Anisotropy of torsional rigidity of sheet polymer composite materials

Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.     

Multifibre polymer composites: Prediction of deformation and thermophysical properties

Conclusions A theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermophysical characteristics of hybrid polymer composites reinforced with anisotropic fibres of several types. The theoretical solutions were obtained by generalizing the self-consistent method for the case of a three phase model. The effects of brittle fibre breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of a short-term loading and a long-term creep. It has been shown that a creep of viscoelastic fibres plays a principal role in creep of the hybrid composite. It is just this creep that significantly increases the fibre damage during creep of the composite.A variant of the solution has been proposed for predicting the thermorheologically complex behavior of hybrid composites containing not only elastic but also viscoelastic thermorheologically simple components with different temperature-time shift factors. The peculiarities of thermal expansion of hybrid composites and the possibilities for a purposeful control of thermal expansion coefficients by hybridization were studied. The considered thermal interval included a region of transition of the polymer matrix from a glass state into a viscoelastic one.The control tests were performed for specimens of organic/glass, organic/carbon, glass/carbon and organic/boron polymer composites with different ratios of fibre volume contents. On the whole, the obtained accuracy of predicting the characteristics of the examined hybrid composites may be considered as acceptable for engineering applications.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 299–313, May–June, 1994.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Calculation of elastic characteristics and creep functions of hollow-sphere plastics by the effective medium method

Conclusion Solutions for the elastic characteristics and the creep functions of a composite containing hollow spherical fillers as applies to the four-phase nucleus/jacket/binder/equivalent-homogeneous-material model are obtained in the study when the method of self-correspondence is used. It is demonstrated that if the two-stage approach (when the elastic characteristics of the nucleus + jacket system, and the composite are calculated in the first and second stages, respectively) yields an exact solution for the bulk modulus K_* of the composite, it is highly approximate when the shear modulus G_* of the composite is determined. The error of determination of G_* increases considerably (by a factor of 2–2.5 when = 0.4) when Kerner's approximate solution (2) is used in lieu of solution (8) for the three-phase model within the framework of the two stage approach. Dzenis and Maksimov [5] establish by comparison with experimental data that the four-phase model provides a rather exact solution for the elastic modulus of a composite when the bulk content of hollow spheres 0.4. It is also demonstrated that use of Kerner's approximate solution (2) within the framework of the two-stage approach in predicting the creep of a composite yields an inadmissibly high error in the region of the principal relaxation transition of the binder from the glassy to the highly elastic state.This work was sponsored at the Iberoamericana University in 1993 by the Mexican National Council of Science and Technology (CONACYT).Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp. 177–188, March–April, 1994.     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.     

Temperature-frequency dependence of the elastic constants of certain resins

The authors present the results of an experimental investigation of the elastic constants of certain crosslinked and linear polymers in the temperature range from –50 to +110° C and the frequency range from 10¹ to 10⁵ Hz. The elastic constants were determined by both quasi-static and dynamic methods. The range of application of the different methods are characterized with respect to a time scale. It is shown that when certain experimental conditions are observed (strain rate, frequency), the values of the constants obtained by the different methods almost coincide. On the basis of temperature measurements it is postulated that rigid epoxies have a secondary low-temperature dispersion region.Mekhanika Polimerov, Vol. 3, No. 1, pp. 60–65, 1967     

Fracture in Ceramic-Matrix Composites Reinforced with Strongly Bonded Metal Particles

The resistance of a ceramic matrix composite to the cleavage cracking across a field of strongly bonded, uniformly distributed metal particles is studied. The crack trapping and bridging effects of the metal particles are analyzed by means of calculating the strain energy and the traction work. An explicit expression for the critical energy release rate as a function of particle volume fraction has been obtained. The fracture resistance is independent of elastic properties of the matrix and the sample geometry and is predominantly determined by the size/spacing ratio of the particles. It is shown that the theoretical curves agree with experimental data quite well. The methodology developed in this article can be used in studying the fracture resistances of composites with high filler contents and irregular filler geometries.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 303–318, May–June, 2005.     

Adhesion bond and temperature stresses at the polymer - filler interface in polyethylene composites

The temperature stresses in polyethylene composites with fibrous fillers have been estimated. It is shown that they do not represent a threat to the adhesion bond or the cohesion strength of the components of the systems investigated. Model experiments have revealed the presence of an adhesion interaction between the filler and the matrix in the composite itself and have made it possible to estimate the actual threat posed by the temperature stresses. The mechanism of action of the filler particles on the thermal expansion of the composite is explained.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1049–1056, November–December, 1970.     

Dynamic mechanical spectroscopy of polyethylenes with aggregating disperse and hybrid granular-fibrous fillers

Conclusion Based on the results of dynamic experimental studies, it was shown that addition of mineral fillers to polyethylenes does not result in a significant change in the relaxation properties of the polymer matrix of CM. It was found that aggregation of the particles of the granular filler causes a significant increase in the real part of the modulus and a decrease in the mechanical loss tangent of the CM. The possibility of using a modified elastic solution for predicting the effective characteristics of the dynamic viscoelasticity of composites was demonstrated.Translated from Mekhanika Kompozitnykh Materialov, No. 4. pp. 579–586, July–August, 1989.     

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.     

Correlation between the Mechanical Properties and the Amount of Desorbed Water for Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste

The effect of the amount of desorbed water on the mechanical properties of composites based on low-density polyethylene and linen yarn production waste (LW) is analyzed by statistical methods. It is shown that the amount of absorbed water decreases during the desorption process at room temperature both for specimens modified and unmodified with diphenylmethane diisocyanate (DIC.) The most sensitive to the action of water is the elastic modulus, which decreases considerably under the effect of water and is fully restored in the desorption process. The tensile strain also increases with the amount of absorbed water. It is found that the elastic modulus of the unmodified composite correlates linearly with the amount of desorbed water. Between the amount of desorbed water and the tensile strain, as well the specific work of deformation, a negative linear correlation is revealed. After water desorption, all strength and deformation characteristics of both the modified and unmodified composites are fully recovered.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 515–524, July–August, 2005.     

Structural approach to calculation of the effect of moisture on elastic characteristics of organoplastics

Data have been obtained for the structural calculation of the effect of moisture on the elastic characteristics of organoplastics from the properties of components. The distribution of moisture between the fiber and matrix — the components of a unidirectional composite — is considered. The elastic properties of the fiber are determined by an inverse calculation using the experimental dependences of the composite and matrix on moisture. The moisture effect on the properties of the materials is taken into account with influence functions, which differ by more than 25% for various characteristics. The results can be used for calculating the elastic properties of composites with various reinforcement schemes and at the nonequilibrium distribution of the moisture concentration in an actual environment.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 525–530, July–August, 1998.     

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.     

Estimation of the length distribution of through polymer chains

The contributions of entropy and elastic forces to the tensile modulus of a polymer chain are estimated. The chain length-distribution function in the amorphous region of highly oriented Lavsan is approximately determined from macroscopic stress-strain dependence. It is found that the length distribution has a width of the order of several percent of the length of the amorphous region of the fibril.A. F. Ioffe Physicotechnical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 922–925, September–October, 1974.     

Measuring the stresses in fibers of a loaded composite material by the method of infrared spectroscopy

Conclusions 1. Actual stresses in reinforcement fibers of a loaded composite have been measured by infrared spectroscopy.2. It has been shown that the plain rule of mixtures, not accounting for changes in mechanical properties of the matrix during processing of a composite, does not apply to a hot molded polyethylene-polypropylene composite.3. It is suggested that around the reinforcement fibers there exists an ordered layer of the matrix material capable of carrying a heavy load. A method is proposed, furthermore, for calculating the mechanical characteristics of the composite with such a layer. The volume fraction and the thickness of this hardened layer have been estimated from experimental data.Paper presented at the Third All-Union Conference on Polymer Mechanics in Riga, 1976.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 832–837, September–October, 1977.     

Study of the impact shear strength of polymer materials

A method is proposed for studying the dynamic strength of block polymers in terms of their resistance to impact shear. An original instrument for conducting tests are room and elevated temperatures is described. The results obtained with this instrument for alkathene and styrene carylonitrile copolymer are discussed. It is found that there is a considerable increase in specific shear energy in the region of transition from the glassy to the high elastic state. In the case of alkathene the investigated characteristic falls linearly on the temperature interval studied.Leningrad Kirov Institute of the Textile and Light Industries. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1135–1137, November–December, 1968.     

Theory of the elastic stability of compressible and incompressible composite media

The present article considers general problems of the theory of the elastic stability of composite media in the presence of finite and small precritical deformations with an arbitrary elastic-potential form. Our investigation was conducted for homogeneous and piecewise-homogeneous anisotropic media. Numerical results were obtained for laminar media. We have elucidated the case in which there is internal loss of stability (in the material structure) for compressible materials with small deformations (plane problem) and for incompressible materials with highly elastic deformations (plane and three-dimensional problems) for the Treloar and Mooney potentials.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 2, pp. 267–275, March–April, 1972.     

Nature and mechanism of friction of rubberlike polymers in different physical states

We have investigated the frictional properties of crosslinked butadiene-nitrile and butadiene-styrene copolymers and natural rubber in friction against polished steel under vacuum conditions in the temperature interval from –200 to +150° C, which embraces the glassy and high-elastic states, as well as the transition region between them. The temperature dependence of polymer friction is characterized by two maxima, a principal and a low-temperature maximum. The principal maximum, observed in the glass transition region, is not associated with the mechanical loss maximum observed in the polymers themselves. The temperature dependence of the force of friction is composed of three parts. In the high-elastic region there is an increase in the force of friction with fall in temperature, in accordance with the molecular-kinetic theory of friction of rubberlike polymers. In this region the nature of friction is associated with mechanical losses in the surface layer of polymer. The mechanical losses inside the polymer itself are unimportant. The deviation from the theoretical curve and the fall in the force of friction below a certain temperature in the transition region are chiefly associated with a decrease in the actual area of contact as the polymer passes into the glassy state. In the glassy region the friction is significantly determined by the mechanical losses in the polymer itself associated with the repeated elastic and forced-elastic deformation of the asperities in the layer of polymer in contact with the rigid surface. Therefore the low-temperature maximum is closely related to the mechanical loss maximum observed in the same temperature region in dynamic tests. Apart from this, the friction maximum is also associated with the increase in the forces of adhesion and the reduction of the actual area of contact at temperatures at which a forced-elastic mechanism of compression of the polymer asperities is not realized.Mekhanika Polimerov, Vol. 3, No. 1, pp. 123–135, 1967     

The method of dynamic programming in problems of optimization of temperature fields during thermal treatment of products made from composite polymer materials (CPM)

We state a control problem of stress optimization in cooling of products made from composite polymer materials in terms of dynamic programming. As a criterion of optimization we use the energy functional of elastic deformation, and as control functions we use temperature changes in the outer and inner surfaces of the cylinder.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 61–66, 1987.     

Basic equations of the theory of reinforced media

The author derives the basic equations of the theory of composite elastic media obtained by reinforcing some elastic medium with a large number of linear or planar elastic elements with high strength and deformation resistance. The argument is based on macrostructural considerations. The stress-strain state of each of the reinforcing elements is considered with allowance for interaction with the matrix material. In addition, the "smoothing" principle introduced in [1–3] is applied. This corresponds to approximating the reinforced medium with some equivalent quasi-homogeneous anisotropic medium.The case of a fibrous medium in which the reinforcing elements are rods or filaments [4] is discussed in detail. Allowance for moment effects leads to equations analogous to the equations of the Voight-Cosserat moment theory and its later generalizations. Similar equations are obtained for the case of laminated media, where the reinforcing elements are membranes or plates. On the basis of the viscoelastic analogy [7], the equations of the theory of reinforced media are extended to include the case in which the matrix and/or reinforcing materials are linear viscoelastic.Mekhanika Polimerov, Vol 1, No. 2, pp. 27–37, 1965