B. de Halleux

Two‐conductor line model: Rapid inversion of eddy current data for foil thickness and conductivity determination

An eddy current method based on the theoretical model of a two-conductor line placed over a plane conductive medium is described. We show the performance of the method in determining thickness and electrical conductivity of foils. The expressions for the vector potential and the coil electrical impedance are obtained in the case when the coil is placed over a thin foil. This theoretical model was applied to measurements of a conductive foil using rectangular coils with finite length-to-width were manufactured. Copper and aluminum foils having thicknesses 15-216 mu m were studied experimentally in the frequency range 5-100 kHz. Theoretical values of the electrical impedance of the coils were compared to those measured. Agreement between theory and experiment was excellent. The method allows the determination of the thickness-conductivity product of a thin foil. Consequently, if the foil conductivity is known, we can find the thickness; and if the thickness is known the conductivity can be found. The inversion procedure, employing the Newton-Raphson method with two variables, namely the thickness-conductivity product and the coil lift-off, takes about 100 ms. Using a simplified formula for a very thin foil the inversion time can be further reduced. The formula gives an error in foil thickness determination of less than 2% when foils are thinner than 100 mu m. The agreement between measured conductivity and thickness and those obtained by other techniques is good. The uncertainty of the conductivity and thickness measurement is typically better than 2%, and often +/- 1% is obtained. The integral relations obtained allow the use of a fast inversion procedure that considerably reduces the time of development of eddy current methods and probes. The excellent agreement between theoretical and experimental results strongly suggests that the model can be used with success in numerous other eddy current applications. With a medium accuracy the model can be applied for eddy current measurements using rectangular coils with a length-to-width ratio as low as 5

Thickness and conductivity determination of thin nonmagnetic coatings on ferromagnetic conductive substrates using surface coils

An eddy current technique for determining parameters of a thin nonmagnetic conductive coating on a ferromagnetic conductive sheet metal is reported. Under several conditions the electrical impedance of a coil is shown to be a function of two independent quantities: the substrate permeability-to-conductivity ratio and the coating thickness-conductivity product. Thus, thickness or conductivity of the coating can be determined independently of the variations of magnetic and electrical properties of the substrate. Simple analytic formulae for the electrical impedance of circular and rectangular surface coils are obtained and applied to predict the behavior of split wound surface coils. The performance of the method was tested in the frequency range 20-100 kHz on 1.5 mm thick low carbon steel sheers coated with 15-45 mu m thick aluminum layers and on two series of 0.75-2.0 mm thick hot dip galvanized low carbon steel sheets of 9-20 mu m coating thickness. The experiment was carried out using printed surface coils of rectangular and circular shape. Agreement between theory and experiment is excellent. The mathematical inversion carried out using the obtained formulae and the Newton-Raphson method takes about 450 ms on a Pentium 133 MHz PC. Discrepancies between the eddy current thicknesses and those obtained by other techniques were typically below 1 mu m. An uncertainty in the thickness or conductivity determination better than 2% is obtained. The method has an extremely low sensitivity to variations in the substrate permeability. A large change in the substrate permeability, implying large changes in the coil electrical impedance, does not significantly influence the determined coating thickness. When the permeability change is about a factor of 10, additional errors in the thickness determination typically do not exceed 0.5 mu m

Thickness and conductivity determination of thin coatings on ferromagnetic substrates in the case of cylindrical symmetry

An eddy current method allowing the determination of parameters of a thin nonmagnetic conductive coating on a ferromagnetic conductive substrate is reported. At a single operating frequency, two independent quantities can be determined: a permeability-to-conductivity ratio of the substrate and a thickness-conductivity product of the coating. Thus, thickness or conductivity of the coating can be determined independent of variations of the substrate magnetic and electrical parameters. A simple theoretical formula for the normalized electrical impedance of the test coil is obtained using asymptotic expansions of Bessel functions. The method was applied to the evaluation of electrogalvanized wires in the frequency range 100 kHz-1 MHz. A set of low carbon steel wires with diameter around 2.2 mm, coated with zinc layers having thicknesses in the range 2.7-64.6 mu m, was investigated using two long coils. Experimental data of the electrical impedance were compared to those predicted. Agreement between theory and experiment is excellent for coatings thicker than 12 mu m. Despite discrepancies between theory and experiment for very thin layers arising from various imperfections of the coating and interfaces, the method was applied successfully in the thickness range below 12 mu m. To do this, two parameters: an apparent conductivity of the coating and a thickness offset, were introduced. The mathematical inversion of the experimental data with the two-variable Newton-Raphson method and the asymptotic formula is extremely fast. The technique developed has an extremely low sensitivity to variations of the ferromagnetic substrate conductivity and magnetic permeability. A magnetizing field of 0-23 000 A/m, producing large variations in the substrate magnetic permeability, does not significantly influence results of the coating thickness determination. The agreement between measured thickness and that obtained by a chemical method is excellent, typically within 0.5 mu m. An uncertainty of the thickness or conductivity determination better than 1% is obtained

Quantitative Nondestructive Evaluation Techniques for Investigation of Very Thin Coatings

Coatings are widely used in industry. They provide good electrical conductivity, wear resistance, thermal and electrical insulation, and corrosion protection. Recently submicron range coatings and sophisticated layered composite structures have emerged from the high technology advanced research. A nondestructive evaluation (NDE) of coatings has an immediate goal to ensure satisfactory properties of coated metals, and save often expensive materials. For this purpose two most powerful methods acoustic microscopy and eddy-currents have been used in industry for many years. Two techniques for NDE of micron and sub-micron range coatings by both methods are given in this paper; performance, advantages and limitations are outlined. There are a number of quantitative acoustic microscopy (AM) methods for investigation of thin layers, in this work one of them is discussed. The Doppler continuous wave scanning acoustic microscope has been used for the evaluation of 0.3–5.0 γm thick titanium nitride coatings on steel substrate. Thickness errors are typically within 10 percent. The method has an obvious advantage for nonconductive coatings and substrates and for coatings only slightly different in mechanical properties from the substrate, as nitrogen implantation hardening layers. This potential of the method has been illustrated on tool steel samples having a 0.2 μm thick nitrogen implantation coating. Eddy currents (EC): Operating at a single frequency, using various coils, thickness of conductive coatings on conductive and nonconductive substrates has been determined. Analytical solutions obtained for long coils and surface coils, are mathematically very compact, and allow a real-time evaluation. Aluminum foils of 32–64 μm thick, 0.3–0.8 μm thick metal films sputtered on nonconductive substrates, 15–45 μm thick aluminum coatings on stainless steel, and 2.8–58.5 μm thick zinc coatings on steel substrate have been measured. Agreement between theory and experiment is excellent. Discrepancies between the eddy current thickness and that determined using other methods are typically within few fractions of micron. Encountered problems with measurements on sub-micron range coatings are reported.

Inversion of Eddy Current Data for Conductive Films and Coatings Thickness and Conductivity Measurement

Eddy current testing is currently used to determine the physical characteristics of a conductive specimen and to detect defects by measurements of electrical impedance of an eddy current probe. In this study we developed two systems of coils allowing to determine properties of conductive coatings and foils. A probe contained two plane rectangular coils connected in series and separated by a fixed distance. A coated plate or a foil was placed between the coils and the coil impedance was measured using a digital impedancemeter. The discussed probe had a large length-to-width ratio and was modeled using the simple two-conductor line model, which express solutions in terms of the integrals containing no Bessel but, only common trigonometric functions, which considerably reduces the inversion time. The method allows reproducible measurements on coated conductive sheets. Aluminum 15–45 μm layers have been measured on steel and stainless steel substrates.

Analytical Solutions to the Problem of Eddy Current Probes Consisting of Long Parallel Conductors

Eddy current testing is currently used to determine conductive specimen physical characteristics and to detect defects by measurements of electrical impedance of an eddy current probe. In general, reliable quantitative NDE requires accurate measurements and a theory to interpret them. In some NDE applications related to coated metals inspection eddy current probes which induce planar or linear currents in a sample are used for flaw detection, thickness and conductivity measurements [1]. For probes of this type, e.g. rectangular or meander like coils, there still exists the need of theoretical modeling.

Eddy Current Evaluation of Flaws in Coated Conductors

Thermal protective coatings find an increasing demand in industry. They are currently used in power generating combustion turbine engines, allowing to rise up significantly the allowing to evaluate the magnitude of a flaws in coated conductor surface from a change in the electrical impedance of an eddy current coil. A theoretical solution is based on the finite difference method (FDM) for the two dimensional vector magnetic potential and electric potential around a coated conductive half space with a long surface breaking crack. The diffusion equation was solved by decomposing the coil field by plane waves and taking into account only the main frequency in the coil spatial frequency spectrum. In order to verify obtained results, experimental modeling was carried out. A set of austenitic stainless steel samples electroplated with 60 and 100 μm tin coatings, containing EDM notches of varying depth from 0 up to 600 μm, was manufactured. The specimens were studied experimentally in the frequency range 100–500 kHz using rectangular shape air core surface coils. Comparison between the experiment and theoretical predictions is given.

Efficient Eddy Current Models for Evaluation of Thin Conductive Coatings on Ferromagnetic Substrates

Eddy current testing is widely used to determine physical characteristics of materials and to detect flaws by measurements of the electrical impedance of an eddy current probe. In this paper two analytical models allowing to determine properties of non-magnetic conductive coatings on ferromagnetic conductive substrates, are reported. Operating at a single frequency, two following quantities can be determined: permeability-to-conductivity ratio of the substrate and thickness-conductivity product of the coating [1, 2]. The method was validated using both long solenoids and air core surface coils, and was applied to the evaluation of zinc coatings on steel wires and sheets. The theoretical solutions given for high arguments are compact, and allow fast inversion, respectively around 400 and 10 ms for a pancake surface coil and for a long encircling solenoid. Two series of samples: O2.2 mm low carbon steel electro galvanized wires and 0.75–20 mm thick hot dip galvanized sheets, were inspected. Steel sheet samples with artificial coatings, as aluminum foils glued from both sides, were also examined. Experimental data of the coil electrical impedance were compared to those predicted. Agreement between theory and experiment is excellent. The technique developed has an extremely low sensitivity to the substrate conductivity and permeability variations [2]. A DC magnetic field, significantly diminishing the permeability of the substrate, almost does not influence results of the coating thickness determination. The agreement between measured thickness and that obtained by other methods is excellent. The accuracy of the thickness determination typically about 1 μ is obtained.

Theoretical and Experimental Study on Ultrasonic Transducers

For ultrasonic quantitative NDE, broad-band transducers with reproducible characteristics are needed. To design this type of a probe, one has to carefully match the electrical, mechanical and piezo-electric parameters of all its components. The most important point for a broad-band probe performance is the matching of a piezo-element with a damper. The main goal of this work was a study of physical aspects of the design of broad band ultrasonic transducers with reproducible parameters taking into account possible variations of geometrical, piezo-electrical and acoustical parameters of all the components. The analysis is based on the known equivalent electrical circuit model.

Classification of Objects by the Analysis of the Acoustic Response to an Impact

In this paper, we present a method which allows classifying objects on the basis of the analysis of the acoustic response to an impact, with the final objective being the quality control in a tile manufacturing company.