Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Periodic axial and shear deformation of polymers in the viscous-flow state

Results are given of an experimental investigation of the combined periodic axial and shear deformation of polymers in the viscous-flow state. Specimens in the form of right cylinders were disposed between two parallel plates to which the material adhered completely. The experimental data are compared with those obtained under simple shear. The results indicate that, with combined periodic axial and shear deformation, nonlinear shear deformations affect the axial viscoelastic properties and nonlinear axial deformations affect the shear properties of the material.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 880–885, September–October, 1972.     

Effect of a filler on the strength properties of thermosets

The effect of a filler on the strength properties of polymers in tension is investigated. The thermostructural stresses that develop in the composite during cure are taken into account. Relations are given for the strength of the filled polymer as a function of the percentage filler content. In the process of analyzing the thermostructural stresses an analytic expression is obtained for the linear expansion coefficient of the composite with allowance for the structural distribution of the components. Calculated values of the strength and thermostructural stresses are presented for composites with different filler contents. The theoretical determination of the strength of filled polymers is compared with the results of experimental investigations of composites based on epoxy resin filled with quartz dust.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 97–101, January–February, 1973.     

Region of linearity of the deformation properties of contact-molded glass-reinforced plastic

A study was made of the creep and recovery of contact-molded glass-reinforced plastic in different directions in the plane of the sheet in uniaxial tension. On the basis of experimental data, the region of linearity of the deformation properties of the material under investigation was established. The influence functions in the relations of the theory of viscoelasticity were taken in the form proposed by Bronskii. The dependence of the parameters which determine these functions on direction was investigated. It is shown that, in practice, this dependence is inherent in only one of the parameters, and a relationship which is in satisfactory agreement with the experimental results is proposed to describe it.Moscow Institute of Chemical Machine Building. Scientific-Research Institute for Mechanics, M. V. Lomonosov State University, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 404–410, May–June, 1970.     

Constitutive Modelling of Resins in the Compliance Domain

A rheological HWKK/H model for resins is developed taking into consideration the up-to-date analyses of experimental results. Constitutive compliance equations of linear are formulated for this model in the shear/bulk form, which describes, among other things, the first-rank reversible isothermal creep. The shear (distorsional) deformations are simulated with three independent stress history functions of fractional and normal exponential types. The volume deformations are simulated as perfectly elastic. The model is described by two elastic and six viscoelastic constants, namely three long-term creep coefficients and three retardation times.The constitutive compliance equations of viscoealsticity for resins are also formulated in the coupled form. Formulae for converting the constants of shear/bulk (uncoupled) viscoelasticity into the constants of coupled viscoelasticity are given too.An algorithm for identifying the material constants, based on the creep of uniaxially tensioned bar samples, is formulated in a way that gives unique results. The material constants are fiund for Epidian 53 epoxy and Polimal 109 polyester resins. The creep processes, simulated based on the experimental data, are presented graphically for both the resins examined.     

Experimental and theoretical investigation of a composite beam for bridge structures

Results of an experimental and theoretical investigation of composite beams as elements of bridge superstructure are presented. Experiments on beams of two types — made of wood and the same beams with a composite sheath — were carried out. The rigidity of the beams of the second type was about twice as high as that of the first ones. The classical bending model of composite beams gave deflections smaller than experimental ones. To reconcile these results, the model is refined by including the effect of shear. The deflections are represented as classical ones multiplied by a shear factor which depends on the bending and shear stiffnesses and the span length of the beams. As a result, a good agreement between calculations and experiments is achieved. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 449–462, July–August, 2006.     

Mechanical behavior of a number of polymers at helium temperatures

An experimental investigation of the mechanical behavior of a number of polymers in the range 4.2–240°K has been made. It has been shown that at helium temperature the Poisson ratio is governed by the free volume. It has been established that the dynamic Young's modulus and shear modulus of these polymers at 4.2°K depend on the chemical structure: their values are determined by the mean distance between neighboring macromolecule chains.     

Theoretical-experimental method for determining the averaged elastic and strength characteristics of a honeycomb core of sandwich designs

Analytic formulas for the averaged elastic and strength characteristics of a honeycomb core with a hexahedral structure are derived by introducing the hypothesis about the momentless work of its elements (walls) in the course of loading and during their stepwise exclusion from operation after their buckling in compression-compression or pure shear. The dimensionless coefficients appearing in the structural formulas when solving the problems formulated are to be determined from experimental data on tension, compression, and pure shear in two planes. It is shown that, in tension-compression, honeycomb must be considered as a heteromodular material with averaged elastoplastic properties, for which the relations between averaged stresses and averaged strains in compression and shear change stepwise on some sections (conditional plastic flow).     

Effect of the type of state of stress on the characteristics of the mechanical glass transition process in polymers

The effect of the type of state of stress on the activation energy and relaxation time is investigated with reference to the mechanical glass transition (softening) process in polymers. An expression relating the mechanical glass transition temperature with the structural glass transition temperature, the mean stress, and the stress intensity is obtained for isotropic homogeneous polymers. Experimental data obtained for polymethyl methacrylate in uniaxial tension and compression, pure bending, and shear are presented.All-Union Scientific Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 195–199, March–April, 1971.     

Dynamic loading of polymeric materials

Published material dealing with the dynamic behavior of ductile elastic materials is reviewed. The methods used up unitl now for the investigation of the mechanical characteristics of materials under the conditions of uniaxial stretching and wave propagation are evaluated. There are also presented the basic results of the experimental studies carried out in order to elucidate the effect of rate on the mechanical properties of elastomers, vitrified polymers, glass-reinforced plastics, and crystalline polymers. A review is presented of the experimental and theoretical studies dealing with wave propagation in ductileelastic rods.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 326–338, March–April, 1970.     

Contribution to the theory of forced high-elastic deformation of polymer materials

The large reversible and irreversible deformations of network polymers are examined. Expressions are derived for the stress tensor and for the conventional tensile stress. The uniaxial homogeneous extension curve has a maximum and a minimum if it is assumed that the coefficient of friction depends exponentially on the applied stress. The "necking" condition is derived for uniaxial tension. The results are compared with the experimental data.Mekhanika Polimerov, Vol. 4, No. 2, pp. 255–262, 1968     

The combined compression and shear of a rectangular rubber block

For long rectangular rubber blocks with metal plates bonded to their upper and lower surfaces, approximate force-deflection relations are obtained for the problem of combined compression (or tension) and shear. The results obtained generalise that of Klingbeil and Shield for the case of pure compression alone, as well as incorporating the well known simple shear result. However, unlike the pure compression solution, horizontal and vertical force resultants on the free surfaces cannot both be set to zero, which is a well known characteristic of simple shearing. Here the strategy is adopted of equating to zero only the horizontal force resultants on the free surfaces so that the pure compression approximation of Klingbeil and Shield emerges in the event of zero shear. The force-deflection relations so obtained are illustrated graphically.     

Creep of unidirectional glass-reinforced plastics based on new types of fibers

Theoretical and experimental compressive creep relations for a unidirectional glass-reinforced plastic based on hollow fibers are presented. The agreement between the theoretical and experimental data is shown to be satisfactory. The effect of fiber capillarity on the creep process is unimportant.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Fiber Glass, Moscow; Institute of Mechanics of Machines and Polymeric Materials, Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Mekhanika Polimerov, No. 4, pp. 747–750, July–August, 1971.     

Creep in materials subject to aging

A strain-hardening theory is used in an attempt to describe the creep in aging materials. Samples of commercial celluloid are tested for uniaxial creep under tension and the results are compared with the corresponding theoretical relations. The latter are found to be in fairly good agreement with the test results.Mekhanika polimerov, Vol. 1, No. 1, pp. 61–64, 1965     

Creep and aftereffect of polyethyleneterephthalate films under conditions of uniaxial stress

The results are given for an experimental investigation of creep and aftereffect in polyethyleneterephthalate films stressed in tension. It is shown that the creep is well represented by an exponential relation. A method of determining the corresponding coefficients is described.Mekhanika Polimerov, Vol. 1, No. 2, pp. 59–63, 1965     

Viscosity,rubber elasticity,and viscoelasticity of concentrated polymer solutions

The results of a comparative investigation of the effect of the nature of the polymer and the solvent on the viscosity, rubber elasticity, and viscoelasticity of concentrated polymer solutions in the region of linear mechanical behavior are presented. It is established that in the case of nonpolar polymers the solvent affects only the free volume of the solution, whereas for polar polymers it also affects the entanglement network. This leads to the equality of the viscosities of solutions of nonpolar polymers in different solvents when compared in corresponding states (relative to the glass transition temperature) and to the dependence of the shear modulus of solutions of polar polymers on the nature of the solvent and temperature. It is shown that there is a universal relaxation spectrum in the flow zone for solutions of different polydisperse polymers after normalization with the shear modulus and the natural relaxation time determined as the ratio of the viscosity to the shear modulus.A. M. Gor'kii Ural State University, Sverdlovsk, A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 729–736, July–August, 1973.     

流动稳定性弱非线性理论的重新考虑*

弱非性理论已被广泛用于流动稳定性理论及其它领域.然而其应用对某些问题虽是成功的,但对另一些问题,其结果却常不令人满意,特别是对转捩或自由剪切流中涡的演化这类问题,这时理论研究的目的不是寻找稳态解,而是预测演化过程.在本文中,我们将研究不成功的原因并建议一些改进的办法.     

Numerical simulation of rheological processes in hardening plastics under stress control

The paper concerns the simulation of rheological processes in hardening plastics (resins) under stress control. It is assumed that the resins work in the glassy state, under normal conditions, and the rheological processes are quasi-static and isothermal. The reduced stress levels do not exceed 30% of the instantaneous tensile strength. A resin is modelled as a homogeneous, isotropic, linearly viscoelastic material. The HWKK/H rheological model, developed recently by the author, is used. Short-term, medium-term, and long-term shear strain components are considered and described by one fractional and two normal exponential functions as the stress history (memory) functions. A novel algorithm for the numerical simulation of rheological processes in resins has been developed, which is unified for all stress history functions in the HWKK/H model. The algorithm employs the Boltzmann superposition principle, a virtual table for the classic creep process, and a high-rank Gaussian quadrature. The stress function is approximated with a stair case function. The constitutive equations governing the HWKK/H model are trans formed into an algebraic form suitable for algorithmization. The problem of quasi-exact calculation of the double-improper integral resulting from the fractional exponential function is solved effectively. The algorithm has been tested successfully on selected loading programs of unidirectional tension of epoxide. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 201–212, March–April, 2007.