Water absorption and its effect on rubber strength

The effect of the swelling of rubbers in water and their recovery on the tear strength of the material has been investigated and a mechanism of water absorption is proposed. It is shown that there is a fundamental difference between the mechanism of water absorption and swelling in solvents. The strength of a rubber dried after being kept in water is anomalously high. This effect is explained in terms of the proposed polymer-nonsolvent interaction mechanism.É. A. Ter-Gazaryan State Scientific-Research and Design Institute of Polymer Adhesives, Kirovakan. Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 1, pp. 136–138, January–February, 1970.     

Loss and Birefringence for Arbitrarily Bent Optical Fibres

We present a calculation to determine the radiation losses forarbitrarily bent, weakly guiding optical fibres. Our resultsare derived for the full set of vector Maxwell's equations,and show that the rate of energy loss due to radiation differsfor the various modes. These results are different from thatcalculated from a scalar theory, where the so-called linearlypolarized (LP) modes are used to approximate the electromagneticfield distributions, showing that in this case scalar theoriesgive incorrect loss rates. We also show that different rangesfor the size of the curvature and torsion produce quite differenteffects. In particular, we show that, for smaller amounts ofcurvature and torsion, the modes retain the basic structureof the modes in the straight fibre while losing energy slowlyat differing rates, while, for larger amounts of curvature andtorsion, the modes become distorted by the bending.     

Birefringence and stress-strain diagrams for oriented atactic polymethyl methacrylate and polystyrene films

The stress-strain diagrams of amorphous linear polymers oriented under different conditions are examined; a comparison is made with the parameters of their internal structure. It is shown that the shape of the diagram for rigid polymers is basically determined by the degree of orientation of the links of the macromolecules irrespective of the molecular weight of the polymer and the extension conditions. It is established that the moment of failure can not be determined from this parameter alone. It is found that when the oriented polymer is tested close to the softening point the correlation between the shape of the diagram and the birefringence, characterizing the degree of orientation of the links of the macromolecules, is disturbed.Mekhanika Polimerov, Vol. 2, No. 3, pp. 435–439, 1966     

Effect of temperature on the fracture surfaces of filled systems based on SKS-85 butadiene-styrene copolymer

The tear fracture surfaces of mixtures of SKS-85 butadiene — styrene copolymer (85% styrene) with ordinary (carbon black, chalk) and polymeric (Kapron and cellophane powder) fillers have been investigated on the interval from –60 to +40°C. As the temperature varies within the limits of the glassy state (T_g SKS-85=+24°C) of the filled polymer, the nature of the fracture surface of specimens of filled mixtures, like that of the unfilled polymer, changes; in the region of the temperature transition of the copolymer associated with the mobility of the phenyl groups (–10±5°C) there is a slowing of the fracture process. At temperatures below the T_g of the copolymer the tear fracture surfaces of specimens of mixtures containing ordinary and polymeric fillers differ sharply. The introduction of fillers (20 vol. %) with a coefficient of thermal expansion different from that of the filled polymer considerably reduces the resistance of the material to fracture and leads to a sharp increase in the rate of crack propagation; the introduction of polymeric fillers with coefficients of thermal expansion similar to that of the filled polymer leads to an increase in the resistance of the material to fracture and to a decrease in the rate of crack propagation.Moscow Technological Institute of the Meat and Dairy Industry; State Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 5, pp. 819–826, September–October, 1969.     

Electron diffraction investigation of the fracture surfaces of filled mixtures of SKS-85 butadiene-styrene copolymer

As the result of an electron microscope study of replicas from the fracture surface during the disintegration of samples of mixtures of SKS-85 butadiene-styrene copolymer with 20 vol.% DG-100 carbon black and chalk, in the temperature range from +60 to –60°C, it is shown that, in the region of vitrification of the copolymer and of the loss of the reinforcing effect of the carbon black, there is a sharp change in the character of the fracture micro-surface, and the particles of carbon black become the sites of additional fracture. In the region of the temperature transition of the copolymer, connected with the mobility of the phenyl groups in the same way as in the vitrification region, there is a sharp decrease in the number of particles of carbon black at the fracture surface, while the fracture surface of a mixture with chalk passes selectively along the contact boundary of a polymer with larger particles. The microstructure of the Wallner lines on the surface of a mixture with carbon black, at Tst, is made up of traces of secondary fracture, arising around the particles of carbon black.Moscow Institute of Technology for the Meat and Dairy Industry. M. V. Lomonosov Institute for the Technology of Fine Chemicals, Moscow. É. L. Ter-Gazaryan State Scientific-Research and Design Institute, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 437–444, May–June, 1970.     

Uniform ultimate boundedness of nonlinear nonstationary systems

A certain class of nonlinear, nonstationary systems of differential equations is studied. It is assumed that the right-hand sides of the equations under consideration are homogeneous functions of order smaller than one with respect to the phase variables. The purpose of this paper is to obtain sufficient conditions for the uniform ultimate boundedness of systems of this form. A method for constructing nonstationary Lyapunov functions is suggested and applied to prove that the asymptotic stability of the zero solution of the corresponding averaged system implies the uniform ultimate boundedness of the initial nonstationary system. Classes of perturbations that do not violate uniform ultimate boundedness, even in the case where the order of the perturbations exceeds the homogeneity order of the unperturbed equations, are described. Unlike in previous works, where the results are based on the averaging method, the presence of a small parameter on the right-hand sides of the equations under examination is not assumed. Dissipativity is ensured at the expense of homogeneity orders.     

Stochastic ultimate load analysis:models and solution methods 1

The stochastic ultimate load analysis model used in the safety analysis of engineering structures can be treated as a special case of chance-constrained problems (CCP) which minimize a stochastic cost function subject to some probabilistic constraints. Some special cases (such as a deterministic cost function with probabilistic constraints or deterministic constraints with a random cost function) for ultimate load analysis have airady been investigated by various researchers. In this paper, a generai probabilistic approach to stochastic ultimate load analysis is given. In doing so, some approximation techniques are needed due to the fact that the problems at hand are too complicated to evaluate precisely. We propose two extensions of the SQP method in which the variables appear in the algorithms inexactly. These algorithms are shown to be globally convergent for all models and locally superlinearly convergent for some special cases     

Optimal prediction of the ultimate maximum of Brownian motion

At time 0 start to observe a Brownian path. Based upon the information, which is continuously updated through the observation of the path, a stopping time is determined such that the path is as close as possible to its unknown ultimate maximum over a finite time interval. The closeness is measured by a q-mean or by a probability distance. This can be formulated as an optimal stopping problem. The method of proof relies upon a representation of a conditional expectation of the gain process and the principle of smooth fit (at a single point).     

Attractor and ultimate boundedness for stochastic cellular neural networks with delays

This paper investigates the attractor and ultimate boundedness for stochastic cellular neural networks with delays. By employing the Lyapunov method and a Lasalle-type theorem, novel results and sufficient criteria on the attractor and ultimate boundedness are obtained.