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.     

The velocities of long waves in composites with interphase imperfections

We develop a model of elastic strain of a composite material with interphase imperfections. In the context of this model we construct a continuous model of first order (theory of effective models) for stratified and unidirectional fibrous compounds. We determine the velocities of propagation of long (compared with the size of the structure) waves in any direction. We exhibit the possible characteristic regularities of the influence of interphase imperfections on the value of the velocities. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 100–105.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

On the stability of motion of a movable compound structure with a fluid load

We study the stability of uniform rectilinear motion of a system of solid bodies connected by springs and partly filled with an ideal fluid. The frequency equation obtained is studied as a function of the fundamental parameters of the mechanical system. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 111–116.     

Influence of nanofillers on the thermal and mechanical behavior of DGEBA-based adhesives for bonded-in timber connections

Results of an experimental investigation into the thermal behavior and mechanical properties of a room-temperature-cured epoxy adhesive (diglycidyl ether of bisphenol A, DGEBA) cross-linked with polyetheramines and filled with different fillers, namely nanosilica, liquid rubber (CTBN), and clay, are reported. The nanosilica and liquid rubber increased the flexural strength and elastic modulus of the adhesive systems; the addition of clay particles raised the elastic modulus significantly, but embrittled the adhesive. Establishing a correct cure time is very important for bonded-in timber structures, as it will affect the bond strength. A study on the effect of cure time on the flexural strength was carried out, from which it follows that the adhesives should be cured for at least 20 days at room temperature. The damping characteristics and the glass-transition temperature of the adhesives were determined by using a dynamic mechanical thermal analysis. The results showed that the filled adhesives had a higher storage modulus, which was in agreement with the elastic moduli determined from static bending tests. The introduction of the fillers increased its glass-transition temperature considerably. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 599–614, September–October, 2006.     

Rheological and dynamic thermomechanical propert ies of epoxy composites reinforced with single- and multiwalled carbon nanotubes

An epoxy resin (Epon 828) was filled with single- and multiwalled carbon nanotubes (SWCNT and MWCNT) in two steps by using the high shear mixing and ultrasonication techniques. The melt flow of the composites was characterized in a plate/plate rheometer. The thermomechanical properties of the composites were determined in dynamic mechanical analysis tests performed at various frequencies and temperatures. It was found that the incorporation of SWCNT or MWCNT increased the viscosity and stiffness of epoxy above its glass-transition temperature. The time-temperature superposition principle was employed to estimate the storage modulus of the composites as a function of frequency (f = 10^–33–10³ Hz) in the form of master curves.     

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.     

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.     

Fundamental two-dimensional solutions of electroelasticity for compound piezoceramic bodies

We construct fundamental solutions of the two-dimensional equations of electroelasticity for antiplanar strain of a piezoceramic space with an interphase defect. We study the orders of the powers of the singularities at the vertices of the defect for two cases: an interphase crack and a stiff fiber continuously joined to the upper half-space which has flaked off the lower half-space. The solution is constructed in closed form. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 62–67.     

Nonholonomic Mechanical Systems and Kaluza–Klein Theory

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection and adapted frame fields, we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affine constraints. In the second part of the paper, we show that the Kaluza–Klein theory is best presented and explained by using the framework of nonholonomic mechanical systems. We show that the geodesics of the Kaluza–Klein space, which are tangent to the electromagnetic distribution, coincide with the solutions of Lagrange–d’Alembert equations for a nonholonomic mechanical system with linear constraints, and their projections on the spacetime are the geodesics from general relativity. Any other geodesic of the Kaluza–Klein space that is not tangent to the electromagnetic distribution is also a solution of Lagrange–d’Alembert equations, but for affine constraints. In particular, some of these geodesics project exactly on the solutions of the Lorentz force equations of the spacetime.     

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.     

The equations of the effective two-phase cracked model with finite length cracks

The two-phase effective model of a cracked medium with cracks filled with liquid is extended to the case where cracks have finite length. On the basis of the equations obtained for the generalized effective model, the expressions of kinetic and potential energies and energy streams along axes are derived. This also shows that attenuation is absent. bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 142–153, 1990. Translated by L. A. Molotkov.     

On an effective two-phase model of a medium with cracks of finite length

An effective two-phase model of media with cracks filled with liquid is generalized to the case of finite cracks. Wave propagation in a half-space and in a free layer, described by the new model, is investigated. The results are compared with experimental data and with corresponding results in the case of media with infinite cracks. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 137–155. Translated by L. A. Molotkov.     

Modeling of the Interphase of Polymer-Matrix Composites: Determination of Its Structure and Mechanical Properties

In this work, a model is developed which allows one to determine the thickness and properties of the interphase layer in unidirectional and filled composites, assuming that the materials of the interphase, matrix, and fillers may have a fractal structure, and to predict the properties of composites with interphases. Using a set of computer programs elaborated, the corresponding calculations are carried out for glass-epoxy composites, epoxy carboplastics, and graphite-filled epoxy polymers.     

Interfacial strength of joints between fibers and dispersedly filled epoxy matrices

The concentration dependences of adhesive strength are investigated for fiber/dispersedly filled epoxy matrix systems. The measurements were carried out using an improved model of adhesiometer under normal conditions at a constant rate of loading. It is shown that the adhesive strength as a function of filler concentration has a maximum, which is more or less pronounced. The location of the maximum depends on the nature of filler and particle geometry. The increase in the adhesive strength at the maximum reaches 20–30% in comparison with that for the unfilled epoxy matrix. Since the interfacial strength between steel wire and all the mineral powders investigated is zero, the growth in the adhesive strength upon introduction of a finely divided filler in polymer binders is rather un expected. The possible reasons for the phenomenon observed are discussed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 3–14, January–February, 2007.     

Square and rectangular concrete columns confined by CFRP: Experimental and numerical investigation

The results of an experimental and theoretical investigation into the deformation behavior of CFRP-confined square and rectangular concrete columns under axial loads are presented. Three types of columns are considered: unwrapped; fully wrapped; and fully wrapped, with L-slaped steel angles placed at the corners. A mechanical deformation model for them is proposed, which is based on a nonuniform distribution of the stresses caused by the confining device. The results given by the model are in a good agreement with the experimental results obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 417–442, May–June, 2008.     

Pressure of an elastic half space on a rigid base with rectangular hole in the case of a liquid bridge between them

A model of contact between an elastic half space and a rigid base with a shallow surface rectangular hole is proposed. The hole contains an incompressible liquid and gas. The liquid occupies the middle part of the hole and forms a capillary bridge between the opposite surfaces. The remaining volume of the hole is filled with gas under a constant pressure. The liquid completely wets the surfaces of the bodies. The pressure drop at the liquid–gas interface caused by the surface tension is defined by the Laplace formula. The corresponding plane contact problem for the elastic half space is essentially nonlinear because the pressure of the liquid and the length of the capillary in the contact-boundary conditions are not known in advance and depend on the external load. The problem is reduced to a system of three equations (a singular integral equation for the function of height of the hole and two transcendental equations for the length of the capillary and the height of the meniscus). An analytic-numerical procedure for the solution of these equations is proposed. Dependences of the length of the capillary and the pressure drop at the liquid–gas interface on the external load, volume of liquid, and its surface tension are analyzed. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 150–156, January–March, 2008.     

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.