Normal stresses associated with the flow of non-Newtonian polymer systems

It has been experimentally confirmed that the method of calculating the shear rate dependence of the normal stresses from the flow curve, proposed in [1], gives good results consistent with the experimental data. A series of simple relations proposed for estimating the initial normal stress coefficient are compared with the experimental results and it is shown that there is good agreement between calculation and experiment. In the linear region the Lodge relation, which equates the high-elastic strains to half the ratio of the normal to the shear stresses is satisfied.For communication 1 see [1].Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1971.     

Normal stresses in non-Newtonian polymer flows

The calculation of the normal stresses from the flow curve is considered on the basis of the method of correlation of the frequency and stationary characteristics of flowing polymer systems. Simple expressions are given for finding the initial normal stress coefficient and the high-elastic modulus from the point corresponding to the beginning of non-Newtonian flow. A necessary condition for the appearance of normal stresses is a viscosity anomaly. It is shown that for a bounded value of the initial normal stress coefficient to exist the derivative of the effective viscosity with respect to shear rate must be zero at the initial point.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 506–514, May–June, 1971.     

Effect of the sign of the shear stresses on the shear strength of reinforced plastics

The effect of the sign of the shear stresses on the shear strength has been investigated for a glass-reinforced plastic of the SVAM type with various ratios of the longitudinal and transverse reinforcement in shear in the plane of reinforcement in axes turned through 45° relative to the direction of reinforcement. More than 80 tubularspecimens were tested. The shear strengths T ₄₅ ⁺ and T ₄₅ ^– corresponding to shear stresses of different signs can be found from uniaxial tests in tension and compression in the direction of the reinforcement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 262–268, March–April, 1971.     

Mechanism of shear failure of reinforced rings in bending

The mechanism of failure of a ring due to the shear stresses in the matrix is investigated. It is shown that in the process of shear failure the axial displacement distribution is modified and that the shear failure mechanism depends on the type of loading. The load corresponding to the onset of failure of the ring due to the shear stresses in the matrix does not exhaust the carrying capacity of a reinforced ring with respect to this mode of failure.Institute of Hydrodynamics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 3, pp. 435–444, May–June, 1976.     

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.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Theory of the biomechanism of fractures of the diaphysis of long tubular bones

A new theoretical basis is proposed for the biomechanism of fractures of the diaphysis of long tubular bones resulting from bending deformation. Bone damage is shown to result from the concentration of maximum tensile stresses on the tension side and shear stresses in the compression zone. The origin of fan-shaped cracks and oblique fractures, occurring individually or in combination, is explained in these terms.Altai State Medical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 318–322, March–April, 1971.     

Variant of the variable-modulus theory of elasticity

A variant of the variable-modulus theory — a generalization of the ideas of the classical theory of elasticity in which the observed difference in the moduli of elasticity in uniaxial tension and compression and homogeneous shear is taken into account — is considered. Quasilinear expressions are proposed for the stresses in terms of the strains and the strains in terms of the stresses.Tula Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 363–365, March–April, 1969.     

Relationship between the normal and shear stresses in elastico-viscous liquid flow

A class of elastico-viscous liquids is considered. On the basis of an analysis of the experimental data of a considerable number of authors it is shown that the Weissenberg relation between the shear stresses and the first difference of the normal stresses is limited and a more general expression of the exponential type is proposed.Institute of Thermophysics, Siberian Division, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 1, pp. 126–128, January–February, 1970.     

Interaction of a polymer matrix and short reinforcing fibers

A model of a glass-reinforced plastic with short unidirectional fibers is proposed. The distribution of tensile stresses in the polymer matrix and the fibers and the shear stress distribution at the interface in uniaxial tension are investigated in the elastic formulation.Riga Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1030–1035, November–December, 1971.     

Initial stresses in filament-wound reinforced-plastic rings

Methods of experimentally determining the initial stresses in filament-wound GRP rings are examined and the effect of winding tension is investigated. It is shown that by varying the winding tension it is possible to exercise a considerable degree of control over the magnitude and distribution of the initial stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 505–511, May–June, 1969.     

State of stress of reinforced cylindrical shells with zones of slip

Conclusion Shells with angular reinforcement are more sensitive to delamination in the sense of an increase of the coefficient k_xz which characterizes the concentration of shear stresses. The magnitude of the ratio of the moduli of elasticity of the reinforcement and of the binder has a substantial influence on the concentration of shear stresses: when the values of E increase, the coefficient k_xz decreases (see Table 1).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 896–901, September–October, 1989.The authors express their profound gratitude to Professor Yu. V. Nemirovskii for his constant attention and useful review of the work.     

Anisotropy in the destruction of compact bone material

Conclusions 1. The nature of the destruction of compact bone material upon short-term static compressive and tensile stresses, as well as upon impact bending, is a function of the anistropy of the structure on the osteon level.2. The compact bone material of femoral bones of the age range studied is destroyed by shear for the types of stresses indicated.3. The nature of the destruction of samples of compact bone material for the stresses studied may be generalized for tubular bones.Kurgan Scientific-Research Institute of Experimental and Clinical Orthopedics and Traumatology. Translated from Mekhanika Polimerov, No. 2, pp. 319–324, March–April, 1978.     

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.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Optimal rigidity of a thin-walled orthotropic cylinder in combined tension and torsion

The problem of optimizing the reinforcement of an orthotropic cylinder in combined torsion and tension is considered in relation to the condition of minimum displacement. A numerical example is given. It is shown that the stiffness depends on the ratio of the normal and shear stresses, the elastic moduli, and the parameters.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1121–1123, November–December, 1973.     

Rheological properties of polymers in the fluid state

The possibilities and conditions of correlation are determined for the principal rheological characteristics of single-phase polymer systems measured for one-dimensional shear deformation in steady-state flow regimes, on transition from rest to steady-state flow, and in harmonic vibration regimes. Special significance attaches to the quantitative results of measuring the high-elastic properties of the polymer systems. It is shown that the Lodge theory, describing the flow behavior of high-elastic media, is well-founded in the linear region of deformation, i.e., for the limiting case of shear rates and shear stresses tending to zero, whereas the Mooney-Rivlin-Weissenberg theories are not in accord with the experimental data even in this limiting deformation regime.Topcheiv Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 164–181, January–February, 1969.     

Effect of a uniaxial load on moisture absorption by an epoxy binder

Conclusion The above-developed method of studying the effect of uniaxial compressive and tensile loads on moisture absorption in polymers was tested on epoxy binder EDT-10. It was established experimentally for this material that tensile stresses up to 50 MPa significantly increase the equilibrium moisture content (up to 20% of the initial value). There is a corresponding increase in the rate of moisture absorption during the initial stage of the sorption process — up to 80% of the initial value. No changes in the diffusion coefficient were seen in this case. The application of compressive stresses of up to 40 MPa also had no effect on the kinetics of moisture absorption.Deceased.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 110–115, January–February, 1993.     

Combined bending and axial loading of beams made of materials with low shear strength

The effect of shear stresses on the deflection of glass-reinforced plastic beams in bending with axial loading is investigated in the case of hinged supports. The critical axial compressive load is determined with allowance for shear and the limiting value of the axial tensile load is estimated.Mekhanika Polimerov, Vol. 4, No. 1, pp. 124–130, 1968     

Dynamic stability of a viscoelastic orthotropic cylindrical shell

A method based on the use of Laplace transforms has been developed for reducing the system of equations of motion of a viscoelastic orthotropic cylindrical shell to a single integro-differential equation. The effect of the viscous components on the regions of dynamic instability is investigated (creep due to the action of the shear stresses is taken into account).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1973.