PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 236–246 Author name ./ Structural Integrity Procedia 00 (2019) 000–000

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S'' { x } standard deviation of prior probabilistic distribution of x Y ( a ) correction function β deformation constraint factor Δ K I stress intensity factor range Δ S stress range under constant amplitude loading δ wall thickness φ ( i ) retardation function ω Wheeler crack retardation exponent

A significant number of studies are focused on the investigation of the processes of cyclic damage accumulation and fracture, in a probabilistic formulation (Harris, 1995; Matvienko et al., 2021). These studies are based on the linear fracture mechanics and the hypothesis of linear accumulation of damage without taking into account the effects of crack closure, residual stresses, and the formation of plastic deformations in the zones of propagating cracks after overloads. Models based on the linear damage accumulation hypothesis tend to be overly conservative. In particular, when assessing the probability of fatigue failure, the influence of the crack retardation effect is not taken into account. This effect can lead to a significant change in the cyclic fatigue life and failure probability after a given number of regular loading cycles. The fact that the effect of crack retardation after overloads is often neglected when the statistical description of crack growth processes can be partially explained by the fact that the associated error leads to conservative estimates. However, since the implementation of the risk-based approach requires more accurate estimates of failure probability, the influence of this effect should be taken into account. A significant number of studies are focused on the investigation of the processes of cyclic damage accumulation and fracture, in a probabilistic formulation (Harris, 1995; Matvienko et al., 2021). These studies are based on the linear fracture mechanics and the hypothesis of linear accumulation of damage without taking into account the effects of crack closure, residual stresses, and the formation of plastic deformations in the zones of propagating cracks after overloads. Models based on the linear damage accumulation hypothesis tend to be overly conservative. In particular, when assessing the probability of fatigue failure, the influence of the crack retardation effect is not taken into account. This effect can lead to a significant change in the cyclic fatigue life and failure probability after a given number of regular loading cycles. The fact that the effect of crack retardation after overloads is often neglected when the statistical description of crack growth processes can be partially explained by the fact that the associated error leads to conservative estimates. However, since the implementation of the risk-based approach requires more accurate estimates of failure probability, the influence of this effect should be taken into account. 2. Kinetic equation of a crack and its cycle-by-cycle integration taking into account the effect of crack retardation During operation, structural components are commonly subjected to variable cyclic loading, which includes cycles with increased tension (overloads) or compression (underloads) impacts. The presence of such overload cycles predetermines more complex kinetics of fatigue cracks than that which occurs in the case of the component exposure to regular loading with constant amplitude cycles. The sequences of irregular loading of structural components can be considered as a set of tensile and compressive loads, the effect of which on the kinetics of the crack is repeatedly superimposed on each other. Such a superposition of the effects of overloads and underloads is called the effect of the sequence of loads or the interaction of amplitudes (Schijve, 2009). A single tensile overload (Fig. 1), which leads to crack retardation over a certain time interval, has a significant effect on the growth of a fatigue crack. The graph of the change in the rate of crack growth if a single overload is superimposed on a sequence of regular loading cycles with a constant amplitude has three ranges. In the range I (segment OA ) until the moment of overloading, the kinetics of the crack coincides with the kinetics of the crack in the case of regular constant amplitude loading. Point A corresponds to the moment of application of the overload, which creates a plastic zone from overload R p,OL (Fig.2a), in which residual compressive stresses act, which leads to crack retardation. Throughout range II (segment AB ), while the crack moves inside the plastic zone induced by the overload, it is retarded (Fig.2b). At point B , the plastic zone from the current regular loading cycle reaches the border of R p,OL zone (Fig.2c) and the overload retardation effect ceases to act (segment BC ).