PSI - Issue 36

Oleksandr Andreykiv et al. / Procedia Structural Integrity 36 (2022) 36–42 Oleksandr Andreykiv, Andri і Babii, Iryna Dolinska et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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(2014a ), Popovіch et al. (2014 b), Kharchenko et al. (2014), Polishchuk et al. (2015)). This equipment includes also field sprayers, where the boom length reaches up to 25 m. In the operation process, complex manoeuvre boom loadings take place, in particular, bending oscillations due to the length, as well as shocks caused by obstacle crossings. Therefore, the development of methods for residual lifetime prediction with respect to manoeuvre loadings and corrosive-aggressive environments is of importance for the failure prediction of sprayers. To consider the manoeuvre loading at the residual lifetime calculation of boom elements, the authors apply their developed earlier theory, that has been used for oil pipeline calculations with consideration of the turbulent oil flow, openings and closings of pipe valves and hydraulic shocks (Andreikiv et al. (2018a), Andreikiv et al. (2019), Andreikiv et al. (2016)). The application of this theory allowed us to correctly perform the calculations for elements of power-generating equipment under manoeuvre loading, in particular, a steam turbine wheel and a gas pipeline (Andreikiv et al. (2018b), Dolins’ka (2018)). Besides the manoeuvre loading, this paper considers the influence of the corrosive environment on the residual lifetime of boom elements. It is performed by adaptation of the energy approach developed earlier by the authors based on the first law of thermodynamics (Andreikiv et al. (2011), Andreikiv et al. (2012)). 2. Problem statement and solution method Let us consider a long-range field sprayer boom (Fig. 1). During the operation, boom oscillations occur, resulting in tension, compression and bending cyclic loadings being applied to boom elements. These oscillations are modelled by cyclic oscillations with frequency of 1 Hz. f  In addition, the boom is subjected to n occasional shocks resulting from its movement on an uneven field. They cause variation in steady cyclic loading from the maximum impulse ( 1,..., ) i M i n = with further dumping to the initial amplitude of steady oscillations. In engineering, such a loading mode is called manoeuvre (Andreikiv et al. (2017a), Hevko et al. (2019)). Conventionally, (residual) lifetime of a metallic structure is determined by the lifetime of its weakest link, that is, the most stressed boom element. The boom is a three-dimensional structure subjected to bending, thus, the most loaded element is located at the topmost part (Rybak et al. (2018)). This element is a rectangular tube (Fig. 2, a). Hence, the problem lies in determining the lifetime (number of oscillation cycles N N  = or actual operating time t t  = ), when a crack of size 0 l l = initiates in the tube, growth to the size l l  = , and the boom stops performing its functions (full or partial fracture occurs).

Fig. 1. Scheme of a long-range field sprayer boom.

According to the modern theory of fatigue (delayed fracture mechanics of structural elements under variable loading (Andreikiv et al. (2017a), Rudavs’kyi (2015)), the lifetime N  of a structural element under variable loading is determined by:

i s N N N  = + ,

(1)

i N is the period of fatigue crack initiation;

s N is the period of its subcritical growth.

where