A statistical strength criterion for brittle materials

Published on Nov 9, 2011in Strength of Materials0.592
· DOI :10.1007/S11223-011-9330-9
D. V. Babich1
Estimated H-index: 1
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Abstract
Based on a probabilistic model of brittle microfracture (microdamage) leading to macrofracture of materials, we propose a statistical interpretation of strength criteria, which relate start of macrofracture (manifested by macrocrack formation in tension or internal structure stability loss in compression) with attainment of a certain (critical) value of density of microdefects in the material under study. The criterion is reduced to comparative analysis of microdefect density induced by the particular loading type and its critical value, which is intricnsic to this material and is invariant to the stressed state type.
References3
Newest
Jan 1, 2010·Journal of Strain Analysis for Engineering Design1.63
#1D V Babich (NASU: National Academy of Sciences of Ukraine)H-Index: 1
#2V N Bastun (NASU: National Academy of Sciences of Ukraine)H-Index: 1
The variant of a continuum model describing joint deformation and accumulation of microdamages in elastic-brittle materials is presented. The microdamageability is considered as the process of origin of a system of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The damageable material is simulated by the continuous medium, for which the elastic symmetry and non-linear law of deformation are attributed to the pattern of the ...
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Oct 1, 1998·International Applied Mechanics
#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
The principles of the theory of long-term damage based on the mechanics of stochastically inhomogeneous media are set out. The process of damage is modeled as randomly dispersed micropores resulting from the destruction of microvolumes. A failure criterion for a single microvolume is associated with its long-term strength dependent on the relationship of the time to brittle failure and the difference between the equivalent stress and the Huber-von Mises failure stress, which is assumed to be a r...
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A general expression for the failure probability of a brittle material is developed by using the properties of flaw size distribution and the stress necessary to fracture an inclined crack. A comparison is made with Weibull analysis and an expression for the Weibull modulus, which is known to be an empirical material constant, is related to the properties of the flaw size distribution of a material. Limitations in the application of Weibull analysis are also discussed.
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Cited By9
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Purpose The purpose of this paper is to consider an approximate model of accumulation of microdefects in a material under repeated loading which makes it possible to define theoretical parameters of the fatigue failure (durability, fatigue limit, etc.). The model is involving the relevant law of distribution of ultimate (yield) stresses in the material of these members in combination with the basic characteristics of main mechanical properties of a material (ultimate and yield stresses and assoc...
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#1Natalya Aleksandrova (Siberian State Automobile and Highway Academy)H-Index: 2
#2Vasiliy Chusov (Siberian State Automobile and Highway Academy)H-Index: 2
Last. Yuriy Stolbov (Siberian State Automobile and Highway Academy)H-Index: 1
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The analysis of methods for determining the damage of solids from external loads is performed, and the possibility of their application to asphalt concrete is estimated. As a result, it was found that the principles of deformation and energy equivalence are the most acceptable methods for determining damage. The strength criteria and conditions for plasticity of asphalt concrete are given, obtained by the authors by entering damage into the equations of the limiting state of solids. The method o...
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Based on modern ideas about the destruction of materials, a statistical model of the mechanism of fatigue failure of materials is proposed. The mechanism of failure is associated with the accumulation in the material of scattered microdamages in the process of repeated loading. The criterion for the onset of fatigue failure is the achievement of critical values of the density of microdamages in cyclically loaded bodies that are identified with the density of microdamages formed by separation or ...
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Jun 1, 2018·Arabian Journal of Geosciences1.33
#1Baicun Yang (CAS: Chinese Academy of Sciences)H-Index: 5
#2Lei Xue (CAS: Chinese Academy of Sciences)H-Index: 9
Last. Miaomiao WangH-Index: 2
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Applying the statistical damage theory based on the Weibull distribution to describe rock deformation and failure processes is an important development in rock mechanics. The shape parameter of the Weibull distribution, m, determines the basic shape of the distribution curve; additionally, it also represents a physical characteristic which can be applied when constructing rock constitutive models. To study the evolution of m during rock failure when applying the Weibull distribution to rock mech...
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Jan 1, 2017·Acta Mechanica2.10
#1D. BabichH-Index: 1
#2V. BastunH-Index: 1
Last. T. DorodnykhH-Index: 1
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A structural-probabilistic model of fatigue failure of structures made of elasto-brittle materials and undergoing cyclic loading is proposed. The model is based on the use of the Daniels model of accumulation of defects in the form of flat stochastically dispersed microcracks and of the statistical strength criterion for materials whose failure occurs by forming rupture macrocracks. This statistical criterion is convenient to use in the study of fatigue failure under cyclic loading. The reason f...
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May 12, 2016·Mechanics of Solids0.37
#1D. V. Babich (NASU: National Academy of Sciences of Ukraine)H-Index: 1
#2Tatiana Dorodnykh (NASU: National Academy of Sciences of Ukraine)H-Index: 1
The structural-probabilistic approach to the modeling of combined crack formation and material deformation processes is used to develop a technique for solving bifurcation stability problems for thin-walled structural members made of damageable materials under single and repeated loadings. The example of a uniformly compressed spherical shell is used to show that, under repeated loading, thin-walled structural members made of shear damageable materials can lose stability under loads smaller than...
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#1D. Babich
#2O. Bezverkhyi
Last. T. Dorodnykh
view all 3 authors...
The aim of this paper is to develop a structural approach for the construction of statistical criterion of static and fatigue failure for the transversely isotropic piezoelectric materials. We use a probabilistic model of the mechanism of brittle microfracture. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. Daniel’s structural model of accumulation of microc...
Source
Sep 1, 2015·Key Engineering Materials
#1Dmytro Babich (NASU: National Academy of Sciences of Ukraine)H-Index: 1
#2O. Bezverkhyi
Last. Tatiana DorodnykhH-Index: 1
view all 3 authors...
The present paper addresses the continuum model describing deformation electroelastic materials by using the generalized Eshelby principle. The energy method is based on the principle of equivalence of the deformation energy of fractured piezoelectric materials and the energy of medium, which is modeling these materials as a continuous medium. The key point of this approach is to determine the densities of the released elastic and electric energy.
Source
Aug 1, 2015·Applied Mechanics and Materials
#1Dmytro Babich (NASU: National Academy of Sciences of Ukraine)H-Index: 1
#2Olexander Bezverkhyi (NASU: National Academy of Sciences of Ukraine)H-Index: 1
Last. Tatiana Dorodnykh (NASU: National Academy of Sciences of Ukraine)H-Index: 1
view all 3 authors...
The present paper addresses the continuum model describing deformation and accumulation of microdamages in electroelastic materials based on the generalized Eshelby principle. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The Eshelby method is based on the principle of equivalence of the deformation energy of fractured piezoelectric materials and the energy...
Source
1
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