Page 302 - Biaxial Multiaxial Fatigue and Fracture

286 Z FUKUDA AND H. NISITANI

individual fatigue limits, it is important to understand the physical meaning of the fatigue limit
ratio, r,J a,,, , of torsional to rotating bending fatigue.
Most of the results of the above studies have been discussed using macroscopic criteria for
plastic yielding. For example, it is said that the fatigue limit ratios rJaw of many ductile
materials follow the maximum distortion energy criterion (Mises’ criterion; r J a,=O.58, where
T~, are the yield strengths measured in shear and tensile loading, respectively)[9]. In many
(T,
experimental results, however, the ratio of fatigue limits ( tw/ ow) does not always follow this
macroscopic criterion of yielding. In carbon steels, which are ductile materials, the ratio varies
from 0.55 to 0.7 depending on the microstructure.
According to the tensile and torsional static tests of two kinds of carbon steels in which one
is a fully annealed rolled carbon steel having a clear-banded structure and another is an
annealed cast carbon steel having no banded structure, the clear-banded structure greatly
affects the local strain concentration in torsion, but it hardly affects that in tension [lo].
Taking into consideration these facts, rotating bending and torsional fatigue tests have been
carried out on plain specimens of several kinds of carbon steels which have clear-banded
structure or not, and the fatigue limit ratio ( rJa,) values are herein discussed based on
whether the specimen has a clear-banded structure or not.

FATIGUE LIMIT RATIO OF BENDING AND TORSIONAL FATIGUE [DATA MAINLY
OBTAINED IN THE PAST]

Clu.wificution of fatigue limit
Table 1 shows experimental data, minly obtained in the pst, of fatigue limit ratio of torsional
to bending fatigue for various kinds of materials. The value of fatigue limit ratio r J ow vanes
between 0.5 and 1 depending on the material.
As is well known, fatigue process depends on crack initiation and crack propagation. Crack
initiation is controlled by the maximum shear stress ( tmx) while crack propagation is mainly
related to the maximum tensile stress (amx). They are related to the microstructure or
properties of material in a complex way.
Because of these facts, there are three different cases concerning the dependence of fatigue
limit.
(a) The fatigue limit is controlled by the maximum tensile stress, amax.
(b) The fatigue limit is controlled by the maximum shear stress, rmx.
(c) The fatigue limit is controlled by both amx and tmx.

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

In a defective material, defects, for example inclusions or small holes, are regarded as a kind of
crack. Thus, in this case, crack initiation can be ignored and only crack propagation can be
considered. Gray cast iron or nodular cast iron can be treated in this way, since flake or
spheroidal graphite is regarded as a defect. In this case, the main factor deciding the fatigue
limit is the maximum tensile stress ( omax).
In torsion, the principal stress ( (T 1) is equal to the principal shear stress( r ,), as is shown in
Fig. 1. Therefore, if the fatigue limit is controlled by the maximum tensile stress ( a,) only,