The experimental magnetic susceptibility curves of several soft steel grades, like interstitial free (IF) or low carbon (LC) steels, can be interpreted within the framework of universal scaling functions obtained for systems with quenched disorder, such as the one described by the random field Ising model with supercritical disorder. Mean-field theory (both scalar and site-dependent) is used to explore the behaviour at the proximity of the coercive field, and explicit expressions are derived. As a result, the susceptibility values close to the coercive field can be approximated to a good extend by a Lorentzian function. Theoretical results are compared against a number of experimental curves obtained from interstitial free (IF) and extra low carbon (ELC) steels subjected to isothermal annealing.

We report a comprehensive experimental study to analyze the limiting factors and physical mechanisms that determine the achievable performance of transverse magneto-optical Kerr effect (T-MOKE) ellipsometry. Specifically, we explore different approaches to achieve high sensitivity and reduced acquisition times. The best sensitivity is observed for an incident light polarization with balanced s-p components. We also verify experimentally that the method's theoretical description is accurately describing data for any s-p combination of the incoming light. Furthermore, two alternative measurement strategies are explored by using different measurement sequences for the polarization sensitive optics, which both achieve a very comparable, high quality of results. Signal-to-noise ratios and systematic deviations are measured and analyzed based on a large number of nominally identical measurement repeats, both for entire signal sequences as well as for individual Fourier components of the magneto-optical signal generated by a sinusoidal magnetic field sequence. Hereby, we observe that while higher order Fourier components have a significantly reduced signal amplitude and correspondingly exhibit reduced signal-to-noise and repeatability performance, signal-to-noise ratios always exceed values of 100 even for the lowest signal Fourier component and the lowest signal sample that we investigated, illustrating the extremely precise nature of T-MOKE ellipsometry.

A new technique to calculate an equivalent indirect hysteresis loop, B-ec-H loop, from the distortion of the voltage measured in the magnetic excitation coil is proposed. The aim is to facilitate the industrial implementation of magnetic characterization reducing hardware and error sources of the measuring system, as pick-up coils and their conditioning stages are not necessary. With the B-ec-H technique, the characterization of two sets of materials with very different properties using a simplified electromagnetic system has been achieved. Specifically, the change in the microstructure of annealed low-carbon steel samples was monitored and the hardness of ultrahigh steel sheets was characterized. Moreover, the conventional hysteresis cycles and Bec-H loops are compared, and the obtained lineal relationships between the parameters derived from conventional hysteresis and B-ec-H loops verify that the B-ec-H loops can provide equivalent parameters for magnetic characterization of steel samples as conventional hysteresis loops.

The distortion analysis of magnetic excitation (DAME) method has been recently proposed to facilitate magnetic measurements for non-destructive testing in which pick-up coils are not necessary. This method is based on the distortion effect that the permeability of the sample generates on the voltage across the excitation coil. The aims of the method presented in the present paper are to amplify this distortion effect using a current mode-controlled magnetization and to extract a distortion signal, of high signal-to-noise ratio (SNR), from the voltage measured in the excitation coil by means of a demodulation technique. This methodology is applied to different skin passed steels to characterize the elongation level, which is still a challenge for conventional non-destructive electromagnetic techniques. The relationships between the parameters derived from the distortion and from the hysteresis are studied. Measurements according to the DAME method are performed to verify the improvement in sensitivity for magnetic characterization.

The equivalent indirect hysteresis cycle (B-ec-H cycle) obtained from the distortion of the voltage measured in the excitation coil facilitates the implementation of magnetic nondestructive characterization systems reducing hardware and error sources, as pick-up coils and their conditioning stages are not necessary. The aim of this article is to propose a sine-fitting (SF) algorithm in order to obtain the B-ec-H cycles for nondestructive testing applications. Although the parameters of B-ec-H cycles are not an accurate measurement of magnetic properties, they are equivalent to those of the indirect hysteresis cycles and thus are sensitive to different material processing variables. The B-ec-H cycles of low carbon, dual phase, and ultrahigh strength steels obtained using SF and synchronous demodulation (SD) algorithms are compared. The parameters of B-ec-H cycles obtained using the SF algorithm evidence greater sensitivity to material processing variables and are linearly correlated with parameters of indirect hysteresis cycles.

This experimental study demonstrates that with transverse magneto-optical Kerr effect (T-MOKE) ellipsometry, it is possible to determine the magneto-optical and magnetic properties of insertion layers, even if they are superimposed onto much larger magnetic signals from the surrounding structure. Hereby, it turns out to be especially valuable that with T-MOKE ellipsometry one has full and precise quantitative access to the complex value of the magneto-optical reflection matrix component (beta) over tilde, because small magneto-optical insertion layer signals do not necessarily increase the absolute size of (beta) over tilde, but can lead to observable phase changes of this complex quantity instead. We demonstrate the ability of T-MOKE ellipsometry to precisely detect such small effects and hereby allow for an accurate determination of the alloy concentration dependent onset of ferromagnetism in ultrathin CoxRu1-x insertion layers, that are embedded into a much thicker ferromagnetic structure. In addition, a detailed and quantitative signal analysis allowed us to demonstrate that the CoxRu1-x insertion layers in our samples exhibit a magnetization reversal behavior that is independent of the adjacent Y3Fe5O12 layers, clearly indicating that both magnetic entities are either not or only very weakly coupled.

In this work, two different parametric hysteresis models, the Jiles-Atherton model and the Mel'gui relation, have been combined to form a more general hysteresis operator, suitable for the description of families of experimental B(H) curves obtained for low carbon (LC) steel specimens after isothermal annealing at different temperatures and times. As it has been demonstrated in a number of previous studies, characteristic values of steel hysteresis curves can be used as very efficient identifiers for the monitoring of the different metallurgical transformations that take place during the annealing, such as recovery and recrystallisation processes. It is thus important from a practical point to be able to reproduce the experimental curves obtained under different conditions, as precisely as possible, in order to proceed to the samples characterisation. Hybridisation of the two aforementioned models demonstrated satisfactory results for the reproduction of all considered curves obtained under the different considered annealing conditions.

We present a new methodology that enables a significant sensitivity improvement for transverse magneto-optical Kerr effect (T-MOKE) detection. For this purpose, we developed a novel measurement scheme, in which the polarization detection conditions are changed during the measurement sequence in a pre-defined way. An analytical expression of the associated T-MOKE signal pattern was derived, which allowed us to analyze and classify our experimental data in a straightforward way. Furthermore, this new measurement approach enables the identification of noise and false background signals that might be generated by the sample under investigation, the environment or the detection system itself and it provides a pathway to unambiguously separate all these effects from true T-MOKE signals. These capabilities significantly increase the sensitivity and robustness of T-MOKE detection. The method enabled us to measure magneto-optical signals for samples that are paramagnetic at room temperature or exhibit really small magneto-optical responses, even in the presence of false signals that were far larger in size. Our new methodology was integrated into a scanning wafer tool, which allows for nondestructive, laterally resolved surface characterization measurements and even has the capability of measuring optical and magneto-optical properties simultaneously.

Using nondestructive techniques to quantitatively estimate residual stresses along the depth is necessary to improve the ability to predict the real fatigue life of pieces for many applications. Magnetic Barkhausen noise has been proven to successfully estimate the residual stress at the surface produced by machining, plastic deformation, phase transformation or surface treatments such as shot peening, also allowing one to obtain information of the residual stress depth-profile in shot peened pieces which presented similar depth-profile shapes. However, residual stress depth-profiles with nonmonotonic or different shapes have not been successfully estimated. In the present study, an extended approach is developed in order to estimate these stresses independent of the shape of the residual stress depth-profile. The approach proposed here improves an existing model of the Barkhausen noise spectrum (Kypris-Jiles model) by adding the effect of the attenuation of the applied magnetic field on the Barkhausen noise. This extended approach is used to estimate the residual stress depth-profiles of samples with different depth-profiles using a calibration process. The approach is validated by estimating the residual stress depth-profiles, with errors smaller than 70 MPa in a depth of 130 mu m, in all the samples studied.

The meta-modelling approach based on an adaptive sparse grid interpolator is proposed for tackling the identification problem of parametric hysteresis models for steels with different microstructures. Parametric models of Jiles-Atherton and Mel'gui, respectively, have been considered in this work. The main advantage of the present approach is the separation of the calculation procedure in a computationally demanding off-line phase, which has to be carried out only once, and a very fast on-line evaluation. This decomposition is particularly interesting when a large amount of successive evaluations has to be carried out. Especially in the case that we are interested in a particular family of ferromagnetic materials (e.g. steels subjected to different treatments), where the sought parameters are lying in a specific interval, a single meta-model may be sufficient to be used for the study of a wide range of specimens. The steel samples considered in this study have been obtained from industrially produced low carbon steel, 84% cold rolled, and isothermally annealed in laboratory.