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number. The set of stress changes in service length or in the sample of this service length

transforms in this way into an ordered set of fluctuations, which represents the stress

spectrum. It may be used for reliability calculation and also for testing.

3. FAILURE PROBABILITY OF MACHINE PARTS

Fracture due to fatigue is a result of a complex and stochastic process, and the stress

finite cycle number is a statistical value which can be estimated only on the basis of the

law of probability. Fatigue is a process which has not been studied sufficiently theoreti-

cally to be defined by analytical forms which would make possible the calculation of the

stress finite cycles number. There are several hypotheses about the fatigue process course,

i.e. the crack occurrence process. When a crack occurs it becomes the source of additional

stress concentration, it spreads gradually until the occurrence of complete fracture. The

total finite cycles number up to the fracture

equals the sum of the stress cycle number

until the occurrence of the crack

′

and the stress cycle number in the course of crack

spreading

″

(

′

″

). The crack spreading process has been studied to a significant

degree. This process differs to a high degree, or completely from processes which take

place in the material structure up to the occurrence of cracks. This process is stochastic,

insufficiently studied and it brings a stochastic component into total stress finite cycles up

to fracture. In case of soft and tougher materials (steels) the period of crack spreading is

relatively long, i.e. it may be longer than the period up to the occurrence of the crack.

Calculations in the sense of forecasts of service length of machine parts with cracks in

such cases may have a certain practical significance. In high strength steels the number of

stress cycles up to the occurrence of cracks is relatively big, and crack spreading is very

fast, thus the calculations in relation to crack spreading are not of great practical use.

Up to the occurrence of cracks a process takes place which may be presented most

closely by some assumptions with Markov’s process (Fig. 10). If the process evolved in

one direction, there would be a change at each stress change, from state

into state

+ 1

which entails an increase of the crystal dislocation (fatigue degree). Thus by an one direc-

tion process from state 0 (without fatigue), state

would be reached, which entails the

occurrence of cracks. This would practically be a deterministic process, thus based on the

required energy for the creation of the dislocation, it would be possible to calculate the

required stress cycles number for the occurrence of cracks. The process is not one-

directional, thus from state

, a transition into state

+ 1, or into state

– 1 is possible.

Whether the process is moving forwards or backwards depends to a large degree on the

stress cycle number that will be required for the occurrence of cracks. The transition

probably does not take place, so that transitions occur into neighbouring states, instead

skipping of states is more likely. Big stress amplitudes, probably in large jumps, contri-

bute to the advancing of the fatigue process. Some smaller stress amplitudes may bring an

advanced fatigue process back to some state close to the initial one. It has been proven

that small stress changes (less than 0.5

) do not bring about an increase in the fatigue,

but instead cause relaxation. Depending on the sequence (mixing) of big and small stress

amplitudes the fatigue process may, under same testing conditions, advance faster or

more slowly. The relation of the biggest and smallest stress cycles number up to fracture

under the same testing conditions (same stress value and change, same form, material and

other test sample features, etc.) amounts to

max

min

= 3...5 or even more. This can be

attributed only to the indicated stochastics of the fatigue process.