Page 465 - Biaxial Multiaxial Fatigue and Fracture

Micmcmck Propagation Under Non-Proportional Multiaxial Alternating Loading 449

N, is the number of cycles to failure, while C and z are material parameters. N, is defined by
the point of time when the crack has penetrated the wall. In our facility we are monitoring the
gradient of the inner pressure and the outer pressure. If we have a wall penetrating cracking the
gradient of the inner pressure various very quickly and the outer pressure increases. So we can
determine the point of time of the wall-penetrating of the crack and out of this N,.
it can be seen that for different phase shifts the material parameters are also different.
Furthermore, it can be observed that an increasing phase shift causes a higher life at the same
equivalent load. This indicates that the failure process is not controlled by shear stress
exclusively. Hydrostatic stress plays an important role. Similar results were observed by
Mouguerou [6] and Ogata [7]. For a phase shift of 0 degree the hydrostatic stress reaches its
maximum, while for a phase shift of 180 degrees the hydrostatic stress is minimum. If the
loading amplitudes, at a phase shift of 180 degrees have the same value, the hydrostatic stress
even vanishes. It may therefore be supposed that a higher hydrostatic stress at the same
equivalent stress reduces the lifetime.
To obtain a correlation between the multiaxial experiments with different phase shifts on the
one hand and the uniaxial reference experiments on the other hand, a multiaxiality factor f,
was introduced. Therewith, the Manson-Coffin relation was modified as follows:

C' and z' are material parameters which are extracted from uniaxial fatigue experiments
(C' = 12.63,z' = -0.3395).fm is a function of the multiaxial hydrostatic stress range Aorltiaxia'
referring to the uniaxial hydrostatic stress range AoYa, arising for the same equivalent
plastic strain range A&;:

with ~~~ltiaxial (5)
= 3[ max Trace(5) - min Trace(5)l

From the uniaxial deformation data'determined, it results u = 425.7 and p = 0.2.
The multiaxiality factors out of the different multiaxial experiments were investigated with
Eq. (3). When plotting these multiaxiality factors over the ratio AO~"~"~~' / bounimia' it can be
seen that a linear function could describe this relation quite well:

with h=1.396 and k=0.396. Thus it results a rather good description of the lifetime by the

modified Manson-Coffin relation (Eq. 3). In Fig. 7 the ratio is plotted over the number
of cycles to failure on a double logarithmic scale. It can be seen that the results lie within an