Probabilistic hypothesis of fatigue-damage summation

Abstract

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...

A Probabilistic Physico-Chemical Diffusion Model of the Key Drifting Parameter of Measuring Equipment

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Effects of metal strength statistics on the representation of fatigue life in structural components

“…• firstly, an examination of the general features of the integral (experimental) distributions of the failure number of cycles F(N) with the use of a procedure for forecasting the residual working life, e.g., for a particular specimen with one-packet loading σ a = constant; • secondly, one must consider the two simplest modes of loading, which consist of two packets of cycles with different stresses σ a1 = constant and σ a2 = constant, and also in 1-2 and 2-1 sequences of packet application; and • one needs to formulate a hypothesis or a probabilistic damage summation rule for any multipacket mode [8].…”

Limiting states in calculations on cyclic strength and life estimation

“…In [11][12][13], we find the hypothesis of probabilistic summation for fatigue damage (PSFD), which enables one to use any condition of cyclic loading and any limiting state to calculate the probability function not only for an individual element (calculation point) but also for any complicated construction.…”