PSI - Issue 48

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Shanyavskiy A. et al. / Procedia Structural Integrity 48 (2023) 119–126 Shanyavskiy et al/ Structural Integrity Procedia 00 (2023) 000–000

Nomenclature γ

an experimentally determined parameter describing the rate of damage accumulation

κ the degradation coefficient of the modulus, which is established in the course of computational experiments λ , μ Lamé parameters σ –1 fatigue limit σ̃ –1 fatigue limit in the VHCF region max 1  the value of the maximum main tensile stress σ eq the equivalent stress, which for the case of uniaxial loading coincides with the cyclic stress σ n maximum tensile stress acting on a certain area with a normal n σ U ultimate tensile strength of material τ n maximum shear stress acting on a certain area with a normal n ψ distributed damage function E the Young's modulus of material N the number of cycles The second reason is that the in-service operating conditions do not meet the estimated conditions used in the calculations of durability for the structural element. The main cause for this event can be occurrence of not estimated operational modes, related to, in particular, the resonance conditions. This discrepancy in operating conditions is not a frequent one, however it can be directed to realization of the VHCF regime mechanisms. Finally, as the lifetime increases for a structural element, the behavior of the metal is considered based on the assumption that the realized stress level is below the “fatigue limit”. However, the stress level in a component related to area where the mechanism of VHCF behavior takes place in spite of cracks appear and develop by the surface because of high level of stress concentration. Thus, due to the increase in the in-service operating lifetime of structural elements, the probability of fatigue crack initiation in them by the VHCF mechanism is growing. 2. Fatigue fracture of reducer gears in the transition region from VHCF to HCF The in-service experience shows that, for one reason or another, in the gears of aircraft engine gearboxes, fatigue cracks occur, the propagation of which can lead to the in-service failure of gears at different operating times as was demonstrated by Korablev and Reshetov (1968), Shanyavskiy and Skvortsov (1999), and Shanyavskiy et al. (2017). The allowable stress level in gears with taking into account the safety factor is below the fatigue limit σ –1 , which implies their operation for tens of thousands of hours without failure, if stress concentrators material defects during manufacturing did not occur in them or damage of them did not appear during operation. These assumptions are confirmed by the experience of operating gears, in which the initiation and propagation of fatigue cracks took place during their long service life (Shanyavskiy and Skvortsov (1999)). At the moment of failure of the gears, with cracks initiated by material tears and other defects, their lifetime in-service was more than 10 9 loading cycles, and the cases of crack appearance were sporadic for this type of gear. The indicated lifetime in-service is, at least, an order of magnitude higher than life corresponding to the high cycle fatigue region (HCF), for which the regularities of initiation and propagation of fatigue cracks have been studied and investigated for various types of materials and, mainly, for steels. In the case of increased durability of gears, which are designed according to the safe life principle, up to 10 9 -10 10 cycles, the critical state may occur with the subsurface initiation of fatigue cracks. The surface layer of gears is subjected to carburization in order to increase fatigue strength that leads to reduction of material ductility. Due to the difference in the plasticity of surface layer and bulk material, there is a high probability of a natural initiation of subsurface fatigue crack within the carburized surface layer during the increase in the operating time (Korablev and Reshetov (1968)). Moreover, the mechanisms of subsurface origin formation can be different. These mechanisms are studied and described in detail in Shanyavskiy (2007) and Shanyavskiy et al. (2022).