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.     

Fractional Burgers models in creep and stress relaxation tests

Classical and thermodynamically consistent fractional Burgers models are examined in creep and stress relaxation tests. Using the Laplace transform method, the creep compliance and relaxation modulus are obtained in integral form, that yielded, when compared to the thermodynamical requirements, the narrower range of model parameters in which the creep compliance is a Bernstein function while the relaxation modulus is completely monotonic. Moreover, the relaxation modulus may even be oscillatory function with decreasing amplitude. The asymptotic analysis of the creep compliance and relaxation modulus is performed near the initial time-instant and for large time as well.     

Modeling of primary and secondary creep for a wide stress range

Many materials exhibit a stress range dependent creep behavior. The power–law creep observed for a certain stress range changes to the viscous type creep if the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 5–12 for power–law behaviour) may decrease to the low value of approximately 1 within the stress range relevant for engineering structures. The aim of this paper is to confirm the necessity of the assumption of the stress range dependent power–law–viscous creep transition for the solution of stress relaxation problems affected by creep behavior at elevated temperatures. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. The proposed constitutive model includes a strain hardening function to describe the primary creep stage. To demonstrate the existence of the linear creep behaviour in the low stress range of application area and the influence of the primary creep behaviour on relaxation, several solutions of a uniaxial stress relaxation problem are presented for the loading values relevant to engineering applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Choice of kernels in solving problems involving creep and relaxation

For the memory theory analysis of creep and relaxation processes whose rates have a singularity at the beginning of the process it is proposed to employ a kernel and the corresponding resolvent in the form of a series whose convergence is proved. An estimate of the convergence and an asymptotic formula for large times are also presented. The kernel, the resolvent and their integrals have been tabulated. Theoretical curves are constructed for certain parameters, and it is shown how they can be used in analyzing creep problems when the object is to find relaxation (creep) curves from experimental creep (relaxation) curves. It is noted that, given a suitable choice of parameters, it is possible to use the proposed functions to describe both finite and unlimited creep.Mekhanika Polimerov, Vol. 2, No. 4, pp. 483–497, 1966     

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     

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.     

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.     

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.     

Effect of nanofiller aspect ratio on the stress relaxation and creep response of toughened pom composites

Ternary composites composed of polyoxymethylene (POM), polyurethane (PU), and sodium fluorohectorite (FH) or sodium bentonite (BN) were produced by the melt compounding masterbatch (MB) technique. The related MB was produced by mixing the PU latex with water-swellable FH or BN. The dispersion of the nanofillers in the composites was studied by X-ray diffraction techniques. The crystallization of the POM-based systems was inspected by polarized optical microscopy (PLM). The stress relaxation and creep properties of the composites were determined in short-time stress relaxation and creep tests (creep at various temperatures), respectively. The POM/PU/FH composites produced by the MB technique outperformed the POM/PU blend and the POM/PU/BN system in respect to most of the stress relaxation and creep characteristics. This fact was attributed to the higher aspect ratio of FH compared with that of BN. The master curves (creep compliance vs. time) constructed by employing the time-temperature superposition principle showed that the Findley power law was fully applicable to the experimental results obtained.     

Vibrational creep of polymeric materials

An experimental study of the effect of vibration on the creep process has been carried out in the case of the rigid porous polyurethane PPU-3, as a function of the magnitude of the vibrational loading and the level of basic static stresses. It has been shown that with increase in the velocity amplitude of the dynamic stresses, the creep process is accelerated, without being accompanied thereupon by vibrational heating of the material. The possibility has been established of approximating vibrational creep curves by the integral equation of Volterra, using a discrete series of relaxation times transformed by the vibro-time analogy method.For Communication No. 3, see [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 223–232, March–April, 1970.     

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.     

Thermocreep of polyethylene in the cyclic temperature regime

The shear creep and recovery of low-density polyethylene has been investigated in the constant and cyclic temperature regimes. It is shown that in the cyclic regime the relaxation processes are accelerated and the nonisothermal creep strains become progressively greater than the isothermal strains at the maximum temperature of the cycle. In recovery the relaxation spectra are shifted along the time scale relative to the creep spectra, the shifts for simple shear and uniaxial tension being nonidentical.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 227–235, March–April, 1969.     

Jump conditions in stress relaxation and creep experiments of Burgers type fluids: a study in the application of Colombeau algebra of generalized functions

We discuss stress relaxation and creep experiments of fluids that are generalizations of the classical model due to Burgers by allowing the material moduli such as the viscosities and relaxation and retardation times to depend on the stress. The physical problem, which is cast within the context of one dimension, leads to an ordinary differential equation that involves nonlinear terms like product of a function with a jump discontinuity and the derivative of a function with a jump discontinuity. As the equations are nonlinear, standard techniques that are used to study problems concerning linear viscoelastic fluids such as Laplace transforms and the theory of distributions are not applicable. We find it necessary to seek the solution in a more general setting. We discuss the mathematical and physical issues concerning the jump discontinuities and nonlinearity of the governing equation, and we show that the solution to the governing equation can be found in the sense of the generalized functions introduced by Colombeau. In the framework of Colombeau algebra we, under certain assumptions, derive jump conditions that shall be used in stress relaxation and creep experiments of fluids of the Burgers type. We conclude the paper with a discussion of the physical relevance of these assumptions.     

Investigation of the relaxation process in polycarbonate film

The temperature relaxation of polycarbonate film and the accompanying change in the birefringence path difference are considered. It is shown that at a temperature of about 170°C intense crystallization takes place in the film. The deformation modulus is a function of the density of the network and its degree of orientation. The variation of these parameters with the stretch ratio and temperature is determined experimentally. The creep of polycarbonate film is considered and correlated with the curves representing the fall in the number of chains of the molecular network in pure relaxation.Mendeleev All-Union Scientific-Research Institute of Metrology, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 72–76, January–February, 1973.     

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.     

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     

Estimation of limit strains in disk-type flywheels made of a compliant elastomeric matrix composite undergoing radial creep

Fiber reinforced elastomeric matrix composites (EMCs) offer several potential advantages for construction of rotors for flywheel energy storage systems. One potential advantage, for safety considerations, is the existence of maximum stresses near the outside radius of thick circumferentially wound EMC disks, which could lead to a desirable self-arresting failure mode at ultimate speeds. Certain unidirectionally reinforced EMCs, however, have been noted to creep readily under the influence of stress transverse to the fibers. In this paper, stress redistribution in a spinning thick disk made of a circumferentially filament wound EMC material on a small rigid hub has been analyzed with the assumption of total radial stress relaxation due to radial creep. It is shown that, following complete relaxation, the circumferential strains and stresses are maximized at the outside radius of the disk. Importantly, the radial tensile strains are three times greater than the circumferential strains at any given radius. Therefore, a unidirectional EMC material system that can safely endure transverse tensile creep strains of at least three times the elastic longitudinal strain capacity of the same material is likely to maintain the theoretically safe failure mode despite complete radial stress relaxation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 87–94, January–February, 2000.     

Thermodynamic determination of the shift factor

The methods of the thermodynamics of nonequilibrium processes are used to examine the creep stain-relaxation time; a transition is made from the relaxation time of the degree of advancement of the relaxation process to the strain-relaxation time. Expressions for the temperature and stress shift factors containing experimentally measurable quantities are found starting from the strain-relaxation time.     

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