Novel Techniques in Phase Transformation Characterization in Superduplex Stainless Steel UNS S39274

Abstract

Super duplex stainless steels (SDSS) have a microstructure composed of approximately equal fractions of ferrite and austenite. However, depending on the chemical composition and thermomechanical conditions, precipitation of deleterious intermetallic phases may occur, compromising their properties. This work investigated the influence of isothermal aging time and temperature on the phase transformation of a super duplex steel subjected to heat treatments at 700°C, 800°C and 900°C, for 1 and 2 hours, with water cooling. Initially, all samples were solubilized at 1100°C for 30 minutes for microstructural homogenization. The innovative scanning magnetic microscopy (SMM) technique was used to access variations in remaining magnetization, whose application in steel phase detection has received relatively limited attention in the literature. However, the image processing in SDSS proposed in this work had not yet been reported in the literature, giving the study a pioneering character. Since variations in magnetic properties can result from microstructural changes, this technique, although still requiring further experimentation, presents interesting results. For validation, the results were compared with established methods, such as ferritoscope, vibrating sample magnetometry (VSM), X-ray Diffraction (XRD) and optical microscopy (OM). The results demonstrate that increasing the aging time and temperature promotes a significant reduction in the ferrite fraction (ferromagnetic), accompanied by the dispersed formation of the σ phase and partial transformation into austenite (paramagnetic). Differences between the characterization methods, especially at advanced stages of aging, suggest the possible presence of intermetallic deleterious phases or finely dispersed carbides. As a main result, magnetic techniques are promising for the thorough processing of SDSS.

Keywords:
Superduplex stainless steels; Alpha line phase; Phase transformation; Magnetic microscope; X-ray diffraction

1. Introduction

Superduplex stainless steels (SDSS) are widely used in the oil and gas industry in components such as pipelines, risers, and manifolds. The optimum microstructure is composed of ferrite (δ) and austenite (γ) in an approximate 1:1 ratio, giving them excellent stress corrosion resistance and relatively high mechanical strength when compared to other corrosion resistance alloys. For example, SDSSs can reach yield strengths up to 550 MPa with ultimate tensile strength above 800 MPa in the annealed condition¹,². Cold worked SDSSs can have much higher yield strength, as in cold drawn pipes for tubullars and cases used in oil subsea wells with yield strength higher than 900 MPa¹,³. An important classification criterion for these steels is the PRE (Pitting Resistance Equivalent), whose values in superduplex stainless steels exceed 40, indicating high corrosion resistance⁴. This is due to the high concentration of Cr, Mo, and N and their fine distribution in the microstructure, justifying the use of SDSSs in aggressive environments, such as offshore platforms. However, factors such as phase disequilibrium, and the presence of intermetallic phases rich in chromium (Cr) and molybdenum (Mo) compromise these properties⁵. When free of these secondary phases, denatured duplex stainless steels exhibit high toughness, good weldability, mechanical strength, and corrosion resistance⁶. Such deleterious phases can occur between 350 °C and 1000 °C during isothermal aging⁷, inadequate heat treatments, or processes such as welding⁸, especially at temperatures near 475 °C⁹. Commonly cited deleterious phases are σ, Cr₂N, CrN, secondary austenite, χ, π, G, R, M₇C₃, M₂₃C₆, ε(Cu-rich phase) and τ, largely due to the instability of ferrite. Among these, σ and χ phases are the most dangerous because provoke rapid decrease of mechanical and corrosion resistance properties. The σ phase is a Cr-rich intermetallic also rich in elements such as Mo, Si and W. The interval of temperatures in which σ phase can be formed in SDSSs is large, frequently referred as 600-1000^oC in published TTT diagrams¹⁰-¹². It precipitates from the ferrite phase in reactions involving direct conversion (δ→σ) or involving other phases (δ→χ→σ, δ→σ+γ₂), depending on the temperature. The elements that favor the kinetics of these reactions, notably Cr, Mo, Si and W, are more concentrated in the ferrite phase.

The χ phase is a Mo-rich intermetallic also rich in Cr. It is considered metastable in some references, since its replaced by σ for long aging periods of time (δ→χ→σ), The interval of χ formation is frequently referred to as 700-900^oC¹³,¹⁴ in Mo rich SDSSs. The detection of intermetallic phases in SDSSs requires sensitive techniques, such as SEM combined with EDS and XRD. Among these phases, σ is the most critical due to its negative influence on hardness, ductility and corrosion resistance. The formation of the σ phase can occur in just 5 minutes, between 850 °C and 900 °C, and its mechanism involves nucleation followed by rapid growth. As it is the most common and harmful among the intermetallic phases, its formation is widely studied mainly due to its deleterious effects in toughness and corrosion resistance¹⁵.

Finally, considering the facts mentioned above, this study proposes the development of a method based on scanning magnetometry (SMM) with a Hall sensor, aiming at the detection of changes in remaining magnetization in the test samples that might be related to phase transformations, including the formation of deleterious ones such as σ. The application of SMM in steels is still recent, with little documentation available¹⁶-²¹. For validation, techniques consolidated in the literature were also used, allowing comparison of the results, consisting of SEM, XRD and ferritscope. Heat treatments were applied intentionally to induce imbalances and increase the contrast between the phases. As an innovative aspect to be addressed in the present paper consists in the image processing by means of the ImageJ using the in-built Trainable Weka Segmentation (TWS) tool²². TWS has become a highly effective way of automating image analysis workflows. This one-stop-shop solution pairs the adaptability of machine learning with intuitive interfaces (GUI) inside the ImageJ to solve sophisticated segmentation problems in a broad diversity of scientific fields²³-²⁷. Basically, TWS utilizes a set of the supervised machine learning methods that cast segmentation as a pixel classification problem. Users get involved in the training by annotating a few images manually, delineating regions of interest (ROIs) for various classes or materials. The system automatically derives features from the annotated training instances and learns a classifier to automatically label the remaining pixels in the data. This approach allows researchers to outline complex datasets that can often present artifacts due to scanning procedures and material heterogeneity. Moreover, one has the ability to progressively improve the segmentation by providing corrections to the output of the selected classifier. TWS performs competitively with other ML-based segmentation techniques, particularly in niche scientific domains where flexibility and user accessibility are of utmost importance. Unlike raw pixel-based approaches, TWS employs filters, such as Gaussian blur, Sobel, Hessian to enhance discriminative features, segmenting low-contrast structures more effectively. The only restraints to be emphasized are related to scalability which is less effective compared to GPU-accelerated deep learning on big datasets, and TWS’s performance strongly relies on manual feature and filter selection, unlike end-to-end deep learning. Particularly, in the present paper, the segmentation of the multiple SMM images was performed with classification of the area fractions (%) by magnetic and non-magnetic regions to suggest an initial correlation to the different phases and the obtained results were compared to those from the instrumental analytical methods listed in the ‘Materials and Methods’ section.

2. Materials and Methods

The material analyzed was a SDSS grade UNS S39274, with the addition of tungsten (W) from a cold drawn tube. The chemical composition of the material can be seen in Table 1, having been obtained by optical emission spectroscopy and combustion method (only for N, C and S) ²⁸.

Table 1
Chemical composition (wt %) of steel UNS S39274²⁸.

Chemical composition (wt %)
Cr	Ni	Mo	W	S	P	Mn	Cu	Si	N	C	Fe
24.79	6.60	3.22	1.75	0.002	0.017	0.55	0.51	0.332	0.2550	0.028	Bal.

Eight samples were obtained in the as-received cold drawn (CD). Seven of these samples were subjected to solution heat treatment in a furnace with an inert atmosphere (argon) at 1100 °C for 30 minutes, followed by rapid cooling in water, with the aim of homogenizing the microstructure. Table 2 shows the identification of the test specimens according to their respective heat treatment conditions. These conditions were selected to create samples with varying magnetic phase fractions, allowing evaluation of the new technique.

Table 2
Identification of test specimens by heat treatment condition.

Heat Treatment Condition		UNS S39274
As received		AR
Solubilized at 1100°C for 30 minutes and cooled in water S1100-30	Aged at 700 °C for one hour and cooled in water	A700-1
	Aged at 700 °C for two hours and cooled in water	A700-2
	Aged at 800 °C for one hour and cooled in water	A800-1
	Aged at 800 °C for two hours and cooled in water	A800-2
	Aged at 900 °C for one hour and cooled in water	A900-1
	Aged at 900 °C for two hours and cooled in water	A900-2

For metallographic characterization, electrolytic etching was applied under constant voltage of 3 V in an aqueous solution containing 15 g of sodium hydroxide (NaOH) per 100 mL of distilled water (13.0 wt.% NaOH). The etching time was approximately 15 seconds. The process was interrupted by washing with running water, followed by drying the surface by evaporation with absolute ethyl alcohol, assisted by a jet of hot air. The images were obtained through optical microscopy (OM). The obtained optical micrographs were transformed into the gray-scale (8-bit) to extract Haralick’s textural dimensionless features (Contrast, Correlation, and Entropy), responsible for the pixel organization throughout the recorded images. Haralick’s attributes were obtained at 0, 90, 180 and 270° directions on each image (1 px step)²⁹-³¹.

The mentioned descriptors are derived from the Gray-Level Co-occurrence Matrix (GLCM). This is a statistical technique developed for the examination of the spatial relationships of pixels in an image. The GLCM tabulates frequency of pairs of pixel values occurrence at a specified distance and direction. This, in turn, forms the basis to compute and, eventually, quantify texture.

In particular, the Equation (1) it dealt with the contrast feature is useful at analyzing transition areas, i.e. intensity differences between neighbor pixels and local variations in gray levels in the 8-bit images:

${{\displaystyle \sum }}_{k=0}^{N_g-1}{k}^2{p}_{x-y}\left(k\right)$ (1)

High values ​​of Entropy (See Equation 2) are responsible for the highly disordered and complex surface with varied transitions. Low entropy speaks for the surface to be interpreted as more uniform:

$-{{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_g}p\left(i,j\right)\log \left(p\left(i,j\right)\right)$ (2)

Finally, (see Equation 3) correlation is of the key importance discussing patterns found in images. Highly organized repetitive structures correspond to high values of this attribute, whereas a tendency to randomness is reflected through lower values:

$\frac{{{\displaystyle \sum }}_{i=1}^{N_g}{{\displaystyle \sum }}_{j=1}^{N_g}\left(ij\right)p\left(i,j\right)-{\mu }_x{\mu }_y}{{\sigma }_x{\sigma }_y}$ (3)

N_g – the number of gray levels; i and j - gray-level values of a pair of pixels. i is the gray level of the reference pixel, j of the neighboring pixel separated by a specified distance and direction (angle); $p\left(i,j\right)$ – the normalized GLCM entry, probability of the pair (i,j): $C\left(i,j\right)/R$, where R is the total number of pixel pairs. In symmetric GLCMs, which is applied in ImageJ, each pair contributes twice, so R = 2 ☓number of pairs. As for $C\left(i,j\right)$, it is the count of how many times a pixel i is neighbored by a pixel j (at the given distance and direction).

$p_{x-y}\left(k\right)$is the probability distribution of the absolute difference of gray levels i and j, where k = |i - j| ranges from 0 to N_g-1).

${\mu }_x{\mu }_y$ are the means of the marginal distributions (row and column sums of the GLCM), which are often identical in symmetric GLCM.

${\sigma }_x{\sigma }_y$ - standard deviations of the marginal distributions.

The logarithm $\log \left(p\left(i,j\right)\right)$ is base-2 with an added small constant, e.g. C = 10^-7 to avoid log(0).

Measurements of local magnetic fields near the surface of the samples were performed by Scanning Magnetic Microscopy (SMM), using two ANC-150 piezoelectric stepper motors (Attocube Systems) arranged horizontally structure developed by Lima et al.³². These motors allowed the precise displacement of the samples under the mounted Hall sensor, according to the Chaves et al.³³. The Hall sensor was positioned vertically (Z axis), fixed at a height (h) from the sample surface, varying from 0.2 to 0.4 µm. This sensor was coupled to a mobile support with movement capacity in the XY plane, enabling scanning of the region of interest. The maximum scanning area was 500 x 500 µm, with a minimum resolution (scanning step) of 10 µm in the X and Y directions. The decision to choose a step of 10 µm was due to the fact that the reading area of the Hall sensor is 200 µm², and for step values smaller than this the measurement time increases exaggeratedly, yielding similar results. During the scanning process, the Z component of the magnetic field was recorded as a function of the XY coordinates of the sample surface. To mitigate external interferences, such as the Earth's magnetic field (~500 mG) and power grid noise (~5 mG, 50 Hz), all measurements were performed inside a magnetic shielding capsule made of µ-metal, with an attenuation factor greater than 500³³,³⁴. It’s important to state that during the scanning process, no external magnetic field is applied to the sample. After data acquisition, it is crucial that, before the analysis process, the data is processed with the aim of eliminating noise and making the signal measurable. For this purpose, a program was developed in MatLab®, identified as “Mapper”. The Mapper program was previously used and described in³³-³⁵. The total number of the collected images was 65 (Figures S1-S5, Supplementary Material).

Multiple SMM maps (500 x 500 px) from different ROIs on the subject samples were processed and analyzed using ImageJ (1.54p, Java 1.8.0_322 – Win 64bit) with a Trainable Weka Segmentation (TWS) available as an additional plugin²²,³⁶,³⁷. As a classificator, the Fast-Random Forest was applied and trained (N_trees = 200, N_threads = 8, batch size = 100, unlimited depth)³⁸. Splitting of the nodes was conducted through the minimization of Gini index (G) using the following Equation (4):

$G=1-{\displaystyle \sum }_{i=1}^C{p}_i^2$ (4)

Where p_iis the proportion of classiat a node, C is a number of classes.

The color tones and the levels (0 - 255) respectively forming three basic channels (R,G,B) by frequency in the collected images were extracted via 3D Color Inspector (ImageJ) and transformed into look-up tables (LUTs) at the number of the tone’s orderliness. Thereupon, levels’ combinations were plotted via histograms (reporting the general distribution across the channels) and tree maps, which are informative in terms of percental portion of each level in specific color channel.

Magnetization measurements as a function of the applied magnetic field were performed at room temperature using the VSM module of a Quantum Design PPMS Dynacool system, within a field range of ±3 T. In SDSS, the FCC phase (austenite) is paramagnetic, while the BCC phase (ferrite) is ferromagnetic. As a result, bulk magnetization measurements are particularly useful for assessing phase transformations induced by heat treatment, especially the conversion of ferrite into deleterious phases. Among the magnetic parameters, the saturation magnetization (M_S) is most commonly used, as it directly correlates with the volume fraction of ferromagnetic phases in the material²⁸-³⁰.

XRD analysis was performed on a Rigaku model MiniFlex II X-ray diffractometer³⁹, using Cu-Kα radiation (λ = 1.78919 Å), with a Ni monochromator and operated with voltage and current of 30 kV and 30 mA, respectively. The acquisitions of the diffractograms of each sample were conducted with angular scanning of 2θ ranging from 20° to 120°, step of 0.05° and time per step of 2s. To identify the microconstituents of the materials, the diffraction peaks of the ferrite, austenite and sigma phases were compared with the Inorganic Crystal Structure Database (ICSD) database⁴⁰, associated, respectively, with the standard files CIF Ferrite (ICSD #632630), Austenite (ICSD #632921) and Cr-Fe-Mo (ICSD #102759). Then, the Rietveld refinement was performed in the HighScore Plus^® software to obtain the volumetric fraction ​​of each of the phases present in the material. A ferrite quantification analysis was performed using a Fischer-MP30 ferritscope, belonging to the department of physics of the FFU⁴¹,⁴². In this case, 10 (ten) measurements were performed for each sample to determine the differences in measurements at different heat treatments and the time they remained in the oven. It is worth noting that the measurements using the ferritscope are directly related to the magnetic permeability of the sample being evaluated, and this equipment does not excite the sample with a strong enough field to reach saturation magnetization. The accuracy of the ferrite phase determination with ferritoscope depends on the previous calibration with samples of the same steel analyzed, which is not always possible. However, with comparative measurements, the ferritscope can be used to detect reactions involving ferrite decomposition.

3. Results and Discussions

Figure 1 shows the optical microscopy images of each of the samples that were analyzed in this work. Under these conditions, observing the longitudinal direction of the previously rolled samples, the microstructure consists of alternating lamellae of elongated austenite and ferrite phases⁴³,⁴⁴. The increase in the austenite fraction (light phase) with increasing treatment temperature is clearly observed when compared to the ferromagnetic ferrite (dark phase).

Figure 1
Optical microscopy of samples etched with 13.0% NaOH (a) As received (AR), (b) S1100-30, (c) A700-1, (d) A700-2, (e) A800-1, (f) A800-2, (g) A900-1, (h) A900-2.

The textural attributes, such as Correlation, Contrast and Entropy quantitatively prove the alterations in the surface organization after processing (Figure 2). The image of the neat sample, AR contrasts to those of the processed steels with the highest Correlation and the lowest Contrast and Entropy in all four measured directions. Further noticeable difference in AR is the total directionality invariance of Correlation, as opposed to Contrast and Entropy, whose values are lower at 0º (pair pixels to the right) and 180º (pair pixels to the left), as compared to 90º (pixel pairs upward) or 270º (pixel pairs downward). However, Correlation in the processed series exhibits similar differentiation between the directions, like in case of another two descriptors: its values along the vertical axes are distinctly lower than in the horizontal directions. This lends support to the validity of the conclusion about the loss of homogeneity in the horizontal patterns due the austenite light regions occurred after heating. With reference to the thermal conditions of the imposed treatment, Correlation gets reduced congruently as with the temperature rise, as with the processing time: in A900-2 it decreases 4.8 (0º or 180º) and 4.9 times (90º or 270º) by comparison with AR. Regarding Contrast, it generally exhibits growth with the temperature, whereas along the vertical directions this descriptor has a significantly higher values maintaining equality of the tendencies from AR to A900-2. Such a discrimination by direction is expectable due to the more frequent co-existence of the pair pixels at elevated intensity difference, once scanned vertically. In all the directions, AR is distinguished though the lowest Contrast vs. other samples. Entropy is less sensitive to the processing regime – it continues relatively stable within 8.2 – 8.8 (0º or 180º) 8.5 – 9.2 (90º or 270º) in all the processed samples. Lower values of the horizontal directions, especially in AR, corroborate the observations in Contrast profile, but it is non-informative for establishing the impact of processing temperature or time.

Figure 2
Haralick’s features extracted from the images of the 13.0% NaOH etched samples – Correlation (a), Contrast (b), and Entropy (c).

The foregoing indicates that the selected treatments were successful in generating samples with different proportions of ferromagnetic phases. However, it’s also important to clarify that ferrite and austenite are not the only phases present in SDSS. The Chi and Sigma phases are also expected to be present in a small but relevant fraction, since they are very rich in Cr, Ni and Mo, raising the local compositional gradients. These changes in phase composition might contribute to variations in the magnetization values obtained as well as the changes in phase volume fraction.

Figure 3(a) presents the diffractograms obtained through XRD, while the Figure 3(b) indicates the percentage results of each phase obtained through quantification by Rietveld refinement. Figure 3(c) shows representative magnetization curves for the as-received samples and for each of the heat treatment performed. The solution treatment provoked a very small increase in the ferrite phase content according to the X-ray analysis, but this was not corroborated by the magnetic curves. The gradual decrease in M_S with heat treatment temperature and time spent in the furnace is attributed to the decomposition of the ferromagnetic phase into austenite and sigma phases, both paramagnetic, Figure 3 (b). This effect was clearly seen in specimens aged at 800^oC, due to the high kinetics of δ decomposition, and less pronounced in the aging at 700^oC. Sample aged at 700^oC for 1h has a ferrite content similar to the solution treated one, while the ageing for 2h caused the formation of secondary austenite (γ₂). Since the Chi phase precipitates are small and dispersed particles, the XRD analysis was not able to detect any significant amount. However, for the scope of this work, this is not an issue. The ferrite phase constitutes the sole significant ferromagnetic phase present, and the contribution of Chi to the magnetic measurements is anticipated to be negligible.

Figure 3
(a) Diffractograms obtained by XRD, (b) Phase amounts (%), obtained from the diffractograms after performing a Rietveld refinement and (c) Magnetization curves versus external magnetic field applied to each of the samples.

The different techniques resulted in quantification discrepancies since they are based in different phenomena and are sensible to different test parameters. As can be seen in Figure 3 (b) (XDR results), ferrite (ferromagnetic phase) initially starts at values between 70 and 80%. As the heat treatment is performed, these values decrease significantly to values close to 10%; the same trend can be seen for the M_S and ferritoscope values in Figure 4. We suggest it to be attributed to transformation of ferromagnetic phase (ferrite into austenite, sigma phase, chi phase and other deleterious phases that appear in the microstructure resulting from the heat treatment performed on the samples.

Figure 4
Comparison of XRD (ferrite fraction) vs VSM (M_S) vs ferritscope results (ferrite fraction).

The XRD analysis is more superficial and susceptible to surface alterations such as specimen finishing and superficial residual stresses. The VSM achieves a volumetric approach but is not capable of differentiating the contribution of each phase to the saturation magnetization if various ferromagnetic phases are present, nor is it able to detect the presence of deleterious phases if there are more than one paramagnetic. In contrast, as stated in methodology section, the ferritscope cannot achieve sample saturation magnetization and is therefore less sensitive than the VSM technique. To perform phase quantification, the material is subjected to a magnetic field that will interact with the ferromagnetic phase and the changes caused in the sample will generate an induced magnetic field (magnetic permeability). This induced magnetic field, read by the second coil, results in a voltage proportional to the volumetric percentage of the ferromagnetic⁴¹,⁴². In the case of the scanning magnetic microscope (SMM) technique applied to the remaining magnetization analysis of superduplex steel, Figures 5 and 6 show that it is a very promising technique for this purpose. It can satisfactorily match the results obtained by more established techniques in the literature, such as those presented in Figure 4. This suggests that SMM is promising for this type of analysis and, with further testing and validation, could be used to correlate with phase quantification. Furthermore, despite being a relatively rare technique in steel analysis, it still offers room for improvement in many parameters to achieve much more accurate results.

Figure 5
The individual examples of the SMM images submitted to processing (1-5); and their corresponding segmented and classified binary images (6-10). To facilitate the reading of the maps, a general scale was presented for all of them where all the maps are of 5µm×5µm area and the remanent magnetic field value varies between 3 and -3x10^-4T.

Figure 6
The variances of the area fractions for the magnetic phase calculated from the TWS-classified SMM binary images

Keeping in mind that the magnetic field is a vector quantity, the opposite extremes on the map scales indicate the presence of magnetically active regions (Figure 5, 15). Hence, for training the algorithm, the segmentation of the remaining magnetization distributed over maps was undertaken for two-color criterion. The non-magnetic zones, correspondingly, were close to zero on the color scales. The black and white (BW) binary images were saved from the probability maps at the Otsu threshold. White ROIs were assigned to the target phase, whose area fractions (Area %) were calculated within the ImageJ interface (Figure 5). To facilitate the interpretation of the results, a simple classification (magnetic/non-magnetic) was suggested, and the area fractions of two phases only are normalized to 100%.

The collected area fractions of the target remaining magnetization regions formed variances and were subjected to the statistical analyses (Figure 6). The AR sample is characterized by the lowest standard deviation (5.2) of the area fractions among the subject samples, where its mean value is 68.3%. The processed samples’ standard deviations lie within 7.3 – 9.0 because of the excessive non-uniformity of the image patterns provoked by the thermal treatment. Besides, heating up > 700 °C leads to the decrease of the magnetic phase’s mean area fraction to more than 50%.

Since the area’s percentage variances do not meet criteria for the ANOVA (normal distributions and homoscedasticity), in order to compare them, the nonparametric means comparison (NMC) based on the Dunn’s method⁴⁵ for control for joint ranks was applied, where the variance of the AR (neat sample) was assigned as a reference (‘control’) and compared to the rest of the variances attributed to the processed samples (Table 3).

Table 3
The Dunn’s NLC summary*.

Processed Sample	Control	Score Mean Difference	Std Err Dif	Z	p-Value
A700	AR	-7.19	8.978	-0.800	1.0000
S1100-30	AR	-25.47	9.965	-2.556	0.0423
A900	AR	-36.14	9.226	-3.9178	0.0004
A800	AR	-42.88	8.854	-4.843	<.0001

• ^*
  Score Mean Difference - the mean of the rank score of the observations in each Processed Sample minus the mean of the rank scores of the observations in the Control, where a continuity correction is applied. Std Error Dif - the standard error of the Score Mean Difference. Z - the standardized test statistic, which has an asymptotic standard normal distribution under the null hypothesis of no difference in means. p-Value - the p-value for the asymptotic test based on Z.

The analysis of the NLC provided an idea of non-significant difference between the AR and A700 which means that heating at 700 °C did not induce the disproportion between the suggested magnetic and non-magnetic components, as compared to the neat sample. A short heating (30 min) at 1100 °C causes a slight downshift of the mean % of the area occupied by “magnetic phase”, but the p-value at 0.0423 is not low enough to declare the significant difference even at ≈ 3.5 times higher score mean difference. Another two regimes, at 800 and 900 °C, give an accurate account of noticeable decrease of the magnetic phase (p << 0.05), whose score mean differences are > 30. Hence, it favors the view that prolonged (≥ 1h) thermal treatment leads to SMM-detectable decrease of the “magnetic phase’s” concentration corroborating the findings from the instrumental measurements (ferritoscope, XRD or VSM).

Another, more sophisticated perspective from the digital colorimetry is conducive to interpreting the magnetic/non-magnetic phase ratios from their combinations of the 8-bit RGB scheme (Figure 7). The 3D scatter plots illustrate the color dots at varied sizes in respect to the specific tones found in the analyzed images shown in Figure 4. The deeper color is, the higher levels within the scale of 0 – 255 are. The size bears in a direct relation to the portion of specific level within each channel. In AR, for one, there are no deep blue dots and only red and yellow dots represent the magnetic phase (Figure 7(a)). The samples S1100-30 and A700 poses as red and deep blue dots in conformity with magnetic field, but the gamma of green dots is larger, whereas the dots themselves are bigger (Figure 7 (b) and (c)). The portion of the green dots in the samples heated at 800 and 800 ºC is the largest, as compared to AR, S1100-30 or A700 (Figure 7 (d) and (e)). The magnetic phase in A800 is mostly represented by red and yellow dots and although in A900 the deep blue together with red dots are found, the huge portion of green at the specific tonality (the massive dot) is observed proving the incrementally increased non-magnetic phase’s fraction. These qualitative findings served as a guide for further proceeding to comprehensive quantitative analysis of the tones as combinations of the levels (RGB) at various frequencies.

Figure 7
The 3D color scatter plots: AR (a), S1100-30 (b), A700 (c), A800 (d) and A900 (e).

Keeping in mind that in the RGB system pure Red, Green or Blue channel correspond to (255, 0, 0), (0, 255, 0) and (0, 0, 255), the profiles in the studied samples’ images are individual as by calculating the 0-255 levels portions in each channel (see the tree maps), as through the dominating modes of the levels combinations (see the histograms) - Figure 8. Establishing the numerical interconnections between the tone’s distribution histograms and the tree maps offers certain insights into the magnetic properties’ changes caused by heating.

Figure 8
The tone distribution histograms and 8-bit RGB levels portions tree maps: AR (a), S1100-30 (b), A700 (c), A800 (d) and A900 (e).

First of all, the tree map for AR reports high levels of red and green channels in combination with low level of blue: two most intensive tones, (248, 248, 8) and (248, 218, 8) are responsible for more than 22% of the overall combinations. Blue component is contributed by low level (0, 0, 8) at 66.87% and, hence, the magnetic phase portion is predominantly attributed to the high-intensity red channels: the identified 128, 158, 188, 218 and 248 levels make approx. 97% of all the levels in the red component. Highest levels of the Green channel, in its turn, whose total portion is ca. 29%, are interfered with R > 128. Next, the S1100-30 sample`s profiles changes drastically: the 248 level’s portion for the Green component increases 1.6 times (74%) as compared to the neat sample – moreover, the total portion of the 128-248 levels takes almost 94%. Besides, the visible repartition of the levels inside the Red and Blue channels takes place. In Red, the 248 is significantly reduced, whereas the 8 level takes 16.37% - the latter is concentrated in the regions where the blue component is prevalent at 248 (Figure 8 (b)). Despite the presence of Blue component, which together with Red channel form the magnetic regions, the grown Green’s portion reflected 35% reduction of the magnetic area on the image after processing at 1100 °C even for a short period.

The consequent heating (Figure 8 (c)(e)), at 700, 800 and 900 °C, leads to a monotonous decrease of the 248 level in the Red channel (from 35.9 to 19.9%), whereas the total portion of high levels inside the Green channel grows up to 95.41% and takes up to 85.4% in combination with Red or Blue channels to form the color profile (900 °C). It is important to note, in the Red and Blue channels the 248 levels got depressed - 16.19 and 11.19%, respectively. In the light of above, five tones from the RGB histograms responsible for the non-magnetic phase can be selected (Figure S6): (188, 248, 68), (158, 248, 98), (128, 248, 98), (128, 248, 128), (98, 248, 128). Their sum frequency percentage (Figure 9) undergoes congruent tendencies reflected in the Figure 4 and Figure 6. The AR sample’s initial sum frequency of the listed tones takes the minimal value (ca. 21%) and increases up to ca. 31% in S1100-0.5. As we determined, a moderate increase of the sum frequencies (ca. 23%) together with the non-magnetic phase’s concentration at the temperature of 700 °C, occupies markedly much higher percentage reaching 51.4% at 900 °C.

Figure 9
The five-tone sum frequency percentage vs. samples.

The reason to choose a group of the RGB-tones is based on non-monotonic dependence of each single component in accordance to the thermal treatment mode (Table 4). For instance, the most intensive tone of (128, 248, 98) taking 31% alone amongst the all tones in A900, contributes less than 2% to all the frequencies in A800. This tone, however, has almost equal portion in the S1100-0.5 and A700 samples. Other four tones share the common trait while any further processing of AR is undertaken – the encountered extrema in the individual tones do not reflect the adequate observations over the heat maps. Such alterations of the tones through the whole series, from one sample to another one, can be explained through the anisotropic effects on the samples’ surface interacting with the Hall sensor. To strike a compromise between the sensor’s height variation (0.2-0.4 µm) and the data post-processing with further transformation into the maps, we have a firm belief that such a range of the tones is representative to assign them the “non-magnetic phase” and embody the segmentation via WTS.

Table 4
The partial frequency percentage (%) of five selected tones.

(R, G, B)	AR	S1100-30	A700	A800	A900
(158, 248, 98)	7.11	5.708	3.238	13.204	4.687
(98, 248, 128)	0.387	4.305	2.295	1.591	3.298
(188, 248, 68)	6.569	8.818	6.382	10.936	6.786
(128, 248, 98)	0.572	6.423	6.748	1.767	31.646
(128, 248, 128)	5.494	5.473	4.187	15.878	5.06

We can carefully assume that specifically these tones can be proposed to calibrate the images suggesting the “non-magnetic phase” quantification using color scheme in parallel to the area % computed from the binary images. This fact needs verification in our future chemometric research, where the chosen instrumental measurements is supposed to be calibrated with the processed images. The SMM images processing did not outperform the expected resolution between the heating intervals (1 or 2 h) for a set temperature (700, 800 or 900 °C). However, it gave an estimate of differentiation among the temperature regimes which affected the magnetic properties on the studied samples. There is a strong evidence for the proportional variation in the “magnetic phase” concentrations summarized in Figure 3. Hence, the proposed conjunction of SMM with trained WTS classificator has proven to be an additional complementary tool to monitor the ferromagnetic concentration via images inspection for the selected processing environment. The present protocol requires further testing and possible adjustment or calibrations under various temperature conditions, also in the case of material’s surface pretreatment. In the latter instance, not only the segmentation of the respective suggested phases, but also quantitative description of the image texture would be relevant.

4. Conclusion

The proposed heat treatments were able to produce samples with varying ferromagnetic properties, as noted by the OM results and the different quantification techniques. Although various techniques produced different measurements, a clear but non-linear decrease in the suggested “ferromagnetic phase” was observed with increasing temperature and time of heat treatment. The higher discrepancy between XRD and magnetic measurements were observed in the as-received sample, mostly due to the influence of the cold drawing process which introduces strain-hardening effects. The XRD measurements pointed higher ferrite (ferromagnetic phase) content when comparing to the magnetic methods. This might be due to the higher susceptibility to surface phenomena and residual strain hardening effects from the manufacturing process. In this sense, the SMM presented results more aligned with the VSM and Ferritoscope. Ferritoscope might be used to qualitatively compare different samples, but it’s not as sensible as the VSM since it doesn’t achieve saturation magnetization. The SMM was able to detect and distinguish varying intensities of remaining magnetization that might indicate the presence of magnetic and non-magnetic phases reflected through the areas on the resulting images. The findings obtained after image processing and data analysis are promising, although they require to be calibrated via established and known samples to accurately quantify the phase volume fraction as through the digital colorimetry, as via binary images segmentation. In this work, it was measured the remaining magnetic field, but there is also the possibility of measuring the induced field.

Supplementary Material

The following online material is available for this article:

Figure S1

The images collected for AR sample.

Figure S2

The images collected for S1100-30 sample.

Figure S3

The images collected for A700 sample (1 and 2h).

Figure S4

The images collected for A800 sample (1 and 2h).

Figure S5

The images collected for A900 sample (1 and 2h).

Figure S6

Five principal tones responsible to the proportion of the non-magnetic phase on the SMM images.

Table S1

LUT-700.

Table S2

LUT-800.

Table S3

LUT-900.

Table S4

LUT-CR174.

Table S5

LUT-Sol-1100-30.

5. Acknowledgements

This study was financed in part by the Coordenaçã ode Aperfeiç oamento de Pessoal de Nível Superior−Brasil (CAPES) - Finance Code 001 and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), (Process No. 312460/2023-6) and FAPERJ (grant No. JCNE E-26/201.260/2022), (grant No. E-26/210.305/2022). Nazarkovsky is thankful for the financial support received from Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) (grants E-26/202.671/2023 and E-26/200.612/2025). Also, Nazarkovsky is thankful to Prof. S. Paciornik (DEQM-PUC Rio, Brazil), Prof. B. Marinkovic (DEQM-PUC Rio, Brazil), and Dr. D. Kirmayer (HUJI, Israel).

• Data Availability
  The dataset that supports the results of this study is not publicly available.

6. Referencias

• ¹ Conceição JN, Correa EO, Gonzaga AC, Pardal JM, Tavares SSM. Mechanical properties of UNS S39274 superduplex stainless steel work hardened and solution annealed. Mater Res. 2022;25:e20220108. https://doi.org/10.1590/1980-5373-mr-2022-0108
  » https://doi.org/10.1590/1980-5373-mr-2022-0108
• ² ASTM: American Society for Testing and Materials. Specification for seamless and welded ferritic/austenitic stainless steel pipe. West Conshohocken, PA: ASTM International; 2022. https://doi.org/10.1520/A0790_A0790M-22
  » https://doi.org/10.1520/A0790_A0790M-22
• ³ ISO: International Organization for Standardization. ISO 13680:2024 - Oil and gas industries including lower carbon energy — Corrosion-resistant alloy seamless products for use as casing, tubing, coupling stock and accessory material — Technical delivery conditions. Geneva: ISO; 2024.
• ⁴ ASTM: American Society for Testing and Materials. ASTM A 890/A 890M–91: ferrous castings; ferralloys. 1st ed. West Conshohocken (PA): ASTM International; 1999.
• ⁵ Weber J. Materials for seawater pumps and related systems. 1st ed. Winterthur: Sulzer Brothers Limited; 1986.
• ⁶ Gunn RN. Duplex stainless steels microstructure, properties and applications. Anti-Corros Methods Mater. 1998;45(2). https://doi.org/10.1108/acmm.1998.12845bae.001
  » https://doi.org/10.1108/acmm.1998.12845bae.001
• ⁷ Callister WD. Materials science and engineering an introduction. 5th ed. New York: John Wiley & Sons; 2012. 895 p.
• ⁸ Verma J, Taiwade RV. Effect of welding processes and conditions on the microstructure, mechanical properties and corrosion resistance of duplex stainless steel weldments: A review. J Manuf Process. 2017;25:134-52. https://doi.org/10.1016/j.jmapro.2016.11.003
  » https://doi.org/10.1016/j.jmapro.2016.11.003
• ⁹ Tavares SSM, Pardal JM, Abreu HFG, Nunes CS, Silva MR. Tensile properties of duplex UNS S32205 and lean duplex UNS S32304 steels and the influence of short duration 475 ^oC aging. Mater Res. 2012;15(6):859-64. https://doi.org/10.1590/S1516-14392012005000116
  » https://doi.org/10.1590/S1516-14392012005000116
• ¹⁰ Gunn RN. Duplex stainless steels: microstructure, properties and applications. Abington: Abbington Publishing; 1997. https://doi.org/10.1533/9781845698775
  » https://doi.org/10.1533/9781845698775
• ¹¹ IMOA: International Molybdenum Association. Practical guidelines for the fabrication of duplex stainless steels. London: IMOA; 2009. 62 p.
• ¹² Charles J, Bernhardsson S. Duplex stainless steels. 1st ed. Beaune: Les Éditions of Physique; 1991.
• ¹³ Pohl M, Storz O, Glogowski T. Effect of intermetallic precipitations on the properties of duplex stainless steel. Mater Charact. 2007;58(1):65-71. https://doi.org/10.1016/j.matchar.2006.03.015
  » https://doi.org/10.1016/j.matchar.2006.03.015
• ¹⁴ Wang R. Precipitation of sigma phase in duplex stainless steel and recent development on its detection by electrochemical potentiokinetic reactivation: A review. Corros Commun. 2021;2:41-54. https://doi.org/10.1016/j.corcom.2021.08.001
  » https://doi.org/10.1016/j.corcom.2021.08.001
• ¹⁵ Lo KH, Shek CH, Lai JKL. Recent developments in stainless steels. Mater Sci Eng Rep. 2009;65(4–6):39-104. https://doi.org/10.1016/j.mser.2009.03.001
  » https://doi.org/10.1016/j.mser.2009.03.001
• ¹⁶ Tumanski S, Liszka A. The methods and devices for scanning of magnetic fields. J Magn Magn Mater. 2002;242–245:1253-6. https://doi.org/10.1016/S0304-8853(01)01023-X
  » https://doi.org/10.1016/S0304-8853(01)01023-X
• ¹⁷ Cambel V, Karapetrov G, Novosad V, Bartolomé E, Gregušová D, Fedor J, et al. Novel Hall sensors developed for magnetic field imaging systems. J Magn Magn Mater. 2007;316(2):232-5. https://doi.org/10.1016/j.jmmm.2007.02.104
  » https://doi.org/10.1016/j.jmmm.2007.02.104
• ¹⁸ Xiao C, Zhang Y. A method of magnetic scanning imaging for detecting defects in ferromagnetic materials. Meas Sci Technol. 2011;22(2):025503. https://doi.org/10.1088/0957-0233/22/2/025503
  » https://doi.org/10.1088/0957-0233/22/2/025503
• ¹⁹ Cano ME, Pacheco AH, Cordova T, Mazon EE, Barrera A. Superficial magnetic imaging by an xy-scanner of three magnetoresistive channels. Rev Sci Instrum. 2012;83(3):033705. https://doi.org/10.1063/1.3694002
  » https://doi.org/10.1063/1.3694002
• ²⁰ Ignat’ev VK, Orlov AA, Perchenko SV, Stankevich DA. A hall microscope for measuring magnetic properties of films. Tech Phys Lett. 2017;43(8):687-90. https://doi.org/10.1134/S1063785017080090
  » https://doi.org/10.1134/S1063785017080090
• ²¹ Gudoshnikov S, Tarasov V, Liubimov B, Odintsov V, Venediktov S, Nozdrin A. Scanning magnetic microscope based on magnetoimpedance sensor for measuring of local magnetic fields. J Magn Magn Mater. 2020;510:166938. https://doi.org/10.1016/j.jmmm.2020.166938
  » https://doi.org/10.1016/j.jmmm.2020.166938
• ²² Arganda-Carreras I, Kaynig V, Rueden C, Eliceiri KW, Schindelin J, Cardona A, et al. Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification. Bioinformatics. 2017;33(15):2424-6. https://doi.org/10.1093/bioinformatics/btx180
  » https://doi.org/10.1093/bioinformatics/btx180
• ²³ O’Mahoney T, Mcknight L, Lowe T, Mednikova M, Dunn J. A machine learning based approach to the segmentation of micro CT data in archaeological and evolutionary sciences. bioRxiv. 2019;859983. https://doi.org/10.1101/859983.
• ²⁴ Salum P, Güven O, Aydemir LY, Erbay Z. Microscopy-assisted digital image analysis with Trainable Weka Segmentation (TWS) for emulsion droplet size determination. Coatings. 2022;12(3):364. https://doi.org/10.3390/coatings12030364
  » https://doi.org/10.3390/coatings12030364
• ²⁵ Lormand C, Zellmer GF, Németh K, Kilgour G, Mead S, Palmer AS, et al. Weka trainable segmentation plugin in ImageJ: a semi-automatic tool applied to crystal size distributions of microlites in volcanic rocks. Microsc Microanal. 2018;24(6):667-75. https://doi.org/10.1017/S1431927618015428
  » https://doi.org/10.1017/S1431927618015428
• ²⁶ Kataras TJ, Jang TJ, Koury J, Singh H, Kaul M. ACCT: automatic cell counting with Trainable Weka Segmentation. Scientific Reports. 2022. https://doi.org/10.21203/rs.3.rs-1743231/v1
  » https://doi.org/10.21203/rs.3.rs-1743231/v1
• ²⁷ Kharma N, Mazhurin A, Saigol K, Sabahi F. Adaptable image segmentation via simple pixel classification. Comput Intell. 2018;34(2):734-62. https://doi.org/10.1111/coin.12173
  » https://doi.org/10.1111/coin.12173
• ²⁸ Gonzaga AC. Microestrutura, propriedades mecânicas e de resistência à corrosão do aço inoxidável superduplex uns S39274 (deformado e solubilizado) [tese]. Rio de Janeiro: Centro Federal de Educação Tecnológica Celso Suckow da Fonseca; 2024.
• ²⁹ Haralick RM, Shanmugam K, Dinstein I. Textural features for image classification. IEEE Trans Syst Man Cybern. 1973;SMC-3(6):610-21. https://doi.org/10.1109/TSMC.1973.4309314
  » https://doi.org/10.1109/TSMC.1973.4309314
• ³⁰ Calandra I. A workflow for quality control in surface texture analysis applied to teeth and tools. J Archaeol Sci Rep. 2022;46:103692. https://doi.org/10.1016/j.jasrep.2022.103692
  » https://doi.org/10.1016/j.jasrep.2022.103692
• ³¹ Bloise N, Fassina L, Focarete ML, Lotti N, Visai L. Haralick’s texture analysis to predict cellular proliferation on randomly oriented electrospun nanomaterials. Nanoscale Adv. 2022;4(5):1330-5. https://doi.org/10.1039/D1NA00890K
  » https://doi.org/10.1039/D1NA00890K
• ³² Lima EA, Bruno AC, Carvalho HR, Weiss BP. Scanning magnetic tunnel junction microscope for high-resolution imaging of remanent magnetization fields. Meas Sci Technol. 2014;25(10):105401. https://doi.org/10.1088/0957-0233/25/10/105401
  » https://doi.org/10.1088/0957-0233/25/10/105401
• ³³ Chaves JF, Noris LF, Yokoyama E, Osorio GFG, Mendoza LAF, Araujo JFDF. Multisensor magnetic scanning microscope for remanent magnetic field measurements. Sensors. 2024;24(7):2294. https://doi.org/10.3390/s24072294
  » https://doi.org/10.3390/s24072294
• ³⁴ Silva JFC. Microscópio magnético de varredura adaptável para medição de campos remanentes [dissertação]. Rio de Janeiro: PUC; 2023.
• ³⁵ Araujo JFDF, Reis ALA, Yokoyama E, Medina CD, Osorio GF, Luz-Lima C, et al. Construction of a Hall effect scanning magnetic microscope using permanent magnets for characterization of rock samples. J Magn Magn Mater. 2023;569. https://doi.org/10.1016/j.jmmm.2022.170304
  » https://doi.org/10.1016/j.jmmm.2022.170304
• ³⁶ Arganda-Carreras I, Kaynig V, Rueden C, Eliceiri KW, Schindelin J, Cardona A, et al. Bioinformatics. Bethesda (MD): Trainable Weka Segmentation I; 2017.
• ³⁷ Arganda-Carreras I, Kaynig V, Rueden C, Eliceiri KW, Schindelin J, Cardona A, et al. Bioinformatics. Bethesda (MD): Trainable Weka Segmentation II; 2017.
• ³⁸ Breiman L. Random forests. In: Ceci M, editor. Machine learning. Berlin: Springer; 2001. p. 5-32.
• ³⁹ Subramanian M. Department of Public Safety and Oregon State Police. Tokyo: Rigaku Miniflex II; 2024.
• ⁴⁰ Horstmann W. Inorganic Crystal Structure Database (ICSD). Eggenstein-Leopoldshafen, Germany: FIZ Karlsruhe; 2024.
• ⁴¹ Helmut-Fischer. Catálogo do Feritscope® FMP30: Measurement of the Ferrite Content in Austenitic and Duplex Steel. Sindelfingen, Germany: Helmut Fischer GmbH; 2019.
• ⁴² Helmut-Fischer. Operators Manual FERITSCOPE® FMP30: Determination the ferrite content of austenitic and DUPLEX stainless steel and determination of the ratio of martensite in austenitic stainless steels. Sindelfingen, Germany: Helmut Fischer GmbH, Institut für Elektronik und Messtechnik; 2008. 240 p.
• ⁴³ Ramírez Londoño AJ. Precipitação de fases intermetálicas e austenita secundária na ZAC de soldagens multipasse de aços inoxidáveis duplex [tese]. São Paulo: Universidade de São Paulo; 2001. https://doi.org/10.11606/T.3.2001.tde-02012002-175418
  » https://doi.org/10.11606/T.3.2001.tde-02012002-175418
• ⁴⁴ Ramirez AJ, Lippold JC, Brandi SD. The relationship between chromium nitride and secondary austenite precipitation in duplex stainless steels. Metall Mater Trans, A Phys Metall Mater Sci. 2003;34(8):1575-97. https://doi.org/10.1007/s11661-003-0304-9
  » https://doi.org/10.1007/s11661-003-0304-9
• ⁴⁵ Dunn OJ. Multiple comparisons using rank sums. Technometrics. 1964;6(3):241-52. https://doi.org/10.1080/00401706.1964.10490181
  » https://doi.org/10.1080/00401706.1964.10490181

Edited by

• Associate Editor:
  Hugo Sandim.

• Editor-in-Chief:
  Luiz Antonio Pessan.

Data availability

The dataset that supports the results of this study is not publicly available.

Publication Dates

• Publication in this collection
  15 May 2026
• Date of issue
  2026

History

• Received
  17 Feb 2026
• Accepted
  08 Apr 2026