**1. Introduction**

The need to reduce greenhouse gas emissions and, due to the Paris Agreement, the need for countries to achieve climate neutrality in the second half of the 21st century have resulted in modifications to structural components. One such change is the production of components with a reduced thickness or cross-sectional area. However, the negative effect of such an approach is the significant impact of even small heterogeneities on the structural strength of the part, which may threaten the safe use of the structure. Therefore, it is necessary to frequently evaluate the structure with nondestructive testing.

Carbon structural steels are the primary construction materials that have a specific chemical composition defined for these varieties, and are delivered in the form of sheets and other rolled products with fixed, typical cross-sections. The chemical composition of structural carbon steels is designed for their intended use. In Europe, the requirements for such steels are specified in the European standard EN 10025. Examples of carbon structural steels are S195, S235, S355, S420, and S460. The letter S in the steel designation indicates "carbon structural steel" and the number following it specifies the minimum yield stress for this steel grade in MPa. The EN 10025 standard defines the yield stress as a value at which irreversible plastic deformation of a rod with a diameter of 16 mm will occur.

In engineering practice, the yield strength is a point on the graph of stress dependence on the strain, which means exceeding the stresses below, with material behaving according to Hook's law. That is, if the stress does not exceed the yield strength, the material behaves

**Citation:** Chady, T.; Łukaszuk, R.D.; Gor ˛acy, K.; Zwir, M.J. Magnetic ˙ Recording Method (MRM) for Nondestructive Evaluation of Ferromagnetic Materials. *Materials* **2022**, *15*, 630. https://doi.org/ 10.3390/ma15020630

Academic Editors: Giovanni Bruno and Christian Müller

Received: 20 November 2021 Accepted: 12 January 2022 Published: 14 January 2022

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perfectly elastic. After exceeding the yield strength, at least part of the deformation of the material will be permanent. The yield strength is a number characteristic for a given material. In practice, it means the maximum stress that a part or structure can carry without permanent damage. For structural carbon steels, this limit is relatively easy to determine.

Carbon structural steels are ferromagnetic and retain their ferromagnetic properties up to a temperature of about 770 ◦C—in this respect, they have properties such as their main component, iron. This distinguishes them from alloy steels in which the Curie temperature strongly depends on other alloying elements present in their composition: Ni, Cr, Mn, Co. This dependency in some configurations of constituents may even lead to the loss of ferromagnetic properties at ambient temperature (e.g., austenitic steels).

The conditions of magnetic materials can be examined in a nondestructive way using the following methods:

The magnetic flux leakage method relies on analyzing changes in the magnetic field distribution around the tested object. Magnetizing the material with an external magnetic field excites the magnetic flux in the material. If the flux encounters any geometrical inhomogeneities with significantly lower permeance, it breaks out of the material and can be registered by the magnetic sensor [1,2]. Flux leakage allows the inspector to localize and identify surface and subsurface flaws [3]. The inevitable advantages of this technique are high efficiency and no requirement for direct contact with the tested object [4,5]. However, it also has some disadvantages, such as susceptibility to the flaw orientation, the need to demagnetize the object after inspection, a sensitivity that is dependent on the distance between sensor and material, and difficulty detecting small and stress-induced changes [6–8].

The Barkhausen noise method is based on the phenomenon occurring in ferromagnetic material. The structure of any such material is made up of magnetic domains separated by domain walls. Each domain contains dipoles oriented in one privileged magnetization direction [9,10]. The external magnetic field will cause the movement of the domain walls. If any inhomogeneities occur in the material's internal structure, the walls change their position discontinuously. This process is accompanied by a sudden change in magnetization and an induction of voltage pulses in the sensor coil [11]. This technique is suitable for detecting surface and subsurface changes, determining grain dimensions or hardness, and assessing stress levels [12,13]. Some benefits of this method include good sensitivity, a simple examination procedure, no requirement for surface preparation, and quick residual stress recognition [14,15]. This method suffers several drawbacks: the necessity of sensor calibration and a non-standardized measurement approach [16,17].

The Magnetic Memory Method is a relatively novel approach to the nondestructive inspection of ferromagnetic materials. It was proposed by Dubov in 1997 [18]. Under the influence of Earth's magnetic field or applied stress, the intrinsic magnetic domains irreversibly change their position and direction [19]. The process of stress influence on magnetic materials has been known for a long time as an inverse magnetostrictive effect or Villari effect [20]. At the core of the metal magnetic memory method is the detection of a self-magnetic leakage field, indicating the inhomogeneities of the internal structure caused by the effect mentioned above [21]. The significant advantages of this method are no requirement to prepare the surface or premagnetize or demagnetize the material, low-cost measurement equipment, simplicity, time-saving inspection procedure, and the possibility to detect and localize the stress zones, thus avoiding a sudden catastrophic accident [22–25]. The disadvantages of this technique include a weak field forcing the use of sensitive sensors and its applicability only if no external, strong magnetic fields act on the material before or during the inspection [25,26].

### **2. Materials and Methods**

The proposed new method for nondestructive testing of magnetic materials is somehow like those discussed in Section 1, particularly the magnetic memory method.

In the case of the proposed Magnetic Recording Method (MRM), the tested object has to be magnetized in a strictly defined way, e.g., quasi-triangular or quasi-sinusoidal pattern. If external factors such as static stresses act on the material, the residual magnetization changes. By analyzing changes in the magnetic field caused by residual magnetization, it is possible to determine the intensity and direction of the structural influences.

The samples used in the experiments were made of structural S355 steel. Due to its beneficial properties and low-cost production, S355 is widely used in modern industry branches such as civil engineering, offshore, shipbuilding, and automotive [27–34]. The chemical composition of S355 is as follows: Mn—1.45, Al—0.33, P—0.23, Si—0.21, C—0.17, S—0.08 [32]. The exemplary magnetic properties of the steel S355 are as follows [35]: a relative peak permeability of 1500, a saturation point of 1.7 T at 6.9 kA/m, a coercive field of 310 A/m, and a residual flux density of 1 T (measured on the major loop).

Each sample was cut out of a hot-rolled plate using a waterjet cutter to avoid jagged metal edges. The shape and dimensions of the samples produced in this way are shown in Figure 1.

**Figure 1.** Sample shape and dimensions with depicted measurement area.

The measuring procedure consisted of four steps. In the first step, the sample was magnetized in a strictly defined manner. The magnetizing element consisted of the magnets configured in the array to generate a quasi-sinusoidal magnetization pattern in the sample. A simplified view of the magnetizing element is shown in Figure 2. It was constructed using 100 neodymium plate magnets, 2 mm high, 15 mm wide, and 30 mm long, made of N38 material, and magnetized in the length direction (30 mm). The material N38 (Nd2Fe14B) has the following magnetic parameters: remanence *Br* = 1.2 T; coercivity *Hcb* ≥ 899 kA/m; coercivity *HcJ* ≥ 955 kA/m; energy density (*BH*) max ≥ 287–310 kJ/m3. The magnets were separated from each other with a tape 0.12 mm thick. On one side (facing the magnetized sample), a 0.8 mm thick PTFE (polytetrafluoroethylene) spacer was glued to the array of magnets to facilitate sliding and ensure a permanent lift-off. The magnetic field in the gap between the magnets and the magnetized sample was 0.97 T. It was measured with a GM08 Gaussmeter manufactured by Hirst Magnetic Instruments (Falmouth, United Kingdom) with a PT7810 Hall effect probe. The array was manually moved above the sample surface with a lift-off of 0.8 mm in a direction parallel to the *y*-axis from one edge to the other edge of the sample (Figure 2). The magnets were moved at a speed of around 5 mm/s. In this way, the plate was magnetized relatively evenly in the *y*-axis direction. If necessary, the uniformity of the magnetization could be improved by using a motorized mechanical scanner.

**Figure 2.** The array of magnets over the sample under magnetization.

In the second step, the magnetic field caused by the residual magnetization of the sample was measured with a three-axis magnetometer (HMC5883L) moved in the *x*- and *y*-directions over the sample surface (lift-off 0.3 mm) in the area depicted in Figures 1 and 2. The third step of the procedure included filtering two-dimensional signals and then averaging, which results in obtaining one-dimensional signals. In the last stage, onedimensional signals were analyzed and their characteristic parameters, such as amplitude and frequency, were determined. A flowchart of the procedure designated for this purpose is shown in Figure 3.

**Figure 3.** The measuring procedure.

In all cases, data measured for selected *y*-coordinates were used for the analysis. The scanning paths were chosen in such a way as to avoid the influence of the edge effect on the calculation of characteristic parameters. The selected signals were used to calculate an average signal. Next, a low-pass, fourth-order, digital Butterworth filter (*f* / *fN* = 0.4, *fN*—Nyquist frequency) was used to remove external interferences of the measured signals. After filtration, the characteristic parameters of the signal were calculated. Several cycles of the signal were selected to determine the signal period, and thus its frequency (Equation (1)):

$$f\_{\text{Ra}} = \frac{1}{T\_{\text{Ra}}} \tag{1}$$

where: *α*—*x*, *y,* or *z* component of the magnetic field, *fBα*—frequency of a given magnetic field component, and *TBα*—magnetic field period of a given component. Then, the windowed central part of the signal (corresponding to the magnetic field measured in the middle part of the sample) was utilized to calculate the mean peak-to-peak value (Equation (2)):

$$\overline{B}\_{app} = \frac{1}{n} \sum\_{i=1}^{n} B\_{app} \tag{2}$$

where: *<sup>B</sup>αpp*—the peak-to-peak value of magnetic field component (*α* could be *x*, *y,* or *z*), *n*— the number utilized in calculations of peak-to-peak values of *B<sup>α</sup>*, *<sup>B</sup>αpp*—mean peak-to-peak value of magnetic field component.

Furthermore, additional calculations: relative mean change in magnetic field (Equation (3)) and relative frequency change in the magnetic field (Equation (4)) were performed to assess the variations in magnetization of the samples after their stress-loading.

$$
\Delta \overline{B}\_{\mathfrak{A}} = \frac{\overline{B}\_{app}^{before} - \overline{B}\_{app}^{after}}{\overline{B}\_{app}^{before}} \cdot 100\% \tag{3}
$$

$$
\Delta f\_{\text{Ba}} = \frac{f\_{\text{Ba}}^{\text{before}} - f\_{\text{Ba}}^{\text{after}}}{f\_{\text{Ba}}^{\text{before}}} \cdot 100\% \tag{4}
$$

where: *α*—could be *x*, *y,* or *z* component of the magnetic field, *Bbef ore αpp* —mean peak-to-peak value of the magnetic field for the non-stressed samples, *Ba f ter αpp* —mean peak-to-peak value of the magnetic field for the samples after tensile loading, *f bef ore Bα* —signal frequency for the non-stressed samples, *f a f ter Bα* —signal frequency for the samples after tensile loading.
