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are achieved, and the crack at fracturing spreads out circularly. The number of finite

cycles number is equal to the number of rotations of the test sample. Figure 10b shows

the manner of introducing the longitudinal force in the testing of the engine screw, piston

rods, and other similar parts exposed to longitudinal variable forces. The change of force

occurs through hydraulic machines with a change of force of sufficiently high frequency.

The rotating machine parts such as gears, shafts, couplings, etc. are tested with the help of

devices with closed power circuits (Fig. 11c). Two identical pairs of gears, i.e. transmis-

sions are conjugated in the circuit (“back to back”). The load is achieved by flexible

deformation of parts in the circuit, in stationary state, with the moment created by the

weight on the lever of appropriate length. In such a state, screws are tightened on the

coupling, weights and levers are removed, and the “conserved” load–stress in the parts

remains in the circuit, which remains also in the state of rotation. The number of stress

cycles is the same as the number of rotations.

4. FAILURE PROBABILITY IN THE RANGE OF FINITE LIFE STRENGTH

In the logarithmic coordinate system the fatigue strength curve – Wöhler’s

–

curve

is a straight line. By logarithm of exponential equations

, we get

log

+ log

log

, and by substituting

= log

, log

, it follows that

. The

straight line is defined by two points. It is sufficient to perform the testing for two stress

levels and use these results for determination of required data for any stress level using

equations of the indicated straight line.

For the realization of the testing process it is necessary to choose two stress levels to

which the test samples will be exposed to, and choose the number of test samples (parts)

which are to be tested at chosen stress levels. The difference between chosen stress levels

should be as big as possible so that the direction of the obtained straight line is as precise

as possible. The upper level should be as close as possible to the yield strength without

entering the plasticity range. The lower level should be as close as possible to the endur-

ance limit, without entering the range of dissipation of the endurance limit. The decision

about the values of these stresses is made on the basis of experiences gained in previous

research work or on the basis of testing one or a few pieces. Figure 12 gives an example

of research results of rotating test samples related to bending. The test was performed at

reversed stress

= 973 N/mm

(

= 1500 N) and

= 810 N/mm

(

= 1250 N). To each one of these stresses,

= 10 test specimens were exposed. In the

range of finite life strength, the failure (fracture due to fatigue) occurs after some finite

number of cycles, in the case of all test specimens. Finite numbers of cycles are the result

of the stochastic process and are realized by the law of coincidence. After classification

into the growing series of numbers, a set of values is obtained of these numbers,

, given

in the table in Fig. 12. For two stress levels, two sets of finite cycles numbers are obtained

by testing. The failure probability for each one is a cumulative probability

where

is the number of failed specimens at the finite numbers of cycles, which are

smaller or equal to the number

for which the probability is calculated,

– total number

of tested specimens with stress for which the probability is calculated. This expression is

valid for big samples (big sets

). For small samples, the above indicated approximate

expressions are used. The most suitable for applications is the first expression which has

been used for calculation of failure probability in the table in Fig. 12. The failure prob-

abilities,

, determined in this way have been entered in Weibull’s coordinate mesh, and

the set of points for stress

= 973 N/mm

and for

= 810 N/mm

have been approxi-

mated by straight lines. The parameters of Weibull’s distribution have been determined