Computer analysis of the configurations of magnetic fields of subsurface discontinuities of finite dimensions and arbitrary shapes in tested objects of finite length by the method of spatial integral equations

Using software developed by the authors and based on the method of spatial integral equations, the spatial configurations of the magnetic fields of tested objects of finite length that contain subsurface discontinuity flaws of finite dimensions and arbitrary shapes are studied. It is possible to take into account the influence of both uniform and nonuniform magnetizing fields, including real sources; an arbitrary geometry of tested objects; and a nonlinear character of the magnetic properties of materials. It is shown that software can be used in studies of the influence of the geometrical parameters of a defect on the topography of the informative magnetic field in the testing zone.     

Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field

The magnetic traction on a deformable ferromagnetic material is deduced based on the classical magnetoelastic model. The vibration frequency of a ferromagnetic beam subjected to an inclined magnetic field is analyzed by employing formulations of the magnetic force. The result for the condition of longitudinal magnetic field is the same trend as that of the previous experiment carried out by Takagi et al. [Analysis and experiment of dynamic deflection of a thin plate with a coupling effect. IEEE Transactions on Magnetics 1992;28(2):1259–62]. Moreover, experimental tests have been carried out to study the free vibration of a magnetic plate subjected to an inclined magnetic field.     

Non-linear analysis of skew thin plate by finite difference method

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed.     

Effect of the number of surface flaws in a group on their magnetic field

The effect of the number of surface flaws in a group on the value of their magnetic field in air above a ferromagnetic article is considered.Translated from Defektoskopiya, Vol. 40, No. 8, 2004, pp. 3–9. Original Russian Text Copyright © 2004 by Zagidulin, Muzhitskii, Bizyulev.     

Effect of a gap in the electromagnet-object magnetic circuit on the magnetic field of surface flaws in different steels

The dependences of the magnetic-field strength of surface flaws in various steels on the electromagnet current have been studied for different gaps in the magnetic circuit. It is shown that an anomalous ratio of the magnetic-field strengths of flaws in hard and soft magnetic materials holds in the entire range of gap changes. The dependence of the ratio of the magnetic-field strengths of a flaw, which are obtained for different gaps in the magnetic circuit, on the electromagnet current has an extremum in the region of weak currents and, at high currents, tends toward to a constant value, which is determined by the value of the set gaps. The results are considered, taking their interrelations with the magnetic properties of materials and processes of their magnetization in the presence of a demagnetization factor into account.     

Computational relationships for the development of software for calculating magnetostatic fields from flaws in arbitrarily shaped ferromagnetic products

Based on the integral equation for the stray magnetic field strength inside a magnetized article, computational relationships have been derived in the form of a matrix equation that is convenient when developing software for modeling the distribution of magnetization in arbitrarily shaped articles with different flaws and for calculating and imaging external magnetic fields of the magnetized article. On this basis, a program has been developed that is most suitable for the case where the article boundaries and flaws can be sufficiently accurately defined on a three-dimensional grid with identical rectangular cells.     

A finite strip method for the post-locally-buckled analysis of plate structures

A finite strip method is presented for the post-locally-buckled analysis of prismatic thin walled structures under end compression. Sample problems are analysed and the economy of the method compared with the finite element method is demonstrated.     

Modifications in the linear current model of a discontinuity flaw in a ferromagnetic piece

In order to achieve a better agreement between experimental data and theoretical results, we have introduced the magnetic field due to magnetized regions above flaw faces to the linear current model of the flaw.     

The measurement of magnetic field strength near the surface of a ferromagnetic object

A technique for measuring field strength near the surface of a ferromagnetic object using a polarized local tape magnetic carrier (LTMC) is described. The calibration characteristics of a demagnetized and polarized LTMC made of И4701-35 tape are given.     

Modeling magnetic fields measured by surface probes embedded in a cylindrical flux conserver

Calculating magnetic fields at the surface of a flux conserver, perfect conductor, for displaced plasma currents is useful for understanding modes of a Z-pinch. The magnetic fields measured at the flux conserver are a sum of the magnetic fields from the plasma current and the eddy currents which form in the walls to keep the flux constant. While the magnetic field at the wall from the plasma current alone is easily calculated using the Biot-Savart law, finding the eddy currents in the flux conserver which satisfy the boundary conditions can be a tedious process. A simple method of calculating the surface magnetic field for a given Z-pinch displacement off-axis is derived for a cylindrical flux conserver. This relationship does not require the explicit calculation of the eddy currents, saving time when analyzing surface magnetic probe measurements. Analytic expressions can be used to describe the surface magnetic field which increase the understanding of the magnetic probe measurements.     

A method for improving the accuracy of evaluating the dimensions of flaws in walls of tubular elements of structures

An algorithm for evaluating the real accuracy of the basic measuring instrument (exterior or in-tube flaw detector) in measuring parameters of flaws of a particular inspected tube was proposed on condition that the basic measuring equipment has no systematic error, while a verification instrument is considered as “absolutely” precise or “reference.” A statistical method of increasing the accuracy of evaluating the dimensions of flaws in thin-walled tube elements was developed on the basis of a correlation between the dimensions of flaw parameters. It can be taken as a basis for finding real values of parameters of flaws and for performing reliable calculations of the residual strength and residual life, for scheduling optimal periods for the next inspection of pipelines, and for ranging segments of a pipeline by a risk criterion, thus providing optimal scheduling of repairs.     

A study of the possibility of detecting surface defects in ferromagnetic products using a pyroelectromagnetic method

A new method for detecting surface cracks in ferromagnetic products by means of combined magnetization and defect zones by the temperature relief of a surface using an infrared camera (infrared imager) is proposed. Its physical principles and testing procedure are outlined. Experimental data obtained on steel specimens with surface microcracks are given.     

Experimental studies of the reflection coefficient of a film that visualizes magnetic fields in the zone of a flaw during testing of ferromagnetic objects

The character of changes in the light-reflection coefficient in the zone of indicator patterns of flaws on a magnetic-field-visualizing film was determined during magnetic testing of ferromagnetic plates. The flaw detection in specimens was performed in an applied field directed in parallel to the inspected surface. External light radiation was directed perpendicular to the specimen surface and the magnetic-field-visualizing film that were placed on it.     

Extrusion of rate-sensitive materials using a viscoplastic constitutive equation and the finite element method

The flow of a rate sensitive material in a forming process in general and an extrusion process in particular has been analysed by using a constitutive equation in the form where such a material is treated as a viscous, non-Newtonian incompressible fluid flow. The discretized form of the flow equation is obtained using the principle of virtual work and the finite element technique. Velocities and pressures are used as primary variables in the formulation.The method which is presently applied to the axisymmetric steady state extrusion of rate sensitive materials can readily be extended to unsteady problems. The two rate-sensitive materials choosen are an aluminium having a definite yield stress and a Pb-Sn eutectic alloy having no detectable yield limit. The results of the present analysis are compared with available experimental values or with that obtained by other methods and in general good agreement is found to exist.     

A decrease in the error of the statistical method for estimating the parameters of flaws in magnetic flaw detection

A method for increasing the accuracy of evaluating the dimensions of flaws during magnetic flaw detection in steel sheets and pipes, which is based on the division of a set of flaws into subclasses using a certain generalized parameter in accordance with the criterion of minimization of an appropriate estimate, is described. The results of applicability of this method to the evaluation of the depths of flaws of the metal loss type are presented.     

Measuring the surface area of a cell by the method of the spatial grid with a CSLM—a demonstration

The spatial grid is a method for estimating the surface area of particles. A stack of perfectly registered sections is the essential prerequisite for its use. The confocal scanning light microscope provides such a stack by optical sectioning. The spatial grid method is briefly described and applied to an osteocyte lacuna in dry mineralized human mandible. This type of cell was chosen because of its very complex shape. The variance of the area estimate is studied and compared with the results of a simulation.     

Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method

In this paper, a finite element formulation is developed for analyzing the axisymmetric thermal buckling of FGM annular plates of variable thickness subjected to thermal loads generally distributed nonuniformly along the plate radial coordinate. The FGM assumed to be isotropic with material properties graded in the thickness direction according to a simple power-law in terms of the plate thickness coordinate, and has symmetry with respect to the plate midplane. At first, the pre-buckling plane elasticity problem is developed and solved using the finite element method, to determine the distribution of the pre-buckling in-plane forces in terms of the temperature rise distribution. Subsequently, based on Kierchhoff plate theory and using the principle of minimum total potential energy, the weak form of the differential equation governing the plate thermal stability is derived, then by employing the finite element method, the stability equations are solved numerically to evaluate the thermal buckling load factor. Convergence and validation of the presented finite element model are investigated by comparing the numerical results with those available in the literature. Parametric studies are carried out to cover the effects of parameters including thickness-to-radius ratio, taper parameter and boundary conditions on the thermal buckling load factor of the plates.     

Analytical estimation of measurement uncertainty in surface plate calibration by the Moody method using differential levels

Surface plate quality influences the calibration of artifacts, instruments, working gauges and, by extension, the quality of manufactured parts. A statement of uncertainty for the surface plate calibration is needed for conformance testing and for estimating uncertainty in calibrations that rely on the surface plate. An analytical approach to the estimate of uncertainty for a common measurement method is given. The residual height at each position on the surface is expressed in terms of the measurement parameters and the measured angles. Uncertainty of each residual height value is then derived following the common methods for propagation of uncertainty. The maximum uncertainty is at the center of the surface and the calculated bounds on error compare well with values of closure from actual measurements. The uncertainty of height values is proportional to the spacing of the measurement positions and to the squareroot of the number of positions. Using data from many plates of various size and quality, a generalized uncertainty in flatness for the measurement method was estimated. The derivations also allow calculations for specific applications. Finally, a method is proposed for reporting uncertainty in surface slope which is required for estimating uncertainties of items calibrated on a surface plate.     

Free vibration analysis of aboveground LNG-storage tanks by the finite element method

Recently, in proportion to the increase of earthquake occurrence-frequency and its strength in the countries within the circum-pan Pacific earthquake belt, a concept of earthquake-proof design for huge structures containing liquid has been growing up. This study deals with the refinement of classical numerical approaches for the free vibration analysis of separated structure and liquid motions. According to the liquid-structure interaction, LNG-storage tanks exhibit two distinguished eigenmodes, the sloshing mode and the bulging mode. For the sloshing-more analysis, we refine the classical rigid-tank model by reflecting the container flexibility. While, for the bulging-mode analysis, we refine the classical uncoupled structural vibration system by taking the liquid free-surface fluctuation into consideration. We first construct the refined dynamic models for both problems, and present the refined numerical procedures. Furthermore, in order for the efficient treatment of large-scale matrices, we employ the Lanczos iteration scheme and the frontal-solver for our test FEM program. With the developed program we carry out numerical experiments illustrating the theoretical results.