PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 256–265 ReznikovD.O./ Structural Integrity Procedia 00 (2019) 000–000

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distributions of random variables can be adjusted, for example, during the implementation of Bayesian procedures (Karandikar, Kim, Schmitz,2012; Makhutov, Reznikov, 2021) . The effect of crack retardation after tensile overloads will be neglected in this work, which is acceptable in engineering calculations, since it leads to conservative estimates of cyclic durability and fracture probability. 2. Mathematical model for describing the kinetics of a crack under combined constant amplitude regular loading and random overloads Consider a pipeline structural component containing an axial crack on the inner surface (Fig. 1). During operation, the component is exposed to internal pressure, which changes cyclically with a constant amplitude, and a series of overloads, the intensity of which is assumed to be independent, equally distributed random variables distributed according to the normal law (Fig. 2).

Fig.1. Structural component.

Fig.2. Load history.

The history of operational loading is represented as a sequence of two blocks (Fig. 3): a block of constant amplitude loading with the stress range Δ S and a block of overloads Σ 1 ,Σ 2 ,…,Σ k . In this case, the amplitude values of overloads are assumed to be independent random variables distributed according to the normal law. Let us first consider the kinetics of a crack under the action of the first loading block consisting of cycles with a constant stress range Δ S and stress ratio R r . We will assume that the crack kinetics is described by the modified Paris equation:

m

1 R        I

da

,

(1)

C K

 

dN





r

r