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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3. Statistical mathematical model of functional change of coalescence factor in the zone of coalescence of two identical surface cracks Processing of the obtained experimental data set of simulation modeling of surface crack coalescence, interpretation and analysis of the regression analysis obtained results of the coalescence factor = ( 4 ; ) was performed using a specialized software program Statistica (Santorico et al. (2010)). It should be noted that the regression analysis is used to construct a mathematical model of the studied process by selecting a probable dependence that relates the response to the input factors (Fig. 1). After checking the adequacy of the approximating model by Fisher's F-test and evaluating the statistical significance of the regression equation factors by Student's t-test and the subsequent transition from coded notation of input factors to natural quantities, we obtained the regression equation that functionally describes the change of coalescence factor γ coal during the coalescence of two semi-elliptic surface cracks into one major surface crack: = 3.42 + 2.47 ( 4 ) − 6.63 ( ) − 16.82 ( 4 ) ( ) + 28.34 ( 4 ) 2 + 6.84 ( ) 2 . (2) The obtained regression equation can be used to determine the nature of the functional change of the coalescence factor γ coal during coalescence of surface cracks, depending on their relative geometric dimensions a/ 4 c , and the geometry of the coalescence zone of the cracks a coal / a within the variation of variable factors 0,075 ≤ a /4 c ≤ 0.250; 0.1≤ a coal / a ≤0.95. According to the obtained regression equation, the response surface (Fig. 3, a) and the two-dimensional cross section of the response surface (Fig. 3, b) of the change of the coalescence factor in the zone of coalescence of identical surface cracks as a functional = ( 4 ; ) are built.

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Fig. 3. The response surface (a) and the two-dimensional cross-section (b) of the response surface of the change of the coalescence factor in the zone of coalescence of identical surface cracks as a functional = ( 4 ; ) . Analysis of the regression equation factors, response surface and its cross-section indicates on a significant effect of crack geometry (ratio of surface crack depth to the sum of axes of two cracks 4 c on the sample surface) and the position of the deepest point of the saddle-shaped contour a coal during coalescence, which is categorized by ratio a coal / a . The factor that has the greatest (dominant) influence on the change of the approximated values of the coalescence factor γ coal is the ratio a coal / a . The ratio a/ 4 c has a less significant effect on the change of the