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RELIABILITY AND SAFE SERVICE OF STRUCTURES

Milosav Ognjanović, Faculty of Mechanical Engineering, Belgrade, S&Mn

INTRODUCTION

The failure process consists of the part taking place from the occurrence of cracks and

the part covering crack spreading. The crack spreading process is determined by many

known parameters and has been studied in fracture mechanics. The process of crack

occurrence is not known enough and is stochastic. It takes place chaotically, the finite

cycles number may vary even several times at completely identical fatigue conditions. In

case of high strength steel the crack spreading speed is great, thus the participation of the

finite cycles number in the course of crack spreading in the total finite cycles number is

small. The cycles number of stress fluctuation until the occurrence of a crack, which is

stochastic (chaotic), dominates. Those are the basic reasons why mathematical statistics is

used in the analyses and calculations of machine parts loaded in this way. This approach

always presents a possible practical solution when physical laws have not been

completely clarified and when deterministic methods are not applicable. Due to the

stochastic behaviour of the failure process, i.e. the critical stress, and also due to

stochastic work conditions, i.e. service stresses, two solutions are used in practice. One

consists of the application of safety factor which entails “bridging over” the distribution

range of these stresses and elimination of risks of every possible failure. The other

consists of using statistical indicators which make possible entrance into the range of

“controlled” risk at the occurrence of failure which is expressed by the respective

probability – reliability. The rationality of design solutions is small in the first case, and

the mass and dimensions are big. In the second case along with the risk of a smaller

number of machine parts failed, a significant reduction of dimensions and mass are also

achieved, and the design solutions become more compact.

In order to establish a relation between the probability of service conditions (load and

stress) and the probability of failure under such conditions, extensive experimental data

from both ranges are required. The service conditions are defined by the regime of

exploitation, i.e. the stress spectrum in the length of service. These spectrums, i.e.

regimes, are obtained by measurements, follow-ups, analyses, and statistical research of

service conditions of machine systems of respective types in typical exploitation condi-

tions. The failure probability is determined on the basis of a large number of tested

samples of machine parts until fracture. Only based on extensive statistical data and

theoretical knowledge is it possible to establish a reliability model of respective machine

system components. It is based on empiricism and is a good substitute for not well under-

stood fatigue process, as well as for the stochastics of exploitation conditions.

1. SAFETY FACTOR AND RELIABILITY CORRELATION

The safety factor is the ratio of critical stress (at which failure begins) and work stress

which is the consequence of service load acting on the machine part. Failure does not

occur if in each possible case the work stress is less than the critical. Neither the critical