Elasticity of the crystal lattice of polyethylene terephthalate

The elasticity of the crystal lattice of polyethylene terephthalate was studied along and across the axes of the polymer molecules. The elastic modulus across the chains depended on the degree of crystallinity and the interplane distances in the directions of thea and b parameters of the unit cell. The nature of the elastic deformation in the crystal lattice was analyzed, and its elastic modulus along and across the axes of the chains was calculated. On loading biaxially oriented amorphous-crystalline polymers with a tensile stress applied in the direction of one of the orientation axes of the polymer, the stresses in the crystallites oriented along and across the external applied force and the amorphous regions in series with them were equal to the stress in the sample averaged over the cross section.Deceased.Translated from Mekhanika Polimerov, No. 6, pp. 982–986, November–December, 1972.     

Elasticity of composites with irregularly oriented shape-anisotropic filler particles

A variant of determining the elastic characteristics of composites containing irregularly oriented shape-anisotropic filler particles of two types (short fibers and thin platelets) is considered. The effective elastic constants of the composites are calculated by using the method of orientational averaging of elastic characteristics of isolated transversely isotropic structural elements reinforced with unidirectionally oriented short fibers or coplanarly arranged thin platelets. The superposition of elastic properties of the irregularly oriented structural elements, with account of their orientational distribution in the composite material, is accepted. The calculation results are compared with experimental data for the effective elastic moduli of polymeric composites reinforced with short glass fibers and of polymeric nanocomposites containing the platelet-type particles of organically modified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 285–300, May–June, 2006.     

Anisotropy of elasticity of a composite with irregularly oriented anisometric filler particles

The effects of orientation and shape of filler particles on the elastic properties of composites have been analyzed. The elastic constants of a composite with irregularly oriented filler particles were calculated by using the method of orientational averaging of the properties of a representative structural element. The elastic constants of the structural element were found according to a known generalized Eshelby solution for a finite concentration of ellipsoidal inclusions. The diagrams of elasticity anisotropy for a transversely isotropic structural element and an orthotropic composite with irregularly oriented inclusions are presented. A quantitative estimate for the degree of anisotropy of elastic properties of composites is suggested. Data on the influence of shape anisometry of inclusions on the anisotropy coefficient of filled composites are also reported.     

Elasticity of the intercrystallite zones and the mechanical properties of oriented polymers

As a result of a study of the behavior under load of the elements of the supermolecular structure of oriented amorphous-crystalline polymers it is shown that the stresses on the crystallites and the amorphous zones in series with them in the direction of the chain axes are equal to the mean stress applied to the specimen along the orientation axis. The nature of the elasticity and deformability of the amorphous zones is analyzed. A relation is obtained between the strength properties of oriented polymers and the number of load-carrying chains in the amorphous zones.Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 1002–1007, November–December, 1969.     

Theoretical and maximum attainable strength of various uniaxially oriented polymers (film,fibers)

The theoretical strength of various ideally oriented synthetic fibers was calculated. The calculation was based on an assumption that the rupture of polymers involves simultaneous breaking of molecular chains and pulling asunder the chain ends. The temperature-time dependence of the strength of fibers was analyzed and the maximum attainable strength of fibers of various kinds was calculated to show that it is 2–5 times higher than that recorded in practice. The main causes of the difference between the attainable and attained levels of strength are associated with imperfections of the supermolecular structure and an insufficient degree of orientation of materials of this kind. The principal means of obtaining high strength levels of synthetic fibers were discussed.Mekhanika Polimerov, Vol. 2, no. 6, pp. 845–856, 1966     

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.     

Transverse compression of PPTA fibers

Results of single transverse compression testing of PPTA and PIPD fibers, using a novel test device, are presented and discussed. In the tests, short lengths of single fibers are compressed between two parallel, stiff platens. The fiber elastic deformation is analyzed as a Hertzian contact problem. The inelastic deformation is analyzed by elastic-plastic FE simulation and by laser-scanning confocal microscopy of the compressed fibers ex post facto. The results obtained are compared to those in the literature and to the theoretical predictions of PPTA fiber transverse elasticity based on PPTA crystal elasticity.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).3TEX, Inc. 109, MacKenan Drive, Cary, North Carolina 27511, USA. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 533–544, March–April, 2000.     

Small deformations of oriented polymers

On the basis of a phenomenological analysis of the temperature dependence of the modulus of instantaneous elasticity and the stress relaxation process, it is suggested that in the region of small deformations there are no breakages of the macromolecules that might affect the elasto-relaxational behavior of highly oriented polymers (fibers) as in the region of large deformations. To judge from the values obtained for the energy constants, these properties are determined by the number of intermolecular bonds in the amorphous regions (modulus of instantaneous elasticity) and the physical events associated with the reorganization of these bonds and hindered rotation of the chain units (relaxation process).S. M. Kirov Leningrad Institute of Textiles and Light Industry. Translated from Mekhanika Polimerov, No. 6, pp. 976–980, November–December, 1971.     

Strength of biodegradable polypropylene tapes filled with a modified starch

The possibility of creating composite materials with high deformation and strength characteristics based on polypropylene (PP) and a natural polysaccharide in the form of a modified starch (MS) has been studied. The modified starch is shown to interact chemically with functional groups of PP, thereby positively affecting the physicomechanical properties, structure, and water absorption properties of films and oriented flat fibers based on starch-filled PP. The strength characteristics of both oriented and unoriented composites are 1.5–2.0 times as high as those of the initial PP. The water absorption ability of the materials varies symbatically with content of MS, which points to the dominant contribution of interactions at the PP-MS interface. The introduction of MS into synthetic polymers offers a possibility of producing new ecologically safe materials with high strength characteristics. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 389–400, May–June, 2006.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

Macromolecular mechanics

The fundamentals of "macromolecular" mechanics are outlined and approximate quantitative relations are established between the parameters of the mechanical properties of elastically stretched macromolecules and the characteristics of the mechanical properties of polymers determined at significant uniaxial deformations. This new scientific approach is based on the assumption of "framework connectivity." The conditions of internally compensated mechanical equilibrium at the molecular level are investigated. Several variants of simple geometric models of the "framework" reinforcing the stretched polymer are proposed. A system of quantities characterizing the mechanical properties of the polymer and the "framework" is developed. According to the theory, the stress in the "framework" macromolecules, considered as a molecular elastic continuum, substantially exceeds the stress in the stretched polymer. The nature of the internal stresses and elastic aftereffect in glassy crystalline polymers subjected to significant deformation is reinterpreted.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 221–231, March–April, 1971.     

Correlation of the elastic characteristics of Arimid PM with the elasticity modulus of its crystal lattice

Studies were made of the elastic characteristics (longitudinal elasticity modulus, elastic recovery) of Arimid PM fibers and of the longitudinal elasticity modulus of the crystal lattice of these samples. The elasticity modulus of the crystallites was determined by x-ray diffraction studies of loaded fibers. It is shown that the studied samples practically instanteneously recover their starting length after removing the load; the sample and its crystal lattice have comparatively low elasticity moduli with nearly identical values. Based on this data, reasons are discussed for the high elastic recovery of Arimid fibers and for the low elasticity modulus of its crystal lattice.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 771–773, September–October, 1972.     

Intermolecular interactions in fiber-forming linear polymers and certain of their mechanical properties

Values of the specific volumetric intermolecular interaction energies of a series of linear polymers have been calculated on the basis of data on the interatomic and intermolecular interactions of the functional groups in the polymer molecules. It is shown that the specific volumetric intermolecular interaction energy is closely correlated with the elastic and relaxation properties of the polymers, which makes it possible to predict a series of mechanical properties of chemical fibers.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 790–795, September–October, 1971.     

Deformation properties of some glass-like polymers

Problems of deformation in amorphous, glass-like polymers are considered. The deformation and strength properties of PMMA (polymethyl methacrylate) were studied, for different temperatures and conditions of deformation. It was established that the long-term resistance to deformation of glass-like polymers subjected to forced elastic deformation, as judged by the time lapse to "neck" formation, is described by a longevity equation, allowance being made for the displacement of the origin with respect to the coordinates.Yu. V. Mirgorod participated in the experimental part of this work.Tambovsk Institute of Chemical Machine Construction and Experimental Laboratory of Polymer Physics, V. I. Lenin State Pedagogic Institute, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 717–720, July–August, 1972.     

Nonlinear stress-strain relations for carbon-reinforced plastics under continuous static loading

The specific characteristics of oriented reinforced polymers are quite fully taken into account by a nonlinear anisotropic theory of the same type as the nonlinear theory of elasticity or the deformation theory of plasticity, based on the use of tensor-linear relations containing two quadratic forms of the stress components without the introduction of higher-order tensors. The possibility of extending this theory to the case of uniaxial deformation of carbon-reinforced composites is demonstrated.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 49–53, January–February, 1976.     

Patient-specific model of lung deformation using spatially dependent constitutive parameters

Breathing-induced spatially dependent lung deformation is predicted using patient-specific elastic properties with the contact–impact analysis model. The lung geometry is derived from 4D CT scan data of real patients. The spatially varying Young’s modulus for the patient is obtained from a previous study that used inverse deformation of the lung. The compact–impact analysis is implemented using the finite element method. The predicted lung deformation is compared with the results based on linear elasticity. The results are consistent with physiology, indicating large deformations near the diaphragm and smaller values at remote locations on the lobe. The effect of non-linearity of elastic property is most significant at the remote locations where the diaphragm-induced deformation is significantly attenuated.     

Mechanism of the increase in strength and heat resistance of oriented polymeric materials modified by graft copolymerization with vinyl monomers

The mechanical properties and structures of oriented films and fibers composed of polyethylene, polymethyl methacrylate, and other amorphous and crystalline polymers modified by the synthesis of uniformly distributed graft and block copolymers of methyl methacrylate, acrylonitrile, vinylidene chloride and other monomers have been the subject of a comparative investigation. The effect of the grafted polymers on the molecular mobility, relaxation processes, and solubility of the materials is explained by reference to a universal physical "crosslinking" mechanism. A theory of the interrelation between the structure and physical properties of the materials, the nature of the polymers, and the grafting conditions is developed and used to analyze the experimental data on a broad range of systems.V. I. Lenin Belorussian State University, Minsk. Translated from Mekhanika Polimerov, No. 6, pp. 968–975, November–December, 1973.     

Strength and deformability of reinforced polymers in tension normal to the fibers

The strength and deformability of reinforced polymers in tension across the fibers is investigated. It is assumed that the polymer deforms as an ideal elastoplastic body. Relations are obtained for the nature of the deformation of the polymer between the fibers and the strength and deformability of the composite with allowance for the structural distribution of the components. Theoretical stress-strain diagrams are presented for composites with different reinforcement densities and resin elasticities. The theoretical values of the strength and deformation of reinforced polymers with the load applied across the fibers are compared with the results of experiments on model specimens of epoxy-Thiokol polymers.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 682–687, July–August, 1970.     

Strength properties of oriented amorphous linear polymers in relation to their structure

Tensile tests have been conducted at room temperature on uniaxially oriented films of a number of amorphous linear polymers. It has been shown that the mechanical properties of the oriented polymers in the glassy state are chiefly determined by two parameters of the structure—the degree of orientation of the macromolecule segments and the concentration of stressed chains per unit volume, irrespective of the molecular weight of the polymer and the orientational stretching conditions.Mekhanika Polimerov, Vol. 3, No. 3, pp. 455–460, 1967