Principles of the micromechanics of material damage. 1. Short-term damage

Published on Oct 1, 1998in International Applied Mechanics
路 DOI :10.1007/S10778-007-0018-6
L. P. Khoroshun19
Estimated H-index: 19
(NASU: National Academy of Sciences of Ukraine)
Sources
Abstract
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 random function of coordinates. The stochastic elasticity equations for porous media are used to determine the effective moduli and the stress-strain state of microdamaged materials. The porosity balance equation is derived in finite-time and differential-time forms for given macrostresses or macrostrains and arbitrary time using the properties of the distribution function and the ergodicity of the random field of short-term strength as well as the dependence of the time to brittle failure on the stress state and the short-term strength. The macrostress-macrostrain relationship and the porosity balance equation describe the coupled processes of deformation and long-term damage
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References7
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#1S. Chandrakanth (IISc: Indian Institute of Science)H-Index: 2
#2PC Pandey (IISc: Indian Institute of Science)H-Index: 14
A continuum isotropic ductile plastic damage model has been derived in the framework of internal variable theory of thermodynamics. The damage model is based on the concept of effective stress and the principle of strain equivalence. The damage model shows non-linear variation with respect to plastic strain, and is sensitive to stress triaxiality. The predictions using the model compare well with experimental results of certain aluminium alloys. This damage model can be used for such metals to s...
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#1V. N. Aptukov (RAS: Russian Academy of Sciences)H-Index: 2
#2V. L. Belousov (RAS: Russian Academy of Sciences)H-Index: 1
Based on phenomenological thermodynamics a new approach is suggested for formulating kinetic equations for the increase in damage in the general case of a damage tensor measure of the second rank.
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The classical method of solving problems concerning the delayed fracture of structural materials and elements is based on analysis of their stabilized stress strain state and the use of parametric relations which include the time or number of cycles to failure. Researchers have developed another approach employing the concept of internal variables along with a system of evolutionary equations and failure criteria. Entropy, internal energy, empirical temperature, internal time, strain hardening, ...
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#1J. A. CollinsH-Index: 1
The Role of Failure Prevention Analysis in Mechanical Design. Modes of Mechanical Failure. Strength and Deformation of Engineering Metals. State of Stress. Relationships Between Stress and Strain. Combined Stress Theories of Failure and Their Use in Design. High-Cycle Fatigue. Concepts of Cumulative Damage, Life Prediction, and Fracture Control. Use of Statistics in Fatigue Analysis. Fatigue Testing Procedures and Statistical Interpretations of Data. Low-Cycle Fatigue. Stress Concentration. Cree...
#1John F. KnottH-Index: 28
#1Waloddi WeibullH-Index: 4
Cited By78
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
A structural theory of the coupled processes of deformation and short-term damage of unidirectional fibrous composites with physically nonlinear components whose stress鈥搒train curves have a descending section is developed. The damage process is modeled as the collapse of dispersed microvolumes followed by the formation of quasispherical micropores. A strain-based failure criterion formulated for the second invariant of the deviatoric macrostrain tensor is used as a condition for the short-term d...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
#2E. N. Shikula (NASU: National Academy of Sciences of Ukraine)H-Index: 15
A theory of long-term damage of fibrous composites with physically nonlinear matrix is proposed. The damage of the matrix is modeled by random micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its critical value, which is the tensile strength, according to the Huber鈥揗ises criterion, and assumed to be a random function of coordinat...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
#2E. N. Shikula (NASU: National Academy of Sciences of Ukraine)H-Index: 15
A theory of long-term damage of laminated materials with physically nonlinear components is proposed. The damage of components is modeled by random micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its critical value, which is the tensile strength, according to the Huber鈥揗ises criterion, and assumed to be a random function of coor...
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#1L. V. Nazarenko (NAS: National Academy of Sciences)H-Index: 1
UDC 539.3 A model of deformation of composite materials with physically nonlinear components is generalized to the case of materials in the form of a matrix reinforced by unidirectional infinite fibers. It is assumed that the matrix is isotropic and deforms nonlinearly and that the fibers are linearly elastic and have orthotropic symmetry. As initial equations, we use the stochastic differential equations of the physically nonlinear theory of elasticity. We transform these equations into integra...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
#2Lidija NazarenkoH-Index: 2
A statistical model describing the coupled deformation and damage of composites with porous transversely isotropic and orthotropic components is proposed. The mechanism of microdamage of such composites is studied assuming that the microstrength of the material is inhomogeneous. A single microdamage is modeled by an empty quasispherical pore forming in place of a microvolume damaged in accordance with the Huber鈥揗ises failure criterion. The ultimate microstrength is assumed to be a random functio...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
A structural theory of the coupled processes of deformation and short-term damage is set up for the following materials whose stress鈥搒train curves have a descending portion: homogeneous physically nonlinear materials and particulate composites with two physically nonlinear components. Damage is modeled by randomly arranged micropores formed in place of damaged microvolumes. The short-term damage criterion for a microvolume is a strain-based failure criterion formulated in terms of the second dev...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
#2E. N. Shikula (NASU: National Academy of Sciences of Ukraine)H-Index: 15
The studies on the theory of deformation and short- and long-term damage of physically nonlinear homogeneous and composite materials are systematized. In the case of short-term damage, a single microdamage is modeled by an empty quasispherical pore occurring in place of a microvolume damaged by the Huber鈥揗ises criterion. The ultimate microstrength is assumed to be a random function of coordinates. In the case of long-term damage, the damage criterion for a single microvolume is characterized by ...
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#1L. P. Khoroshun (NASU: National Academy of Sciences of Ukraine)H-Index: 19
#2E. N. Shikula (NASU: National Academy of Sciences of Ukraine)H-Index: 15
The studies on the deformation and short- and long-term damage of homogeneous and composite materials are systematized. In the case of short-term damage, a single microdamage is modeled by an empty quasispherical pore formed in place of a microvolume damaged in accordance with the Huber鈥揗ises or Schleicher鈥揘adai failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. In the case of long-term damage, the damage of a single microvolume is characterized by i...
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#1D. V. Babich (NASU: National Academy of Sciences of Ukraine)H-Index: 1
A structural approach combined with the energy method is used to construct a continuum model of the joint process of deformation and scattered cracking in elastic-brittle isotropic materials. The proposed approach allows one to match the form of the symmetry of the effective deformation properties and damageability of the material depending on the stress state character.
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