Estimation of the macroscopic stress-strain curve of a particulate composite with a crosslinked polymer matrix

The main focus of the present paper is the estimation of the macroscopic stress–strain behavior of a particulate composite. A composite with a cross-linked polymer matrix in a rubbery state filled with an alumina-based mineral filler is investigated by means of the finite-element method. The hyperelastic material behavior of the matrix is described by the Mooney–Rivlin material model. Numerical models on the basis of unit cells are developed. The existence of a discontinuity (breaking) in the matrix at higher loading levels is taken into account to obtain a more accurate estimate for the stress–strain behavior of the particulate composite investigated. The numerical results obtained are compared with an experimental stress–strain curve, and a good agreement is found to exist. The paper can contribute to a better understanding of the behavior and failure of particulate composites with a polymer matrix.     

Application of the method of conditional moments to investigating the deformation properties of orthotropic composites with fiber microdamages

A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a fibrous composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random function of coordinates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algorithm for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams for an orthotropic composite in uniaxial tension are obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17–30, January–February, 2009.     

Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite

Analysis results for the elastic properties of a composite with a small amount of coplanarly arranged platelike filler particles are presented. The geometrical form of the particles is described by an oblate ellipsoid of revolution. The calculations are performed by formulas obtained by using the Eshelby approach for media with a low concentration of inclusions. The effect of anisometry of the ellipsoidal particles and of the ratio between the elastic moduli of the filler and matrix on the effective elastic constants of the composite is discussed. Calculation results are compared with experimental data for the elastic moduli of a nanocomposite containing completely exfoliated particles of an unmodified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 493–504, July–August, 2008.     

Operational properties of a heat-insulation composite with expanded polystyrene crumbs

The operational properties (strength, heat conductivity, hygroscopic sorption, vapor permeability, and frost resistance) of a heat-insulation composite of density 150–350 kg/m³ are investigated. The matrix consists of an aerated concrete substance and a disperse filler of expanded polystyrene crumbs obtained by crushing the household polystyrene package waste. The macro-and microstructure of the composite are considered. It is found that the operational properties of the material directly depend on its density, determined by the amount of the cementing substance in the matrix. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 591–604, July–August, 2008.     

Structural theory of elastomeric composites based on fiber systems — Invariant description

A three-dimensional theory of elastomeric composites with elastomeric matrices reinforced by systems of fibers is presented. The theory is based on a structural approach in which the matrix and the reinforcement of the composite are considered separately without reduction to a medium having continuously changing characteristics. The approach is based on the idea of a vector field of macroscopic displacements given by the positions of the axial lines of the fibers in the curret (deformed) configuration of the composite. The vector field determines the current macroscopic configuration, the tensor fields of the measures of macroscopic strain, and the field of the macroscopic stress tensor in the composite. The displacement, strain, and stress fields in the elastomeric matrix and the fibers of the reinforcing systems are regarded as derivatives of the field of macroscopic displacements of the medium. Relations are presented to describe the kinematics of the fibers in the current configuration of the composite, including the evolution of their orientation and the frequency of their planar and spatial distribution. Equations are obtained for the macroscopic motion of the fiber-reinforced matrix, and the dynamic variational principle that governs this motion is established. The elastic macroscopic potential of the matrix is found and related to the components of the macroscopic stress tensor. The procedure to be followed in constructing the constitutive equations of the composite is described. The proposed system of equations, relations, and algorithms is closed and can be used to solve problems involving the deformation of products made of fiber-reinforced elastomers and the creation of elastomeric composite products, based on fiber systems, that possess the requisite properties.     

Investigation of the mechanical behavior of two-component granular composites in terms of structural models

A structural model is suggested for elastomers filled with particles of two fractions — with diameters exceeding 10 μm and submicronic ones. In each fraction, the particle diameter varies randomly, but between the fractions, the average particle diameter differs by several orders of magnitude. It is assumed that the small particles, together with the matrix, behave as a homogeneous medium relative to the large ones. By using this model, the mechanical behavior of composites based on elastomers filled with different volume contents of solid particles is investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 191–200, March–April, 2007.     

Boundary-value problem in the correlative approximation of the method of quasi-periodic components for a unidirectional fiber composite

The boundary-value problem in the correlative approximation of the method of quasi-periodic components and a numerical algorithm based on the boundary element method for determining the nonuniform stress fields in the matrix of a unidirectional fiber composite with a disordered structure are considered. The numerical results and analysis of the probability density function, for example, for normal stresses at some points of the interface of absolutely rigid fibers of the composite are presented. Perm State Technical University, Russia. Translated from Mekhanika Kompozytnykh Materialov, Vol. 35, No. 5, pp. 629–642, September–October, 1999.     

Failure of particulate reinforced polymers

In this presentation, a review is given on the main effects of mineral particulate fillers (with an aspect ratio of about unity) on the deformation and fracture of amorphous and semicrystalline thermoplastic and thermosetting polymers. Elastomeric modifiers, polymer blends, and filled elastomers are not considered here. Fillers are generally used to reduce cost as well as the thermal sensitivity of mechanical properties of the matrix material and to improve, if possible, the strength and toughness. The addition of particulate fillers influences all stages of the fabrication and use of the resulting composites. We focus on the effects of a stiff second phase on elastic moduli, matrix structure, and on deformation, creep, and failure mechanisms. As the main mechanisms, particle-matrix debonding, void formation, and matrix microshear yielding are identified. Toughness is less sensitive to the quality of adhesion since particle-matrix debonding and formation of voids can be tolerated. If well controlled, debonding contributes to deformation (formation of voids should be well distributed in space and time). Reference is also made to the surprising and positive effect of CaCO₃ particles on the toughness and impact resistance of HDPE, which increases at small interparticle distances due to interfacial effects on lamellar growth in the ligament area. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 305–316, March–April, 2000.     

Creep and Long-Term Strength of Press-Powder Composites

The mechanical state of a press-powder filler for pyroautomatics system units of aerospace equipment during their long-term storage is investigated. With the use of the endochronic approach, the rheological properties of a dispersedly reinforced composite are simulated based on the conceptions of linear and nonlinear creep. Analytical expressions of constitutive relations of creep and strength for the composites are obtained. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 803–818, November–December, 2005.     

Deformation of orthotropic composites with unidirectional ellipsoidal inclusions under matrix microdamages

In the present paper, a model of deformation of stochastic composites under microdamaging is developed for the case of orthotropic composite, when the microdamages are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by three-axial ellipsoidal inclusions with orthotropic symmetry of elastic properties. It is assumed that the loading process leads to accumulation of damages in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a composite with orthotropic components are taken as the basic relations. The fracture criterion is assumed to be given as the limit value of the intensity of average shear stresses occurring in the undamaged part of the material. Based on the analytical and numerical approach, an algorithm for the determination of nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the matrix. Using the numerical solution, nonlinear stress-strain diagrams for the orthotropic composite in the case of biaxial extension are obtained. Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 121–130, January–March, 2008.     

The passage of a bending wave through an inhomogeneity in an absolutely rigid rib backing an elastic plate

The wave properties of a system consisting of an elastic plate and an absolutely rigid infinite rib with a defect on a segment are examined. An elastic inclusion and a gap are two kinds of defects under study. The Green's function method is applied to the diffraction problem and transforms it to singular integro-differential equations on an interval. For the case of short defects, the nonresonance and resonance asymptotics of the scattering pattern are obtained. These results show that the coefficient of penetration for a gap is much larger than that for an elastic inclusion if the frequency is nonresonant. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210. 1994, pp. 22–29. Translated by I. V. Andronov.     

Scattering of a plane acoustic wave on a periodic array of piston radiators embedded into a rigid screen

The stationary scattering of a plane acoustic wave on a periodic or a doubly periodic set of piston radiators elastically connected with a rigid screen is considered. The screen separates two half-spaces filled with media possessing different acoustic properties. The model considered takes into account energy losses in the elastic ties between the piston radiators and rigid screen. The problem solution in the case where only one half-space is filled with an acoustic medium is found as a special case. The results of numerically analyzing the reflection coefficients of a plane wave as functions either of the frequency of the incident wave or of the angle of incidence of the plane acoustic wave for different values of the parameters involved are presented. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 125–137. Translated by G. L. Nikitin.     

Influence of particle size on the fracture toughness of a PP-based particulate composite

The main focus of this paper is a numerical investigation of the fracture behavior of a particulate composite (CaCO₃-PP). The composite is modeled as a three-phase continuum and simulated numerically on a microscale by using finite elements. The propagation of a microcrack in a matrix filled with rigid particles covered by an interphase is analyzed. The stress distribution is determined for a variety of particle sizes and material properties of the interphase. The final results, in agreement with experimental data, confirm that the microcrack behavior depends on particle sizes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 411-418, May-June, 2009.     

Estimation of limit strains in disk-type flywheels made of a compliant elastomeric matrix composite undergoing radial creep

Fiber reinforced elastomeric matrix composites (EMCs) offer several potential advantages for construction of rotors for flywheel energy storage systems. One potential advantage, for safety considerations, is the existence of maximum stresses near the outside radius of thick circumferentially wound EMC disks, which could lead to a desirable self-arresting failure mode at ultimate speeds. Certain unidirectionally reinforced EMCs, however, have been noted to creep readily under the influence of stress transverse to the fibers. In this paper, stress redistribution in a spinning thick disk made of a circumferentially filament wound EMC material on a small rigid hub has been analyzed with the assumption of total radial stress relaxation due to radial creep. It is shown that, following complete relaxation, the circumferential strains and stresses are maximized at the outside radius of the disk. Importantly, the radial tensile strains are three times greater than the circumferential strains at any given radius. Therefore, a unidirectional EMC material system that can safely endure transverse tensile creep strains of at least three times the elastic longitudinal strain capacity of the same material is likely to maintain the theoretically safe failure mode despite complete radial stress relaxation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 87–94, January–February, 2000.     

Properties of a composite prepared using a concentrate of carbon nanotubes in polyethylene

Results of an investigation into the properties of polyethylene (PE) with small, no more than 5 wt.%, additions of multiwall carbon nanotubes (CNTs) are reported. Specimens of the composite were prepared using a concentrate containing 31.6 wt.% of nanotubes in the polyethylene matrix. The concentrate was fabricated by a patent in situ polymerization method. Experimental data on the influence of CNT additions on the thermograms of differential scanning calorimetry, the crystallinity of the polyethylene matrix, and the indices of mechanical properties (yield stress, strength, elastic modulus, ultimate elongation, and long-term creep) of PE/CNT composite are obtained. A theoretical analysis of elastic properties of the PE/CNT composite was carried out by using the Mori–Tanaka theory of an equivalent medium. The calculation results are compared with experimental data.     

Effect of interphase layers on the elastic properties of a carbon-nanotube-reinforced composite

A variant of a stepwise analysis of the elastic properties of a carbon-nanotube-reinforced composite with account of the effect of interphase layers between the nanotubes and the polymer matrix is reported. The preliminary calculation of the elastic constants of a structural element incorporating a nanotube and an interphase layer and the subsequent calculation of independent elastic constants of a composite with such transversely isotropic structural elements oriented in one direction are both performed by using the Mori–Tanaka theory of an equivalent medium. The calculations are carried out for a wide range of ratios between the elastic moduli of the interphase layer and matrix. The elastic constants of a composite with randomly oriented nanotubes are obtained by using the method of orientational averaging.     

Stressed state of an anisotropic body with elliptical holes, elastic inclusions, and cracks

A method is proposed for studying the two-dimensional stressed state of a multiply connected anisotropic body with cavities and elastic and rigid inclusions, as well as planar cracks and rigid laminar inclusions. Generalized complex potentials, conformal mapping, and the method of least squares are used. The problem is reduced to solving a system of linear algebraic equations. Formulas are given for finding the stress intensity factors in the case of cracks and laminar inclusions. For an anisotropic plate with a single elliptical hole or a crack and an elastic (rigid) inclusion, some numerical results are presented from a study of the effect of the rigidity of the inclusion and the closeness of the contours to one another on the distribution of stresses and the stress intensity factor. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 175–187, 1999.     

Deformation of composites with arbitrarily oriented orthotropic fibers under matrix microdamages

In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using the numerical solution, the nonlinear stress–strain diagrams are predicted and discussed for an orthotropic composite material for various cases of orientation of inclusions in the matrix.     

A fractal model of reinforcement of elastoplastic nanocomposites

Within the framework of fractal analysis and percolation theory, an alternative model of reinforcement of filled polymers is offered. Practically, this model can be used only to describe the reinforcement of nanocomposites, because, according to the treatment considered, a pronounced reinforcement can be reached only at ratios of filler particle diameter to the statistical segment length of about 10 and less. A theoretical calculation showed a good qualitative and quantitative agreement with experiments. The type of reinforcement mechanism of composites is determined by the type of the space (fractal or Euclidean) in which the structure of the polymeric matrix is formed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 797–802, November–Decem ber, 2006.     

Analysis of contact stresses in structural joints of composite shell with steel banding

Based on the generalized Timoshenko-type shell theory, a numerical-analytical procedure for determining contact stresses from the interaction between a cylindrical composite shell and rigid bandings is proposed. Specific cases of loading and contact interaction (ideal contact through an adhesive interlayer) are considered. The contact problems are reduced to the solution of a Fredholm integral equation of the second-kind. A calculation analysis is performed. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–120, January–February, 2000.