# Application of Magnetic Adaptive Testing for Nondestructive Investigation of 2507 Duplex Stainless Steel

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}) [7]. The appearance of the σ-phase dramatically decreases the ductility of duplex stainless steel. Considering that these steels are widely used as construction materials, a nondestructive inspection of this process is of extremely great practical importance.

## 2. Materials and Methods

#### 2.1. Sample Preparation and Hardness Testing

_{0}thickness of the samples was around 10 mm, the w

_{0}width was around 15 mm and the l

_{0}length of the cut samples was 100 mm. The specimens were cold-rolled by a double cylinder rolling machine with a 300 mm diameter. The cold rolling direction was perpendicular to the direction of the hot rolling during manufacturing. In every rolling step, the thickness reduction was 0.25 mm.

_{0}− h)/h

_{0}∗ 100 (%)

#### 2.2. DC Magnetometer Measurements

#### 2.3. Magnetic Adaptive Testing

^{2}, and 18 mm, respectively, corresponding to the sizes of the specimens. For magnetization, an excited coil, which was wound and placed on one of the legs of the yoke, was used. A linear and triangular waveform of the magnetizing field was applied with an amplitude that was increased step by step, generating one minor loop during each step. The magnetizing field that was pumped into the sample was proportional to the magnetizing current.

_{a}, h

_{b}), with a suitably chosen step, Δh

_{a}= Δh

_{b}. If the permeability values determined from the measured permeability loops are used, this is called a permeability, or m, matrix. (Other matrices can also be calculated, such as the hysteresis loops matrix, whose elements include the integrated permeability along the field, h

_{a}). A 3D representation of a permeability matrix is shown in Figure 5. The sweeping magnetizing field, h

_{a}, is given on the X axis and the amplitude of the corresponding minor loop, h

_{b}, is given on the Y axis, while the calculated permeability (from the measured loops) is given on the Z axis.

## 3. Results

_{a}= 100 mA (see Figure 8 at the first arrow, which is close to the maximal permeability of samples), h

_{a}= 100 mA MAT descriptors were calculated at the beginning. Figure 9 demonstrates how the MAT descriptors (m matrices) depended on the temperature of the heat treatments of the seven investigated series of samples, if the matrices were calculated using field values of h

_{a}= 100 mA and h

_{b}= 1300 mA. This MAT parameter offered the largest sensitivity.

_{a}= 100 and h

_{b}= 1300) for the samples having rolling reductions from 0 to 61.9%. A field value of h

_{a}= 100 mA corresponds to the magnetizing field, where the maximal permeability was experienced (see Figure 8). The MAT descriptors of unannealed but differently cold-rolled samples differed significantly from each other. The heat treatments caused a significant reduction in this parameter. This behaviour is clearly different from that shown in Figure 7.

_{a}= 1200 and h

_{b}= 1300) is considered as a function of the temperature of the heat treatment (see Figure 10), another type of correlation can be observed, as shown in Figure 9. The sensitivity is smaller in this case, but the figure is more or less the same as Figure 7. The differences between the magnetic parameters belonging to the rolling reductions of 10.3 and 20.3 are attributed to measurement errors.

_{a}= 1200 and h

_{b}= 1300) MAT descriptors were equal to the saturation induction measured by DC magnetometry, the correlation between MAT descriptors taken from different regions of permeability and saturation inductions is shown in Figure 12. It highlights that if the (h

_{a}= 1200 and h

_{b}= 1300) descriptors are considered, a very good and almost linear correlation exists between these two differently measured magnetic parameters, as shown by the blue triangles in Figure 12. In regions of lower magnetization, the difference becomes more and more pronounced, as shown by black squares in Figure 12. By taking MAT descriptors from the low magnetizing region, (h

_{a}= 100 and h

_{b}= 1300) the difference becomes significant (as demonstrated by the black squares).

_{a}= 1200 and h

_{b}= 1300) MAT descriptors are taken into account, but the different sample series are marked by different colours. The parameter in this figure is the temperature of the heat treatment. The equivalence of (h

_{a}= 1200 and h

_{b}= 1300) MAT parameters and the saturation induction is evident, regardless of the individual samples.

_{a}= 100 and h

_{b}= 1300) m matrix elements are considered by marking the different sample series again with different-coloured symbols. The correlation also seems to be good in this case, but only for those samples that were heat-treated. Samples without heat treatment (T = 20 °C) behaved very differently. These considerations are shown in Figure 14.

_{a}= 100 and h

_{b}= 1300) m matrix elements were found to yield the best correlation between hardness and magnetic parameters. This correlation is shown in Figure 15. Interestingly, cold rolling causes a rapid and significant decrease in hardness if unannealed samples (the black squares) are considered, and there is an almost linear but less pronounced correlation between the magnetic parameters and the hardness due to cold rolling and heat treating at temperatures of 800 and 850 °C. Conversely, the magnetic parameters of the samples hardly seemed to be dependent on the hardness when heat treated at temperatures of 700 and 750 °C. As demonstrated in Figure 15a,b, the actual temperature value of the heat treatment seems to be important (Figure 15a) rather than the value of deformation (Figure 15b).

_{a}= 1200 and h

_{b}= 1300) are used for the magnetic characterization of the material, the correlation with the hardness is different, as shown in Figure 16. The difference in the MAT parameters vs. the hardness values is significant in the cases of deformed but unannealed samples.

_{a}= 1200 and h

_{b}= 1300) m matrix elements.

_{a}= 100 and h

_{b}= 1300) m matrix elements are demonstrated better, if—for illustration—the two groups of samples are considered separately. This is illustrated in Figure 18, where the MAT descriptors are shown for cold-rolled but unannealed samples (Figure 18a) and for cold-rolled samples annealed at a temperature of 800 °C (Figure 18b). The regression factors of the linear fit are also indicated in the graphs.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A specimen set. It contains an initial sample and six differently cold-rolled samples. All of them were heat-treated at 800 °C for 30 min.

**Figure 3.**Block diagram of the MAT measuring system: The soft magnetic yoke (grey) magnetizes the blue tested object via the red driving coil (through the green non-magnetic thin spacers; this spacer is not necessary in all measurements) using a series of minor hysteresis loops with increasing amplitudes. The yellow sensing coil picks up the resulting signal, which carries information on the actual differential permeability, µ, of the closed magnetic circuit (and, thus, on the quality of the tested object). The amplitude at which the signal displays the top sensitivity with respect to the material quality of the object is singled out as the most responsive MAT measurement.

**Figure 6.**DC magnetization curves of undeformed heat-treated samples: saturation polarization vs. magnetic field.

**Figure 7.**Saturation polarizations of all samples as a function of the temperature of the heat treatment. The parameter is the rolling reduction.

**Figure 9.**(h

_{a}= 100 and h

_{b}= 1300) MAT descriptors of all samples as a function of the temperature of heat treatments. The parameter is the rolling reduction.

**Figure 10.**(h

_{a}= 1200, h

_{b}= 1300) MAT descriptors of all samples as a function of the temperature of the heat treatment. The parameter is the rolling reduction.

**Figure 11.**Modification of MAT descriptors as functions of rolling reductions for two annealing temperatures.

**Figure 12.**m matrix elements taken from four areas of permeability as functions of the saturation polarization. In this figure, all measured points are taken into account.

**Figure 13.**(h

_{a}= 1200 and h

_{b}= 1300) m matrix elements for all samples, indicating the actual heat treatments as functions of the saturation polarization.

**Figure 14.**(h

_{a}= 100 and h

_{b}= 1300) m matrix elements for all samples, indicating the actual heat treatments as functions of the saturation polarization.

**Figure 15.**(h

_{a}= 100 and h

_{b}= 1300) m matrix elements for all samples, indicating the actual heat treatments as functions of the hardness (

**a**) and indicating the actual rolling reductions (

**b**).

**Figure 16.**(h

_{a}= 1200 and h

_{b}= 1300) m matrix elements for all samples, indicating the actual heat treatments as functions of the hardness.

**Figure 17.**Saturation polarizations of all samples, indicating the actual heat treatments (

**a**) and the rolling reductions (

**b**) as functions of the hardness.

**Figure 18.**(h

_{a}= 100 and h

_{b}= 1300) MAT descriptors as functions of the hardness if the two groups of samples are considered separately, as follows: cold-rolled but unannealed samples (

**a**) and samples that are cold-rolled and annealed at a temperature of 800 °C (

**b**).

Fe | C | Mn | S | P | Si | Cu | Ni | Cr | Mo | Nb | N | Ti |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Rest. | 0.021 | 0.822 | 0.0004 | 0.023 | 0.313 | 0.178 | 6.592 | 24.792 | 3.705 | 0.008 | 0.264 | 0.005 |

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**MDPI and ACS Style**

Vértesy, G.; Mészáros, I.; Bögre, B.
Application of Magnetic Adaptive Testing for Nondestructive Investigation of 2507 Duplex Stainless Steel. *Sensors* **2023**, *23*, 3702.
https://doi.org/10.3390/s23073702

**AMA Style**

Vértesy G, Mészáros I, Bögre B.
Application of Magnetic Adaptive Testing for Nondestructive Investigation of 2507 Duplex Stainless Steel. *Sensors*. 2023; 23(7):3702.
https://doi.org/10.3390/s23073702

**Chicago/Turabian Style**

Vértesy, Gábor, István Mészáros, and Bálint Bögre.
2023. "Application of Magnetic Adaptive Testing for Nondestructive Investigation of 2507 Duplex Stainless Steel" *Sensors* 23, no. 7: 3702.
https://doi.org/10.3390/s23073702