Strength of a half space weakened by a plane circular crack

The methods of the mechanics of brittle fracture and the theory of generalized cleavage fracture are used for the approximate solution of the problem of strength of a half space weakened by a plane circular crack. A simplified computational scheme is proposed for the evaluation of the fracture load in the case of free (tensile) fracture. The results of theoretical investigations are experimentally confirmed by testing concrete specimens. __________ Translated from Problemy Prochnosti, No. 6, pp. 122–132, November–December, 2006.     

Heating of a half space containing an inclusion and a crack

Two-dimensional stationary problems of heat conduction and thermoelasticity for an elastic half space containing an elastic cylindrical macroinclusion and a thermally insulated crack are investigated. The problems are reduced to systems of two singular integral equations on closed (the boundary of the inclusion) and nonclosed (crack) contours. The numerical solutions of these systems are obtained by the method of mechanical quadratures for an inclusion in the form of an elliptic cylinder and a rectilinear crack in a half space heated by a friction heat flow uniformly distributed over a part of the surface of the half pace. For the problem posed for two cases of matrix-inclusion compositions (steel-aluminium and aluminium-steel), the numerical solutions are presented in the form of the plots of the stress intensity factors as functions of the dimensions of the inclusion and the distance between the inclusion and the crack.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 4, pp. 34–40, July–August, 2004.     

Influence of a circular crack on the electromagnetic field in a conductor

The problem of scattering of low-frequency electromagnetic fields on circular cracks is reduced by the method of small parameter to a system of hypersingular integral equations of the Newton-potential type. For the solution of these equations, we propose to use the method of orthogonal polynomials of two variables. It is shown that the electric dipole whose moment is proportional to the normal component of the sounding field is an electrodynamic analog of the crack.     

Interaction of a crack with the boundary of a half space under impact loading

We studied the interaction of a crack subjected to the action of a dynamic load (whose dependence on time is described by the Heaviside function) with the boundary of an elastic half space. We present the plots of the stress intensity factors for the case where the half space contains a disk-shaped crack perpendicular or parallel to its boundary and the crack lips are loaded by impact forces.Pidstryhach Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 6, pp. 46–50, November–December, 1995.     

Penny-shaped interface crack between an elastic layer and a half space

The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.     

The electromagnetic field scattered by a crack in a piecewise-homogeneous medium: Theory of nondestructive testing

Summary Two-dimensional electromagnetic-wave diffraction has been considered for a system composed of a thin defect and a cylinder in a half-space, with the solution obtained by means of integral equations, which are solved by means of mechanical quadratures. The performance in the various integral representations has been examined. The scattered fields have been calculated for various geometrical and physical parameters. Conclusions arc drawn on how the latter affect the excited field.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 2, pp. 94–100, March–April, 1990.     

Stress intensity near a crack in the composition of a half space and a layer under harmonic loading

We consider a three-dimensional problem for an elastic bimaterial body formed by a half space and a layer and containing a circular crack. The surface of the crack is subjected to the action of stationary torsional forces. The problem is reduced to the solution of a system of boundary integral equations of Helmholtz-potential type for the unknown jumps of displacements on the crack surfaces. The dynamic stress concentration in the vicinity of the crack contour is investigated. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 27–32, March–April, 2008.     

Generation of electromagnetic waves by electrons rotating in a radial electrostatic field in free space

A theoretical analysis is made of mechanisms for the generation of electromagnetic waves by electrons rotating in a radial electrostatic field formed by a positively charged filament in free space. A dispersion equation is obtained to describe the interaction between the waves and nonrelativistic electrons. It is shown that electromagnetic fields can be generated by means of Čerenkov resonance. The frequencies and growth rates of the emitted waves are determined and their dependence on the parameters of the problem is investigated. Pis’ma Zh. Tekh. Fiz. 25, 1–4 (November 12, 1999)     

Thermoelastic state of a half space containing a thermally active elliptic crack perpendicular to its boundary

By the method of boundary integral equations, we solve the problem of stationary heat conduction and thermoelasticity for a semiinfinite body containing an elliptic crack perpendicular to its boundary in the case where the crack surfaces are kept at a certain temperature. The boundary of the body is unloaded and either thermally insulated or kept at temperature equal to zero. We study the influence of crack depth and its location on the stress intensity factor at a given constant temperature. __________ Translated From Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, Pp. 45–52, March–April, 2006.     

Theoretical investigation of the possibility of independent electromagnetic testing of two local inclusions in a conducting half space

We study the problem of finding the electromagnetic field of a plane wave scattered by two inclusions placed in an isotropic conducting nonmagnetic half space and develop a technique for numerical calculation of the equivalent dipole moments for both independent and interacting inclusions. The equivalent voids of dipole moments and their electromagnetic fields are analyzed numerically. The results of this investigation can be used in designing methods and equipment for independent electromagnetic nondestructive testing of several inclusions.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 80–89, July – August, 1994.     

Finite element analysis of a subsurface crack

The problem of a subsurface crack parallel to the surface of a half space was studied by the finite element method. Without using the interface or gap elements over the crack faces, the crack faces would penetrate into each other for the traction-free boundary condition under shear loading, which is physically impossible. Using the gap elements, this problem was avoided, and a contact zone was observed near one crack tip. The size of the contact zone decreases but the maximum contact pressure at the closed crack tip increases as the crack approaches the surface. For tensile and shear loadings, both K _I (mode I stress intensity factor) and K _II (mode II stress intensity factor) increase as the crack approaches the surface. For shear loading there is no K _I at the closed tip and the K _I and K _II at the open tip are comparable as the crack approaches the surface.     

Head waves in a piezoelectric half space

Head waves are an interesting phenomenon that is often ignored in harmonic piezoelectric wave study. They present a noise source in SAW devices, but carry useful information in seismology and ultrasonic NDE. In this work, a model based on exact Newtonian and Maxwell's equations of motion is used instead of the commonly used quasi-static approximation, because the former behaves better analytically than the latter and correctly describes certain waves that the latter cannot even predict, We identify three types of head waves. One type, called electromagnetic acoustic (EMAC) head waves, is new and unique to piezoelectric materials. The directivity of a head wave depends only on its critical angles, while the intensity changes with the kind of source that excites it. The polarization, on the other hand, is constant, independent of the observation angle and the kind of the excitation source. It is found that a metallized surface reduces the number of head waves in a piezoelectric medium and affects intensities of existing head waves, but does not change their propagation characteristics. Numerical examples are given for all three types of head waves, for both mechanical and electrical sources, and with both free and metallized surfaces     

Interaction between a surface crack and a subsurface inclusion

A numerical method for the integration of the singular integral equation resulting from the interaction of a surface crack with a subsurface inclusion is presented. The crack is modelled as a pile-up of dislocations, and the dislocation density function is partitioned into three parts: A singular term due to the load discontinuity imposed by the inclusion, a square root singular term from the crack tip, and a bounded and continuous residual term. By integrating the singular terms explicitly the well behaved residual dislocation density function only has to be determined numerically, together with the intensity of the square root singular term. The method is applied to the determination of the stress intensity factor for a surface crack growing towards and through a circular inclusion whose diameter is equal to the distance from the free surface, and to the determination of the characteristic stress intensity factors when the crack enters the inclusion and leaves it for arbitrary ratios between the inclusion diameter and the distance from the surface.     

Direct use of discrete complex image method for evaluating electric field expressions in a lossy half space

A modelling technique is proposed for direct use of the discrete complex image method (DCIM) to derive closed-form expressions for electric field components encountered in the electric field integral equation (EFIE) representing a lossy half space problem. The technique circumvents time consuming numerical computation of Sommerfeld integrals by approximating the kernel of the integrals with appropriate mathematical functions. This is done by appropriate use of either the least-square Prony (LS-Prony) method or the matrix pencil method (MPM) to represent electric field expressions in terms of spherical waves and their derivatives. A comparison is made between the two methods based on the computation time and accuracy and it is shown that the LS-Prony method performs two?three times faster than the MPM in approximating the integral kernels depending on the platform. The main feature of the proposed technique is its ability for direct inclusion in the kernel of computational tools based on the method of moments solution of the EFIE. This can be viewed as an advantage over the conventional DCIM approximation of spatial Green's functions for mixed potential integral equation for cases where the problem in hand can be more efficiently represented by the EFIE (e.g. the thin-wire EFIE). The accuracy of the proposed technique is validated against numerical integration of Sommerfeld integrals for an arbitrary electric dipole inside a lossy half space.     

Analysis of the field of a plane SH-wave scattered by a finite crack on the interface of materials

We solve the problem of diffraction of plane elastic SH-waves on a crack of finite width located in the plane interface of two different perfectly joined isotropic elastic materials. The problem is solved by the Wiener-Hopf method. An approximate solution of the Wiener-Hopf equation is obtained. The numerical results in the far-field zone are presented for a broad frequency band. The specific features of distribution of the radiation field in the zone of critical angles are analyzed. The probability of excitation of lateral waves is investigated and the possibility of detection of defects is discussed. A simple experimental procedure is proposed for the NDT evaluation of crack width in a test bench based on measuring the modulus of the field of displacements in the zone of critical angles. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 5–16, November–December, 2006.     

A strong electromagnetic field generated by a dipole

A strong electromagnetic field generated by a steep current pulse passing in a conductor dipole was measured. The current was created by an ultrashort voltage pulse formed in a coaxial transmitting line of a high-current picosecond electron accelerator.     

Torsion of a nonhomogeneous transversely isotropic half space

The statical Reissner Sagoci problem for a transversely isotropic, nonhomogeneous elastic solid is investigated. The modulus of rigidity of the medium is assumed to be variable as a power of the radial coordinate in the form $\text{r}{}^{\mathrm{\beta }}\text{(β ? 0)}$. The expressions for stresses, displacement and torque are given.     

Sublimation in a UHF electromagnetic field

An analytic expression describing sublimation in the presence of a UHF electromagnetic field is obtained and verified experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 2, pp. 243–249, August, 1977.     

Two bonded half planes with a crack going through the interface

The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.     

Technique for producing crack arrest by electromagnetic heating

Abstract

Crack arrest in current conducting materials by electromagnetic heating can be used effectively to extend the service life and improve the safety and reliability of structures and components. Theoretical analysis and experimental investigations have shown that due to heat concentration around the crack tip, small welded joints are formed by metal melting. Thus, the formation of the main crack source is prevented. From metallography, it has been found that a typical fine phase transformation microstructure can be obtained in the crack tip region as a result of rapid heating and cooling. The intensity, ductility, and wear capacity are promoted under the combined influence of superfine structure, thermal compressive stresses, and phase transformation compressive stresses. Microcracking and subsequent main crack propagation can both be prevented. The basic principles of the electromagnetic heating effect and the results of experimental work based on the theory are presented.