Page 471 - Biaxial Multiaxial Fatigue and Fracture

Microcmck Propagation Under Non-Proportional Multiaxial Alternating Loading 455

s = 2.4e-’ + 1.45 (14)
The dependence of t, on h is determined by the energy release rate in terms of the equivalent
stress and strain in the linear elastic case [9]:

Thus and since the regime of short cracks starts at a crack length a=kd, AJ can be written as

AJ=AJ*[$)

and Eq. (8) as
da
dN

with AJ* denoting the value of AJ for a crack of the length a=kd. Now, McDowell and Bennet
had ideas how Eq. (8) can be extended to describe crack propagation also in the regime of
micro cracks [8]. We adopted some of these ideas and modified Eq. (17) for the description of
crack propagation in both, the regime of micro cracks (a < kd) and the regime of short cracks
(a 2 kd ), as follows:

da
dN
with

mp =1 for arkd

mp =cp(%r for a<kd

c, and b, denote additional material and temperature dependent parameters. Accordingly the
mean value of the crack growth rate da/dN becomes in the regime of micro cracks for high
loading levels (Ne,/& +O) nearly independent on the crack length a (m, +O) like it is
discussed in the previous section.
Assuming that the lifetime fractions for micro crack nucleation and for long crack propagation
can be neglected in comparison to fractions for micro and short crack propagation Eq. (1 8) can
be used for lifetime prediction. For our material, the sonic emission observations indicate that
the lifetime fraction up to micro crack nucleation is rather small in comparison to whole
lifetime. Due to the thin wall thickness of the used specimens the cracks leading to failure and
wall penetration, respectively, can be considered to be small so that the lifetime fraction for
long crack propagation is assumed to be negligible in comparison to the whole lifetime. So we