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Article

Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects

by
Roman Kvit
1,
Petro Pukach
2,
Tetyana Salo
1 and
Myroslava Vovk
1,*
1
Department of Advanced Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, Ukraine
2
Department of Computational Mathematics and Programming, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
Modelling 2024, 5(4), 1568-1581; https://doi.org/10.3390/modelling5040082
Submission received: 17 August 2024 / Revised: 30 September 2024 / Accepted: 17 October 2024 / Published: 19 October 2024

Abstract

Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are uniformly distributed cracks that do not interact with each other, the plane of which is normal to the surface, and the depth is much less than its length on the surface. The cracks’ depth and angle of orientation are random values, and their joint distribution density is specified. Plates made of this material are under the influence of biaxial loading. The probability of failure, along with the mean value, the dispersion, and the variation coefficient of the plate’s strength, taking into account the surface defects under different types of stress, were determined. Their dependence on the type of loading, the size of the plate, and the surface structural heterogeneity of the material were studied graphically. Joint consideration of the influence of the interrelated properties of real materials, such as defectiveness and stochasticity, on strength and fracture, opens up new opportunities in creating a theory of strength and fracture of deformable solids.
Keywords: probability of failure; surface defects; isotropic material; failure loading; stochasticity; integral probability distribution function probability of failure; surface defects; isotropic material; failure loading; stochasticity; integral probability distribution function

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MDPI and ACS Style

Kvit, R.; Pukach, P.; Salo, T.; Vovk, M. Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects. Modelling 2024, 5, 1568-1581. https://doi.org/10.3390/modelling5040082

AMA Style

Kvit R, Pukach P, Salo T, Vovk M. Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects. Modelling. 2024; 5(4):1568-1581. https://doi.org/10.3390/modelling5040082

Chicago/Turabian Style

Kvit, Roman, Petro Pukach, Tetyana Salo, and Myroslava Vovk. 2024. "Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects" Modelling 5, no. 4: 1568-1581. https://doi.org/10.3390/modelling5040082

APA Style

Kvit, R., Pukach, P., Salo, T., & Vovk, M. (2024). Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects. Modelling, 5(4), 1568-1581. https://doi.org/10.3390/modelling5040082

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