PSI - Issue 59

Mykola Pidgurskyi et al. / Procedia Structural Integrity 59 (2024) 322–329 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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process of their propagation take a significant part (from 50 to 90%) of the structure life service from the beginning of operation to the limit state. Therefore, the objects of calculation are welded frames, bridge beams, cabs of trucks, in which edge cracks and internal through-thickness cracks as well as surface fatigue cracks are developing. The calculation model should take into account the main features of the real object and the factors influencing the results of the calculation on one hand and should also allow the possibility of calculation by existing methods and programs on the other hand. The main factors influencing durability are geometry of the structural element and the whole structure, type and parameters of the loading process that determine the stress-strain state (SSS), mechanical properties (resistance characteristics of crack development) of the material in the area of fatigue cracks. In real designs, the cross-sections of rolling elements can be represented in the form of channels, I-beams, T beams, angles, closed profiles, etc. Within the linear fracture mechanics of materials the research of SSS of frame structures, in the presence of crack defects in them, in practice it is reduced to determination of stress intensity factor (SIF). Such problems, taking into account the real loads and geometry of structures, are quite complex in mathematical terms, so the direct application of analytical methods in engineering problems is quite limited (Panasiuk (1992), Andreikiv and Darchuk (1992), Andreikiv et al. (2018)). Promising in this regard are numerical methods, the most effective of which is the finite element method (FEM) (Dunn et al. (1997), Pawar et al. (2016), Pidgurskyi et al. (2021)], which due to its versatility, quite simple interpretation and well-developed mathematical software can get rid of the difficulties that arise when using analytical methods (Panasiuk (1992)). It should be noted that the reliability of the results obtained by FEM is related to the accuracy of the created model. A number of researchers (Zheng et al. (2015)) determine the SIF for cracks that develop in complex structural elements, experimentally, using tensometry and others methods. This method deserves attention, especially for load bearing structures, although it is difficult to interpret for problems with a different element configuration. Therefore, it is expedient to construct relatively simple dependences for the SIF determination in engineering problems, in which lower accuracy of calculation is compensated by low complexity (boundary interpolation method (Andreikiv (1982)), the method of change in section inertia moment during crack propagation (Kienzler and Hermann (1986)). Analysis of the operation of frame structures of mobile machines shows that one of the main types of loads are bending moments (Lyashuk et al. (2023), Syrotyuk et al. (2021), Hevko et al. (2021)). Thus, the boundary interpolation method was used to estimate the SIF for the edge crack that initiate in the flange of the channel (Andreikiv and Darchuk (1992), Rybak (1985)). This problem is asymmetric. Two extreme cases are considered: a small crack compared to the width of the flange, and a large crack approaching the neutral axis. For these cases, the correction function is interpolated to determine the SIF of the real crack that develops in the channel under bending loading. Despite the relative simplicity of the method, the solution of the problem significantly depends on the choice of the relative crack length, which is included in the polynomial of the correction function for SIF when considering individual stages of crack propagation. 2. Methodology of research In order to avoid a significant part of the shortcomings, quite simple and visual engineering method of SIF determining for thin-walled cross-section profiles using the change in inertia moment of the profile cross-section are proposed, the base of which are presented in the paper (Kienzler and Hermann (1986)). In this work, a formula is proposed for determining SIF of normal separation for a crack in strip with rectangular cross-section loaded with a bending moment M :

1 1 1 I I  



K M 

(1)

,

1      2

where M is the bending moment, N∙m ; δ is strip thickness, m; 1 I and 2 I are inertia moments of cross-section without a defect and with a defect, respectively, m 4 .