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.     

Study of the strength of plastic sandwich construction

Results are given for edge-supported sandwich panels with a honeycomb core tested in bending in two directions. The experimental data are compared with theoretical results obtained from equations proposed by the authors. It is established that in designing honeycomb panels for bending in two directions it is possible to treat the panel material as virtually isotropic in the plane of the laminations and to use the authors' equations for determining the deflections and the normal and shear stresses.Mokhanika Polimerov, Vol. 1, No. 5, pp. 45–50, 1965     

Results of an experimental investigation of the residual stresses in wound glass-reinforced plastics

The results of an experimental investigation of the residual stresses in wound glass-reinforced plastic rings are presented. The residual stresses were determined by the Davidenkov method. The dependence of the maximum tensile and compressive circumferential stresses on ring thickness and polymerization temperature is investigated. The experimental data are compared with the results of calculations based on the theory proposed in [1, 2].Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1116–1119, November–December, 1970.     

Strength of glass-reinforced plastics in the complex stress state

A new criterion of strength is proposed for anisotropic materials of the glass-reinforced plastic type. This criterion takes into account not only the different ultimate strengths in tension and compression in each direction but also the dependence of the ultimate shear strengths on the sign (direction) of the shear stresses. The criterion is given in tensor invariant form, so that it can be rewritten for any direction of the glass fibers. The criteria proposed by other authors, in particular, R. Hill's condition of plasticity [1], follow from the new generalized criterion as special cases. The results of experiments conducted both by the authors of the present article and by other investigators provide good confirmation of the proposed criterion.Mekhanika Polimerov, Vol. 1, No. 2, pp. 70–78, 1965     

Calculating 3D stresses in layered composite plates and shells

Advanced failure criteria for fiber composites account for all six components of the stress tensor. Plate and shell analysis, however, is sensibly performed by assuming the plane state of stress, which results in global displacements, cross-sectional membrane forces, and bending moments of suitable accuracy. Based on these results, equilibrium conditions can be applied to locally determine the stress components in the transverse direction. Therewith, the transverse shear stresses require first derivatives and transverse normal stresses even second derivatives of the membrane stresses. Higher-order finite elements would be necessary if these stress components are to be determined on the element level. To ease this deficiency, a procedure is proposed based on neglecting the in-plane derivatives of the membrane forces and twisting moments as well as the mixed derivatives of the bending moments. This allows us to reduce the order of differentiation by one. Applicability of this procedure is demonstrated by calculating the transverse shear and normal stresses for layered composite structures of different geometric dimensions and various stacking orders under mechanical as well as thermal loads. Comparison with results from 3D analyses shows excellent accuracy and efficiency of the proposed procedure.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Deutsches Zentrum für Luft- und Raumfahrt e.V. (German Aerospace Center), Institute of Structural Mechanics, D-38022 BRAUNSCHWEIG, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 491–500, July–August, 1998.     

Bending strength of oriented glass-reinforced plastics

The authors consider the effect of the low shear strength and shear stiffness of oriented glass-reinforced plastics (GRP) on the stress distribution and type of failure in bending. On the basis of relations obtained in [1] it is shown that the effect of shears on the magnitude and law of distribution of the normal and shear stresses is important only for very short beams made of materials with a low shear stiffness. An experimental study of the nature of failure in bending has revealed that the chief cause of extension of the region of shear failure of oriented GRP is the low shear strength of the material, and has made it possible to establish the limits of this region for three typical materials. Anisotropy of the elastic properties has little effect on the type of failure in bending.Mekhanika Polimerov, Vol. 2, No. 4, pp. 535–542, 1966     

Moduli of elasticity of polymer melts

The physical significance of the so-called initial modulus, determined in measuring the rheological properties of thermoplastic melts from the initial slope of the time dependence of the stresses at given constant shear rate, is considered. It is shown that this quantity is related with the ratio of the shear and normal stresses.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 534–538, May–June, 1969.     

Some questions relating to the strength of glass laminate

The ultimate strength of glass laminate is investigated in the plane-stress case, in which the directions of the principal stresses do not coincide with the axes of anisotropy of the material and one of the principal stresses is equal to zero. The experimental data are compared with the results of calculations based on expressions describing the onset of the limiting state proposed in [1]. The agreement is satisfactory.Mekhanika Polimerov, Vol. 4, No. 1, pp. 64–66, 1968     

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.     

Calculation of the residual stresses in coiled objects made on the layer-by-layer hardening principle

The effect of the technological mode of winding with layer-by-layer hardening on the residual-stress distribution in coiled glass-plastic objects is analyzed by the method outlined in [1, 2]. The computing scheme of [3, 4] is used to calculate the stresses arising at the winding stage. The results are compared with experimental data.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 284–289, March–April, 1972.     

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.     

Normal stresses during periodic shear deformation

It is shown that the disagreement between the theory and the experimental values of the variable component of the normal stresses during periodic shear is due to lack of consideration of the stiffness of the specimen and its ratio to the stiffness of the measuring device in the direction of action of the normal force (in particular, in measurements made where the instrument is of the cone-plane type). Measurements on fused low-density extrusion polyethylene (LDEP) reveal that if these parameters of the instrument and specimen are taken into account, the theory agrees satisfactorily with experiment. Details of the measurement devices are given.Presented at the Seventh Symposium on the Rheology of Polymers, April 10–14, 1972.Institute of Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 321–328, March–April, 1974.     

Effect of a local load on an orthotropic glass-reinforced plastic shell

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 95–101, January–February, 1970.     

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.     

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.     

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.     

Stresses in plastics reinforced with anisotropic fibers and subjected to transverse normal loading

The question of the stress distribution in plastics reinforced with anisotropic fibers and subjected to transverse normal loading is considered. The stresses in the components are determined by the methods of the theory of elasticity using stress functions. The theoretical relations obtained are used to construct diagrams showing the distribution of the tangential, radial, and shear stresses in the composite and the isoclines of the concentration coefficient for a carbon-reinforced plastic. The results obtained for the carbon-reinforced plastic are compared with the analogous results for a glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 244–252, March–April, 1973.     

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Mechanism of failure of reinforced beams in bending

The mechanism of shear failure is investigated. A theoretical analysis makes it possible to determine the limits of shear failure of reinforced beams in relation to the geometric parameters of the beam, the mechanical properties of the reinforcement and the resin, their volume content, and the loading and support conditions. The results obtained are consistent with the experimental data of [1]. 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 and the support conditions.Institute of Hydrodynamics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekahnika Polimerov, No. 4, pp. 698–709, July–August, 1973.     

Refined stability theory for sandwich shells with transversally stiff core. 2. Linearized equations of neutral equilibrium

Neutral equilibrium equations of the refined theory of stability for sandwich shells with a transversally stiff core are constructed and used for studying local mixed forms of stability loss (FSL), as well as admitting different variants of simplification, depending on the type of precritical state and realized FSL. The generalized Reissner variational principle used for deriving the stability equations allows us to refine transverse shear stresses in the core as compared to [1]. A method for a highly accurate definition of these stresses is proposed. Namely, after the integration of three-dimensional equilibrium equations over the transverse coordinate, the number of free constants and the number of static conditions to be satisfied are equalized according to the actual stress distribution across the thickness.Science and Technology Center for Study of Dynamics and Strength. Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 786–795, November–December, 1997.