Effect of gamma radiation on the cracking and mechanical properties of Kapron (polycaprolactam)

The results of a mechano-optical investigation of irradiated oriented polycaprolactam film are discussed. After irradiation comparatively large cracks running at right angles to the orientation axis appear in the film; these are responsible for the reduced tensile strength and deformability of the polymer.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad; Lenin Tadzhik State University, Dushanbe. Translated from Mekhanika Polimerov, No. 4, pp. 756–758, July–August, 1971.     

Fractographic study of macrocrack propagation in oriented Kapron

The fracture surface of an oriented Kapron monofilament has been studied at electron-microscope and optical magnifications with the object of establishing the details of the micromechanism of crack propagation associated with the fracture of polymeric materials. Microparabolic figures can be observed in the specular zone of the fracture surface. This relief may be assumed to originate in the interaction of the main crack and the submicroscopic cracks present in loaded polymers. In the region of high main-crack velocities it is possible to observe a self-oscillatory motion of the tip of the main crack leading to the formation on the fracture surface of a system of bands parallel to the main crack front.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 645–648, July–August, 1971.     

Critical behavior of a monoaxial chiral helimagnet

We analyze the critical behavior of magnetically ordered phases appearing in a monoaxial chiral helimagnet in a weak external magnetic field. Using the formalism of the equations of state in the critical region, we determine the temperature dependence of the order parameters for the conical phase and the soliton-lattice phase. We calculated the critical exponents and show that they coincide with those in the three-dimensional Heisenberg model.     

Experimental evaluation of the strength of one-piece Kapron nuts

The strength of one-piece Kapron nuts has been investigated in static loading tests. Graphs of the load versus the number of turns, which reflect the distribution of the load over the turns, are presented. The types of failure of threads of five standard sizes with different profiles are analyzed. It is concluded that there is an important difference between the usual thread calculation model based on the strength of the turns in shear, bearing and bending and the actual loading of the turns of polyamide nuts cooperating with steel screws.Dnepropetrovsk Metallurgical Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 752–754, July–August, 1968.     

Breakage of the polymer chains in Kapron oriented at various temperatures

Infrared spectroscopy has been used to detect a considerable reduction in the number of broken macromolecules in Kapron oriented at elevated temperatures, particularly in the region above 140°C. This is a consequence of weakening of the hydrogen bonds and an increase in the mobility of the amide groups in the crystalline parts of the polymer as the temperature rises.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 649–653, July–August, 1971.     

Relation of the reinforcing action of fillers with molecular motion in polymers

In the case of filled systems based on butadiene-styrene copolymers, it has been shown that the attainment of mobility of kinetic segments in definite temperature regions leads in amorphous polymers to an increase in their strength and reinforcement effect, and also to a change in the morphology of the breakdown surface in these temperature regions. The established regularity has been examined from the point of view of the adhesion theory of reinforcement.Moscow Institute of Meat and Milk Industry. Central Scientific-Research Laboratory of Chemical Packaging Materials, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 909–911, September–October, 1972.     

Plane stretching of thermoplastics

Plane stretching tests over a wide temperature interval have been used to construct moldability curves for several thermoplastic resins produced in the USSR. These curves are found to have two maxima in the temperature range studied. The effect of the strain rate, heterogeneity of the material, and the addition of fillers, plasticizers, and cross-linking agents upon the formation of these maxima is discussed.Mekhanika Polimerov, Vol. 1, No. 2, pp. 137–145, 1965     

Natural convection on a vertical stretching cylinder

The flow and natural (or mixed) convection due to a vertical stretching cylinder is studied. Using similarity transforms, the Navier-Stokes and energy equations reduce to a set of nonlinear ordinary differential equations. Asymptotic analysis for large Reynolds numbers shows the relation between axisymmetric flow and two-dimensional flow. Due to the algebraic decay of the similarity functions, numerical integration is performed using a compressed coordinate. The axial velocity is composed of forced convection due to stretching and natural convection from the heated cylinder. The heat transfer increases with both the Reynolds number and the Prandtl number. The result is also a rare similarity solution of the free convection and Navier-Stokes equations.     

Brownian motion reflected on Brownian motion

 We study Brownian motion reflected on an ``independent' Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian path. We show that there exist two different natural local times for a Brownian path reflected on a Brownian path. Received: 25 October 2000 / Revised version: 30 March 2001 / Published online: 20 December 2002     

Effect of random noise on chaotic motion of a particle in a ϕ6 potential

The chaotic behaviors of a particle in a triple well ϕ⁶ potential possessing both homoclinic and heteroclinic orbits under harmonic and Gaussian white noise excitations are discussed in detail. Following Melnikov theory, conditions for the existence of transverse intersection on the surface of homoclinic or heteroclinic orbits for triple potential well case are derived, which are complemented by the numerical simulations from which we show the bifurcation surfaces and the fractality of the basins of attraction. The results reveal that the threshold amplitude of harmonic excitation for onset of chaos will move downwards as the noise intensity increases, which is further verified by the top Lyapunov exponents of the original system. Thus the larger the noise intensity results in the more possible chaotic domain in parameter space. The effect of noise on Poincare maps is also investigated.     

Effect of bounded noise on chaotic motion of duffing oscillator under parametric excitation

A harmonic function with constant amplitude and random frequency and phase is called bounded noise. In this paper, the effect of bounded noise on the chaotic behavior of the Duffing oscillator under parametric excitation is studied in detail. The random Melnikov process is derived and a mean-square criterion is used to detect the chaotic dynamics in the system. It is found that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the noise in frequency increases. The threshold of bounded noise amplitude for the onset of chaos is also determined by the numerical calculation of the largest Lyapunov exponents. The effect of bounded noise on the Poincaré map and power spectra is also investigated. The numerical results qualitatively confirm the conclusion drawn by using the random Melnikov process with mean-square criterion for larger noise intensity.     

Natural convection on a vertical radially stretching sheet

The natural convection on a vertical radially stretching surface is studied. The resulting flow is a new exact similarity solution of the Navier-Stokes and energy equations. Asymptotic properties and uniqueness are shown.     

Cooling of a stretching sheet in non-Newtonian flow

An analytical solution has been developed for the temperature distribution in a stretching sheet undergoing cooling in a non-Newtonian viscoelastic fluid. A solution has also been obtained for the temperature field in the boundary layer. Sufficient conditions for convergence of the solutions have been established.     

Effect of uv irradiation on the mobility of the molecular chains in polyethylene

Conclusions 1. A decrease in the mobility of molecular chains in polyethylene after UV irradiation was discovered by the spin probe method. This decrease is proportional to the time of irradiation.2. A discontinuity lacking in unirradiated polyethylene was found on the curve for the logarithm of the rotational correlation time of the spin probe in polyethylene as a function of the inverse temperature. It was shown that the nature of the discontinuity is related to a "thawing out" of the rotational motion of the chains in the crystalline phase.Institute of the Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel. Translated from Mekhanika Polimerov, No. 4, pp. 603–608, July–August, 1976.     

Effects of manifolds and corner singularities on stretching in chaotic cavity flows

It has been assumed that the stretching field in chaotic flows evolves as the result of a random multiplicative process [F.J. Muzzio, C. Meneveau, P.D. Swanson and J.M. Ottino, Scaling and multifractal properties of mixing in chaotic flows, Phys. Fluids A, 4, 1439–1456, (1992); F. J. Muzzio, P.D. Swanson and J.M. Ottino, Partially mixed structures produced by multiplicative stretching in chaotic flows, Int. J. Bifurc. Chaos, 2, 37–50 (1992)]. This assumption has been used to derive an asymptotic scaling formalism of distributions of stretching values that has useful predictive capabilities. Deviations from this scaling were thought to be limited to cases with regular islands. However, as is shown in this paper for the chaotic cavity flow, deviations from the proposed scaling can also occur for globally chaotic flows as a result of the joint action of unstable manifolds of hyperbolic periodic point and of singularities at the corners of the cavity. A detailed examination of random multiplicative stretching, the conditions necessary for its validity, and the intensity of manifold interaction effects is performed here for the cavity flow.