<i>Statistical Strength Theory</i>

Volkov, Shulamit; Weiss, George H.

doi:10.1063/1.3050941

Cited by 13 publications

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“…The term "incipient fracture" refers to any local rupture of the continuity of the material-cavity or micro-or macrofracture of any configuration and size. The eorreemess of this hypothesis is confirmed by the basic theorems of the statistical theory of brittle strength [2, 3]. According to this theory the total breaking of the material of the medium occurs upon attainment by the mean stress of the "local strength" -corresponding to the weakest "imperfection," that is, the strength of the entire system is determined by the strength of the weakest place ("imperfection").…”

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Kinetics of the propagation of fractures in the process of explosive breaking of rocks

Mambetov¹,

Mosinets²

1965

Soviet Mining Science

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The explosive breaking of rocks is the formation and development of fractures. This process therefore should be related primarily to the laws of formation and propagation of fractures, the study of which is of definite interest for over-all development of the theory of breaking of rocks.During the propagation of a shock wave in a rock mass,there is "predestruction" of the mass along a system of natural microfractures in a volume of 75-88% of the total volume of breaking; with the subsequent expansion of the detonation products the pressure of the latter expands the forming "predestruction" fractures to the point of total rupture of the structural bonds of the medium [1].The breaking of a rock mass permeated by a chaotic system of natural micro-and maerofraetures therefore must be related primarily to the laws of propagation of the fractures, and not their formation, since from the very beginning there is no lack of strain in the incipient fractures. This assertion corresponds to modern points of view concerning the structure of real solid bodies. The term "incipient fracture" refers to any local rupture of the continuity of the material-cavity or micro-or macrofracture of any configuration and size. The eorreemess of this hypothesis is confirmed by the basic theorems of the statistical theory of brittle strength [2, 3]. According to this theory the total breaking of the material of the medium occurs upon attainment by the mean stress of the "local strength" -corresponding to the weakest "imperfection," that is, the strength of the entire system is determined by the strength of the weakest place ("imperfection"). It is assumed that these imperfections are statistically distributed throughout the entire volume. In rocks, the presence of such imperfections can be caused by tectonic dislocations and local changes of the rocks due to secondary processes.The condition for breaking of fractured media can be written as in [4, 5]: v,,,e _ _ 2~/''~ %AtR321~, 4 V~--V~where V is the velocity of propagation of the fractures, in cm/sec; K is the cohesion modulus of the medium, in kg" em'S/~; R is a constant characteristic of the material, in kg" cm -s/2" s$c -i/2; CS is the velocity ofthetransverse wave, in cm/sec; Cp is the velocity of the longitudinal wave, in cm/sec; 2/o is the length of the initial fractures, in cm; At is the time of application of tensile stresses, in sec; Or is the tensile stress acting at the ends of the fracture, in kg/cm 2.The specific impact of the compressive stresses, necessary and sufficient for a uniform and stable propagation of fractures through the entire volume to be broken, corresponding to the ultimate rate of transformation of the elastic energy of the shock waves into surface energy of the fractures, can be defined as

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Kinetics of the propagation of fractures in the process of explosive breaking of rocks

Mambetov¹,

Mosinets²

1965

Soviet Mining Science

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“…), процесс разрушения носит более сложный характер. Некоторые принципиальные результаты, характеризующие этот вид разрушения, получены в исследова-ниях П. У. Бриджмена [6], А. А. Гвоздева [7], С. Д. Волкова [8,9], О. Я. Берга [1,4].…”

Section: физические основы критерия прочности бетонаunclassified

Stresses in Cement-Concrete Pavement Surfacing Caused by Thermal Shock

Пшембаев¹,

Ковалев²,

Shevchuk³

2016

Nauka teh.

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Belаrusian National Technical University, 2016Реферат. Среди различных воздействий на покрытие автомобильных дорог следует выделить так называемый термиче-ский удар. В зимний период эксплуатации дорожных покрытий на поверхности бетона образуется слой льда. Обычно для его удаления с поверхности дорожного покрытия применяется хлористый натрий, который понижает температуру замер-зания воды и вызывает таяние льда при отрицательной температуре. Поэтому в бетоне, находящемся непосредственно под тающим слоем льда, резко снижается температура, что приводит к значительным напряжениям. Такое явление полу-чило название термического удара (локальное значительное изменение температуры). Этот процесс недостаточно изучен, имеет практическую значимость для оценки прочности и долговечности цементно-бетонного покрытия и поэтому актуа-лен. Целью исследований авторов являлись разработка математической модели и определение допустимых градиен-тов термического удара для цементно-бетонного дорожного покрытия. Для нахождения напряженно-деформированного состояния цементно-бетонных покрытий автомобильных дорог использовали конечно-разностный метод. Составлена компьютерная программа, позволяющая выполнять расчет дорожного покрытия при различных законах распределения температуры по его глубине. Получены закономерности распространения деформаций и напряжений в цементно-бетонном покрытии автомобильных дорог при термическом ударе. Установлен допустимый параметр распределения тем-ператур по толщине покрытия. При расчете использован критерий прочности, основанный на процессе образования и развития микротрещин в бетоне. Выявлено, что термический удар вызывает на поверхности цементно-бетонного по-крытия значительные градиенты температур, приводящие к большим нормальным напряжениям в поверхностном слое бетона. Возможность появления микротрещин в дорожном покрытии определяется характеристиками прочности матери-ала, условиями закрепления плиты и градиентом температур.Ключевые слова: температура, градиент, напряжения, прочность, бетон, критерий, покрытие, автомобильная дорога, конечные разности, обледенение, граница, сплошность, микротрещины

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“…The energy of a single microcrack in field (2) is defined by E M H ik ik = -. If the normalized distribution function has the following form [4]:…”

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“…This assumption is based on the experimental data of [4], where it was shown that ¿ = 1inside a microcrack.…”

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Development and application of radiowave photoelasticity for the fracture analysis of dielectrics

2011

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The radiowave photoelasticity method is developed and is justified for use in the fracture mechanics of dielectrics. The damage tensors of a material with microcracks are considered. The basic equations of the method are given. The time-dependence of microcrack density is analyzed. Numerical results are presented and analyzed Keywords: radiowave photoelasticity method, dielectrics, damage, microcrack density Introduction. The development of theoretical (analytic, numerical) and experimental methods for stress analysis of modern structures and their elements (plates, shells) made of homogeneous and inhomogeneous anisotropic materials is of importance for various branches of engineering. There is an increasingly urgent need for experimental methods for studying the time-dependent mechanical behavior of isotropic and anisotropic bodies, especially if they have crack-like stress concentrators.The most complete results on the development of the photoelastic method are presented in [8]. Among them are photoplasticity [8], photoviscoelasticity [13], integral photoelasticity [1], dynamic photoelasticity [6,8], and radiowave and infrared photoelasticity [9].The fracture of bodies (materials) involves the nucleation and propagation of cracks that create free surfaces under loading. This process is considered in static, kinematic, and dynamic aspects. The fracture of a material is known to be a complex process, even in the ideal case (isotropic homogeneous material). The process is even more complicated if the material is anisotropic or has plastic strains, residual strains, defects, or inhomogeneities. Fracture theory devotes particular attention to fatigue failure due to gradual crack growth under cyclic or long-term loading. In these cases, fatigue failure results from the accumulation of irreversible damage in the material. Cracks (changes in the material) start developing in bodies long before their failure (either plastic or brittle).Dynamic photoelasticity [6] in the macrofracture mechanics of anisotropic materials was addressed in the papers [14-18] which analyzed the stress-strain state (SSS) of isotropic and anisotropic plates with cracks subject to creep or dynamic loading.The present paper develops the radiowave photoelasticity method for the stress analysis of solid bodies. It is based on the distribution of electromagnetic waves in anisotropic and isotropic bodies (dielectrics and semiconductors including ceramics, plastics, ferrite, etc.) opaque to visible light. This method is advantageous over photoelasticity by making it possible to analyze the SSS of dielectrics using the invisible (ultrahigh frequency) spectrum of electromagnetic waves.Our goal is to justify the use of polarized radio-waves for examining (detecting and analyzing) microcracks in dielectrics.1. Macroscopic Damage Tensor. The nucleation and propagation of submicrocracks in dielectrics can be described based on the dislocation model [3] because cracks are generated by some type of incompatibility in a continuum. A crack is represented by a s...

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Statistical Strength Theory

Cited by 13 publications

References 0 publications

Kinetics of the propagation of fractures in the process of explosive breaking of rocks

Kinetics of the propagation of fractures in the process of explosive breaking of rocks

Stresses in Cement-Concrete Pavement Surfacing Caused by Thermal Shock

Development and application of radiowave photoelasticity for the fracture analysis of dielectrics

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