Local magnetic flux density measurements for temperature control of transient and non-homogeneous processing of steels

Measuring temperatures during high-temperature processing of steels is usually limited to surface measurements that cannot directly assess the internal temperature distribution. Here, we demonstrate the feasibility of using a magnetic flux density measurement system to assess transient and non-homogeneous temperature fields in a modern high-strength steel, within the intercritical temperature range where microstructural evolution defines their key mechanical properties. The system accurately detects the Curie temperature and distinguishes temperature change rates within the processed volume. The magnetic measurements are also sensitive to the volume above Curie temperature and its shape, as revealed when integrated with thermal computational simulations. The electromagnetic signal provides real-time qualitative and quantitative information relevant to the metallurgical conditions enabling future intelligent control systems for the production and processing of steels. Contactless measurements of temperature-dependent electromagnetic properties can enable through-thickness temperature monitoring solutions, opening up opportunities for non-destructive full-field imaging of steels during thermal and thermomechanical processing.


Results
Experimental setup. We developed a magnetic measurement system tailored to identify temperature evolution in the ideal range for thermomechanical processing of HSS. Figure 1 shows schematic representations of the measurement setup created to monitor the magnetic flux density during thermal and thermomechanical cycles. The setup consists of a S700MC HSS test specimen clamped to a non-magnetic copper chassis (Fig. 1a) containing the measurement system. Inside the chassis, a permanent magnet generates a magnetic field, → H , that interacts with the steel specimen, changing the magnetic flux density, → B , according to the relation μ → = ⋅ → B H R , assuming that magnetic permeability, μ R , is a scalar since the material is considered isotropic. Two (for redundancy) Hall-effect sensors, positioned between the magnet and the steel, monitor the local magnetic flux density. The location of these sensors was chosen based on the results of the computational analysis presented in the 'Computational analysis' section. Thermocouples positioned at the half-thickness of the processed zones, according to Fig. 1b, measured the temperatures. The chassis was water cooled to protect the magnet and the magnetic sensors from the effects of the high temperatures. An oxy-fuel flame was used as the heat source for the thermal cycles (Fig. 1c), and plastic deformation induced by a rigid friction stir welding (FSW) 48,49 tool was the heat source for the thermomechanical cycles (Fig. 1d). These two heat sources were selected to decouple the purely thermal effect from any eventual effect of the material flow during the thermomechanical processing that might affect the magnetic measurements. Non-electrical heat sources were selected to avoid any coercive electromagnetic interaction with the magnetic measurement system. A more detailed description of the experimental setup and procedure is described in the 'Methods' section and in the Supplementary Information file accompanying the online version of this publication.
Phase transformation and Curie temperatures of S700MC steel. DSC measurements with different heating and cooling rates (detailed in the 'Methods' section) revealed the presence of three distinct peaks in each cycle. These are labelled 1, 2 and 3 in Fig. 2a. The endothermic peaks inside 1 identify the body centered cubic α iron (e.g. ferrite) → face centred cubic γ iron (austenite) phase transformation between austenite onset temperature, A C1 , and austenite finish temperature, A C3 , in the heating stage. The exothermic peaks inside 2 mark the γ → α transformation region between the ferrite onset temperature, A R3 , and ferrite finish temperature, A R1 , in the cooling stage. The peaks inside 3 identify T C and their magnitude is smaller than the phase transformation peaks. As with other steels 27 , the phase change temperatures depend on the heating/cooling rate but T C is quite stable.
A closer analysis of the endothermal reactions during heating at 50 °C/min is presented in Fig. 2b. The peak between 700 and 800 °C corresponds to the ferromagnetic to paramagnetic transformation and its lowest point defines T C = 740 °C. The peak between 800 and 900 °C marks the α ↔ γ phase transformation. We extrapolated the A C1 and A C3 temperatures by tracing the baseline of the peak and intersecting it with the tangents to the inflection points of the curves. The temperature where the negative slope tangent intersects the baseline defines A C1 = 826 °C and the temperature where the positive slope tangent intersects the baseline defines A C3 = 882 °C. The austenite to ferrite transformation onset and finish temperatures on cooling, A R3 and A R1 , were determined following the same methodology (Fig. 2c). Since for the 50 °C/min cooling, the T C is inside the [A R1 , A R3 ] temperature range, the magnetic transformation occurs within the phase transformation and the energetic contributions from these two phenomena are added forming a single exothermic peak. Considering the relation of the T C with the equilibrium transformation temperatures [A 1 , A 3 ], an acceptable approximation is [A 1 , Computational analysis. To estimate the temperature distribution for the experimental part of this work and to support the design of the magnetic measurement system, we performed computational thermal analyses using the Finite Element Method (FEM). The analysis established the full temperature fields and identified the volume of material that reaches temperatures above T C , thus, changing from μ R ≫ 1 to μ R ≈ 1 and becoming paramagnetic, hereafter the paramagnetic volume, V paramagnetic (Fig. 3). The conditions for the steady-state thermal analysis are described in the 'Methods' section. Superimposing the modelled V paramagnetic on the etched cross section images of the test specimens reinforces the good agreement between the V paramagnetic obtained by computational analysis and the thermomechanically-affected zones (TMAZ) obtained experimentally, further confirming the validity of the model.
In a multi-physical approach, we then integrated V paramagnetic into a magnetostatic computational analysis to study the interaction of the magnetic field with the test plate upon the ferromagnetic to paramagnetic transformation. The results provide a visualization of the difference between the magnetic flux density in the presence of a V paramagnetic in the fully ferromagnetic condition: μ R ≫ 1 when T < T C (Fig. 4a,c); versus V paramagnetic in the paramagnetic condition: μ R ≈ 1 when T > T C (Fig. 4b,d). These results were used to support the design of the magnetic measurement system. The optimal position for the sensors is where the magnetic flux density experiences the greatest variation, comparing the ferromagnetic to paramagnetic states. This occurs mainly inside the paramagnetic volume itself and in its immediate vicinity. Since the inside of the material is inaccessible and the heat sources occupy the space above the V paramagnetic , the magnetic sensors were positioned below V paramagnetic .
Experimental measurements of temperature and magnetic permeability during thermal and thermomechanical cycles. The magnetic measurement system, introduced in the 'Experimental setup' section, was used to monitor the magnetic flux density and the temperature during the thermal and thermomechanical cycles (see details in 'Methods' section). The different cycles are identified according to heat source -Flame or FSW tool -and maximum temperature above or below the Curie temperature: T MAX > T C or T MAX < T C . www.nature.com/scientificreports www.nature.com/scientificreports/ In Figs. 5 and 6, the plotted temperature curves correspond to the thermocouple that registered the highest temperature in each measurement (i.e. the one closest to the heat source). The magnetic measurements are represented as magnetic flux density variation, Δ → B , from a baseline defined as the initial value of → B . Positive values  The results for the Flame_T MAX < T C cycle are presented in Fig. 5a. The maximum temperature does not go over T C and there is no drop in magnetic flux density, indicating that T C was not reached anywhere in the specimen. Similarly, in the FSW_T MAX < T C cycle (Fig. 5b) the maximum temperature measured did not exceed T C and no drop in Δ → B occurs. It is worth mentioning that even though the whole processed volume of the steel specimens is kept below the Curie temperature the Δ → B moves slightly away from the baseline. This phenomena of sensitivity of the magnetic measurement to different temperatures below the T C is reported by other authors [50][51][52] .
The Flame_T MAX > T C measurements are shown in Fig. 6a. T MAX surpassed T C and, accordingly, the magnetic flux sensors detected a clear decrease in signal strength, followed by a return to the baseline when the temperature dropped below T C at the end of the cycle. The magnetic sensors registered the signal decrease about Δt 1 = 12.8 seconds before the thermocouple recorded values above T C . This offset is due to the fact that the thermocouple provides a point measurement while the magnetic measurement is immediately sensitive to the change in μ R , caused by temperatures above T C , anywhere in the volume of processed material, starting from the vicinity  www.nature.com/scientificreports www.nature.com/scientificreports/ of the power source. This delay is opposite during the cooling, for the same reason. Note that Δt 2 < Δt 1 which reflects the difference in temperature change rate between heating and cooling periods.
The FSW_T MAX > T C measurements, presented in Fig. 6b, exhibit all the same characteristics as those described for Flame_T MAX > T C , and contain additional distinguishable features of the notable significance. The distinguishable effect, depicted in Fig. 6b, is an inverse systematic relation between the Δ → B rate and the heating rate. During the dwell phase of the thermomechanical cycle, the temperature curve exhibits two different heating rates, represented by blue dotted lines marked = . Gauss/s. This means that the measurement system not only accurately detects the T C , but is also sensitive to the effect of temperature change rates within the processed volume. This quantitative effect is of the upmost importance because it has not been found in the existing literature and it opens up the possibility of implementing new intelligent control systems. As an example, the Δ → B signal can be used as an input for a control system to maintain the temperatures during steel production or processing inside the [≈A 1 ,T C ] range. The results of a more detailed investigation of the sensitivity of the Δ → B to the volume above Curie temperature, V paramagnetic , will be presented next.
Magnetic flux density measurements versus material volume above Curie temperature. We estimated V paramagnetic , i.e. the volume of material with T > T C , at five different instants during the heating phase of Flame_T MAX > T C and FSW_T MAX > T C via computational analysis. Figure 7 shows the relationship between V paramagnetic and the change in magnetic flux density ∆ → B relative to the initial value Observing the visual representations of the paramagnetic volumes we can identify two different stages in the evolution of V paramagnetic . The first stage is dominated by an increase in the thickness of V paramagnetic (i.e. ∆ ∆ ∝ V t, where t is the thickness) and is more pronounced in V paramagnetic Flame is sensitive to the shape of the paramagnetic volumes and to the way those shapes evolve over time.

Discussion
The peak temperatures and the temperature change rates control the grain size evolution, precipitation and solution, which along with the strain hardening are responsible for the microstructure of steels and their mechanical properties. These phenomena depend mostly on the thermal and thermomechanical history across the intercritical temperature domain 12 , where the Curie temperature lies and the α ↔ γ phase transformation of iron structures occurs.
We developed a non-destructive, contactless, magnetic-based measurement system that exploits the temperature dependence of the electromagnetic properties to assess temperature domains inside a volume of processed steel. By monitoring the change of magnetic flux density near the Curie temperature, our system provides www.nature.com/scientificreports www.nature.com/scientificreports/ real-time qualitative and quantitative information related to the temperature field within the intercritical temperature domain. This enables the development of intelligent systems capable of assessing and controlling the phenomena that govern the metallurgical and mechanical properties of steels, which is of special relevance in the thermal and thermomechanical processing of modern high-strength steels. Examples of processes associated with an external heat source resulting in thermal processing, approximated in the paper by the thermal cycles using the flame as external the heat source, are i) with fusion: oxi-fuel welding and cutting, laser welding and cutting, electron beam welding, electric arc based welding and cutting; ii) without fusion: heat treatment, e.g. plasma, flame, high-frequency induction (where the sensor can be integrated with the induction coil). Examples of processes associated with thermomechanical processing, where the heat source is internal, i.e. the material, by energy dissipation during its bulk plastic deformation, are the FSW (partially addressed in the paper by the thermomechanical cycles using the plunge and dwell stages of a FSW tool), the friction welding, forging, hot rolling during steel production.
The multiphysical research plan encompassed DSC experimental measurements, computational thermal analysis and dedicated design and implementation of the magnetic-based measurement system. The DSC measurements with different heating and cooling rates were used to establish, with precision and reliability, the Curie temperature, T C ≈ 740 °C, and the transformation temperatures, [A R1 , A C3 ] = [702 °C, 882 °C], of the S700MC high-strength steel used as test specimen. The transformation temperatures considered were the ones obtained with the 50 °C/min rate as they are the ones closer to real processing conditions. The Curie temperature showed no dependence on the heating or cooling rates. The computational thermal analysis was used to support the design of the magnetic measurement system and identify the volume of material that reaches temperatures above T C , thus, changing from μ R ≫ 1 to μ R ≈ 1 and becoming paramagnetic.
The results show that our magnetic flux density measurements can be used to detect the magnetic transformation of the processed volume when it reaches the Curie temperature. Above this temperature, it is also sensitive to the effect of temperature change rates within the processed volume. Additionally, based on the multiphysical approach, the measurements provide sensitive data related to the evolution of the processed volume, namely, it can discern between different heating and cooling rates and between the effects of different changes in shape (Δ thickness vs Δ diameter). There is a ∆ → B associated with a small magnetic permeability increase below the Curie temperature indicating that the temperatures inside processed volume are changing, this may also represent a valuable information for a control system and should be studied in more detail.
The new and distinguishable results presented in this work result from two major differences in the implemented research plan when compared with the state of the art in this field, namely: (i) the measurements of the magnetic properties are performed during transient thermal processing with complex non-homogenous conditions; (ii) besides an external purely heat power source (i.e. a flame), the work included thermomechanical processing. In this case, the specimen materials become the heat power source, due to the heat generated by internal viscous energy dissipation during the non-homogeneous plastic deformation of the material and superficial frictional energy dissipation in the contact with the rigid FSW tool. The internal energy dissipation decreases as the www.nature.com/scientificreports www.nature.com/scientificreports/ temperature increases and, so, the thermomechanical processing resulted in steady-state heating rates, different for different stages of the deformation. This yielded the opportunity for the magnetic measurement system to show unique capabilities, besides accurately detecting the T C , such as being sensitive to the effect of temperature change rates within the processed volume. For full temperature range measurements other complementary measurement methods, such as pyrometers and infrared thermography systems, can be integrated via data fusion processes.
This through-thickness, contactless, monitoring solution (that can provide real-time data on the temperatures and temperature rates inside a volume of material under non-uniform and transient conditions) will contribute to bring steel production and processing in line with the new digitalization paradigm by providing large amounts of information rich data that can be readily available to support highly integrated, smart, cyber-physical manufacturing systems 53 . Going digital in the fabrication of steel-based structural systems and products, will allow zero-defect factories with safer working conditions and lower environmental impact.
The next steps will be to expand the capabilities of the measurement system from a single Hall-effect sensor configuration to multiple sensors forming an array. This will provide data with spatial resolution and enable image reconstruction of the processed volume of material. With a dedicated multiphysical solution, integrating computational simulation of the metallurgical evolution and thermal analysis with the non-destructive real-time magnetic measurement system presented here, it will be possible to deliver a full field imaging solution for application in intelligent automated control systems for steel production and processing.

Methods
Material. The base material used in this study was a S700MC high-strength steel produced by TMCP, whose chemical composition is: [max. wt.%] 0.059 C; 0.205 SI; 1.79 Mn; 0.007 P; 0.002 S; 0.026 Al; 0.083 Nb; V; 0.013; 0.113 T. The specimens used in the thermal and thermomechanical processing cycles were 100 × 100 × 4 mm plates. For the thermal cycles (oxy-fuel flame heat source), a region of reduced thickness (2 mm) was produced on the middle of the plates, by removing Ø 25 × 2 mm of material by machining as depicted in Fig. 1c, to concentrate the heating effect. Similarly, for the thermomechanical cycles (FSW tool heat source) a Ø 10 mm and 3.5 mm deep hole (Fig. 1d) was drilled at the center of the plates to remove a volume of material roughly equivalent to that of the tool probe.
Differential scanning calorimetry (DSC). Differential scanning calorimetry measurements were performed on a NETZSCH STA 449F1 equipment, capable of a maximum heating rate of 50 °C/s. A sample of the S700MC steel (approximately 1.5 × 2 × 3 mm and 75 mg) was placed inside an Al 2 O 3 ladle and the measurements were carried out under a protective Argon atmosphere. The thermal cycles comprised four stages: 1 -holding at 100 °C; 2 -heating (at 50, 20, 10, and 5 °C/min); 3 -holding at 1000 °C; and 4 -cooling (at 50, 20, 10, and 5 °C/min). The cycles were carried out three times per heating/cooling rate. The holding times were 5 min.
Computational analyses. Transient thermal computational analyses were performed using the commercial ANSYS Workbench 19.0 software. The purpose of these analyses was to obtain the temperature fields in agreement with the temperature measurements obtained experimentally via thermocouples and to estimate the volume of material that reached temperatures above T C . The geometries used were the same as shown in Fig. 1a and 1c, with the specific sample geometry for each heat source (i.e. a region of reduced thickness in the case of the flame as heat source, and the negative of the FSW tool in the case of the FSW tool as the heat source). The meshes were comprised of about 3.8 million (flame as heat source case) and 3 million (FSW tool as heat source case) tetrahedron elements. The maximum element size was 0.5 mm in the steel plates and 1 mm in all other bodies. The loading condition representing the flame was a heat flow with a normal distribution applied on the surface of the reduced thickness region of the steel specimen body. The analysis was carried out in one step. The loading conditions representing the effect of the heat flow from the FSW tool were applied on the surfaces corresponding to the negative of the tool geometry. The analysis was carried out in two steps. The first step with heat flow applied only on the surfaces corresponding to the probe, and the second step adding the heat flow contribution on the surfaces corresponding to the shoulder. The final results were obtained by adjusting loading conditions iteratively until the simulated temperature fields were in close agreement with the thermocouple measurements for each case. In both cases, the initial temperature was 25 °C, and a constant temperature of 25 °C was applied to the surfaces corresponding to the inside of the copper cooling tubes. An emissivity of 0.3 was considered at the top surface of the steel specimen, excluding the heat flow loading surfaces. All other outside surfaces were adiabatic. The material models used were those for Steel 1010, Copper, Titanium, and Air, available in the materials library of the ANSYS Workbench 19.0 software. The results were validated by comparing the temperature fields above the T C , obtained computationally, with the heat-affected zones evaluated in cross-sections of samples extracted from the center of the processed specimens. A table with the material thermal properties, figures and graphs supporting the methods implemented in the thermal analyses are included in the "Suplementary Information" file available with the online version of this paper.
The magnetostatic computational analyses were performed using the ANSYS Maxwell R18.0 software. The geometries were the same as in the thermal analyses. The meshes were comprised of 2.8 million tetrahedron elements (in both the flame and the FSW tool analyses). The volumes obtained from the thermal analysis were integrated into the magnetostatic model and the analyses were carried out for different values of magnetic permeability (μ R ≫ 1 vs μ R ≈ 1) in those volumes. The material models used were those for Steel 1010, Copper, Titanium, Air and NdFe35, available in the materials library of the ANSYS Maxwell R18.0 software. A table with the magnetic properties considered for the materials is included in the "Suplementary Information" file available with the online version of this paper. (2019) 9:17900 | https://doi.org/10.1038/s41598-019-54503-5 www.nature.com/scientificreports www.nature.com/scientificreports/ Thermal and thermomechanical cycles with temperature and magnetic flux density measurements. Thermal and thermomechanical cycles were carried out on S700MC HSS using non-electrical heat sources to avoid any coercive electromagnetic interaction with the magnetic measurement system. Two heat sources were applied to the specimens: For the thermal cycles it was an oxy-fuel flame, which is a purely thermal heat source; and for the thermomechanical cycles it was the thermomechanical processing, which is an indirect heat source via internal friction dissipation during the plastic deformation induced in the HSS specimen by the plunging and rotation of a rigid FSW tool. The tool material was a non-magnetic polycrystalline cubic boron nitride in a tungsten rhenium metal matrix. Thermocouples were inserted into small holes reaching the half thickness of the processed zone of the specimens. A spacing of 5 mm was kept between each thermocouple as shown in Supplementary Figure S2 in the Supplementary Information file.
The 'Experimental setup' section described the main features of test setup, depicted in Fig. 1. The magnet used to generate the magnetic field was a Ø 15 × 8 mm NeFeB permanent magnet with N42 magnetization in the axial direction. The distance from the magnet to the test sample was such that the interaction between the field and the sample generates the largest field intensity variation when the material changes from ferromagnetic to paramagnetic (and vice versa) without saturating the signal from the Hall-effect sensors. A good compromise between these two conditions was achieved at a distance of 13 mm, directly under the processed zone. The two sensors used to measure the magnetic flux density were SS496A1 ratiometric Hall-effect sensors. These were positioned in 2 mm deep slots machined on the copper chassis at ±5 mm from the center of the plate. The positioning of these sensors, relative to the permanent magnet and the test plate, was supported by the results of the magnetostatic computational analysis. The chassis was water cooled to protect the magnet and the magnetic sensors from the effects of the high temperatures. Furthermore, a 3 mm thick thermal barrier (air gap for the thermal cycles and a Ti plate for the thermomechanical cycles) was placed between the copper chassis and the steel test piece for additional protection of the magnet and the sensors from the high temperature, and also to provide additional backing support in the case of thermomechanical cycles. The data from the Hall-effect sensors and the thermocouples was acquired via a NI USB-6008 module and a NI-9212 module, respectively. A custom-made application was created in LabVIEW to control and synchronize the data acquisition and recording. The data acquisition rate used was 10 Samples/s (10 Hz) which was sufficient to capture with high resolution all the magnetic flux density gradients in the tested thermal and thermomechanical transient processes.

Data availability
Supplementary information is available in the document accompanying the online version of this publication.