Page 130 - Biaxial Multiaxial Fatigue and Fracture

Long-Life Multiaxial Fatigue of a Nodular Graphite Cast Iron 1 I5

Crack observations

For all stress states tested, fatigue cracks in nodular iron specimens nucleated and
propagated on maximum principal stress planes. Typical fatigue cracks under uniaxial tension,
torsion and equi-biaxial tension are shown in Fig. 7.
Cracks for torsion or tensile loading showed some tortuosity as the crack linked up
numerous microstructural features, Le., graphite nodules or shrinkage pores. However, it can be
observed from Fig. 7 that the crack direction is fairly well defined. During equi-biaxial loading
the cracks grew generally in the plane normal to the hoop stress, but in comparison to the
torsion or tensile cracks there is significantly more branching and tortuosity. In these tests the
stress state was nearly equi-biaxial. Both numerical calculations and strain gage measurements
showed that the axial stress was only about 2% greater than the hoop stress. The Mode I crack
driving force was thus nearly equal in all directions.
For comparison, a torsion fatigue crack for normalised low carbon steel C45 tested in
completely reversed torsion is shown in Fig. 8. Material was received as 40 mm diameter bar
stock and later machined into the tubular specimens shown in Fig. 5a. Measured hardness was
BHN=193. As the figure shows, small cracks in this C45 initiate on both 0' and 90" planes for
torsion only loading. This is a well-documented phenomenon for ductile metals. Crack growth
along the specimen surface is via Mode II crack growth and into the depth of the material by
Mode III growth. After shear cracks reach a length of several hundred microns, crack
branching along k45" planes occurs. For near-fatigue limit testing, the crack branching occurs
rather late in the total life of the material.
Cracks produced by uniaxial tension fatigue are similar for both C45 and nodular cast iron,
i.e. initiation and propagation is macroscopically always normal to the direction of maximum
principal stress. For this reason it is very difficult to distinguish between shear and tensile
dominated materials based only on axial tension fatigue loading.

Effect of second principal stress on fatigue

While the dominant failure mechanism of the nodular iron is due to Mode I crack growth, the
fatigue limit stresses for torsion and equi-biaxial tension cannot be compared directly to the
uniaxial fatigue limit without additional considerations of the stress state. Because failure in
nodular iron is controlled by the nucleation and growth of small cracks from inclusions and
pores, the second principal stress influences the fatigue strength. As previously discussed,
crack driving force near a notch is greater in the case of h= -1 as compared to A=O. Endo
and Murakami 1221 and Beretta and Murakami [23] used fracture mechanics arguments to
estimate the fatigue strength in torsion to be approximately 80-83% the fatigue limit in tension
for materials dominated by Mode I failure from small defects.
In materials where the fatigue limit strength is controlled by the propagation / non-
propagation of cracks nucleating at individual small holes or inclusions, it may be expected
that the biaxial fatigue limit is higher than that for uniaxial fatigue, but the authors are not
aware of experimental work on this subject. Once cracks have nucleated and growth can be
modelled by linear elastic fracture mechanics, the role of the second principal stress is reduced.
While only limited data is available, the trend is that transverse stress only marginally affects
the Mode I crack propagation. Brown and Miller [26] reported the effect of biaxial stress on
Mode I crack growth for AIS1 3 16 stainless steel. At low stresses the effect of the transverse stress