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

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, t...

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Main Authors: Roman Kvit, Petro Pukach, Tetyana Salo, Myroslava Vovk
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Modelling
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Online Access:https://www.mdpi.com/2673-3951/5/4/82
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author Roman Kvit
Petro Pukach
Tetyana Salo
Myroslava Vovk
author_facet Roman Kvit
Petro Pukach
Tetyana Salo
Myroslava Vovk
author_sort Roman Kvit
collection DOAJ
description 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.
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spelling doaj-art-2f920eb63f8240e09269741b0859f8ae2025-08-20T02:56:54ZengMDPI AGModelling2673-39512024-10-01541568158110.3390/modelling5040082Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface DefectsRoman Kvit0Petro Pukach1Tetyana Salo2Myroslava Vovk3Department of Advanced Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, UkraineDepartment of Computational Mathematics and Programming, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, UkraineDepartment of Advanced Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, UkraineDepartment of Advanced Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, UkraineBased 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.https://www.mdpi.com/2673-3951/5/4/82probability of failuresurface defectsisotropic materialfailure loadingstochasticityintegral probability distribution function
spellingShingle Roman Kvit
Petro Pukach
Tetyana Salo
Myroslava Vovk
Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
Modelling
probability of failure
surface defects
isotropic material
failure loading
stochasticity
integral probability distribution function
title Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
title_full Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
title_fullStr Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
title_full_unstemmed Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
title_short Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects
title_sort statistical modeling and probable calculation of the strength of materials with random distribution of surface defects
topic probability of failure
surface defects
isotropic material
failure loading
stochasticity
integral probability distribution function
url https://www.mdpi.com/2673-3951/5/4/82
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