Page 304 - Biaxial Multiaxial Fatigue and Fracture

288 T FUKUDA AND H. MISITAMI
3 3

Fig. 1. Principal stress and principal shear stress in torsion

the relation between both fatigue limits of bending and torsion becomes cJ,=Z, in torsion.
Then, the fatigue limit ratio of torsional fatigue to bending fatigue is obtained by the following
equation:

This equation corresponds to the maximum tensile stress criterion, which is related to the
macroscopic criterion of yielding ( Zs/(7,= 1).
A defective material, which contains sharp defects like gray cast iron, mostly follows the
Eq.(l). However, in the artificial defects of small circular holes or nodular cast irons, it is
necessary to consider the stress concentration of a circular hole. Since the maximum stress due
to the stress concentration of a circular hole is equal to approximately 3 0 in bending and 4 t
in torsion ( (J Z the ratio of fatigue limits is reduced to the following equation:

Nisitani presented some experimental results for an annealed rolled carbon steel bar with a
small hole [13]. In the case of a single hole specimen, Z J (J,was equal to approximately 0.75,
whereas it was equal to about 0.9 in the case of the connected hole specimen, It was also
shown that TI,,,'^^ was equal to approximately 0.9 (not 0.75) for a nodular cast iron. This
means that spheroidal graphite is not always independently distributed and is regarded as a
kind of connected hole.
As is mentioned above, the fatigue limit of a defective material including cast iron is mainly
controlled by the maximum tensile stress, and the value of fatigue limit ratio Z J 0, follows
Eq.(3), depending on the type or distribution of defects, etc.

Z,/(7,=0.75 - 1 (3)

In the case where the fatigue limit is controlled by the maximum shear stress only
(non-defective material)

If the cracks once initiated do not stop propagating, the fatigue limit is determined by whether
a crack initiates or not. According to the successive observations by Nisitani, age-hardened
Al-alloy corresponds to this case [15]. In this material a crack initiates in a fairly small region