Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Study of microbuckling of fiber-reinforced composite materials

On the basis of the theory of microbuckling of lamina-reinforced composites and formula predicting the critical composite stress for microbuckling in the shear mode _cs published in the literature, a FORTRAN program for study of the behavior of microbuckling of fiber reinforced composites has been developed. Some types of composite materials (reinforcement of different fibers and epoxy matrix) have been studied. Graphics and curves, accounting for the dependences of the compressive stress at failure _cs from the reinforcement volume k, specimen length L, and shear modulus of resin G_r have been obtained. The comparison of the theoretical diagrams presented here and experimental and theoretical results, published in the literature shows good agreement. The basic conclusion of the work presented here is that the study could be used for other fiber reinforced composites (with different mechanical properties of matrices and fibers).Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 531–538, July–August, 1996.     

Temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region

The possibility of using temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region is demonstrated and an additional applicability criterion — similar slopes of the isotherms of the amplitude dependences of the dynamic functions — is formulated. In the case of heavily filled rubbers it may be necessary to determine the constants of the Williams-Landel-Ferry equation and the reference temperature T_S from the experimental data — they may not coincide with the universal values. Master curves of the dynamic functions are obtained for a series of shock-absorbing rubbers at a shear strain amplitude =0.01.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 751–754, July–August, 1973.     

Prediction of the relaxation properties of materials based on heat-resisting polymers

Conclusions The PB0, P0D, and PI materials were used to show the possibilities of simulating the long-term relaxation processes for a new group of polymer materials using the time analogies in the linear and nonlinear regions of the viscoelastic properties. The results show that the generalized dependences of compliance and relaxation modulus widen the time range of lead of the relaxation processes by approximately six to seven decimal orders. Satisfactory results were obtained in comparing the generalized dependences with the results of the long-term reference experiment carried out in the same basic conditions.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 778–783, September–October, 1984.     

Effect of filler on the viscosity and viscoelasticity of melts of low-density polyethylene. Communication 2

Conclusions 1. A filler causes a change in the viscoelastic functions of melts, which in general cannot be described in linearly transformable coordinates.2. With rising filler concentration, the maximum of the frequency of the relaxation spectrum N(s) increases, but the frequency corresponding to the maximum decreases.3. The dynamic viscosity and rigidity of matrices and composites as functions of frequency are satisfactorily described by a three-parameter relationship. The relationship derived contains parameters of the degree of filling. Using the dimensionless viscosity '/_o and deformation frequency '₁ it was possible to obtain a relationship which is invariant with respect to the filler in a limited range of change in and which can be used for approximate calculations.4. The initial shear modulus of a composite with a filler concentration corresponding to formation of a secondary network can be lower than the shear modulus of the matrix.For communication 1 see [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 122–126, January–February, 1977.     

Rheological characteristics of melts of low-molecular-weight branched polyethylene in the region of critical molecular weights

The viscosity and the first difference of the normal stresses have been measured at stationary shear rates from 5.68 to 4500 sec^–1 for melts of low-density polyethylenes obtained by thermal degradation of commercial polyethylene in a nitrogen atmosphere. In addition, the complex modulus has been measured on the angular frequency range from 0.396 to 198.5 sec^–1. Three regions of molecular weights differing with respect to the value of the exponent in the relation ₀ = kM have been established. At > normal stresses are observed in the region of shear rates corresponding to a linear dependence of the shear rate on the shear stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga; Plastpolymer Research and Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 963–967, November–December, 1973.     

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.     

Multicritical phenomena in flow of viscoelastic liquids. 2. Zaremba-Fromm-De Witt liquid model generalized to the relaxation time spectrum

The effect of the relaxation time spectrum on the critical, i.e., limiting, conditions of stable shear flow of viscoelastic liquids at small Reynolds numbers was investigated. The approach developed in [1] was generalized to the Zimm, Rouse, Spriggs, and Ferry-Landel-Williams (FLW) viscoelastic relaxation time spectra. The FLW spectrum depicts the plateau of the viscoelasticity of high-molecular-weight polymer melts. The problem of the frequency dependence of the components of the complex shear modulus at different steady-state flow rates for the case of periodic shear directed both parallel to steady-state flow and orthogonal to it was solved for all of the listed models. The results of the experiment on superposition of periodic shear on the steady-state flow of a moderately concentrated solution of polyisobutylene were compared with the results of calculating the effect of steady-state flow on the frequency viscoelastic functions for liquids whose viscoelasticity is approximated by a Spriggs relaxation time spectrum. The calculation showed that in flow of liquids approximated by Rouse, Zimm, or Spriggs spectra, only parallel and orthogonal elastic losses of stability occur and dissipative loss of stability does not. Three types of instability (two elastic — parallel and orthogonal - and one dissipative — parallel) predict the prospects for use of the FLW spectrum. For this model, like the models using the Rouse and Zimm spectra, the shear rate at which instability is generated, especially dissipative instability, is a function of the number of relaxation times considered in the calculation. It was found that the predicted generation of dissipative instability begins for shear rates qD^* greater than the critical rates of generation of elastic parallel qE^* and elastic orthogonal qE^* instabilities, in contrast to the ZFD model which predicts that qE^*<qD^*<qE^*. The critical shear rates are correlated with the appearance of supermolecular viscoelastic structures caused by shear flow, called elastic-dissipative by analogy with dissipative structures.For communication 1 see [1].Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 119–135, January–February, 1997.     

Experimental determination of the shear modulus of compact bone tissue

Various methods of experimentally determining the shear moduli G₁₂, G₁₃, and G₂₃ of compact human bone tissue have been examined. The results of the study confirm the previous view that compact tissue has properties similar to those of a transversally isotropic material. It has been established that the shear modulus along the diaphysis of the tibia at the level of girdles 9–24 does not change significantly. There is a definite difference in the rigidity characteristics with respect to the regions of the cross section. The highest values for the shear modulus were established in the angle regions of the cross section. There is a linear dependence of the shear stress ₁₂ on the torsional angle ₁ within the experimental range of stresses (₁₂90 kg/cm²).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 697–705, July–August, 1972.     

Rheology of filled polymers. Steady-state shear flow and periodic deformation. 1. Relaxation time spectra,viscosity

Conclusions 1. The validity of the temperature-frequency superposition in the finite relaxation region has been confirmed for a concentrated solution of PIB filled with solid dispersed particles;2. the apparent heat of activation of the viscoelastic relaxation times increases at and above a certain filler concentration (c=15%);3. in the case of fillers for which the apparent heat of activation of the viscoelastic relaxation times is independent of the filler concentration, the filler only shifts the frequency functions of the components of the complex shear modulus along the logarithm of the modulus axis and the relaxation time spectrum H() along the log H axis. In this case G_C/G_M=G_C/G_M=_OC/_OM=_rel;4. the effective filler concentration for ccrit, as determined from the concentration dependence of the initial viscosity, exceeds the nominal filler concentration by a factor of 2.4 to 2.8;5. at a filler concentration c>c_crit, the contour of the relaxation time spectrum changes on account of the formation of a secondary filler structure;6. when the filler concentration ccrit, the dependencies of the viscosity on the shear rate for the composites and the matrix can be reduced with respect to two parameters;7. possible methods for the reduction of flow curves by means of linear coordinate transformations have been systematized.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1075–1083, November–December, 1977.     

Torsion testing of polyvinyl chloride sheet

The behavior of polyvinyl chloride sheet in torsion has been studied. Normal round test pieces were tested at strain rates of 0.3 and 1 rpm. The specimens were cut in the longitudinal and transverse directions of the sheet. The principal strength and plasticity characteristics of the material in torsion were obtained. During the tests torsion diagrams (M_t vs. ) were recorded. The specimens failed in shear. The shear modulus was determined on a special table device. The experiments showed that the shear modulus, limit of proportionality, and tensile strength have the same values in both longitudinal and transverse directions. The values of the angle of twist at failure are large and vary over a wide range.Mekhanika Polimerov, Vol. 1, No. 5, pp. 19–24, 1965     

Some Asymptotic Formulae for q-Shifted Factorials

The q-shifted factorial defined by (a : q^k) _n = (1 – a) (1 – aq^k)(1 – aq^2k)... (1 – aq^{(n – 1)k}) appears in the terms of basic hypergeometric series. Complete asymptotic expansions as q 1 of some q-shifted factorials are given in terms of polylogarithms and Bernoulli polynomials.     

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.     

Creep on an initial small interval

The creep processes of hereditary media on a small initial interval are described, using as influence functions the resolvent functions for the generators of the Dirac function, which are employed as relaxation kernels. Equations are constructed for determining the instantaneous modulus and the parameters of these functions from experimental stress-strain diagrams obtained at three different constant loading rates.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1970.     

Elastic properties of certain polymer matrices at low temperatures

A study is made of the viscoelastic behavior of the polyimide DFO and polybenzoxasol (PBZ) at low temperatures. Pulsed ultrasound is used to measure ultrasonic velocity in polymers at the frequency f=5 MHz within the temperature interval 4.2–240 K. Data obtained from acoustic measurements is used to calculate the dynamic elastic modulus, shear modulus, compressive bulk modulus, Poisson's ratio, and certain thermophysical characteristics (Debye temperature, specific heat, coefficient of linear expansion, Grünheisen parameter). It is established that the investigated polymers have low dynamic moduli at 4.2 K. Their values change by 18–20% within the temperature range 4.2–240 K. The polymers also have a large free volume at the temperature of liquid helium. The results show that polyimide DFO and PBZ have good service properties at low temperatures.Paper presented at the IX International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Moscow State Academy of Automotive and Tractor Engineering, Russia. Translated from Mekhanika Kompozitmykh Materialov, No. 4, pp. 454–459, July–August, 1996.     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

Bending of prestressed glass-reinforced plastic beams

Initial waviness of the fibers and prestressing are investigated in relation to their effect on flexural stiffness and strength for beams with low shear strength. It is shown that prestressing the reinforcement increases the flexural stiffness but at the same time adds to the shear correction as a result of an increase in the modulus of elasticity E_x in the direction of reinforcement and the insensitivity of the shear modulus G_xz to prestress. It is established that prestressing increases the shear strength and the degree of anisotropy . Materials of two types are investigated: unidirectional (AG-4S) and cloth-reinforced (SKT-11).Mekhanika Polimerov, Vol. 3, No. 5, pp. 888–893, 1967     

On predicting unsteady non-Newtonian blood flow

The influence of the non-Newtonian stress–strain relation of blood on the oscillatory shear index (OSI) and mean wall shear stress (WSS) are described. A mathematical non-dimensional model based on the momentum equation for a modified Casson’s fluid is formulated in terms of the dimensionless yield shear stress . An original direct numerical procedure is presented to predict the flow patterns. Results obtained by using a finite difference approach show a difference in OSI when blood is assumed to be a Newtonian fluid instead of a modified Casson’s fluid. The calculation of the OSI in human normal conditions under the Newtonian approach differs in 5% from the result obtained from using the Casson model.     

Resin cure monitoring system based on nondestructive dielectric spectrometry

An on-line indirect cure monitoring prototype system is described based on dielectric spectrometric measurements (frequency dependences of the dielectric modulus and/or dielectric permittivity and/or dielectric loss factor and/or relaxation spectrum). A key block of the system is the Dielectric Spectrometer. Model DS 7056-C interfaced with a standard PC. A variation of the dielectric frequency spectra during the cure process for two epoxy systems based on araldite resins LY556 and LY561-1 are considered as an illustration of capabilities of the described hardware and software.Institute of Polymer Mechanics, Riga, Latvia LV-1006. Published in Mekhanika Kompozitnykh Materialov, Vol. 32. No. 3, pp. 401–409, May–June, 1996.     

Best approximation of periodic functions by trigonometric polynomials in L2

Estimates are gotten for the best approximations in L₂ (0, 2) of a periodic function by trigonometric polynomials in terms of its m-th continuity modulus or in terms of the continuity modulus of its r-th derivative. The inequality E_n–1(f)L₂<(C _2m ^m _m(2/n;f)L₂(1 const) is proved, where the constant (C _2m ^m )^–1/2 is unimprovable for the whole space L₂ (0, 2). Two titles are cited in the bibliography.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 513–522, November, 1967.