Formation of a linearly extended destruction zone in the body of transparent polymers

The action of pulsed laser radiation on solid transparent polymers has been studied. Analysis has been made of different methods of concentrating the light field: focusing to a point and focusing to a caustic. High effectiveness of injury to the material during the use of the method of linearly concentrated focusing is shown.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 354–356, March–April, 1976.     

Molecular mechanism of orientation in polymers

On the basis of calculations in which the behavior of the chain under load is investigated, it is suggested that, apart from the rotational isomerism mechanism, at low temperatures and high stresses the instability of the folded configuration may play an important part in polymer orientation. A distinctive feature of the proposed mechanism is the high rate of orientation, which for an isolated chain is of the order of the speed of sound.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 3, pp. 525–528, May–June, 1976.     

Molecular mechanism of oriented crystalline polymers

It is shown with reference to linear polyethylene that the deformation of an oriented crystalline polymer takes place as a result of elongation of the coiled parts of the macromolecules in the amorphous zones owing to conversion of gauche into extended trans isomers. The decrease in coiled isomer content when the specimen is deformed by approximately 5% is accompanied by a small number of chemical bond breakages. Repeat deformation by the same amount does not result in any additional breakage of polymer chains.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of The USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 584–588, July–August, 1973.     

Effect of submicroscopic crack formation and relaxation phenomena in polymers

The development of submicrocracks and the changes taking place in their concentration during loading and unloading cycles were studied by the low-angle x-ray scattering method in oriented amorphous-crystalline polymers (capron and polypropylene). The deformation () of the polymers was compared with the changes in submicrocrack concentration (N_cr).A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 387–392, May–June, 1970.     

Kinetics of crack growth in polymers during repeated loading with a small number of cycles

We have shown that crack propagation, especially in its initial stage, is greatly inhibited by the deformation process involved in hardening. It was established that loading repeated at intervals leads to a brief increase in crack-propagation rate during each loading period, as a result of the development of excessive stresses and the heating effect at the crack apex caused by the finite rate of the relaxation processes.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 247–251, March–April, 1972.     

Extrusion of a plastic material from a circular sector with a small apex angle and a sink at the vertex

The plane inertialess extrusion of a perfect rigid-plastic material from a circular sector, the angle of which serves as a small parameter, is investigated using the asymptotic integration. The flow was initiated by the approach of the two sides of the sector and the existence in it of a sink of specified power. The principal velocity and stress approximations are obtained and the domains of applicability of the asymptotic expansions and the inertialess (quasistatic) solutions are found. Analogies are drawn with the solutions of the classical Prandtl problem and several of its extensions.     

Singularities at the tip of a crack on the interface of piezoelectric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezoelectric media under various boundary conditions on the crack surfaces. The singularity exponents form the spectrum of a certain polynomial pencil, and although explicit formulas are not available, this spectrum is described completely though. The mathematical results apply to problems in fracture mechanics. In this way the Griffith formulas are obtained for increments of energy functionals due to the growth of the crack, and the notion of energy release matrix is introduced. Normalization conditions for bases of singular solutions are proposed to adapt them to energy, stress, and deformation fracture criteria. Connections between these bases are determined, and additional properties of the deformation basis related to the notion of electric surface enthalpy are established. Bibliography: 44 titles. Dedicated to Vsevolod Alekseevich Solonnikov Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 241–271.     

An experimental-analytical hybrid model for the elasto-plastic stresses at a crack

The primary obstacle preventing the analytical determination of physically sensible stresses at a crack tip is the presence of a mathematical singularity there. This singularity is best known in its elastic form; however it persists even in elasto-plastic crack-tip stresses. To overcome the difficulty we adopt the following strategy: we attempt to capture initial elastic stresses experimentally, than track subsequent elasto-plastic stress distributions analytically.We infer a finite stress at a crack tip from the experimental behaviour of cracked specimens at fracture when the specimens are made of a truly brittle material. Given a size-independent result, we argue that the crack-tip stress at fracture must equal the ultimate stress for such a material; thus dividing by the applied stress at the same point gives a measure of the stress concentration factor, K_T. The approach is checked for size independence and against hole configurations with known theoretical, yet physically reasonable, K_T. Then the effective experimental KT are taken as inputs for the second phase of the study in which we model the crack as being a smooth notch having the same stress concentration factor as found experimentally. In this way our configuration initially shares the same stresses at the crack tip as we inferred physically. Next we track effects of incremental plastic flow on a set of finite element grids. Satisfactory resolution in return for modest computational effort is obtained by employing a substructuring method. The accuracy in both the elastic and the elasto-plastic regime is checked against trial problems with exact solutions. Thereafter, physically interpretable stress distributions ahead of the crack are determined for a range of materials and for varying load levels.     

Effect of the conditions of bond formation and destruction on the adhesion of polymers to synthetic fibers

It is shown that the adhesion of linear polymers can be measured by shearing a monofilament relative to a microblock of adhesive [1]. Experiments have been performed on polypropylene, polyethylene terephthaliate, polycaprolactam, polyvinyl alcohol, and glass fibers. Broad variation of the diameter, structure, and physicomechanical properties of the various kinds of oriented fibers had practically no effect on the adhesion. The physicochemical properties of the adhesive solutions at the moment of application to the fiber likewise do not affect the adhesion which, other things being equal, is determined by the nature and supermolecular structure of the polymers in the contact zone.Belorussian Lenin State University, Minsk. Branch of the Karpov Scientific-Research Physicochemical Institute, Obninsk. Translated from Mekhanika Polimerov, No. 6, pp. 1042–1048, November–December, 1970.     

Mechanical behavior of a number of polymers at helium temperatures

An experimental investigation of the mechanical behavior of a number of polymers in the range 4.2–240°K has been made. It has been shown that at helium temperature the Poisson ratio is governed by the free volume. It has been established that the dynamic Young's modulus and shear modulus of these polymers at 4.2°K depend on the chemical structure: their values are determined by the mean distance between neighboring macromolecule chains.     

Problem of an elastic half-plane with a crack emerging orthogonally at the boundary

The problem of the half-plane, in which a finite crack emerges orthogonally at the boundary, is studied. On the edges of the crack a self-balancing load is applied. A detailed investigation is carried out for an integral equation with respect to the unknown derivative of the displacement jump, to which the problem can be reduced. The exact solution of the integral equation is constructed with the aid of the Mellin transform and the Riemann boundary value problem for the halfplane. The asymptotic behavior of the solution at both ends of the crack is elucidated. First the asymptotic behavior of the solution at the point of emergence of the crack is obtained and the dependence of this asymptotic behavior on the type of the load is established. For a special form of the load one obtains a simple expression of the stress intensity coefficient. In the case of a general load, the asymptotic behavior is used for the construction of an effective approximate solution on the basis of the method of orthogonal polynomials. As a result, the problem reduces to an infinite algebraic system, solvable by the reduction method.Translated from Dinamicheskie Sistemy, No. 4, pp. 45–51, 1985.     

Numerical computation of the stress-strain state at the end of a crack under dynamic load

We obtain the values of the stress intensity factor at the end of a stationary crack under dynamic load using a numerical method. We compare the results with the existing experimental data. We establish that it is possible to apply the proposed method to compute stationary cracks under dynamic load. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 61–65.     

A note on the stress singularity at a penny-shaped crack in three-dimensional electrostriction

Zusammenfassung Diese Mitteilung behandelt eine vollständige Bewertung der Spannungs-Singularität am Rande eines flachen kreisförmigen Spaltes unter der Einwirkung von Elektrostriktion. Die Ergebnisse bestätigen die Schlussfolgerungen, welche früher bei zweidimensionalen Problemen gezogen wurden.Die der Elektrostriktion zuzuschreibende Singularität zeitigt eine rein radiale Spannung, welche nicht dazu neigt, die schon bestehenden Spalten ihrer Ausdehnungs-Oberfläche entlang auszubreiten.

---

---

Research supported by the National Science Foundation under grant NSF GP 22567.

---

Research supported by the United States Atomic Energy Commission.     

The end zone of a shear crack propagating at an intersonic velocity

An asymptotic solution of the problem for a shear crack propagating at an intersonic velocity is given that determines the size of the end zone, the distribution of the displacement jump in it and the dependence of the propagation velocity on an effective stress intensity factor, introduced in this paper. Numerical data are presented for the case of linear softening in the end zone and a comparison is made with the results for the Leonov–Panasyuk–Dugdale model. It is established using an effective stress intensity factor that the propagation is unstable at velocities close to the velocity of transverse waves; it becomes stable when approaching the velocity of longitudinal waves.     

Comparison of the mass spectra of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation

The compositions of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation have been studied and compared by means of mass spectrometry. For those polymers in which in both cases breakdown of the macromolecules begins with the basic chain, the volatile products are the same. For polymers in which breakdown of the molecules in thermal degradation begins with the stripping of side groups, the volatile products of thermal and mechanical degradation are different. This confirms and extends the ideas of the kinetic theory of fracture concerning the relationship between the processes of mechanical fracture and thermal degradation of polymers.Mekhanika Polimerov, Vol. 3, No. 1, pp. 80–88, 1967     

The stress state of an elastic composite cone with centre of rotation at the apex

The torsion of a composite cone that has a centre of rotation at its apex is investigated in a spherical system of coordinates. A composite cone is a cone with one shear modulus, inserted into a conical funnel having another shear modulus and with ideal mechanical contact between its surface and the inner surface of the conical funnel. The auxiliary problem of a composite cone with its apex truncated by a spherical surface is considered first. The outer surface of such a conical body is not loaded, but a load that reduces to a torque is applied to its spherical surface. The auxiliary problem is reduced to a one-dimensional discontinuous boundary-value problem using a specially constructed integral transformation. The exact solution of this boundary-value problem is constructed. The limit is then taken in the solution obtained as the radius of the spherical surface tends to zero for the purpose of obtaining an exact solution of the problem of the torsion of a composite cone that has a centre of rotation at the apex.