PSI - Issue 81

Ivan Pidgurskyi et al. / Procedia Structural Integrity 81 (2026) 47–53

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4. Statistical Mathematical Model of the Functional Variation of the Interaction Factor of Two Identical Surface Cracks Processing of the obtained dataset from the simulation experiment on surface cracks interaction, as well as interpretation and analysis of the regression analysis results for the interaction factors γ int = f ( a / t ; a / c ; t s / c ), were carried out using specialized software (Statistica). It should be noted that regression analysis is employed to construct a mathematical model of the process under investigation by selecting a plausible functional relationship that links the response variable to the input factors. After verifying the adequacy of the approximating model using Fisher’s F -test and assessing the statistical significance of the regression equation factors using Student’s t -test, followed by transformation of the input factors from coded form to their natural values, a regression equation was obtained. These equations functionally describe the variation of the interaction factor γ С for the inner points C of semi-elliptical surface cracks: ( , , ) = 1.0109 + 1.0440 −0.0576 −0.2509 +0.6136( ) 2 +0.1043( ) 2 +0.3185( ) 2 − −0.6832( ∙ )−1.2209( ∙ )+0.0750( ∙ ); (1) and interaction factor γ A for the deepest point A of each identical surface crack: ( , , ) = 0.9824 + 0.1251 +0.1015 +0.0535 +0.4079( ) 2 +0.0442( ) 2 −0.0494( ) 2 − −0.3757( ∙ )−0.1306( ∙ )−0.1044( ∙ ). (2) The response surfaces of the interaction factors γ С (positions a , b ) for the inner point and γ A (positions c , d ) for the deepest point are shown in Fig. 6. Analysis of the data (Table 1) and the response surfaces (Fig. 6), constructed on the basis of Equations (1) and (2), indicates that the parameter exerting the greatest influence on the variation of the interaction factors γ С and γ A is t s / c , namely, the reduction in the distance between identical coplanar surface cracks on the specimen surface.

Fig. 6. Response surfaces of the interaction factor γ С the inner points C (a, b) in the mutual interaction zone of two identical surface cracks and the interaction factor γ A for the deepest points (c, d), as a function γ int = f ( a / t ; a / c ; t s / c ).