Micromechanics of long-term damage of particulate composites with unlimited microdurability

The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components is modeled by randomly dispersed 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 limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and relevant curves are plotted in the case of unlimited microdurability Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 7–17, November 2008.     

The nonlinear mechanics of continual damage and its application to problems of creep and fatigue

The results of investigations of the mechanics of continual damage of materials and structural elements are reviewed. The focus is on nonlinea models of damage accumulation for problems of creep and high-cyclic fatigue. Nonlinearity criteria are formulated, and methods of construction of nonlinear models are analyzed. Approaches to the solution of problems of prediction of long-term strength and lifetime under creep and interaction of creep and fatigue are considered. S. P. Timoshenko Institute of Mechanics, national Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 31–66, March, 2000.     

Deformation and long-term damage of physically nonlinear particulate composites

The theory of long-term damage is generalized to particulate composite materials with physically nonlinear components. The damage of the components is modeled by randomly dispersed 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 limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of are developed. The effect on the nonlinearity of the matrix on the damage and macrodeformation curves is examined     

Solving initial–boundary-value creep problems

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation     

Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed 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 limit, which is the ultimate strength, according to the Huber–von Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential power function     

Deformation and long-term damage of fibrous materials with the stress-rupture microstrength of the matrix described by a fractional-power function

The theory of long-term damage is generalized to unidirectional fibrous composites. The damage of the matrix is modeled by randomly dispersed 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 limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by a fractional power function     

Theory of long-term microdamage of physically nonlinear homogeneous materials

A theory of long-term damage of physically nonlinear homogeneous materials is proposed. Damage is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in a physically nonlinear material at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses are developed and the corresponding curves are plotted. The effect of the nonlinearity of the material on its macrodeformation and damage is analyzed     

Deformation and long-term damage of layered materials with stress-rupture microstrength described by an exponential power function

The theory of long-term damage of homogeneous materials is generalized to layered materials. The damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the exponential power dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of exponential power microdurability function     

Coupled deformation and long-term damage of layered materials with stress-rupture microstrength described by a fractional-power function

The theory of long-term damage of homogeneous materials is generalized to layered materials. The damage of the components (layers) is modeled by randomly dispersed 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 limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of a fractional power microdurability function     

Coupled processes of deformation and long-term damage of fibrous materials under thermal loading

A theory of long-term damage of fibrous composites under thermal loading is set up. The damage of the matrix is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Schleicher–Nadai failure criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated taking into account the thermal component. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. Corresponding curves are plotted. The effect of temperature on the deformation and microdamage of the material is studied     

Application of a gradient approach to estimation of the local strength

Some problems associated with the use of the gradient approach for estimating the local strength are considered. It is shown that a physically unjustified choice of the gradient function in the strength criterion can lead to contradictory results. Institute of Physicotechnical Problems of the North, Siberian Division, Russian Academy of Sciences, Yakutsk 677891. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 222–228, July–August, 1999.     

云母石英片岩的三轴蠕变试验研究

在三轴蠕变试验的基础上,通过对径向蠕变和轴向蠕变的比较研究,得出云母石英片岩的蠕变变形和长期强度特点:径向蠕变变形比轴向蠕变变形敏感,以径向蠕变长期强度作为长期强度更合理;围压越大,对径向变形的约束能力越强,径向蠕变长期强度和轴向蠕变长期强度均增加,径向蠕变长期强度与轴向蠕变长期强度的比值减小。同时指出进行径向蠕变研究的意义。     

Subcritical crack growth in an aging plate with variable elastic modulus

The paper addresses subcritical growth of a crack in a thin isotropic plate made of an aging viscoelastic material with time-dependent elastic modulus. The behavior of the material is described by Arutyunyan’s creep theory. To simulate fracture, a modified Leonov–Panasyuk–Dugdale model and a critical crack opening displacement criterion are used. An equation describing the subcritical growth of the crack is derived assuming that Poisson’s ratio is constant. As an example, the critical loads are determined, and curves of subcritical crack growth are plotted for a specific material. The results are compared with the case of constant elastic modulus     

Deformation and long-term damage of particulate composites with stress-rupture microstrength described by a fractional-power function

The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components is modeled by randomly dispersed 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 limit, which is the tensile strength, according to the Huber-Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of limited microdurability Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 3–12, October 2008.     

Deformation and long-term damage of particulate composites under thermal loads

A theory of long-term damage of particulate composite materials under thermal load is proposed. The damage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed     

Deformation and long-term damage of orthotropic composites with limited stress-rupture microstrength

The theory of long-term microdamage of homogeneous materials based on the mechanics of stochastically inhomogeneous materials is generalized to a composite with orthotropic inclusions. The damage of the composite components is modeled by randomly dispersed 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 limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. Given macrostresses or macrostrains, an equation of damage (porosity) balance in the composite components at an arbitrary time is derived. The time dependence of microdamage and macrostresses or macrostrains in a discrete-fiber-reinforced composite with limited stress-rupture microstrength described by a fractional-power function is plotted     

Micromechanics modeling of strength for nanocrystalline copper

We present a model in this paper for predicting the inverse Hall–Petch phenomenon in nanocrystalline (NC) materials which are assumed to consist of two phases: grain phase of spherical or spheroidal shapes and grain boundary phase. The deformation of the grain phase has an elasto-viscoplastic behavior, which includes dislocation glide mechanism, Coble creep and Nabarro–Herring creep. However the deformation of grain boundary phase is assumed to be the mechanism of grain boundary diffusion. A Hill self-consistent method is used to describe the behavior of nanocrystalline pure copper subjected to uniaxial tension. Finally, the effects of grain size and its distribution, grain shape and strain rate on the yield strength and stress–strain curve of the pure copper are investigated. The obtained results are compared with relevant experimental data in the literature.     

Influence of heating on the deformation and long-term damage of unreinforced materials

A theory of long-term damage of homogeneous materials under thermal load is proposed. The damage of the material is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed, and respective curves are plotted. The effect of temperature on the macrodeformation and damage curves is studied     

Coupled processes of deformation and damage of composites with orthotropic inclusions and unbounded rupture-stress function

The theory of long-term damage of homogeneous materials, which is based on the equations of the mechanics of stochastically inhomogeneous materials, is generalized to composite materials reinforced with orthotropic ellipsoidal inclusions. The microdamage of the composite components is modeled by randomly dispersed micropores. The failure 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 limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. Given macrostresses or macrostrains, an equation of porosity balance in the composite components at an arbitrary time is formulated. The time dependence of microdamage and macrostresses or macrostrains is established in the case of unlimited stress-rupture microstrength described by an exponential power function