Table of contents

This paper consists of a general report of the Joint Conference of The Non-Destructive Testing Group and the Société Française de Métallurgie, held in the Lecture Theatre of the Institution of Mechanical Engineers from 2nd to 4th May 1960. It includes a list of all the papers presented at the Conference, with references, where available, for those which have been or are being published, and is followed by four of the papers presented at the Conference.

The physical basis of all non-destructive testing is emphasized. It is suggested that the `structure' (in a general sense) of non-destructive testing is based on two principal forms of energy, viz. the spectrum of electromagnetic radiations and fields and the spectrum of particle movements or vibrations in solids. The two are involved together or separately and are interpretable in terms of the structure (in a more physical sense) of the material, i.e. the electrons, atoms, molecules, crystal structure, etc.

A unified scheme of relationships is suggested. Reference is made to a fundamental unity of the equilibrium physical properties of a perfect crystal so that physical methods of examination are similarly inter-related. The `real' materials of industry, and in particular metals, can be regarded as derived from perfect single crystals by the introduction of increasingly serious forms of lattice `imperfection' or irregularity such as solid solution strains, vacancies, domains, dislocations, etc., leading to the eventual appearance of grain boundaries, poly-phase structures, segregation, etc. The way in which various physical properties are used to interpret materials in those terms is indicated.

The methods for studying surface deformation used in the National Engineering Laboratory are described. Deformed metal surfaces show an enhanced photoelectric emission which is studied with the aid of open-ended Geiger-Müller counters or electron multipliers. Oxide films stripped from deformed metal surfaces are studied by electron-microscopy and changes in chemical reactivity by radioactive tracers. Surface topography is an important factor in lubrication and wear research and is being studied with the aid of interferometry, phase contrast and electron microscopy. Replica techniques are often applied with advantage.

Some recent developments in the examination of materials with the aid of the magnetization curve are described. The well-known method of estimating internal stresses by means of magnetic measurements has recently been much refined so that a quantitatively correct estimate of the internal stresses arising from plastic deformation of nickel and even iron can be made. In special cases even inhomogeneous stresses can be magnetically estimated and the approach to saturation is related to the dislocation density. A fair amount of information about non-magnetic inclusions and precipitates in a magnetic material can be derived from a critical assessment of its coercivity. On the other hand, the measurement of torque curves and of rotational hysteresis allows a comprehensive analysis of the shape, size and density of magnetic precipitates. Finally, the use of magnetic viscosity measurements for structure studies is mentioned.

Attempts to solve Maxwell's equations for regions inside electrical conductors generally meet with insuperable mathematical obstacles, unless a uniform magnetic field can be assumed to exist. In many practical instances the field will be non-uniform, since it is generated by currents flowing along wires. The lack of formulae for realistic geometrical arrangements is keenly felt in two cases. They are the prediction of eddy-current power losses and the development of electromagnetic methods for non-destructive testing.

A metallic body can be considered to consist of an infinite number of closed filamentary circuits, coinciding with the streamlines of induced currents. It is then shown, for the most general case, how to express the current at any point in the metal by an infinite series of increasing powers of the frequency of a sinusoidal current flowing in an energizing filament. The coefficients of the series are functions of conductor geometry, electrical conductivity and magnetic permeability, but not of the current itself. This opens the way to measurements on scale models, the long numerical calculation of coefficients by digital computers and the tabulation of normalized coefficients for geometrically similar systems.

Some possible causes of the `anomalous eddy-current loss' in magnetic laminations are briefly reviewd in order to illustrate the differing opinions that are still being held on this subject. It would, therefore, seem advisable to re-examine the methods of measuring eddy-current losses with reference to the theory of coupled circuits, and thereby determine whether the classical formulae are sufficiently good approximations. Experiments for this purpose are discussed.

The paper is concerned with the calculation and measurement of the stresses involved in the twisting together of two cylindrical rubber rods, which may be taken as a model of a two-ply cord. Two cases were examined: in the first the rods are initially without twist, while in the second they contain initial twist. The forces measured are the couple about the `cord' axis and the tension along this axis, as functions of `cord' twist and `cord' axial extension. The forces are calculated on the basis of Rivlin's equations for the stresses in a rubber cylinder subjected to combined axial extension and torsion, corrections being introduced for the effects of lateral pressure between `plies' on the tensile force, the non-circularity of section resulting from this lateral pressure on the couple due to torsion and bending, and for the effect of torsion on the bending couple.

For the case of zero initial twist in the rods the agreement between calculated and observed forces is good. When initial twist is present, however, there are significant differences, which are not fully understood.

The finely divided magnetic solids, encountered in dense medium coal preparation and iron-ore beneficiation plants, show a wide variation in their residual magnetism after passage through an alternating current demagnetizer. High residual magnetism is associated with considerable oscillation of the suspended particles in the alternating magnetic field. It is shown that this behaviour cannot be unambiguously correlated with the magnetic properties of the bulked material, and a test based on settling characteristics is preferred as a means of differentiating the materials.

The mathematical expressions for the field intensities external to spheroids or an ellipsoid with uniform magnetization are given. They are useful in predicting fields external to (a) open-structure magnetic devices such as metallic or ferrite films, twistors or splinters, and (b) spheroidal and ellipsoidal samples which are often used in magnetic measurements.

Curves are plotted to indicate the spatial variation of field intensity with the dimensional ratio of a spheroid as a parameter. In the region near the spheroid, field intensity is normalized against field intensity at the boundary. In the region far from the spheroid, field intensity is normalized against that of a dipole of the same dipole strength as the spheroid.

Measurements of the packing of spherical particles poured into a cylindrical container show that the intensity of deposition, the height of drop and the elasticity of the particle material influence the packing equally. Minor departures from perfect sphericity tend to mask the influence of elasticity.

Optimum packing of poured spherical particles occurs when the energy increment imparted to the bed by each impacting particle exceeds a critical value, the rate of renewed application of increments is above a critical value and the intensity of deposition is below a critical level. Within a critical range of deposition conditions, sufficient energy may be imparted to spherical particles to activate a process of ordered packing, initiated at a wall. These conditions are fulfilled when 0.125 in. diameter spheres fill a 3 in. diameter glass cylinder at 1400 particles per second with impact velocities greater than 120/{½(1 + e_m)}¹² in/s, e_m being the resilience of the particle material.

Determinations of wall effect show that these conclusions and the derived mechanism of packing are valid for the packing of an infinitely extensive bed.

Flow experiments give an equation relating to S in terms of measurable quantities, where is the inter-granular porosity of the bed, and S is the envelope surface area of the granules in 1 cm³ of bed. Heywood's shape factors for the granules give a second equation relating to S. Using the two equations and S can be determined uniquely. If the tortuosity factor be taken to be π/2 in the equations given previously (Jones 1956), connecting the friction factor λ and the Reynolds number (Re), then λ = 16/(Re) for granular beds, as for long straight tubes.

A molecular fluorescence method of comparing the thickness of transparent films (in the range 3 × 10^-6 to 10^-2 cm) is described. An instrument for use in the middle of this range (10^-4 cm) is also described and results show that its accuracy is to better than ±2%.

This paper describes the use of an analogue computer to generate certain conformal transformations of the circle, these being of use in the analysis of stress patterns in the neighbourhood of holes of various shapes. The relationship between the form of transformation and the shape produced is also discussed.

Necessary and sufficient conditions for the existence of a simplifying transformation of a set of physical equations are given, whereby the physical variables involved become a less numerous set of dimensionless parameters. The proof provides a method for performing this transformation and for deciding whether it is unique, and this method is described. Whilst such a transformation is always possible for a single physical equation whose form is algebraic, its existence and description is not always apparent when more than one such algebraic equation is affected and the transformation is required to apply consistently to each, or when the equations are not algebraic. The method described is applicable not merely to sets of general equations, but to any collection of power-products of physical variables whose consistent transformation is desired.

In a loaded lamina of complicated shape stress concentrations arise which it is difficult to calculate. A model in the form of an electrolytic tank may be used to find the resultant stress at any point in a loaded lamina. The tank is made of an insulating material in the same shape as the lamina and filled with an electrolyte. It is fitted with electrodes to represent the areas over which the load is applied. The loads are represented in magnitude by the alternating currents flowing through the electrodes and in direction by the relative phase angles of the currents. The electric current at any point in the model tank can be sampled with a probe consisting of two fine wires a short distance apart. The resultant stress at a point in the loaded lamina is proportional to the electric current at the corresponding point in the model tank. This approach offers a valuable addition to means already available for finding stress concentrations in laminae of complicated shape.

Numerous formulae have been given for the calculation of the electromechanical coupling factor of piezoelectric disks in terms of the resonant and anti-resonant frequencies. These formulae, which are derived either on the basis of an analysis of the mechanical motions of a disk, or by considering the equivalent electrical circuit give widely divergent values of coupling factor.

It is shown that when an equivalent circuit which takes account of the overtones is used, the corresponding value of coupling factor obtained is in agreement with that of the mechanical analysis.

Curves, and a nomogram are given to enable coupling factor to be quickly calculated from the equations of the mechanical analysis without approximation.

A technique is described for the staining of germanium p-n-p alloyed junction transistors using chemical deposition of copper. It is shown that copper is deposited preferentially on p-type regions and, in so doing, reveals certain features associated with regrowth processes. Other structural effects which are revealed may be connected with strain induced in the semiconductor by thermal cycling.