S. S. Volkov
THE EFFECT OF DAMAGE AT AN ENSEMBLE OF MICROSTRUCTURE POINTS ON THE MARGIN OF SAFETY IN STRUCTURALLY HETEROGENEOUS MATERIALS
DOI: 10.17804/2410-9908.2019.5.060-072 Fracture concentration regions are considered in a microstructure under loading. A mathematical model of a micro-heterogeneous medium with random properties of elements is used for the calculations. The initial data in the problem includes the characteristics of the distributions of random elastic moduli and ultimate strengths in the microstructure elements. The microstructure strength condition is a difference between stresses and ultimate strengths for a multitude of points of a given configuration. The probability of stress simultaneously exceeding the ultimate strength in a given set of elements determines the probability of fracture in this ensemble of points and relative damage at the micro level. A multidimensional normal distribution is used to calculate damage. The structure of the correlation matrix of distribution takes into account the kind of the damage concentration region. The relationship between critical microstructure damage and the margin of safety is determined. Examples of calculating the probability of fracture in two, three, and four microstructure elements are given.
Keywords: random properties, microstructure damage, multidimensional probability distribution, ultimate strength, margin of safety  References:
1. Yokobori T. An Interdisciplinary Approach to Fracture and Strength of Solids, Groningen, Wolters-Noordhoff Scientific LTD, 1968.
2. Vildeman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of Non Elastic Deformation and Fracture of Composite Materials]. Nauka Publ., Moscow, 1997. (In Russian).
3. Volkova T.A., Volkov S.S. Microstructure damage related to stress- strain curve for grain composites. Theoretical and Applied Fracture Mechanics, vol. 52, iss. 2, 2009, pp. 83–90. DOI: 10.1016/j.tafmec.2008.02.004.
4. Sih G. C. Fracture mechanics in retrospect in contrast to multiscaling in prospect. In: Proceedings of the 17-th National Conference of Italian Group of Fracture, ed. by A. Finelli and L. Nobile, Bologna, June 16–18, 2004, pp. 15–37.
5. Trusov P.V., Volegov P.S., Yanz A.Yu. Two-scale models of polycrystals: Evaluation of validity of Ilyushin’s isotropy postulate at large displacement gradients. Physical Mesomechanics, 2016, vol. 19, no. 1, pp. 21–34. DOI: 10.1134/S1029959916010033.
6. Surikova N.S., Panin V.E., Derevyagina L.S., Lutfullin R.Ya., Manzhina E.V., Kruglov A.A., Sarkeeva A.A. Micromechanisms of deformation and fracture in a VT6 titanium laminate under impact load. Physical Mesomechanics, 2015, vol. 18, no. 3, pp. 250–260. DOI: 10.1134/S1029959915030091.
7. Schastlivtsev V.M., Tabatchikova T.I., Yakovleva I.L., Klyueva S.Yu., Kruglova A.A., Khlusova E.I., Orlov V.V. Microstructure and properties of low-carbon weld steel after thermomechanical strengthening. The Physics of Metals and Metallography, 2012, vol. 113, no. 5, pp. 480–488. DOI: 10.1134/S1029959915030091.
8. Pugacheva N.B., Bykova T.M., Trushina E.B., Malygina I.Yu. The Structural State and Properties of a Deposited Coating for an Internal Combustion Engine Valve. Diagnostics, Resource and Mechanics of materials and structures, 2018, iss. 5, pp. 74–85. DOI: 10.17804/2410-9908.2018.5.074-085. URL: http://dream-journal.org/issues/2018-5/2018-5_186.html (accessed 30.11.2019).
9. Zaitsev A.V. Second-order moment functions for the random structure of unidirectionally reinforced fibrous composites. In: Vestnik UGTU-UPI. Mekhanika microneodnorodnykh materialov i razrushenie [Herald of UGTU-UPI, Mechanics of Micro-Heterogeneous Materials and Fracture]. Ekaterinburg, UGTU-UPI Publ., 2006, no. 11 (82), pp. 161–167. (In Russian).
10. Smirnov S.V., Konovalov A.V., Myasnikova M.V., Khalevitsky Yu.V., Smirnov A.S., Igumnov A.S. A Computational Model of V95/sicp (7075/ Sicp) Aluminum Matrix Composite Applied to Stress-Strain State Simulation under Tensile, Compressive and Shear Loading Conditions. Diagnostics, Resource and Mechanics of materials and structures, 2017, iss. 6, pp. 16–27. DOI: 10.17804/2410-9908.2017.6.016-027. Available at: http://dream-journal.org/issues/2017-6/2017-6_133.html (accessed 14.10.2019).
11. Panin V.E., Derevyagina L.S., Lebedev M.P., Syromyatnikova A.S., Surikova N.S., Pochivalov Yu.I., Ovechkin B.B. Scientific Basis for Cold Brittleness of Structural BCC Steels and Their Structural Degradation at Below Zero Temperatures. Phys. Mesomech., 2017, vol. 2 (2), pp. 125–133. DOI: 10.1134/S1029959917020023.
12. Panin S.V., Marushchak P.O., Vlasov I.V., Eremin A.V., Byakov A.V., Syromyatnikova A.S., Stankevich R. Structure and Fatigue Durability of 09mn2si Pipe Steel after Long-Term Operation in Far North Conditions. Diagnostics, Resource and Mechanics of materials and structures, 2017, iss. 4, pp. 81–85. DOI: 10.17804/2410-9908.2017.4.081-085. Available at: http://dream-journal.org/issues/2017-4/2017-4_164.html (accessed 14.10.2019).
13. Mironov V.I., Emelyanov I.G., Vichuzhanin D.I., Kamantsev I.S., Yakovlev V.V., Ogorelkov D.A., Zamaraev L.M. A Method for Experimental Investigation of Degradation Processes in Materials. Diagnostics, Resource and Mechanics of materials and structures, 2019, iss. 2, pp. 16–27. DOI: 10.17804/2410-9908.2019.2.016-027. Available at: http://dream-journal.org/issues/2019-2/2019-2_246.html (accessed 30.11.2019).
14. Mitropolsky A.K. Tekhnika statisticheskykh vychisleniy [The technique of Statistical Computations]. Nauka Publ., Moscow, 1971. (In Russian).
15. Volkova T.A., Volkov S.S. Microstructure damage at ensemble of points for grain composites. Theoretical and Applied Fracture Mechanics, 2010, vol. 54, iss. 3, pp. 149–155. DOI: 10.1016/j.tafmec.2010.10.010.
16. McLean D. Mechanical Properties of Metals, Wiley, New York, 1962. С. С. Волков
ВЛИЯНИЕ ПОВРЕЖДЕННОСТИ АНСАМБЛЯ ТОЧЕК МИКРОСТРУКТУРЫ НА ЗАПАС ПРОЧНОСТИ СТРУКТУРНО-НЕОДНОРОДНЫХ МАТЕРИАЛОВ
Рассматриваются зоны концентрации разрушений в элементах микроструктуры деформируемого материала. Для расчетов используется математическая модель микронеоднородной среды со случайными свойствами элементов. Исходными данными задачи являются характеристики распределения случайных модулей упругости и предела прочности в элементах микроструктуры. Микроструктурное условие прочности представляет собой разницу между напряжениями и пределом прочности для множества точек данной конфигурации. Вероятность одновременного превышения напряжением предела прочности в данном множестве элементов определяет вероятность разрушения этого ансамбля точек и относительную поврежденность на микроуровне. В расчетах поврежденности используется многомерное нормальное распределение. Структура корреляционной матрицы распределения учитывает вид зоны концентрации разрушений. Найдена зависимость между величиной критической микроструктурной поврежденности материала и запасом прочности. Проведены примеры расчетов вероятности разрушения в двух, трех и четырех элементах микроструктуры.
Ключевые слова: случайные свойства, поврежденность микроструктуры, многомерное распределение вероятностей, предел прочности, запас прочности Библиография:
1. Yokobori T. An Interdisciplinary Approach to Fracture and Strength of Solids. – Groningen : Wolters-Noordhoff Scientific LTD, 1968.
2. Вильдеман В. Э., Соколкин Ю. В., Ташкинов А. А. Механика неупругого деформирования и разрушения композитных материалов / под ред. Ю. В. Соколкина. – М. : Наука. Физматлит, 1997. – 288 с.
3. Volkova T. A., Volkov S. S. Microstructure damage related to stress- strain curve for grain composites // Theoretical and Applied Fracture Mechanics. – 2009. – Vol. 52, iss. 2. – P. 83–90. – DOI: 10.1016/j.tafmec.2008.02.004.
4. Sih G. C. Fracture mechanics in retrospect in contrast to multiscaling in prospect // Proceedings of the 17-th National Conference of Italian Group of Fracture / ed. by A. Finelli and L. Nobile, Bologna, June 16–18, 2004. – P. 15–37.
5. Trusov P. V., Volegov P. S., Yanz A. Yu. Two-scale models of polycrystals: Evaluation of validity of Ilyushin’s isotropy postulate at large displacement gradients // Physical Mesomechanics. – 2016. – Vol. 19, no. 1. – P. 21–34. – DOI: 10.1134/S1029959916010033.
6. Micromechanisms of Deformation and Fracture in a VT6 Titanium Laminate under Impact Load / N. S. Surikova, V. E. Panin, L. S. Derevyagina, R. Ya. Lutfullin, E. V. Manzhina, A. A. Kruglov, A. A. Sarkeeva // Phys. Mesomech. – 2015. – Vol. 18, no. 3. – P. 250–260. – DOI: 10.1134/S1029959915030091.
7. Microstructure and properties of low-carbon weld steel after thermomechanical strengthening / V. M. Schastlivtsev, T. I. Tabatchikova, I. L. Yakovleva, S. Yu. Klyueva, A. A. Kruglova, E. I. Khlusova, V. V Orlov // The Physics of Metals and Metallography. – 2012. – Vol. 113, no. 5. – P. 480–488. – DOI: 10.1134/S1029959915030091.
8. The Structural State and Properties of a Deposited Coating for An Internal Combustion Engine Valve / N. B. Pugacheva, T. M. Bykova, E. B. Trushina, I. Yu. Malygina // Diagnostics, Resource and Mechanics of materials and structures. – 2018. – Iss. 5. – P. 74–85. – DOI: 10.17804/2410-9908.2018.5.074-085. – URL: http://dream-journal.org/issues/2018-5/2018-5_186.html (accessed 30.11.2019).
9. Зайцев А. В. Моментные функции второго порядка случайной структуры однонаправленно армированных волокнистых композитов // Вестник УГТУ-УПИ. Механика микронеоднородных материалов и разрушение : сборник научных трудов. – Екатеринбург : УГТУ–УПИ, 2006. – № 11 (82). – С. 161–167.
10. A Computational Model of V95/sicp (7075/ Sicp) Aluminum Matrix Composite Applied to Stress-Strain State Simulation under Tensile, Compressive and Shear Loading Conditions / S. V. Smirnov, A. V. Konovalov, M. V. Myasnikova, Yu. V. Khalevitsky, A. S. Smirnov, A. S. Igumnov // Diagnostics, Resource and Mechanics of materials and structures. – 2017. – Iss. 6. – P. 16–27. – DOI: 10.17804/2410-9908.2017.6.016-027. – URL: http://dream-journal.org/issues/2017-6/2017-6_133.html (accessed 14.10.2019).
11. Scientific Basis for Cold Brittleness of Structural BCC Steels and Their Structural Degradation at Below Zero Temperatures / V. E. Panin, L. S. Derevyagina, M. P. Lebedev, A. S. Syromyatnikova, N. S. Surikova, Yu. I. Pochivalov, B. B. Ovechkin // Phys. Mesomech. – 2017. – Vol. 2 (2). – P. 125–133. – DOI: 10.1134/S1029959917020023.
12. Structure and Fatigue Durability of 09mn2si Pipe Steel after Long-Term Operation in Far North Conditions / S. V. Panin, P. O. Marushchak, I. V. Vlasov, A. V. Eremin, A. V. Byakov, A. S. Syromyatnikova, R. Stankevich // Diagnostics, Resource and Mechanics of materials and structures. – 2017. – Iss. 4. – P. 81–85. – DOI: 10.17804/2410-9908.2017.4.081-085. – . URL: http://dream-journal.org/issues/2017-4/2017-4_164.html (accessed 14.10.2019).
13. A Method for Experimental Investigation of Degradation Processes in Materials [Electronic resource] / V. I. Mironov, I. G. Emelyanov, D. I. Vichuzhanin, I. S. Kamantsev, V. V. Yakovlev, D. A. Ogorelkov, L. M. Zamaraev // Diagnostics, Resource and Mechanics of materials and structures. – 2019. – Iss. 2. – P. 16–27. – DOI: 10.17804/2410-9908.2019.2.016-027. – URL: http://dream-journal.org/issues/2019-2/2019-2_246.html (accessed 30.11.2019).
14. Митропольский А. К. Техника статистических вычислений. – Москва : Наука, 1971. – 576 с.
15. Volkova T. A., Volkov S. S. Microstructure damage at ensemble of points for grain composites // Theoretical and Applied Fracture Mechanics. – 2010. – Vol. 54, iss. 3. – P. 149–155. – DOI: 10.1016/j.tafmec.2010.10.010.
16. Мак Лин Д. Механические свойства металлов / пер. с англ. Л. И. Миркина ; под ред. Я. Б. Фридмана. – Москва : Металлургия, 1965. – 431 с. 
Библиографическая ссылка на статью
Volkov S. S. The Effect of Damage at An Ensemble of Microstructure Points on the Margin of Safety in Structurally Heterogeneous Materials // Diagnostics, Resource and Mechanics of materials and structures. -
2019. - Iss. 5. - P. 60-72. - DOI: 10.17804/2410-9908.2019.5.060-072. -
URL: http://dream-journal.org/issues/2019-5/2019-5_274.html (accessed: 30.03.2025).
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