11.2. Fatigue (Wohler’s) curve under the symmetrical cycle. Fatigue strength
For the design analysis under the action of the repeated variable stresses, it is necessary to know the mechanical material characteristics. They are determined by the test way with the specimen fatigue on a special machine.
The specimen test under the symmetrical stress cycle is the most simple and widespread one. The principle machine scheme for the specimen test in bending is shown in Fig. 11.4.
The
specimen 1 is fixed in chuck 2 of the machine spindle rotating with
some angular velocity. Pillow 3 through which the force F passes the
constant direction is placed at the specimen end. It is easy to see
that under it the specimen is subjected to the bending action with
the symmetrical cycle. Indeed, the tension stress
acts at the most dangerous point A
of the section I-I
because the cantilever bends the concave downward. However, after
that as the specimen rotates on half revolution, the point
A
will be down in the compressive zone and the stress will be equal to
The point A
will be up again after the next half revolution of the specimen and
so on. Under the passage through the neutral axis the stress at the
point A
will be equal to zero.
The test is
taken in the following sequence. Take 10 similar specimen usually of
the diameter 6-10 mm with a polished surface. The first specimen is
loaded up to the considerable stress
in order to destroy it under the comparatively small revolution
number N1
(the
cycle).
B
esides
the maximum cycle stress for the maximum stress point of the section
is kept in mind. In bending, it is known, the maximum stress arises
at the extreme section points and it is determined by the formula
Fig. 11.4. Fig. 11.5.
The test
results are put on the diagram which is drawn in coordinates
(Fig. 11.5).
The point A
appears on the diagram with the coordinates N1
and
after the test of the first specimen.
Then the
second specimen is tested under a smaller stress
Naturally it is destroyed under the larger cycle number N2.
On the diagram the point B is put with the coordinates N2
and
and so on.
Having tested all specimens and having united the points A, B, C and so on by smooth lines, we get a curve ABCD which is called the fatigue (Wohler’s) curve.
This curve
is typical as it goes practically horizontally (the region CD)
starting from some stress. It means that under some stress
the specimen can bear an infinitely large cycle number N2
not being destroyed. The experience of the steel specimen test under
the normal temperature shows that if the specimen has not been
destroyed up to the cycle
(it is approximately 54 h under 3000 r.p.m.) the specimen is not
destroyed and under more protracted test.
A preliminary given maximum duration of the test in the fatigue is called the test base.
For steel specimens in usual conditions the test base is equal to 106 cycles.
The maximum
cycle stress in the absolute value under which the fatigue rupture
doesn’t occur up to the test base is called the fatigue
strength
For symmetrical cycles R=1
in this case the fatigue strength is denoted by
The limited
fatigue strength
term is introduced for details of the limited function period as the
maximum (by absolute value) cycle stress corresponding to the given
cycle number is less than the base number.
Analogically
the tests are carried out on other machines, the limits of the
fatigue under the axial forces action
in torsion
and under the combined deformations are found.
At the present for many materials the fatigue strength is found and represented in the reference book. It can be seen from these data that for the majority metals the fatigue strength of the symmetrical cycle is less than the yield point.