Evaluation of integral operators of viscoelasticity

A method of calculating the integral operators of viscoelasticity from arbitrary continuous functions is proposed for the case where the relaxation (creep) function is given in tabulated or graphic form. The problem of constructing the creep function from an experimentally known relaxation function is solved.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1115–1117, November–December, 1973.     

Investigation of the mechanical properties of acrylics under conditions of creep,stress relaxation,and harmonic vibration

The dynamic and static (creep, stress relaxation) mechanical properties of various acrylics have been investigated. A relation is established between the structure and the macroscopic mechanical properties. The previous thermal history and the characteristics of the state of stress are shown to affect the nature of the relaxation processes and the mechanical properties of the acrylics. Generalized stress relaxation curves are constructed. The mechanical glass transition temperatures of the acrylics investigated are determined.Lenin Moscow State Pedagogic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 157–159, January–February, 1973.     

Creep of polymer materials under periodically varying loads

A method is proposed for constructing the creep curves of a material whose nonlinear memory properties are described by Rozovskii's nonlinear integral equation [2] (with allowance for the stress dependence of the relaxation time) under given periodic loading from known creep curves recorded at constant stress. In deriving the theoretical relation certain simplifying assumptions are made (the creep strain accumulated in 1–2 cycles is small, no vibration [4–6]). An experimental check shows that the proposed method can be used to predict the behavior of a material under periodic loading with an accuracy sufficient for practical purposes.Mekhanika Polimerov, Vol. 2, No. 3, pp. 330–336, 1966     

Method of determining the volume and shear characteristics of elastico-viscous hereditary media from uniaxial-tension (compression) experiments

A method is proposed for determining the elastic constants — instantaneous modulus of elasticity, Poisson's ratio, shear modulus, bulk modulus, and the shear and volume influence functions — the shear creep kernel, the shear creep rate kernel, and the corresponding relaxation kernels from the data of creep or relaxation tests.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 754–758, July–August, 1969.     

A molecular model of creep and stress relaxation in crystalline polymers

A possible model of defect formation in a polymer crystal lattice is considered. The results of an investigation of creep and stress relaxation in crystalline polymers are interpreted on the basis of the model proposed.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 6, pp. 969–975, November–December, 1971.     

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.     

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.     

Equations of three-dimensional deformation of linear viscoelastic media

An equation is proposed relating the stress and strain tensors in time for the three-dimensional deformation of linear viscoelastic media whose properties are determined by four parameters. A method is indicated for determining these parameters based on simple creep or relaxation tests. Values of the parameters are given for certain polymer materials. For such materials, there is an upper limit of the stress state below which an equilibrium limit state is possible. A creep kernel is proposed for the case of no equilibrium limit state, and a resolvent constructed with account for the variation of stress and strain in time.Mekhanika Polimerov, Vol. 1, No. 4, pp. 35–42, 1965     

On the theory of anisotropic creep of unidirectional glass-reinforced plastics

The basic relations of the theory of anisotropic creep of unidirectional glass-reinforced plastics (GRPs) in a three-dimensional stress state are found using a model of a material with inhomogeneous structure and the rheological properties of the resin. These relations are suitable for investigating the stress state of GRPs for resin stresses not exceeding certain values. The phenomena of simple creep and stress relaxation are studied with reference to a unidirectional GRP with an epoxy-maleic resin matrix.Mekhanika Polimerov, Vol. 1, No. 2, pp. 64–69, 1965     

Use of the results of auxiliary experiments in solving problems in the linear theory of viscoelasticity

The approximate method of solving problems of the theory of linear viscoelasticity with arbitrary creep and relaxation kernels, proposed in [2], is substantiated and generalized. The essence of this method consists in the approximation of the functions depending on the Laplace — Carson transforms of the mechanical characteristics of a viscoelastic body by means of certain combinations of the transforms of the creep and relaxation kernels. The expressions obtained as a result of the approximation enable the inverse transforms of the unknown functions to be found without difficulty.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 963–969, November–December, 1968.     

Acoustic creep of glass-fiber-reinforced plastic

A method of investigating acoustic creep of polymer composites developing under the effect of static tensile forces and small amplitudes of dynamic stresses with a frequency of 20 kHz acting coaxially with the static loads is considered. Results of investigating acoustic creep of glass-fabric-reinforced plastic are presented. It is shown that the presence of a high-frequency stress component regularly accelerates relaxation processes and reduces considerably the deformation resistance of the material. Generalized curves simulating the long-time static creep of reinforced plastic are constructed by the method of temperature-time, stress-time, and vibration-time analogies. The results of prediction are compared with the control experiment.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 397–404, May–June, 1973.     

Determination of regular discrete relaxation spectra from the viscoelastic functions

A procedure for determining regular discrete relaxation spectra from the viscoelastic functions is presented as a generalization of a previously proposed procedure for determining the conditional rheological characteristics in a piecewise-exponential approximation of the experimental creep, relaxation, and – curves. The calculated data are in good agreement with the experimental results.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 801–807, September–October, 1971.     

Viscoelastic characteristics of the interaction between structures and soils

The shear coefficients of a body relative to the soil and the shear creep and relaxation kernels are determined from the data of creep and relaxation tests.Urazbaev Institute of Mechanics and Earthquake Resistance of Structures, Academy of Sciences of the SSR, Tashkent. Translated from Mekhanika Polimerov, No. 2, pp. 207–211, March–April, 1973.     

Investigation of the one-dimensional problem of nonlinear creep

A method of analyzing experimental creep curves of a nonlinear viscoelastic material to obtain relaxation curves is examined. It is assumed that the family of creep curves in question cannot be represented as a product of the stress function and a function of time. The investigation is carried out using the memory theory. The sum of the exponentials for curves not having a singularity at the start of the process is taken as the creep kernel [1]. A method of approximation by the sum of the exponentials is given. For processes with an initial singularity it is proposed to use the corresponding kernel, for which the resolvent is given.Mekhanika Polimerov, Vol. 2, No. 5, pp. 678–687, 1966     

Some relationships between the specific functions and constants of visoelastic media

It is proved that the shear, lateral creep, and relaxation functions can be expressed in an elementary way by the longitudinal creep and relaxation functions and the elasticity modulus of the bulk.I. M. Gubkin Moscow Institute of Petrochemical and Gas Industry. Translated from Mekhanika Polimerov, No. 5, pp. 810–814, September–October, 1973.     

Rheological characteristics of orthotropically reinforced polymeric materials

It is proposed to calculate the rheological characteristics of orthotropically reinforced polymeric materials using a model in accordance with which the composite is assumed to consist of layered blocks, the planes of the layers having one of three possible orientations with given probabilities. The effective rheological characteristics of each block are exactly determined, while those of the composite as a whole are determined in the Voight or Reuss approximations. The first scheme is convenient for calcuating the shear modulus operators, the second for calculating the Young's modulus and Poisson's ratio operators. A numerical computer analysis has been made for the Young's moduli. It is shown that for the anisotropic composites in question each of the technical elastic moduli is characterized by two resolvent Q* operators of real or complex argument. The conditions under which one of the Q* operators can be neglected are determined. The integral representation of the kernel of the Q* operator of complex argument is given in the case where the latter is fractional-exponential with fractional index =–1/2 and the corresponding curves are presented.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 276–283, March–April, 1972.     

Analysis of nonlinear polymer creep

The relaxation properties of polyethylene are analyzed. The nonlinear time-dependent stress-strain relations and the creep and relaxation equations are obtained from the experimental creep data. The analysis is based on an appropriate variant of the nonlinear memory theory with singular functions whose parameters, together with the modulus of elasticity, are determined by the method described in [1].Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 410–414, May–June, 1969.     

Low-cycle fatigue of a composite substance containing a dispersed filler in cyclic compression

Conclusions 1. The lifetime of a composite material having a dispersed filler has been examined under conditions of low-cycle compression.2. It has been shown that, in distinction from materials of fibrous structure, the lifetime of this material is determined, not by a breakdown in the continuity of structure, but the deformability of the polymer matrix.3. The absence of a correlation between the static and fatigue strengths of composite mateials from cold and hot curing is caused by the different effect of the structure of the cured binder as a component of the material on the ultimate static characteristics and creep, whose relaxation character is more clearly expressed.4. Creep of the binder and the strength of the microspheres are the main factors which determine the lifetime of the material in question in cyclic compression.All-Union Scientific-Research Institute of Synthetic Resins, Vladimir. Translated from Mekhanika Polimerov, No. 4, pp. 653–657, July–August, 1978.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965     

Creep of a multilayer cylinder under nonisothermal loading

A method is proposed for calculating the creep of a multilayer cylinder under nonisothermal loading with allowance for the temperature dependence of the physico-mechanical characteristics of the material. Numerical examples are considered. The states of stress and strain of the viscoelastic and elastic components of a two-layer cylinder are compared.Baranov Central Institute of Aviation Engine Construction, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 321–327, March–April, 1969.