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     

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     

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     

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     

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     

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 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     

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     

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

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 layers 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 layers is studied     

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.     

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.     

Long-term damage of discrete-fiber-reinforced composites with transversely isotropic inclusions and stress-rupture microstrength described by an exponential power 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 discrete-fiber-reinforced composite materials. 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. Given macrostresses and macrostrains, an equation of damage (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 stress-rupture microstrength described by an exponential power function Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 19–29, February 2009.     

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     

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     

Elastic properties and long-term damage of transversely isotropic composites with stress-rupture microstrength described by a fractional-power function

The damage process is modeled by randomly dispersed micropores occurring in places of destroyed microvolumes according to the stress-rupture microstrength, which is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, according to the Huber–Mises criterion, and is a random function of coordinates. Given microstresses or microstrains, the equations of porosity balance at an arbitrary time are derived. Together with the macrostress–macrostrain relationships for a discrete fibrous composite with porous components, they describe the coupled processes of deformation and long-term damage. A specific problem with a bounded stress-rupture microstrength function is solved Translated from Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 71–81, January 2009.     

Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized by its stress-rupture strength 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 or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied     

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

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 __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 108–121, February 2007. For the centenary of the birth of G. N. Savin.     

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part I: Theoretical formulation

The present two-part study aims at investigating the specific effects of Mohr–Coulomb matrix on the strength of ductile porous materials by using a kinematic limit analysis approach. While in the Part II, static and kinematic bounds are numerically derived and used for validation purpose, the present Part I focuses on the theoretical formulation of a macroscopic strength criterion for porous Mohr–Coulomb materials. To this end, we consider a hollow sphere model with a rigid perfectly plastic Mohr–Coulomb matrix, subjected to axisymmetric uniform strain rate boundary conditions. Taking advantage of an appropriate family of three-parameter trial velocity fields accounting for the specific plastic deformation mechanisms of the Mohr–Coulomb matrix, we then provide a solution of the constrained minimization problem required for the determination of the macroscopic dissipation function. The macroscopic strength criterion is then obtained by means of the Lagrangian method combined with Karush–Kuhn–Tucker conditions. After a careful analysis and discussion of the plastic admissibility condition associated to the Mohr–Coulomb criterion, the above procedure leads to a parametric closed-form expression of the macroscopic strength criterion. The latter explicitly shows a dependence on the three stress invariants. In the special case of a friction angle equal to zero, the established criterion reduced to recently available results for porous Tresca materials. Finally, both effects of matrix friction angle and porosity are briefly illustrated and, for completeness, the macroscopic plastic flow rule and the voids evolution law are fully furnished.     

Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials

The mechanisms of interfacial debonding of particle reinforced rheological materials are studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived and expressed in terms of the interfacial energy. The particle size effect on interface debonding can then be analyzed easily owing to the fact that critical stress is inversely proportional to the square root of particle radius. By taking PP/CaCO₃ system as an example, the present energy criterion is compared with the mechanical debonding criterion, and it is found that under the condition that bond strength is equal to matrix strength and particle radius not over 0.2μm, the mechanical debonding criterion can be automatically satisfied if the energy criterion is satisfied. A relation between critical time and interface energy is calculated by using the energy criterion. The influences of the particle volume fraction and the parlicle size, the loading rate and the relaxation time of the matrix on the critical time of interfacial debonding are also discussed. Supported by the National Natural Science Foundation of China (19632030 and 19872007) and Natural Science Foundation of Jiangsu Province.     

Accelerated aging of unidirectional hybrid composites under the long-term elevated temperature and moisture concentration

Despite their high performances, composites with polymer matrix are very sensible to the increase in temperature and moisture concentration. During long years of services, both phenomena cause a critical transient hygrothermal transverse stresses, particularly at first-ply; i.e. at two edges of the composite plates. Therefore, significant degradation of hygrothermal characteristics and ultimate strengths of materials are occurred. To get an explicit relation between the durability and the damage probability of the composite, quadratic failure criterion in stress space is used. This criterion enables us to find a direct relation between transient hygrothermal stresses produced by the increase in temperature and moisture concentration and the ultimate strengths. It is necessary to calculate the strength ratio R from initial to saturation time for each condition imposed of temperature and moisture concentration. The strength ratio gives a point of view on the damage probability of the composite plates, where the rupture occurs if R = 1. In order to limit the consequences of simultaneous effects of temperature and moisture concentration, unidirectional hybrid composites in graphite epoxy was proposed. To reach this aim, hygrothermal transverse stresses are calculated through the thickness of unidirectional hybrid plate. Finally, the strength ratio was evaluated along of the plate with a gradual increase in temperature and moisture concentration.