Page 314 - Biaxial Multiaxial Fatigue and Fracture

298 T FUKUDA AND H. NISITANI

easily initiated in the ferrite grain in torsional fatigue of carbon steel which has a clear-banded
structure.

Fatigue test

The S-N curves of all specimens are shown in Fig.12. Table 4 shows the fatigue limits (7,and
Z, and the fatigue limit ratios of torsional fatigue to rotating bending fatigue ( T,,/ a,) of all
materials. In anisotropic materials which have a clear-banded structure (S20C, S45C), the
ratios are 0.55-0.57, and in isotropic materials which have no banded-structure (SC450,
S45C-DA, S45C-H), the ratios are 0.65-0.68. As is mentioned above, in the torsional fatigue
of carbon steel, which has a clear-banded structure, the large local strain concentration occurs
in the ferrite. On the other hand, in the rotating bending fatigue of the same steel, the local
strain concentration hardly occurs in the ferrite band. This produces a relative reduction of the
torsional fatigue limit. Namely, the fatigue limit ratio ( T J (7,) depends on whether the
specimen has a clear-banded structure or not, and does not follow the macroscopic criterion for
plastic yielding (Mises’ criterion; tS/ us =OS). The fatigue behavior of a specimen is related to
the local microstructural details of the specimen. On the other hand, the macroscopic yielding
is related to the average properties of the specimen. This is the reason why the criterion for
macroscopic yielding is not applicable to fatigue loading under combined stresses in general.
In discussing the results of fatigue tests under combined stresses (bending and torsion), it is
important to consider whether the material used has a banded structure or not.

Classification of fatigue limit ratio T,J U,

The fatigue limit ratio Z J (7, varies between 0.5 and 1 depending on the material as is shown in
Table 1. The fatigue process consists of crack initiation and crack propagation. Therefore, by
considering crack initiation, crack propagation, microstructure and type of defect, the value of
fatigue limit ratio can be classified as is shown in Table 5.

CONCLUSIONS
(1) The local deformations are not uniformly distributed in both static tension and static torsion,
and therefore most of local strains are not the same as the applied macroscopic strain.
(2) A clear-banded structure greatly affects the local strain in static torsion but it hardly affects
that in static tension. That is, large shear strain concentration in torsion occurs in the ferrite
band sandwiched between pearlite bands but the mean normal strain in tension in a ferrite
band is nearly equal to that of a pearlite band.
(3) Because of the above conclusion, the fatigue cracks of carbon steel with a clear-banded
structure are initiated more easily in torsional fatigue than in bending fatigue. That is the
reason why the fatigue limit ratio of the steel is close to 0.58 (Mises’ criterion).
(4) The fatigue limit ratio ( rJ(7,) depends on whether the specimen has a clear-banded
structure or not, and does not follow the macroscopic criterion of yielding. In discussing
the results of fatigue tests under combined stresses (bending and torsion), it is important to
consider whether the material used has a banded structure or not.