Long-Term Strength Criteria for Some Polymer Materials under a Plane Stress State

The problem of the choice and experimental justification of long-term failure criteria for isotropic polymer materials in creep under a plane stress state is considered. The criteria are defined by a linear two-parameter interpolation relating two stress-tensor invariants which limit the interpolation range with respect to the conditions of viscous and brittle failure and take into account the signs of principal stresses. The base experiment for determining material constants includes standard tests on long-term strength in uniaxial tension and a test on long-term strength under a plane stress state. The failure criteria have been approved in constructing unified long-term strength diagrams for thin-walled tubular specimens made of rigid polyvinylchloride and high-density polyethylene under the action of internal pressure, pressure with axial tension, torsion, and axial tension with torsion.     

Plane-stress creep of a glass-reinforced plastic

The creep behavior of an orthotropic glass-reinforced plastic based on Polimal'-109 resin and 19-S4 glass fabric is described. A special device for testing tubular specimens in plane-stress creep has been designed. The loading conditions include combined torsion and tension, internal pressure, and loading along the principal directions of anisotropy. Constitutive equations describing creep and recovery are proposed for the two-dimensional case.Warsaw. Translated from Mekhanika Polimerov, No. 3, pp. 398–410, May–June, 1971.     

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.     

Effect of the conditions of formation of glued joints on their thermophysical properties

A correlation has been experimentally established between the thermal resistance of adhesive films and the internal stresses that develop during the curing process. During cure the thermal resistance varies in parallel with the internal stresses. It is assumed that the development of thermal resistance is determined by the tension produced in the film by the development of the internal stresses.Voronezh Forest Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 754–756, July–August, 1973.     

Anchoring and a Load Transfer Technique in Uniaxial Tension of Unidirectional High-Strength Composites

A simplified analytical method for calculating the stress-strain state in uniaxial tension of unidirectional composite specimens with glued wedges is developed. A numerical analysis of the influence of geometry and mechanical parameters of the specimens on the maximum stresses is carried out. The calculations are refined by finite-element modeling. Tests of the specimens have proved the suitability of the suggested technique of anchoring and load transfer in uniaxial tension of unidirectional high-strength composites.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 319–334, May–June, 2005.     

Superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders

A mathematical model of superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders is constructed. The macroscopic stresses of the reinforced material are additively determined by matrix stresses and by tensile or constrained compression stresses in the reinforcing fibers. The model is based on the numerical solution of two boundary-value problems, one of which corresponds to the butt-end torsion and the other to the coaxial torsion and axial shear. The boundary-value problem on joint deformations is solved with the use of the displacement field determined from the solution to the boundary-value problem on butt-end torsion. The results obtained by applying this method to homogeneous and axially-radially reinforced thick-wall cylinders subjected to butt-end torsion with subsequent coaxial torsion and axial shear are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 465–492, July–August, 2007.     

Shape-Preserving Approximation of Spatial Data

We present a new method for the construction of shape-preserving curves approximating a given set of 3D data, based on the space of quintic like polynomial splines with variable degrees recently introduced in [7]. These splines – which are C ³ and therefore curvature and torsion continuous – possess a very simple geometric structure, which permits to easily handle the shape-constraints.     

Yield surfaces in local strain theory

The initial yield surfaces for biaxial tension and combined tension and torsion are determined on the basis of the local strain theory. The limit surfaces of the resultant stress on a local plane in tension (torsion) are obtained. A plastic strain probability factor is introduced and its values are calculated for various loading paths.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 594–598, July–August, 1971.     

Theoretical and experimental investigation of anisotropic damage in textile-reinforced composite structures

In the present work, a phenomenological plane-stress damage-mechanics-based model for textile-reinforced composites is presented and its predictive capability is evaluated by carrying out a series of experimental tests. Damage variables are introduced to describe the evolution of the damage state and, as a subsequence, the degradation of material stiffness. For calculating the nonlinear stress and strain distribution of complexly loaded composites with a textile reinforcement, a special emphasis has to be placed on the interaction between the fiber failure due to the stress in the fiber direction and the matrix failure due to the transverse and shear stresses. This demands the formulation of realistic failure criteria taking into account the microstructural material behavior and different fracture modes. The new failure criteria, like the fracture mode concepts, consider these fracture modes, as well as further fracture types, in the reinforcement plane. The failure criteria are based on equations for failure surfaces in the stress space and damage thresholds in determining the stiffness degradation of the composite. The model proposed was used to characterize the strength and the failure behavior of carbon-fiber-reinforced composites. For this purpose, several unidirectional and bidirectional tests were performed to determine the specific properties of the material. The specimens were investigated by using acoustic emission techniques and strain-controlled tension and torsion tests.Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 791–810, November–December, 2004.     

The Geodesics of Metric Connections with Vectorial Torsion

The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields coincide with the Levi-Civita geodesics of a conformally equivalent metric. By pullback, this yields a systematic way of constructing invariants of motion for such connections from isometries of the conformally equivalent metric, and we explain in as much this result generalizes the Mercator projection which maps sphere loxodromes to straight lines in the plane. An example shows that Beltrami's theorem fails for this class of connections. We then study the system of differential equations describing geodesics in the plane for vector fields which are not gradients, and show among others that the Hopf–Rinow theorem does also not hold in general.     

Torsion of a composite,viscoelastic prismatic bar of rectangular cross-section

The generalization of Ilyushin's approximation method is used to determine the stresses in the quasistatic problem of torsion of a composite, layered viscoelastic prismatic bar of rectangular cross-section. Numerical computations are carried out for the special case of a step function torsional moment.     

Analysis of the transition zone in combined metal/reinforced-plastic shells

The bending stresses in the conical joint zone of cylindrical shells composed of two different materials are determined for the case of internal pressure. The effect of the length of the joint on these stresses is investigated using parameters typical of steel and glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 465–475, May–June, 1971.     

Deformation of tape-wound cylindrical shells under internal pressure

The state of stress of a cylindrical shell would from glass tape at arbitrary angles to the generator is examined. The pressure dependence of the strains and stresses is obtained for uniform internal pressure, and the question of rationalization of the structure of the shell material is investigated. To describe the deformation characteristics associated with failure of the resin under load, a perfectly plastic model is introduced. The results of an experimental determination of the relative elongations are presented for the case of active loading and unloading.Mekhanika Polimerov, Vol. 3, No. 5, pp. 915–920, 1967     

A New Static Failure Criterion for Isotropic Polymers

A new static failure criterion for isotropic polymers with different strengths in tension and compression based on exponential dependence between the mean stress and the von Mises equivalent stress is proposed. The two material parameters introduced can be determined by two simple tests - the uniaxial tension and compression. The locus of the criterion is nearly conical for low hydrostatic pressures and tends to a cylindrical form if an increased hydrostatic pressure is applied. The validity of the criterion is demonstrated by experimental strength data taken from the literature for several polymers in the case of superimposed hydrostatic pressure.     

Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Temperature stresses in a long hollow viscoelastic cylinder with variable inner boundary

As distinct from existing solutions for the state of stress and strain, in addition to the stresses created by internal pressure acting on the moving inner surface, the thermal stresses created by a temperature field are also taken into account. A solution is obtained using tabulated singular kernels of the hereditary theory of viscoelasticity.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 219–226, March–April, 1969.     

Programmed winding of glass-reinforced plastics

It is proposed to employ a variable winding tension designed to give a required initial stress distribution. The program is constructed on the basis of solutions describing the loss of tension associated with winding and the softening of the resin during heat treatment. The problems are solved in the elastic formulation. Programs are obtained for three cases: constant tension in a ring sill on the mandrel, compensation of the stresses that develop after removal from the mandrel, and compensation of the thermoelastic stresses that develop during cooling.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 48–53, January–February, 1970.     

Experimental study of the effect of technological parameters on the residual stresses in thin-walled coiled parts

The effect of the parameters of heat treatment and programmed winding under tension on the residual stresses in thin-walled coiled parts made from glass plastic by the "dry" winding of a heated glass strip on an unheated mandrel is studied experimentally. The effect of the thickness of the parts on the maximum radial residual stresses is considered. A method is proposed for regulating the residual stresses in parts with very thick walls.Translated from Mekhanika Polimerov, No. 1, pp. 75–80, January–February, 1972.     

Influence of hydrostatic pressure on the lifetimes of polymers

Under uniaxial tension, the lifetimes of polymers under hydrostatic pressure are longer than under atmospheric pressure. This effect is attributed to a change in the failure mechanism under pressure owing to retardation of the free-radical chain reaction of breakage of the macromolecules under omnidirectional compression.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 207–213, March–April, 1976.     

Load bearing capacity of multilayered sectional tubular rods made of composites

Conclusion We investigated the load bearing capacity of a new class of tubular rods made of composites, viz., peripherally and radially sectional. It was discovered that under conditions of tension, compression, bending, and combined loading by compression and torsion the number of macrolayers, strengthening by a carcass or external lagging have practically no effect on the rigidity and strength of peripherally and radially sectional rods. The nature of failure of sectional and monolithic rods is the same. Ways were shown of increasing the load bearing capacity of the rods under consideration with the object of bringing their mechanical properties up to the level of monolithic rods by improving the technology of assembly and by using high-strength film glues.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 85–92, January–February, 1990.