Verification of the validity of the Dugdale-Barenblatt model by the method of caustics

The method of caustics was used for the study of the validity of the Dugdale-Barenblatt model for the solution of the stress-distribution in cracked plates made of elastic-plastic materials. According to this method the. stress-singularity at the crack-tip is transformed into an optical singularity by applying strict mathematic laws. The optical singularity can be experimentally defined with high precision and accuracy and thus yields a means for the accurate evaluation of the stress-field at the vicinity of the crack-tip. The optical singularity is derived by a concentration of the strongly deviated light rays reflected from the close vicinity of the crack-tip, which is highly deformed. These rays form a singular surface in space, which when projected into a reference plane forms a strongly illuminated curve (caustic).An experimental study on metallic flat plates was undertaken, which contained a single transverse crack and were subjected in pure tension. Different types of steels were selected for specimens, with stress-strain curves varying between elastic-perfectly plastic and elastic-strongly strain hardening. The front surfaces of the specimens were hand polished and the optical set-up was arranged to yield a virtual image of the exterior caustic from reflections from the front face. By introducing the assumptions of the D-B model into the Muskhelishvili-Westergaard formulation for the cracked plate, the equations for the caustic and its initial curve may be expressed and solved for various loading steps. By comparing the thus obtained theoretical forms of caustics with the corresponding experimental curves it was possible to determine the area of the validity of the D-B model in terms of the mechanical properties and the shape of the stress-strain curve for each material.     

On the spectrum of the electric field integral equation and the convergence of the moment method

Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self‐coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low‐order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd.     

Influence of the coefficient of vaporization on the parameters of the gas near the surface

The dependence of the coefficient of concentration jump on the coefficient of vaporization for a diluted binary mixture, when the concentrations of the components are significantly different, has been investigated. The analytical expression of the concentration jump for the case where the frequency of collisions of molecules is in proportion to their velocity has been obtained. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 121–126, March–April, 2007.     

Multi-segment FEA of the human lumbar spine including the heterogeneity of the annulus fibrosus

This study pursues the numerical validation of human lumbar spine segments. By means of the finite element (FE) method, computational analyses are carried out of various load cases. In particular Flexion–Extension, Lateral Bending and Axial Torque are considered. By means of a literature review the underlying constitutive data is verified. In this context, the heterogeneity of the annulus fibrosus, the transversely isotropic stress response of the spinal ligaments and aspects of the FE discretization are particularly emphasized. The numerical results show good agreement with experimental investigations for Extension and Axial Torque for a FE model that accounts for intact human lumbar spine response. In Flexion and Lateral Bending, however, the results of the intact FE-model do not properly account for the experimental data. A good correlation for these load cases can be found by taking disc degeneration into account in the FE-model. This fact shows that tissue degeneration plays a key role in the current validation process and must be accounted for if the lumbar spine specimen is employed for spinal implant evaluation. A degenerated FE-model that represents the stage of degeneration of the specimen and fits the experimental data for all load cases could not be found in this study and warrants further work in this area.The authors are deeply indebted to Centerpulse Orthopedics Ltd., Winterthur, Switzerland (www.zimmer.com) for financial aid and support of this research. Additionally, the authors thank Darrell Goertzen for his work involving the experimental testing.     

A method for the determination of the parameters of the hysteresismodel of magnetic materials

Many methods have been proposed for the determination of the hysteresis loops of magnetic materials, and many mathematical approaches have been proposed to find a good model for the hysteresis phenomenon. However, very few attempts have been made to determine the parameters of the hysteresis model experimentally. This paper shows how, starting from a digital method for the experimental determination of the hysteresis loop under different maximum induction values, the parameters of a hysteresis model can be automatically estimated with good accuracy. Due to its good behavior in terms of accuracy and to the comparative ease in determining its parameters, the Preisach model for rate-independent hysteresis phenomena was chosen. Experimental determination of the model and consequent hysteresis loop computation were carried out. An accuracy below 1% was attained over the peak induction range from 0.49 T to 1.68 T and the frequency range from 50 Hz to 100 Hz     

Method of including the anisotropy of the optical properties of the surface and the nonunidimensionality of the system in determining the effective radiation

Based on the method of successive substitutions, an integral equation is derived in which multiple reflections are explicitly identified. This equation is used provide simple methods of estimating the local effective radiation of two-dimensional and three-dimensional systems of surfaces, with due regard for the anisotropy of their optical properties. A cylindrical cavity confined by the surface of a right circular cylinder with a side pyrometric hole is treated as an example. The results obtained by the suggested method are compared with the data of direct solution of an integral equation for the two-dimensional problem.     

On the estimation of the toughness of surface microcracks

Hardness testing is a method frequently used for evaluating the resistance of body surfaces to the influence of contact loading. The Vickers hardness test is applied for this purpose in a case when the material is sufficiently ductile and no cracks occur in the corners of the indents. Testing of the surface hardness of such materials as glass and ceramics on the basis of the Vickers testing method must take into account the energy that is spent on crack spreading. This paper describes a more exact and accurate method for evaluating resistance to microcrack formation on the surface of a material. To evaluate the conditions for crack spreading, it is necessary to test a specimen under loading in bulk. The suggested procedure involves a bent strip. As bending stresses are known, from the differences in crack length along and across the strip, the resistance of the material surface to crack propagation is determined.     

On the estimation of the toughness of surface microcracks

Hardness testing is a method frequently used for evaluating the resistance of body surfaces to the influence of contact loading. The Vickers hardness test is applied for this purpose in a case when the material is sufficiently ductile and no cracks occur in the corners of the indents. Testing of the surface hardness of such materials as glass and ceramics on the basis of the Vickers testing method must take into account the energy that is spent on crack spreading. This paper describes a more exact and accurate method for evaluating resistance to microcrack formation on the surface of a material. To evaluate the conditions for crack spreading, it is necessary to test a specimen under loading in bulk. The suggested procedure involves a bent strip. As bending stresses are known, from the differences in crack length along and across the strip, the resistance of the material surface to crack propagation is determined.     

Calculation of the amount of gas in the explosive region of a vapour cloud released in the atmosphere

Formulae were derived and calculations made for the amount of gas in the explosive region of a vapour cloud or plume. It appears that, for an instantaneous source, a large fraction of the total amount released (e.g. 50% for methane) can be in the explosive region, irrespective of source strength and meteorological conditions. On the other hand, for a continuous source, the amount in the explosive region is strongly dependent on source strength and meteorological conditions.To assist in the hazard analysis, a computer program was written to calculate the concentration as a function of time for a quasi-instantaneous spill of LNG on water.     

On the comparison of the methods used for the solutions of the governing equation for unsteady unidirectional flows of second grade fluids

In order to solve the governing equation for unsteady unidirectional flows of second grade fluids, the use of the Laplace and the Fourier transform methods are discussed. Three characteristic examples which are unsteady flow between two parallel plates, unsteady pipe flow and unsteady flow over a plane wall are considered. It is found that the solution for unsteady flow in bounded regions obtained by the Laplace and the Fourier transform methods are exactly the same as the case of the unsteady flow of a Newtonian fluid. It is shown that the Laplace transform method for small values of time is useful for flows of Newtonian fluids but it is not convenient for flows in unbounded regions of second grade fluids. Furthermore, it is explained that for some unsteady flows of second grade fluids, the solution obtained by using the Laplace transform does not satisfy the initial condition and therefore the Fourier transform method is used.     

Determination of the characteristics of distribution of the fatigue limits of materials on the basis of the energy approach

We propose a method for the determination of the mean value of the fatigue limit of a material and its mean-square deviation according to the results of standard fatigue tests. The interpretation of these results from the viewpoint of energy enables us to establish the relationship between the individual durability of specimens and their potential ability to withstand fatigue fracture in the form of individual fatigue limits. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 28–33, July–August, 1998.     

An estimate of the effect of the relative dimensions of a standard and the target on the accuracy of the determination of the scattering characteristics of radar targets

A method of estimating the error in measuring the effective scattering surface of a target by the substitution method, resulting from the difference in the linear dimensions of the target and a standard reflector is described. Recommendations are made for increasing the accuracy of measurements of the scattering characteristics of radar targets in the transition and near zones.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 25–26, January, 1994.     

Influence of the geometry of the nozzle on the characteristics of an exhaust jet

Two solutions for the parameters of a turbulent exhaust jet of a dual-duct engine — the traditional solution within the framework of Prandtl equations of the type of boundary-layer equations and calculation of the near-range field within the framework of the Navier-Stokes equations with subsequent calculation within the framework of the Prandtl equations for large distances — have been compared. It has been shown that the influence of the real geometry of the nozzle exit section, including the shift of the center body and the main duct forward from the exit section of the cold secondary duct, can be allowed for by correcting the constant of the source term in the differential equation for turbulent kinematic viscosity. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 37–46, May–June, 2006.     

On the performance of the enthalpy method in the region of a singularity

A test problem is presented which provides a realistic challenge for computational techniques designed for the prediction of temperature distributions in melting/freezing processes. It is shown that a suitably modified finite difference implementation of the enthalpy method produces results that are perhaps adequate for practical purposes. However, the best approach to problems typified by the test problem remains to be found.     

On the asymmetrical dependence of the threshold pressure of infiltration on the wettability of the porous solid by the infiltrating liquid

A general equation has been derived for the threshold pressure of infiltration of liquids into porous solids. From this equation all the known equations for the threshold pressure can be obtained, using different assumptions on the morphology of the porous solid and on the way how the liquid infiltrates the solid. Particularly, the Young-Laplace equation, the Carman-equation, and the modification of the Carman equation, suggested by White and later by Mortensen and Cornie have been reproduced as particular cases of the general equation. A new particular solution of this general equation is also suggested, taking into account that the original solid/gas interface inside the porous body is not fully replaced by the solid/liquid interface during infiltration, especially for the case of non-wetting liquids. The new, general equation consists of three semi-empirical parameters, which should be found experimentally for a given type of morphology of the porous solid and for the given ratio of the surface tension to the density of the infiltrating liquid metal. The new equation provides a value of the threshold contact angle to be between 65.5° and 90°, depending on the morphology of the porous solid. Consequently, the threshold pressure appears to be an asymmetrical function of the contact angle. Based on the new equation, the practical constancy of the threshold pressure is predicted in the interval of the contact angles between 120° and 180°.     

Identification of the Parameters of Multilayer Coatings According to the Thermoelastic Displacements of the Surface of Heating

With an aim to develop a method for the evaluation of the parameters of multilayer coatings, we study the influence of geometric, elastic, and thermal characteristics of materials of three-layered structures on the normal and tangential thermoelastic displacements of points of the surface of the coating in the process of its local heating by axisymmetric stationary heat flows. The absolute values of displacements are estimated for the intensities of heat flow for which the temperature attained at the center of the spot of heating does not exceed 200°C. It is shown that the order of magnitude of the maximum displacements is sufficient for their recording by the methods of holographic interferometry and shearography.     

Acoustic waves in the vicinity of the normal to the surface of piezoelectric crystals

The acoustic wave propagation in the vicinity of the normal to the plane surface confining a piezoelectric crystal of arbitrary symmetry is theoretically studied. An octet formalism arid a perturbation theory have been put forward to describe the wave fields in the region of concern. The developed mathematical approach has been applied to several problems. Specifically, the derivation of the transfer matrix for the normal direction to the surface has been discussed. Furthermore, we have discussed how to estimate the electric potential induced outside the piezoelectric material by a normally incident wave. In addition, an analytical expression has been derived for the numerical factor in the function describing the asymptotic behavior of quasielectrostatic Green's function for half-infinite piezoelectric substrates at small values of the wave vector     

Status Report on the First Round of the Development of the Advanced Encryption Standard

In 1997, the National Institute of Standards and Technology (NIST) initiated a process to select a symmetric-key encryption algorithm to be used to protect sensitive (unclassified) Federal information in furtherance of NIST’s statutory responsibilities. In 1998, NIST announced the acceptance of 15 candidate algorithms and requested the assistance of the cryptographic research community in analyzing the candidates. This analysis included an initial examination of the security and efficiency characteristics for each algorithm. NIST has reviewed the results of this research and selected five algorithms (MARS, RC6™, Rijndael, Serpent and Twofish) as finalists. The research results and rationale for the selection of the finalists are documented in this report. The five finalists will be the subject of further study before the selection of one or more of these algorithms for inclusion in the Advanced Encryption Standard.     

Influence of the properties of thin films on the determination of the relative reflectance of a randomly rough surface

In the determination of the relative reflectance of a randomly rough surface, it is argued in this paper that the measured value of the relative reflectance is influenced by the difference in the optical properties of the thin films used to cover the reference sample on the one hand and the test sample on the other. The influence of the variation in thickness and refractive index of the two films (i.e the variation in optical thickness) is studied. Using numerical examples it is also shown that, for a randomly rough silicon surface, relatively small differences in the above-cited parameters can have a considerable influence on the difference between the measured and true relative reflectances. A procedure is discussed for excluding this influence. In conclusion, an experimental method for determining the true value of the relative reflectance of a randomly rough silicon surface is demonstrated for the system SiSiO₂.