Page 472 - Biaxial Multiaxial Fatigue and Fracture

456 M. WEICK AND 1 AKTAA

applied Eq. (1 8) to calculate the lifetime for our multiaxial tests. The results of this application
are presented in the next section.

Lifetime calculation using crack propagation model. For a cyclic test the lifetime fraction for
micro and short crack propagation and therewith the lifetime is calculated by integrating Eq.
(1 8) as follows:

0

1
*Nf =
cj (N*)"J

For a, = d = 0.02 mm, k = 5, and a, = 0.5 mm (half wall thickness) the material parameters
Cj, "2, , cp , and b,, are determined by fitting the numbers of cycles to failure calculated using
Eq. 20 to the numbers of cycles. to failure observed experimentally. They are independent from
the loading and should be valid for other cases. However they are not verified for other cases as
yet. The resulting values are listed in Table 4. The quality of the fit is illustrated in Table 5 as
well as in Fig. 13 where the calculated lifetimes are compared with the observed ones.

kd 0.1 mm
a, 0.5 mm
mm (N/m)-"'
C j 3.573 1
mi 2.715
4.643
CP
b* 2.736
~ ~ ~ ~ ~ ~~

Table 5. Experimental ascertained AJ, 's ( AJ for a=a,) and herefrom calculated lifetime.