PSI - Issue 36

Ivan Pidgurskyi et al. / Procedia Structural Integrity 36 (2022) 190–196 Ivan Pidgurskyi, Mykola Stashkiv, Mykola Pidgurskyi et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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Analysis of the SIF distribution along the front of the saddle-shaped surface crack shows that the maximum increase of SIFs occurs in the conjugation zone and minimal outside it (Pidgurskyi et al. (2020), Pidgurskyi et al. (2021)). Therefore, the calculation of the durability N coal during the cracks coalescence was carried out on the basis of the integration of the Paris – Erdogan modified differential equation, which describes the average amplitude of the KDFF: = ∫ (∆ 1 ) , (1) where ∆ is the range of the SIF for the deepest point a coal of the series of saddle-shaped contours of the surface crack; a coal is the distance from the deepest point of each of the contours to the front surface of the sample. SIF is determined either directly from the simulation experiment (by FEM for each of the contours that smooth the saddle-shaped front), or by regression equation: = 3.42 + 2.47 ( 4 ) − 6.63 ( ) − 16.82 ( 4 ) ( ) + 28.34 ( 4 ) 2 + 6.84 ( ) 2 , (2) where are the coalescence factors that characterized the ratio of SIF K I at the extreme (deepest) points of the saddle-shaped front of a series of studied contours to the SIF values at the surface points C of the merging cracks: = = 1 . (3) It is worth noting about the good convergence of the results for N coal for both calculation methods (see Table 1). For the case of coalescence of two surface cracks, each of which has the shape parameters a = 5.5 mm and c = 5.5 mm (data of Table 1), the distribution of the SIF values ∆ ( R = 0.25) and the change in the crack growth rate V coal in the coalescence zone depending on the a coal are presented in Fig. 2 a, b.

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b

Fig. 2. Distribution of the range of SIF values in the zone of coalescence of surface cracks (a) and the change of the crack growth rate at the deepest point of the saddle-shaped front in the process of cracks coalescence (b) with geometric parameters: a = 5.5 mm; c = 5.5 mm; a/c = 1 and σ n = 187.5 MPa. Analysis of the SIF distribution and crack growth rates in the coalescence zone shows that their values are maximal at the initial stage of coalescence, then there is a significant decrease in these factors in the range of 0.1 < < 0.5…0.6 and their stabilization at higher values of . Such regularities are characteristic for other a/c ratios for the same length of the major crack (4 c = 22 mm), as well as for other, much smaller sizes of crack. It should be noted that the SIF distribution in the coalescence zone and the shape of the surface cracks significantly affect the durability of the coalescence process N coal (Fig. 3 a, b).