Page 132 - Biaxial Multiaxial Fatigue and Fracture

Long-Life Multiaxial Fatigue of a Nodular Graphite Cast Iron 1 I7

Fig. 8. Fatigue cracks during torsion of C45 low carbon steel.

is small with the biaxial tension (A = 1) having the lowest growth rate. This may be related to
the slightly smaller plastic zone size for this loading case. The difference between the growth
rates increases as the stress levels increase. Only as the nominal stress approached the yield
strength did the above Authors find more significant differences in growth rates. Finite
element analysis shows that under these high loading stresses, the plastic zones are much larger
for A= -1 than those estimated from the elastic solution. In an extensive series of biaxial
loading experiments on 2024 and 7075 aluminium alloys, Liu et al. [27] obtained similar
results. Applied stresses were between 20 to 60 percent of the material tensile strength and the
biaxial stress ratios ranged from -1.5 to 1.75. Mode I crack growth rate for this material was
not affected by the transverse stress and all of the crack growth rate data fell within a single
scatter band.
The current study shows that the fatigue limit for this material is nearly the same for both
uniaxial and equi-biaxial tension. By contrast the fatigue limit during torsion fatigue was
significantly lower. Under equi-biaxial loading the crack driving force was nearly equal in all
directions, so failure in nodular iron is not due to nucleation and crack propagation in a single
plane but cracks are able to progress freely with no strong directional preference. All planes
normal to the surface of the specimen are critical planes.
It is well known that fatigue cracks always form and propagate in the weakest region of a
material subject to high stresses. In his keynote paper on metal fatigue, Miller [28] has
discussed the issue of non-propagating cracks and the fatigue limit both for notched and
smooth specimens. Cracks may cease to grow: (1) as a result of a stress gradient and reduced
crack tip driving force in the region of a stress concentration, or (2) as a result of the crack tip
reaching some microstructural barrier. In an equi-biaxial stress field a fatigue crack will not
have a strong preferential direction. It is therefore reasonable to assume that cracks can more
easily grow around microstructural features that might otherwise halt or greatly retard crack
advance. For this reason, the fatigue limit in biaxial tension for nodular iron is lower than what
is expected based on simple elasticity considerations. Increased crack tortuosity for nearly
equi-biaxial loading as compared to tension or torsion is clearly seen in a comparison of cracks
in Fig. 7.