Acoustic fatigue of polymer materials

An experimental investigation of the fatigue properties of filled rubber under acoustic loading is briefly discussed. It is shown that two processes take place in the material—hardening and softening. A corresponding mathematical model is proposed. The form of the Wöhler fatigue curve in logarithmic coordinates is almost linear for high-frequency cyclic loading and may be assumed linear in the calculations with a risk of not more than 1%.Mekhanika Polimerov, Vol. 3, No. 3, pp. 467–475, 1967     

Delamination of composite plates under tensile load

Conclusions Among the two configurations discussed, the beam has a rather theoretical importance, as an extension and generalization of the cracked beam problem. Unlike this, embedded delaminations can be found often in real constructions. The fact that the maximum value of SERR vs. fibre orientation angle curve for the circular embedded delamination is surpassed by that for the split beam only by three times and by that for the split beam under mode II loading approximately six times means that an embedded delamination can lead to difficulties when the plate is tensed (or compressed — even in an underbuckled state — within the linear approach the non-opening modes of stress concentration will just change their signs when the load changes its sign), especially under a cyclic loading. Of course, the shell model used is fairly rough and does not take in account several features or real delaminations extension and does not allow one to evaluate properly the stress field near the crack front; thus, more analytical and experimental studies would be needed, to establish the crack development process. The 3D analysis is necessary when initiating delaminations are studied, for the beam/plate assumptions can no longer be regarded as necessary since the delamination linear dimensions are comparable to or less than the thickness of the sublaminate.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 45–50, January–February, 1995.     

Elastic constants and state of stress of glass-reinforced strip

The author examines the problem of the state of stress of glass-reinforced strip under short-time loading, when viscoelastic effects are unimportant. The proposed model is composed of a system of parallel identical glass fibers the space between which is filled with a matrix—resin. The change in the elastic constants is found as a function of the volume content of glass reinforcing. Further, the stress distribution between the elementary fibers is investigated for a glass-reinforced plastic in the three-dimensional stress state.Mekhanika Polimerov, Vol. 2, No. 4, pp. 593–602, 1966     

Polymer fatigue from the standpoint of the kinetic theory of fracture

A comparison of the static and cyclic lives of various polymers shows that, whatever the loading regime, fracture may be regarded from the standpoint of the thermal-fluctuation theory. Under comparable test conditions the lifetimes in different loading regimes coincide. The experimentally observed cases of a reduced cyclic as compared with static life do not conflict with the kinetic theory of fracture and can be attributed to hysteresis heating effects or to differences in the structural changes that take place in the test material in different loading regimes.From the standpoint of the kinetic theory, fracture is regarded as a certain process that develops in a body under load and not as a critical event that occurs when a critical stress — ultimate strength — is reached.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 70–96, January–February, 1969.     

Methods of taking into account the nonlinearity of the deformation properties of the material in calculating thick-walled composite rings

The results of an investigation of the deformation properties of unidirectional composites are presented, and engineering models which take into account the effect of the nonlinearity of the properties in the radial direction on the state of stress of rings under pressure are proposed. The relations obtained are checked theoretically — by means of a refined calculation based on the nonlinear theory of elasticity — and experimentally — by loading rings with internal and external pressure by means of rubber cuffs in specially designed apparatus.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 73–84, January–February, 1976.     

Some aspects of the behavior of shock-compressed polymers

The changes in the properties of certain polymeric materials subjected to the action of plane shocks of varying amplitude are discussed. Three loading techniques are employed — single, multiple, and high-frequency multiple loading — each accompanied by a different rise in the temperature of the polymeric material. The results show that the change in physicomechanical properties also varies with the loading technique.Volgograd Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 76–80, January–February, 1970.     

Predicting the transverse strength of unidirectional composites under combination loading

This article presents a mathematical model for predicting the transverse strength of unidirectional fiber composites subjected to combination transverse loading under different conditions. The behavior of the matrix is described by nonlinear physical equations consistent with the strain theory of plasticity for the active loading section. The fibers are assumed to be isotropic and elastic. The boundary-value problem of micromechanics that is formulated includes strength criteria for the matrix and fibers that mark the beginning of their possible failure. The modeling of the fracture process is taken farther through the use of a scheme that reduces the stiffness of the matrix and fibers in the failed regions in relation to the sign of the first invariant of the stress tensor. The method of local approximation is used together with the finite-element method to calculate the stress and strain fields in unidirectional composites with cylindrical fibers in a tetragonal layup. The model is used to study the behavior of an epoxy-based organic-fiber-reinforced plastic subjected to transverse loading in different simple paths — including simultaneous compressive and tensile loads, as well as transverse shear.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 473–481, July–August, 1995.     

Dynamic adhesive strength of fiber-polymer systems

A new device for studying the dynamic adhesive strength is created. A procedure for determining the dynamic adhesive strength in fiber—polymer systems under impact loading (pull-out technique) is developed. The adhesive strength of the interface of polymer—steel wire joints formed by polymers of different chemical nature (epoxy resin, polysulfone, and polypropylene) is examined. It is shown that the dynamic adhesive strength grows as the loading rate increases for all the systems under investigation and that the relationship between the adhesive strength and the loading rate, , over a wide range of rates can be described by two straight lines corresponding to the quasi-static and impact loading, respectively. When passing from the quasi-static to dynamic loading, the character of scale relations of the adhesive strength does not change.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 689–700, November–December, 1999.     

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.     

Effect of the geometry of the structure on the strength distribution of multilaminate tridirectional reinforced plastics

Conclusion The proposed analytical method makes it possible to predict the strength distribution of an LRP of the type [0/±]_s from its structure (the geometry of the packet, the number of layers, and the strength properties of the layers) in a plane stress state. Allowance is made for the random character of the strength properties of the layers, which makes it possible to evaluate the reliability of the LRP for both determinate and random loading. A criterion was formulated for the optimum design of the structure of an LRP with respect to ensuring maximum reliability for specific loading conditions. We also evaluated the effect of the parameters of the structure and the characteristics of the plane stress state on reliability. According to the results of a numerical analysis performed with the above-developed structural model of the failure of an LRP — with allowance for the random character of the strength properties of the layers — the imbalance of the laminated packet which occurs during failure can be ignored. The method used to predict the strength distribution of the LRP, involving determination of the strength distribution law of an RSE and subsequent examination of the loading of parallel-connected RSEs, is promising for other reinforcement schemes as well.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 805–812, September–October, 1988.     

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     

Deformation of teflon in linear and plane states of stress

Teflon specimens have been deformed in accordance with various laws of variation of stress and strain with time under plane stress conditions. Fairly simple expressions describing the relation between the stresses and large (up to 60% relative to the initial dimensions) strains are constructed for a broad class of loading regimes.Scientific-Research Institute of Mathematics and Mechanics, A. A. Zhdanov Leningrad State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 742–746, July–August.     

Complex loading of a polymer material with nonlinear creep

The nonlinear tensor stress, strain, and time relations for a memory-type medium under complex loading are examined using degenerate kernels. The basic expressions for simple loading and the material parameters were determined in [5]. The local strains theory is used to find expressions for the strain components in the presence of stepwise complex variation of the stress components, and these expressions are shown to be in satisfactory agreement with the experimental data for high-density polyethylene.Mekhanika Polimerov, Vol. 3, No. 3, pp. 421–426, 1967     

High-precision modeling of deformation of laminated structures

Precise three-dimensional solutions for homogeneous, two- and three-layer plates of symmetric and nonsymmetric structure over their thickness with orthotropic layers in transverse symmetric and antisymmetric loading normal to the surface of the plates are given. It is shown that the character of stressed states under flexural (antisymmetric) and nonflexural (symmetric transverse compression) loading differs greatly. It is noted that the known refined continual models, which take into account the transverse shear and compression, are all essentially flexural and therefore cannot describe the nonflexural deformations well. In particular, continual shear models in symmetric pressure loading lead to zero solutions. A refined nonflexural continual model of deformation of sandwich plates in bilateral symmetric compression is constructed. The general order of resolving differential equations for continual models does not depend on the number of layers. Approximation functions of the transverse coordinate are obtained with the help of well-founded hypotheses. A high-accuracy variant of the flexural continual model is proposed for antisymmetric loading with account of shear and transverse normal strains, as well as a version combining both models mentioned. A method of precise satisfation of all the constitutive relations for the layers, including the conditions of their contact, is proposed, whereas in the known continual models the dependence between the transverse normal stress and strain is satisfied only integrally, or else the Poisson effect is neglected.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 13–28, January–February, 1999.     

Long-time study of Poisson's ratio for polyethylene stressed in the small strains range

The time dependence of the Poisson's ratio for low-pressure polyethylene has been studied by a method involving superposition of time and temperature (in the short-time range) and by recording creep curves for the longitudinal and transverse strains (under prolonged loading). It is shown that is not constant, its value changing from approx. 1/3 for short loading times to approx. 1/2 under prolonged loading conditions.Mekhanika Polimerov, Vol. 1, No. 3, pp. 52–56, 1965     

Zur Frage der Charakterisierung stationärer Bewegungen in der Hydrodynamik

Summary Helmholtz andKorteweg propose that the steady motion of a viscous fluid under constant extraneous forces having a single-valued potential dissipates—for any given region and assuming that inertia terms in the dynamic equations can be neglected—less energy than any other motion with the same values of velocity at the boundary.—A generalization of this proposition is here given, and an application discussed. The application deals with the motion of a simple macromolecule model in an inhomogeneous field of flow—a motion caused only by the influence ofStokes' friction.     

An estimation of reliability of unidirectional composites by catastrophe theory

In the present work, interest is centered on the theory of fracture and practical approaches to reliability estimation of unidirectional composite materials which are based on it. Fracture mechanics is considered not as a theory of macrocracks but as mechanics of fracture mechanisms of the composites with allowance made for probability estimation. A model of composite material with fibers eliminated from the carrying scheme and parameters specific to the stress-strain-damage state (SSDS) was considered. According to the model, during loading, self-accelerated energy rise is accounted for by structural damages growth — the catastrophe takes place. The model allows us to calculate the critical stress. The composites redistribute forces from overloading zones to neighboring ones by microstructural deformations and damages. It is the effect of reservation of carrying ability. Due to this effect, low-value probability of fracture is sufficiently less for the composite than for homogeneous materials. The approach allows us to evaluate the reliability function for both static loading and fatigue.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Computing Center of the Russian Academy of Sciences, Krasnoyarsk, Russia. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 539–548, July–August, 1996.     

Longitudinal Flexure as a Method for Determining the Flexural Strength of Composite Materials

A method is presented for determining the flexural strength of composites from tests on pinned specimens in axial compression. This scheme is close to the so-called Euler buckling model, but the load is applied eccentrically, and the bar is bent practically from the beginning of loading. An analytical model is proposed for calculating the flexural stress in longitudinal flexure of a thin bar in the case of large displacements. The problem is solved in elliptic integrals of the first and second kinds. The analytical model shows an excellent agreement with experiments. The results obtained are compared with experimental tension data. A device is also designed for testing composite bars in longitudinal flexure. The method offered has an obvious advantage over the conventional three- or four-point bending — the gage zone in this scheme is far away from the loading zone of the test specimen.     

Variants of the local strains theory

By means of the proposed new variants of the local strains theory it is possible to solve a broad class of complex loading problems for initially isotropic materials. The basic equations for a series of variants of incompressible and compressible materials are derived. The author investigates the possibility of using the relations obtained to solve complex loading problems for materials with irreversible plastic strains or with different physical reversible or irreversible creep relations depending on the loading path.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 233–240, March–April, 1970.