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Eddy current (EC) sensors placed in the vicinity of a rail track and sensitive to passing train components are safety-critical components commonly used in the railway sector. From the engineering point of view they form a system with numerous variables including their geometry, the lift-off, magnetic properties of the applied materials, the operating frequency and electrical characteristics of the built-in circuits. Although some simple configurations of the EC devices have been studied experimentally, numerically and analytically, there have so far been no universal algorithm allowing for predicting, understanding and optimizing output signals for arbitrarily device/track/wheel characteristics. A significant step towards such an universal algorithm is presented in this work, combining a linear 3D finite element modelling and a set of analytical formulas derived directly from the constants of the resonance circuit. Functions correlating the magnetic induction space/time characteristics with the circuit outputs are proposed and validated against experiment in three stages: (a) by determination of the signal from a flat thin FeSi plate (i.e. in fully controlled laboratory conditions), (b) by laboratory measurements of a highly degraded rail with uncertain material properties, (c) by tests of a commercial EC wheel detector, with reference to averaged service data. The proposed methodology can be extended to any NDT field where EC devices are applied.

The paper contains an original comprehensive review of finite element analysis (FEA) applied by researchers to calibrate and improve existing and developing electromagnetic non-destructive testing and evaluation techniques, including but not limited to magnetic flux leakage (MFL), eddy current testing, electromagnetic-acoustic transducers (EMATs). Premium is put on the detection and modelling of magnetic field, as the vast majority of ENDT involves magnetic induction, either as a primary variable MFL or a complementary phenomenon (EC, EMATs). FEA is shown as a fit-for-purpose tool to design, understand and optimise ENDT systems, or a Reference for other modelling algorithms. The review intentionally omits the fundamentals of FEA and detailed principles of NDT. Strain-stress FEA applications in NDT, especially in ultrasonography and hole-drilling methodology, deserve as well a separate study.

The magnetic Barkhausen effect is useful for assessing 1D and 2D stress states of ferromagnetic steel objects. However, its extension to technically important materials, such as duplex anisotropic steels, remains challenging. The determination of magnetisation inside the studied object and the electromagnet for various geometries, materials and magnetisation angles is a key issue. Three-dimensional, dynamic finite element analysis has been applied to reproduce time-varying fields inside and outside the prototype of a double-core magnetising setup. Useful relationships between characteristics (peak height and location) and magnetic induction vector have been proposed. The qualitative plausibility of simulation has been validated with an experiment and an analytic formula of skin depth. The angular anisotropy of magnetic Barkhausen effect (MBN) in an isotropic sample has been shown in simulation and confirmed experimentally. The numerical model, despite some limitations, seems to be an efficient tool for calibrating stress/MBN relationships at least in isotropic structural steel components.