Analysis of incremental and differential permeability in NDT via 3D-simulation and experiment

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Highlights

  • In this paper, both NDT incremental and differential permeability methods are simulated via a 3D-FEM modeling taking into account the vector electromagnetic properties of the material.

  • In addition, the dynamic magnetic hysteresis behavior at different operating points is suggested.

  • Analytical algorithms of both permeabilities are described and assessed by comparison to experimental data.

  • The last section is dedicated to the challenges and steps of FEM modelling.

  • The simulated signals are compared and commented as a first validation.

Abstract

This paper investigates differential and incremental permeability in non-destructive testing application, evaluated by two different technologies, 1) using a ‘’yoke probe head’’ principal, via a surrounding coil; and 2) via a local receiver coil situated over the sample. The detected signals are simulated using 3D non-linear finite element method. The dynamic vector hysteresis nature of the ferromagnetic part is considered. The incremental permeability is calculated analytically and the profile is compared to measurement data. The FEM computed signals of both NDT technologies are compared to the experimental results, and show good agreement.

Introduction

The growing demand for new production applications requires fast and reliable control of quality-related material properties. Usually these investigations are realized in laboratory. Several measuring techniques are used; such as optical and electron microscopy for microstructure analysis and destructive testing methods for the determination of mechanical targets like: tensile strength, elongation, hardness, etc. The increasing production rate constraints to use NDT devices in production scale, which allow 100 percent test time in order to monitor manufacturing processes, with the goal to enhance the final components [1]. Many equipment’s and variants of electromagnetic sensors have been developed such as eddy current multi-frequency analysis [2], [3], yoke probe head design [4] and a surface sensor U-shaped yoke [5]. The final aim is to develop functional dependency between micromagnetic measuring quantities and microstructural features and, or material properties (calibration). The complexity of nowadays materials and components requests innovative developments, which are often very consuming in terms of time and money. This explains why the use of NDT techniques remains limited. For this reason, it is necessary to develop analytical and numerical tools in order to predict the a priori electromagnetic behavior of the material in different inspection situations and to reduce the experimental efforts in order to accelerate new developments.

The numerical modelling of incremental permeability methods started in 2009 in the framework of ANR-DSPMMOD (French research project). The aim was to reproduce the electromagnetic signals of incremental permeability in dual-phase steel applications under inline conditions [6]. The conventional simulations were limited due to the time calculation and became complex when taking into account the dynamic hysteresis behavior. A more comfortable and elegant calculation strategy was developed. The time calculation is reduced by a factor of 6 and the computed signals were confronted to measurement in case of dual-phase steel inspection [7]. Later, the research focused on the development of a robust FEM platform for electromagnetic NDT methods, on behalf of the European Symposium research funding. The main results led to an assessment of the numerical NDT tool for a broad range of applications [8]: residual stress [9], hardness of press-hardened parts [10], characterization of the cutting edge of electrical steel [11]. In this context, several improvements were realized especially in magnetic material properties description. Based on the material operating points, the scalar Jiles-Atherton hysteresis formula was selected to describe the magnetic response at each excitation level, via one set of identified parameters. The Bertotti model for dynamic scalar hysteresis, based on losses separation is then proposed [12].

Several experts have been interested by modelling of incremental permeability via 3D non-linear hysteresis integral method [13], where the authors have stated the limit of the model to the quasi-static and high-level excitation amplitude inspection conditions. Other studies have shown possibility to simulate incremental permeability via reduced vector potential formula [14]. Good tendency is found between measurements and modelling. Other simplified simulations, based on a reluctance/impedance lump type modeling typography have been used [15]. The authors have simulated IP-signals for aged 12 Cr-Mo-V-W steel by neglecting the dynamic effect of AC magnetic field. Such modelling is limited to the description of homogeneous magnetic material.

In this paper, both NDT incremental and differential permeability methods are simulated via a 3D -FEM modeling taking into account the vector electromagnetic properties of the material. In addition, the dynamic magnetic hysteresis behavior at different operating points is suggested. Analytical algorithms of both permeabilities are described and assessed by comparison to experimental data. The last section is dedicated to the challenges and steps of FEM modelling. The simulated signals are compared and commented as a first validation.

Section snippets

Analytical calculation of H(B) in dynamic condition

In regards to FEM vector dynamic simulation, the Jiles-Atherton (J-A) is the most attractive model from numerical calculation side in terms of time computation and memory space. In a first step, the scalar inverse H(B) formula is applied [16]. The J-A equations are considered:dMdB=(1-c)dMirrdBe+cdManhdHe1+μ0(1-α)(1-c)dMirrdBe+c(1-α)dManhdHewhere Manh is the anhysteretic magnetization provided by Langevin’s equationManh=MscothHea-aH

  • -

    The Weiss magnetic effective field: He=H+αM

  • -

    Mirr is the

Inspection situations

The sample is magnetized via a single ferrite yoke with the inner and the outer pole distances of 20 mm and 50 mm and with the parameters given in Table 2. The gap between yoke and the specimen is set to 50 µm. The magnetization coil is wound around the yoke (see Fig. 4). The role of each element depends on the used technology.

  • Technology I (Fig. 4.a): it is a yoke probe head concept, where the sample is subjected to superimposed alternating voltage signals under following characteristics: LF(V,f

Conclusion

The selected numerical hysteresis model is able to reproduce the dynamic magnetic behavior of the ferromagnetic parts for various amplitudes and frequencies with high accuracy. The local analytical IP is calculated via J-A formula and validated by comparison to experiments.

The isotropic 3D vector model shows agreement between simulated and measured signals for both NDT technologies. Based on these results, the robustness of the developed 3D FEM tool is proven. Further works are planned for

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported in part by European Commission - Research Fund for Coal and Steel program, under grant agreement N° RFSR-CT-2015-00012, and by German research foundation (DFG), under the program SPP 2086 (SCHU 1010/65-1, LA 2351/46-1, WO 903/4-1).

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