Evaluation of the lifespan indicators of parts subjected to multidimensional cyclic actions

Abstract

Damage in the form of fatigue cracks can arise and corrosion processes can be initiated in the material of a structural element under prolonged simultaneous exposure to variable stresses of different nature. In this connection, it is necessary to construct an adequate mathematical model of the reliability that would make it possible to determine the lifespan of the structure during operation. Accurate values of the lifespan indicators of a part are impossible to obtain in the case of multidimensional loads. For this reason, it is of practical interest to obtain estimates of these indicators, which is the subject of discussion in this article.Damage in the form of fatigue cracks can appear and corrosion processes can be initiated in the material of a structural element under prolonged simultaneous action of variable stresses of different nature. These processes are irreversible, and ultimately result in failure of the element [1]. Thus, the pipelines in a nuclear power plant operate under simultaneous exposure to corrosive media, high pressure and temperature, pressure and temperature pulsations, liquid and vapor flows, radiation, mechanical impacts, and so forth [2]. In practice, most operating objects are subjected to several destructive factors. Thus, in most practical situations multidimensional cyclic loads act on a part.Since the character of each action of periodic loads on a part is random in general, it is desirable to use a stochastic approach to obtaining the lifespan indicators of a part operating under cyclic perturbations. In addition, the part itself is manufactured with a definite accuracy, which is also of a random nature. This makes it necessary to develop reliability-probabilistic computational methods which would be able to answer any questions concerning the lifespan of a system during operation.Accurate values describing the functioning of a system can be obtained only for certain distribution laws for an applied load, even in the case of one-dimensional perturbations [3]. In the case of multidimensional loads, accurate lifespan indicators cannot be obtained even for the simplest load distribution laws, so that it is of practical interest to estimate them. A method for obtaining the lower (pessimistic) estimate of the probability P(t, x) of failure-free operation under conditions of discrete degradation of a part is described in [5]; this method is based on inferences from the Hausdorff estimator [4]. In the present article this method is extended to the case where a multidimensional cyclic load acts on a part.Formulation of the Problem. Consider a part on which act n independent fluxes of periodic perturbations. Let the time intervals between adjacent load cycles of type i τ i1 , τ i2 , τ i3 , ..., τ ik be independent and have the same distribution function F i (t) = F ij (t) = P(τ ij ≤ t), i = 1, 2, 3, 4, ..., n and j = 1, 2, 3, ..., k, with the possible exception of F i1 (t) = P(τ i1 ≤ t) ≠ F i (t).Similarly, we shall assume that each perturbation of the type i changes the damage accumulat...