Page 306 - Biaxial Multiaxial Fatigue and Fracture

290 ?: FUKUDA AND H. NISITANI

limit in bending is equal to that in torsion. Thus considering Omax/ Zmax=2 in bending and U,,J
~,,,=1 in torsion, the fatigue limit ratio of torsional fatigue to bending fatigue is obtained by
the following equation:

This equation corresponds to the maximum shear stress criterion, which is related to the
macroscopic criterion of yielding ( ZJCJ~=O~).

In the case where the fatigue limit is controlled by both a,, and z,,

In annealed metals, the fatigue process can be divided into two different processes, i.e., an
initiation stage and a propagation stage, as is shown in Fig.2 (b) [18,19].
(a) Process ( 1 ): By slip repetitions, the slip band or the grain boundary (or the part near the
grain boundary), which is going to become a crack, is disrupted as a whole and is gradually
turned into a free surface. Then a crack of the size of a crystal grain initiates.
(b) Process (a ): The crack initiated in process ( 1 ) increases in length and depth, and finally
causes the specimen to break.
As is mentioned above, since process ( 1 ) is controlled by the maximum shear stress and
process (n ) is controlled by the maximum tensile stress, the factor deciding the fatigue limit is
not simple to be determined. That is, the fatigue limit in both bending and torsion is determined
by the limting stress for propagation of a non-propagating microcrack.
Considering Omax/ rmax=2 in bending and amax/ rmax=l in torsion, the crack once initiated in
bending is easier to propagate than that in torsion. Consequently, since the fatigue limit in
bending becomes small compared to that in torsion, the value of fatigue limit ratio is more than
0.5, and the following equation holds on the basis of our present data:

2,/(7, = 055 - 0.7 (9
The fatigue limit ratios have frequently been discussed based on the maximum distortion
energy criterion (Mises’ criterion, ~Ju, = OS), which is related to the macroscopic criterion
of yielding [9,20].
In this case, since the fatigue limit depends on the microstructure and the material properties,
and is controlled by both crack initiation and crack propagation, the factor deciding the fatigue
limit is complex to be determined. Therefore, it is difficult to apply the macroscopic criterion
of yielding for deciding the fatigue limit.
In the present study, through the successive observations of fatigue processes and the grid
line method, the physical background of the value of rd 0, in carbon steel will be made clear.

MATERIALS AND EXPERIMENTAL METHODS

The materials used are rolled carbon steel (S20C, S45C) and cast carbon steel (SC450). The
chemical composition is shown in Table 2. Three kinds of specimens were prepared from a
rolled round carbon steel bar (S45C) by heat treatment: the first kind is annealed (S45C), the
second kind is diffusion annealed (S45C-DA) and the third one is quenched and tempered
(S45C-H). Conditions of heat treatment and mechanical properties are shown in Table 3. The
microstructures are shown in Table 4 in the following. In the longitudinal section, the banded