Poisson's ratio of foamed plastics

Six-sided and 14-sided cell models are used as a basis for calculating the Poisson ratio of foamed plastics as a function of the properties of the polymer base and the parameters of the cellular structure. The extremal nature of the dependence of the Poisson ratio on the apparent density of foamed plastics is established and explained.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 1, pp. 45–49, January–February, 1973.     

Special features of the effect of cellular structure on the mechanical properties of foamed plastics

On the basis of the cell model proposed the mechanical characteristics of high-density foamed plastics are calculated. Assuming the general application of the foaming mechanism and the formation of macrostructure, the principle of structural-mechanical superposition of foamed plastics is established. This enables the equivalence of changes in their strength and elastic properties to be indicated over a wide range of variation of the stiffness of the polymer base and the apparent density of the foamed material.Scientific-Research Institute for Synthetic Resins, Vladimirsk. Translated from Mekhanika Polimerov, No. 6, pp. 976–981, November–December, 1972.     

Comparative micromechanical analysis of nonelastic behavior of unidirectional plastics with tetragonal and hexagonal structures

A mathematical model for determining the effective elastic properties and describing the processes of inelastic deformation and damage accumulation of unidirectional fiber-reinforced composites with tetragonal and hexagonal structures is developed. A comparative analysis of the effective elastic moduli of glass, boron, organic, and carbon unidirectional plastics shows that, if the fiber volume fraction does not exceed 0.5, the effective elastic properties calculated by the models presented give closely related results. The calculation results for nonlinear fields of deformation and failure are presented and the limiting strength surfaces of fibrous glass plastics with hexagonal and tetragonal structures are obtained for different transverse loading paths. It is found that the structure of a composite affects significantly its strength properties.Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Perm' State Technical University, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 455–464, July–August, 2000.     

Effect of flame retardants on the properties of monolithic and foamed polyurethanes at low temperatures

The dependence of physical and mechanical properties of monolithic and foamed rigid polyurethanes on the content of flame retardants was investigated at 293 and 98 K. The character of the influence of the content of trichloroethyl phosphate on the ultimate tensile elongation and the coefficient of linear thermal expansion for monolithic and foamed polyurethanes at a temperature of 98 K was established. Latvian State Institute of Wood Chemistry, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 671–676, September–October, 1999.     

Effect of the chemical structure of the polymer matrix on the properties of foam polyurethanes at low temperatures

The dependence of physical and mechanical properties of oligoether-based foam polyurethanes on the molecular mass (M_c) of polymer chains between the nodes of the polymer network and on the content of rigid segments in the polymer is investigated at 293 and 98K. The values of M_c at which the foam plastics have the best mechanical properties at low temperatures are determined. The content of rigid segments in the polymer at which foam polyurethanes have the best combination of the linear thermal expansion coefficient and mechanical properties in tension at a temperature of 98K is found.Latvian State Institute of Wood Chemistry, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 517–526, July–August, 1999.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

Creep of orthogonally reinforced spherofibrous composites

Models of composites with three-dimensional structure, a proposed problem solving method, and Rabotnov's creep operators were used assuming purely elastic deformation of the composite along the orientation of the fibers to determine the viscoelastic properties of composites on inclined surfaces in a three-dimensional stressed state. The formulas used in viscoelasticity theory in the elastic region of component deformation lead to results in satisfactory accord with the reported experimental elastic properties of composites with three-dimensional structure.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 780–786, November–December, 1996.     

Effect of side branches on the properties of cross-linked polyurethanes

Two series of samples of cross-linked polyurethanes: based on diethylene glycol and polypropylene glycol having calculated M_c 1000, were investigated. In synthesis by partial substitution of glycols by fatty acid ester and triethanolamine, long side branches were created in the structure of the polymer. The effect of the mass concentration of these branches on the physicomechanical properties of polyurethanes was evaluated. The different character of the effect of these branches on the properties of two types of polyurethane was demonstrated.Submitted to the Xth International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Latvian State Institute of Wood Chemistry. Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 840–844. November–December. 1997.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.     

Some laws of the elastic properties of oriented fibrous polymers and fibers

The author considers the results of calculations of the limiting values of the elastic properties (modulus of elasticity and load-extension diagram) of the main types of chemical fibers, using a model with "ideal orientation" of the molecules and the derived laws of deformation of polymer chains. A method is proposed for calculating the elastic properties of "ideally oriented" polymers from the velocity of propagation of an elastic deformation pulse and the effective density of the "skeletons" of the polymer chains. Values of the moduli of elasticity of the amorphous regions of the structure of oriented polymers are calculated. The calculated results are compared with experimental data on the elastic properties of fibers.Mekhanika Polimerov, Vol. 2, No. 1, pp. 34–42, 1966Paper read at the XIV All-Union Conference on High-Molecular Compounds, Oriented State.     

Elastoplastic deformation during projectile–wall collision

The Smoothed Particle Hydrodynamics method for elastic solid deformation is modified to include von Mises plasticity with linear isotropic hardening and is then used to investigate high speed collisions of elastic and elastoplastic bodies. The Lagrangian mesh-free nature of SPH makes is very well suited to these extreme deformation problems eliminating issues relating to poor element quality at high strains that limits finite element usage for these types of problems. It demonstrates excellent numerical stability at very high strains (of more than 200%). SPH can naturally track history dependent material properties such as the cumulative plastic strain and the degree of work hardening produced by its strain history. The high speed collisions modelled here demonstrate that the method can cope easily with collisions of multiple bodies and can also naturally resolve self-collisions of bodies undergoing high levels of plastic strain. The nature and the extent of the elastic and plastic deformation of a rectangular body impacting on an elastic wall and of an elastic projectile impacting on a thin elastic wall are investigated. The final plastically deformed shapes of the projectile and wall are compared for a range of material properties and the evolution of the maximum plastic strain throughout each collision and the coefficient of restitution are used to make quantitative comparisons. Both the elastoplastic projectile–elastic wall and the elastic projectile–elastoplastic wall type collisions have two distinct plastic flow regimes that create complex relationships between the yield stress and the responses of the solid bodies.     

New mathematical model for nonuniform deformation of composites

A new mathematical model is suggested for nonuniform deformation of composite materials valid for arbitrary external load gradients. As a basis stochastic equations are suggested for the statics of an elastic microinhomogeneous two-component material with volumetric forces differing from zero. Expressions are obtained for all coefficients in terms of elastic constants of the components and geometric parameters of the structure.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 310–318, May–June, 1995.     

The effect of the concentration and dispersion of quartz on the physicomechanical properties of polyvinylacetate films

Data are given from a study of the effect of the concentration and dispersion of quartz on the structure, the coefficient of thermal expansion, the elastic modulus, the strength, and the extension under tension of polyvinylacetate films. The change in the properties of these films is associated with a change in the structure of the polymer on filling.Institute of Physical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 63–67, January–February, 1972.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

The elastic properties of unidirectionally reinforced composite materials under large deformations are studied. The applied model for deformation of materials is based on the structural macroscopic theory of stiff and soft composites, including micro- and macromechanical levels of analysis of composite media. The properties of unidirectional elastomeric composites are studied in tension and shear in the plane of reinforcement. The microscopic fields in the structural components of composites having poorly compressible and compressible matrices are also analyzed. Changes in the parameters of macroscopic deformation of the composites are examined as functions of the loading parameters and initial conditions of the structure. The evolution of the structural changes in deformed composite materials is described.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 29–50, January–February, 1999.     

Deformation and sliding friction of polyurethane in the presence of a lubricant

The relation between coefficient of friction and elastic and high-elastic strains is investigated with reference to polyurethane subjected to friction in various liquid media. It is shown that a definite relationship between these parameters does exist. The effect of various liquids on the elastic and high-elastic deformation of polyurethane is studied.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 5, No. 2. pp. 357–359, March–April, 1969.     

Investigation of the energy effects accompanying the elastic deformation of uniaxially oriented crystalline polymers

The energy (thermal and mechanical) effects accompanying the elastic deformation of uniaxially oriented crystalline polymers have been investigated; it has been established that, when these polymers are stretched, heat is released. It is shown that the heat release in uniaxial tension is a consequence of localization of the elastic deformation in the poorly ordered regions of the polymer. The relation between the thermoelasticity of uniaxially oriented crystalline polymers and their supermolecular structure is examined.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 785–798, September–October, 1970.     

Numerical identification of properties of particle-reinforced composite materials

The paper deals with numerical identification of the average elastic properties of particle-reinforced composite materials. The finite element method for the determination of deformation energy of the characteristic volume element was used. In earlier analytical investigations, an approximation function of the averaged elastic properties of the composite was derived. An identification procedure allows the estimation of the unknown approximation parameters from numerical experiments. The obtained functions describe precisely the numerical data for any relationships between constituents of the material.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Computer Analysis of Structures, Riga Technical University, Riga PDP-1658, Latvia. Institute of Materials Science, Department of Materials Science, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 383–390, May–June, 1998.     

Calendering mechanics of viscoelastic materials (communication 1)

The kinematics and dynamics of the deformation of a viscoelastic material (rubber mix) between the rolls of a calender are considered. Approximate calculations are presented for the elastic recovery of the sheet after it passes through the nip in terms of the calendering speed, the geometry of the deformation zone, and the rheological properties of the rubber mix. Equations are also given for estimating the vertical thrust and torque.Scientific-Research Institute of the Tire Industry, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 539–545, May–June, 1969.     

Study of prefracture states of rigid polymers. 2. Elastic limit and strength

An explanation is offered for the relation between the magnitude of stresses at the elastic limit (strength) and the strains in rigid polymers. The possibility of high-elastic deformation and orienting processes, which have been considered in [1], is also explained here. Expressions are derived that relate the elastic limit to the strain, the modulus of elasticity, the coefficient of thermal expansion, and the Poisson ratio.For communication 1, see [1].A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 195–201, March–April, 1976.