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 Bibliography:
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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:
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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: 21.11.2024).
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