Method of perturbations of the shape of the boundary in fracture mechanics. Part 2: Inclusions

A brief history of solutions of the elastic problem for a plate with inclusions is given. The method of perturbation of the shape of the boundary for this problem solution is developed for two cases. In the case of an isotropic plate containing isotropic inclusions with turning points on their contours, expansion in terms of a small parameter ∈ and function ζ(z) is used. For the case of an anisotropic plate with an anisotropic or isotropic inclusion, expansion of complex stress functions in terms of the parameter ∈ and Faber polynomialsP _n for some ellipse is applied. The algorithm and its numerical realization are described in detail for the case of noncanonical elastic isotropic inclusions with small, but finite curvature radii at the tips. The limits of applicability of this method concerning both the defects geometry and elastic characteristics of the composition have been established. The convergence of series for the generalized SIF has been studied numerically. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 44–54, November–December, 1997.     

Interparticle interaction in a deformed body. II. Theory of elasticity for a body of theN th coordination order

In the framework of the model of structurally continual media described in the first part of the work [Mat. Sci.33, No. 2, 125–134 (1997)], we construct the theory of elasticity for an anisotropic body of then th coordination order by using the thermodynamic approach. Unlike the classical theory of elasticity for anisotropic bodies, in the constructed theory, the role of bulk forces is played by the forces of interparticle interaction. We introduce matrices of new material constants which characterize the nanomechanical properties of the body from the macroscopic point of view and describe the field of natural elastic waves of a given anisotropic structurally continual medium. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 3, pp. 19–30, May–June, 1997.     

Influence of defect diffusion on the radiation resistance of the heterogeneous photoconductor CdS-PbS

It is shown that the well-known fact that the radiation resistance of CdS improves considerably when PbS is added [A. G. Rokakh, E. V. Elagina, L. P. Matasova, and N. A. Novikova, Composition to Fabricate Film Photoresistors, Author’s Certificate No. 1110351, publ. March 17, 1983] accompanied by the formation of the heterogeneous photoconductor CdS-PbS may be attributed to the gettering of radiation defects by narrow-gap phase inclusions. This gettering occurs because the radiation-stimulated diffusion is considerably more pronounced in the wide-gap CdS-PbS component compared with the narrow-gap component. A model is proposed to explain the radiation resistance of a CdS-PbS system and this is used to determine the steady-state defect concentration profile. Pis’ma Zh. Tekh. Fiz. 25, 55–60 (December 26, 1999)     

A method for the determination of the elastic equilibrium of isotropic bodies with curvilinear inclusions. Part 2. Plane problem

Within the framework of the approach proposed in the first part of the work, the two-dimensional boundary-value problem for an isotropic body with noncanonical elastic inclusion is reduced to a finite system of linear algebraic equations. It is shown that the solution of this problem for elastic inclusions with small radius of curvature at the tip and/or cusps describes the intensity and concentration of stresses in the composition. For some special examples, we reveal the influence of elastic properties of the components of the composition and configuration of the inclusions on its local stress-strain state. It is also established that, unlike the method of perturbation of the shape of the boundary, this method is applicable to the determination of the concentration and intensity of stresses in the vicinity of the tips of elastic inclusions with small radii of curvature, including the inclusions whose elastic properties are close to the elastic properties of the matrix. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 1, pp. 16–26, January–February, 1999.     

Influence of acoustic treatment on the photoconductivity of zinc selenide crystals

It is shown that acoustic treatment of piezoelectric zinc selenide crystals by exciting strong natural elastic vibrations can specifically alter their photoelectric and other properties. Irreversible changes in the stressed-strained state of the crystals under this treatment are responsible for characteristic features in the spectral dependences of the permittivity ε′(λ) and the dielectric loss coefficient ε′’(λ). These dependences plotted in the form of ε*(λ) diagrams on the complex plane and also the spectrum of natural elastic vibrations can be used to monitor the treatment process. Pis’ma Zh. Tekh. Fiz. 25, 24–29 (December 26, 1999)     

Influence of the conditions of formation on the structure and phase composition of subsurface layers of uranium coated with the high-temperature oxide

It is established by x-ray structure analysis that the oxide film formed on the surface of uranium during oxidation by dry oxygen at pressures of 0.1–0.001 Pa and temperatures of 500–700 °C for several hours consists of UO₂ with U₄O₉ inclusions. Near the surface of the uranium the temperature of the α→β phase transition is lowered by 150–160 °C in comparison with the transition in the bulk of the metal, and the low-temperature stabilization of the β phase of uranium is observed. Pis’ma Zh. Tekh. Fiz. 24, 7–11 (June 12, 1998)     

Investigation into threshold stress intensity factors of materials under cyclic loading. Report 2. Prediction of fatigue limits and fatigue crack growth

On the basis of the results described in Report 1 [Probl. Prochn., No. 4, 5–16 (1998)], the author considers the possibility of using threshold stress intensity factors for the prediction of fatigue limits for titanium alloys by the formulas of linear elastic fracture mechanics and presents a substantiation of the method for predicting fatigue crack growth in structural elements. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 5–11, September–October, 1998.     

A Quantum Mechanical Treatment of the Vortex–Vortex Interaction in Anisotropic Superconductors

Using a new Hamiltonian of interaction [Int. J. Mod. Phys. B16, 4809 (1002); B17, 4763 (2003)], we calculate the vortex–vortex interaction energy in anisotropic superconductors. We present here the analytical formulae. The interaction energy has a minimum at a certain vortex–vortex distance. This distance decreases with the increase of the angle θ between the vortex line and the crystalline axis. Also, we calculate the elastic force and the nonharmonicity coefficients of the vortex lattice. Both coefficients decrease with increasing angle. Generally, the interaction energy decreases with the angle increase. Finally, we present the self-energy of a vortex in a lattice, the energy of a single isolated vortex and the lower critical field. Also, the surface of the vortex in the lattice has a form of a rosette with six petals, which are all equals for θ = 0 and become nonequals for θ ≠ 0. The surface of the first isolated vortex has a form of an oval for θ ≠ 0, and becomes a circle for θ = 0. PACS numbers: PACS 74.25.Qt.     

Influence of the magnetic self-field on the formation of a cathode plasma jet in steady-state vacuum arcs

It is shown that magnetic pinching of a cathode plasma jet is initiated after various microjets have merged to form a single jet at a distance r>10³ d from the cathode (d is the diameter of the cathode microspot). The plasma jet acquires the form of a paraboloid of revolution whose surface oscillates about the equilibrium position because of the inertia of the plasma transverse motion. At this point, cooling of the jet ceases. Pis’ma Zh. Tekh. Fiz. 23, 47–53 (June 12, 1997)     

Mechanism of initiation of acoustic emission in crystallization and melting of a substance. II

In[Inzh.-Fiz. Zh.,73,No. 5, 1064–1072 (2000)], the authors investigated one of the possible mechanisms of initiation of the acoustic effect of crystallization (melting) of substances, which was based on the assumption of a stepwise character of motion of the crystal-melt interface. In the present work, consideration is given to another mechanism of initiation of the acoustic effect of crystallization, which is based on the concept of possible enhancement of waves propagating in the liquid and in the crystal during the motion of their interface. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 1073–1079, September–October, 2000.     

Influence of elastic inclusions on the strength and durability of backup rolls of rolling mills

We propose an efficient approach to the evaluation of the influence of elastic inclusions on the strength and durability of large backup rolls of rolling mills. Analytic solutions are obtained for the problem of determination of the durability of rolls and admissible sizes of inclusions under cyclic loads and their critical sizes under static loads. We present the results in the form of the plots and compare them with special cases known in the literature. Ukrainian State University of Forestry Engineering, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 4, pp. 129–132, July–August, 1999.     

Strength of thin-walled structural elements with cracks under the conditions of creep

By using a computational model of growth of high-temperature creep cracks in metallic materials formulated by the authors somewhat earlier [Fiz.-Khim. Mekh. Mater., 42, No. 2, 62–68 (2006)], we develop a procedure for the construction of the diagrams of ultimate stresses for cracked plates. This procedure forms the basis of a method used for the evaluation of high-temperature strength of thin-walled structural elements weakened by cracks. The accumulated numerical results are compared with the experimental data available from the literature. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 33–39, March–April, 2007.     

Possible ionization of mercury atoms by elastic reflection in hyperthermal surface ionization experiments

An elastic collision model baed on data given by Danon et al. [Phys. Rev. Lett. 65, 2038 (1990)] was used to calculate the ionization potential of mercury atoms (V′) at the critical charge transfer distance as a function of the kinetic energy of the atoms (E). The linear dependence V′(E) obtained supports the model of surface ionization of mercury atoms by elastic reflection from a surface. Pis’ma Zh. Tekh. Fiz. 25, 42–45 (July 26, 1999)     

Skew plane shock wave at the interface between two polytropic gases. A heavy-light gas system

In [Inzh.-Fiz. Zh., 72, No. 2, 208–215, 216–225 (1998)] the problem of break decay that occurs when a plane skew shock wave (SSW) arrives at the interface between two polytropic gases of different density (the polytrope indices of both gases remain constant in the entire region of interaction) from the side of the less dense of them is considered in detail. The change in the stationary shock-wave configuration with an increase in the angle of incidence from 0 to π/2 is tracked. In the present work, consideration is given to the development of a stationary shock-wave configuration in the case where the SSW emerges at the interface from the side of the more dense gas. Problems associated with boundary layers and mixing of contacting gases were not considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 4, pp. 802–806, July–August, 2000.     

Correlation dependences between the mechanical characteristics of corrosion-resistant steels

A stability factor of austenite A _γ is proposed for corrosion-resistant steels. By using this factor, the equilibrium phase-structural state of steels can be quantitatively evaluated according to their chemical composition. The factor A _γ is determined by the values of the chromium and nickel equivalents. This factor, together with the generalized Scheffler diagram, enables one to deduce the correlation equations for the mechanical characteristics of steels σ_u, σ_0.2, δ, and ψ. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 1, pp. 54–60, January–February, 2007.     

Thermal stresses in an anisotropic plate with angular inclusions

We reduce the plane problem of anisotropic thermoelasticity for bodies with angular inclusions to a Fredholm system of integral equations. We construct potentials with power singularities at the angular points in the explicit form and present an example of application of the obtained results to the investigation of the dependence of local stresses in a plate with elastic stringer on its physicomechanical characteristics. Lutsk State Technical University, Lutsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 59–68, May–June, 1999.     

Dynamics of discharging of a heat accumulator in an infinite ground massif

Based on the approaches presented in [Inzh.-Fiz. Zh., 77, No. 4, 10–19 (2004)], the problem on discharging of the heat accumulated earlier by single heat exchangers and their combination in an infinite ground massif has been solved. The inefficiency of the accumulation and discharging by single heat exchangers and the high degree of recovery of the accumulated heat in the case of their clustered arrangement have been established. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 6, pp. 70–77, November–December, 2005.     

Modeling of the fracture of elasticoplastic materials capable of undergoing a phase transition

An investigation was made of the fracture of a layer of iron undergoing a polymorphic α-ε phase transition caused by a detonation wave, using an elasticoplastic model of the deformation of a continuous medium with spallation. The influence of the elastic precursor on the spallation was identified. Pis’ma Zh. Tekh. Fiz. 24, 91–95 (September 26, 1998)     

Frictional self-oscillations caused by deformation of the irregularities of the contacting surfaces

A numerical simulation is carried out for the dynamic processes caused by friction during the sliding of solid bodies. It is shown that frictional self-oscillations can arise even in a purely elastic system, in which there is no difference between the static and dynamic coefficients of friction, and the material at each point of a rough surface is deformed linearly. Pis’ma Zh. Tekh. Fiz. 23, 67–73 (March 26, 1997)