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A probabilistic model is examined for evaluation of fatigue damages sustained by material in equipment of the chemical and petrochemical branches of industry. The basis of the expediency of special tests of materials coming under cyclic loads in a σ a = const regime, and the work up of criteria, or "degrees of allowable risk," especially for potentially dangerous fabrications, is given.Criterial considerations regarding an effective deterministic procedure for calculation of cyclic strength and longevity [2] are outlined in [1].A computational probabilistic model, on the basis of which an attempt is made to explain the paradox of the effect of duration, or load history by packets of cycles on longevity, is examined in [3] for a load consisting of two packets of cycles.Experimental data in the form of distribution functions of the failing numbers of cycles F(N) for stress amplitudes σ a = const were adopted as the statistical basis for construction of a probabilistic model. These same data in the form of mathematical expectancies [N] were used in a deterministic approach to obtain the fatigue curve [2].The probability functions are plotted on the basis of a single measure for the components of the probability functions F(N), for which the average failing damage a calculated in accordance with the mathematical expectancies of the failing number of cycles [N] was adopted. The deterministic fatigue curve is plotted with respect to [N] in [2], and the rule of linear summation of fatigue damages (LSFD) can be adopted for this curve on firm grounds.In the probabilistic model under consideration, it is assumed that the standard deviation S logN of the components of the distribution functions F(N) remain unchanged during plotting of the probability functions.To reduce the damage to a single measure, therefore, the F(N) functions are normalized with respect to the mathematical expectancies [N], which have simultaneously similar values of both the damages, and probabilities of attaining the limiting state or failure. For the F 1 (N) and F 2 (N) functions (hereinafter, let us assume that the F(N) functions have a logarithmic scale logN), for example, the mathematical expectancies are [N 1 ] and [N 2 ], for which the damage a is equal to unity, and the probability of failure is close to 0.5 as for conventional monomodal distribution functions.In formulating the probability functions, therefore, the traditional concept of average fatigue damage for which linear summation of damages on the scale a = N/[N] is valid on the one hand, and the linear summation is corrected by accounting for the probabilities that the limiting state will be reached on the other.Here, the most critical parameters of the F 1 (N) and F 2 (N) functions are the mathematical expectancies [N 1 ] and [N 2 ], the standard deviations S logN,1 and S logN,2 , and the threshold numbers of cycles N 01 and N 02 .In conformity with what has been stated above, the F 1 (N) and F 2 (N) functions should be presented in the form of distribution functions of the failing...

In the present report, the results of generalizations and many investigations [1, 2] where it is acknowledged that the appearance of damage in cold collectors is a complicated and multifactor phenomenon are used. It is asserted that the operating temperature of cold collectors (280-290~ at which the effect of a corrosion medium is strongest, is important for explaining the reasons for the damage. It turns out that the fact that, on the one hand, cracking was previously acknowledged to be a more multifactor phenomenon and, on the other, the vibration, as a result of which cases of cracking of equipment metal are most often observed, remains inadequately analyzed, has been neglected.Each structural element possesses mass and elasticity and is potentially subjected to mechanical vibration, though under design conditions of normal operation all elements of the reactor and the first-loop system are regarded as being stationary or quasistationary (they can only move under temperature expansion).Initial data on high-frequency loading in accordance with the standard [3] are obtained after vibrations are discovered during operation and after analysis of the measurements performed on a corresponding element followed by the required calculation. In other words, during operation it is necessary to discover the vibration, collect initial data for calculations, perform the calculations, and then if necessary make a decision about continuing operations.Evidently, pumps and the moving cooling are a source of vibrations [4]. There is no doubt that vibrations of equipment and pipelines are initiated by the main circulation pump, turbulence, and standing waves of pressure in the coolant and steam in the main steam lines, as well as by boiling in the steam generator. It should be noted that in the year before cracking occurred in the cold PGV-1000 collectors --in 1985, a substantial vibration of the main steam lines, which was acknowledged to be caused by hydroacoustic pulsation of the pressure in the steam [5, 6], was discovered in the first power-generating unit of the Zaporozh'e nuclear power plant.Most likely, the situation preceding cracking of cold collectors can be represented as follows. When the reactor plant operates in transient and stationary states, as a result of pressure pulsations on the circulating and multifreqencies of the main circulation pump caused by formation of standing waves of pressure in the first loop and steam lines, the first-loop equipment, the main circulation pipe lines, and main steam lines were subjected to vibrations of different intensity. It appears that the cold collectors of steam generators in some power-generating units of nuclear power plants in Russia and the Ukraine are the weakest point. In other units with VVt~R-1000 reactors, either the quality of fabrication was higher or the assembly and unfastening of the equipment were better or both were present at the same time but vibration did not result in cracking of the collectors in any steam generator in the Roven, Khmel'nitsk, or Kali...

Translated from Gidrotekhnicheskoe Stroite 'stvo, No. 2, February 2014, pp. 32 -36. Use of the probabilistic approach to evaluation of the safety and longevity of the metal in the studs of the No. 2 generating set at the Sayano-Shushenskaya HPP is examined.

Limits are considered to the deterministic approach and the scope for a probabilistic one in calculating the working lives of structural elements, as well as the advantages and shortcomings of these approaches for estimating the safety of objects subject to elevated hazard.In [1], criteria are considered for the limiting states in cyclic strength of a metal, which are now used in standardization documents on strength and safety, and also in determining the cyclic working life of structural elements for the instance of several loads [2].In the first systematic studies on cyclic strength for metals with several loads, it was found that there is an effect from the loading history on the working life. Fairly detailed studies have been made on the simple state consisting of two batches of loading cycles with differing stress amplitudes with 1-2 and 2-1 packet sequences. A paradox was observed: for σ 1 > σ 2 and a 1-2 sequence of packets, some observers found a reduction in working life while others found an increase, and this paradox has as yet not been elucidated.In this connection, emphasis has been given to various approaches to failure and the effects of the loading history on the working life: a search has been made for the physical causes of this in the plastic few-cycle fatigue mechanism in the formation of cracks in stress concentration zones and a search for statistical regularities for states of one-packet and two-packet loading.The existing method of cyclic strength calculation employs safety coefficients on the number of cycles and the stresses [2], and it has been shown that in the linear fatigue damage summation (LFDS), the calculated fatigue curve does not rule out the probability of attaining a limiting state (crack formation) for various stress amplitudes. Then firstly the representation of absolute conservatism in that method of estimating the cyclic strength does not occur, and secondly, when one examines the causes of cracking and the actual crack growth, it is necessary to incorporate the effects from the loading history on the working life and probabilistic formulation of it. In spite of these considerations, calculations on cyclic strength in the formulation of [2] will clearly be performed in the future, since it is almost impossible to abandon at once the deterministic approach, which has been used for quite a long while. It is therefore necessary to consider the limits to that approach and the scope for a probabilistic approach in calculating working life, and also the advantages and disadvantages of those approaches for the corresponding estimates of safety in objects with elevated hazards.Experts should incorporate the terminology and probabilistic specifications introduced by the Federal Law on Technical Regulation, and distinguish between the calculated representation (to some extent sound) and the purely expert [3] representation of the permissible risk for failure in particular constructions, and also the degrees of safety in their use. An expert needs not only personal experience and t...