22.5°) (10)

or, alternatively,:

1 ¨ ¨ © § ˜ ˜

º

·

t

a t k 2 6 9 . 0

i,g

˜ ˜ ˜

(11)

V

V

'

«¬ª

k479.0

¸

» '˜

326,0

2

302,0i

0

a

¹

i

¼

The results are shown in Figure 4 and 5 where predicted values are compared with

the experimental values reconverted in terms of 'Vg,i.

The difference between experimental total life data and estimated residual life is

evident in Figure 3: the mean lines, irrespective of joint thickness and geometry, are all

translated in a way such that the experimental total life to residual life ratio is about 3:1.

However, the most important result is not the position of the scatter band, the centre of

which could easily be translated rightwards, maybe simply assuming a convenient

elliptic crack front, but the substantially unmodified width of the two scatter bands. The

inverse slope of the two curves is about 3, like the exponent m of the Paris’ law.

By changing the parameter m and C in the Paris law, but obeying Gurney’s equation

C·(895.4)m = 1.315·10-4 , the fatigue crack initiation time to total fatigue life ratio now

depends on stress levels (Figure 5). This happens because m is different from the

inverse slope of the Wöhler curves, k|3, see Figure 2. The fact of major importance

remains the capability of the fracture mechanics approach and the NSIF approach to

unify the behaviour of very different geometries.