PSI - Issue 36

Ivan Pidgurskyi et al. / Procedia Structural Integrity 36 (2022) 171–176 Ivan Pidgurskyi, Mykola Pidgurskyi, Petro Yasniy et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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During propagation of a semi-elliptic surface crack (canonical crack shape) in a structural element under cyclic loading, the traditional approach to the analysis of fracture development is quite simple and effective. Stress intensity factors (SIF) are determined by the Newman-Raju equation, and the number of cycles to failure is determined by the Paris – Erdogan equation or dependences that describe the complete kinetic diagram of fatigue life (Anderson (2017), Andreikiv et al. (2020)). With the possible coalescence of surface cracks, the propagation of the major surface crack with a saddle-shaped contour (cracks of non-canonical shape) is observed, which is constantly changing over time. This requires a non standard approach to the analysis of its growth. The difficulties are primarily related to the need of SIF determination along the saddle-shaped contour, which changes under cyclic loading (Coules (2016), Kikuchi (2016), Patel et al. (2010)), because there are no universal calculation dependences for solving this problem. It should be noted that the calculation of SIF must be repeated many times. The finite element method is the most suitable for this (Brighenti et al. (2013)). Significant difficulties are also associated with determination of the shape of the crack contour and the trajectory of its development in the process of cyclic loading (Pidgurskyi et al. (2020), Pidgurskyi et al. (2021)). However, the obtained results are fragmented and not enough to draw general conclusions on this issue. Therefore, the aim of the research is to model the coalescence of identical surface cracks and to develop a mathematical model for SIF determination in the area of the saddle-shaped front of the surface crack. 2. Simulation of coalescence of two identical coplanar surface cracks A simplified approach based on simulation has been proposed to determine the SIF during coalescence of surface cracks. It should be noted that nowadays simulation is the most effective method of studying systems or processes that change over time (Banks et al. (2009), Law (2014)). The simulation modeling methodology of surface crack coalescence meant the solution of two problems, namely substantiation of the coalescence model of two surface cracks into a single major crack (substantiation of crack geometry in a nonstationary process), as well as calculation of formulas that allow to adequately describe SIF along a series of saddle-shaped contours, variable over time, to calculate the residual durability of the structural element according to the experiment (Banks et al. (2009), Law (2014)). Geometrical parameters of the simulation model of coalescence of identical surface cracks are substantiated with the following assumptions: - the process of coalescence of two identical coplanar surface cracks with the sizes of semi-axes a and c and the shape factor a/c was modeled as the development of a major surface crack with axis size 4 c on the surface of element and saddle-shaped contour, which is gradually smoothed out during cyclic loading; - geometric dimensions of surface cracks (lengths of semi-axes a and c , shape factor a/c ) in the process of their coalescence ( ≤ 0.95 ) were considered constant (confirmed by experimental studies (Bezensek et al. (2004)) and comparative results along the crack front (Pidgurskyi et al. (2020)). - the process of smoothening of the saddle-shaped contour was represented by a series of curved lines that simulate the gradual coalescence of cracks within range 0.1 ≤ ≤ 0.95; - conjugation of contours of semi-ellipses was carried out by arcs of circles (fig. 1); Based on the above conditions, a model of the studied object and a block diagram of a simulation of the coalescence of two identical coplanar surface cracks with indication of input and output factors are presented in Fig. 1. The method of conducting a modeling experiment to determine the stress intensity factors along the saddle shaped contour during coalescence of surface cracks is given in (Pidgurskyi et al. (2020)). One of the options (see Table 1) for the SIF distribution along the front of surface cracks during coalescence is presented in Fig. 2. Analysis of the SIF distribution along the front of the saddle-shaped surface crack shows that the maximum increase in SIFs occurs in the saddle-shaped zone and minimal occurs outside it.