Modeling metal forming of a magnesium alloy using an adapted material model

Abstract

Modeling sheet metal forming of materials for lightweight construction requires an understanding of their plastic behavior in different loading directions. The presented work focuses on twin‐roll‐casted magnesium alloy AZ31. It is characterized by unique mechanical properties compared to other magnesium alloys due to the employed twin‐roll‐casting‐process. In general, magnesium alloys with their hexagonal closed‐packed structure possess a complex forming behavior including a deformation‐induced anisotropy evolution. In the context of a fast design approach, an adaptation of the Yield2000‐2d criteria usually used for body‐centered cubic or face‐centered cubic materials is tested. The goal is a simple, versatile material model which parameters are determined just by tensile tests with moderate testing effort. In the investigated model, the yield locus definition is modified by adding a term for the yield exponent evolution during the forming process. The modeling approach is presented and the necessary tests for material data acquisition and evaluation are described. After experimental identification of the model parameters, the material model is applied in a forming simulation. The investigation provides promising results matching well with experimental data. Thus, the application of this model in a fast design step is feasible, offering valuable data like deformed shape, process‐related material properties and induced stresses for further processing.

INTRODUCTION

Resource efficiency and weight reduction are two major goals of lightweight construction as a design philosophy.¹ Hybrid components support these ambitions with their opportunity to design adapted material configurations generating application-specific component properties. In the development process of respective components, the interaction of design, dimensioning and manufacturing has to be considered in order to create advantageous component concepts. For such complex tasks which also includes multistep manufacturing processes, the selective application of finite-element-analysis (FEA) lead to an improvement of the whole design procedure.² Today's hybrid components are often composed of metal and fiber reinforced plastic (FRP).³The metal component contributes high specific stiffnesses and strengths, the latter provides the general strength and ductility.⁴ In this context, magnesium alloys have received increasing attention because of their high strength to weight ratio, making them ideal for industrial applications, such as vehicle components, transportation and aerospace.

Especially in the field of deep drawing, there are different descriptions of the plastic behavior for popular materials like steel or aluminum alloys with a body-centered cubic (BCC) or face-centered cubic (FCC) structure.⁵ Magnesium alloys with their hexagonal closed-packed structure (HCP) show a more complex behavior, resulting in a need for advanced material models and additional efforts in characterization. In this context, effects like material scattering⁶ or the chosen material model⁷ have to be taken into account. Additionally, efforts to reduce the error propagation are of vital importance.⁸ Depending on the chosen materials and respective models, this includes sophisticated test procedures for characterizing the material behavior under tensile, compressive and shear loading.⁹ Furthermore, the modeling of sheet metal forming requires an understanding of the plastic material behavior in different loading directions.¹⁰

This work will present an adapted option for modeling the material behavior of metals independent of their material structure. This simplified approach is intended especially for preliminary studies in the early design process of lightweight components. After a detailed description of the twin-roll-casting process used to manufacture the focused magnesium sheets, a short introduction into the state of the art in modeling of the plastic behavior given. The aim of this work is to evaluate the simplified model which provides a reduced effort for material characterization. The chosen modeling approach is explained comprehensively. Procedures are described in detail for determining the mechanical properties of magnesium alloy AZ31 at forming temperature and, building on that, for deriving the required parameters of the investigated material model. The derived material model is used in the numerical simulation of a deep drawing step of a magnesium sheet. Finally, the results are evaluated in terms of accuracy and efficiency based on established, more complex material models.

STATE OF THE ART Twin-Roll-Casting of Magnesium alloy AZ31

Magnesium alloys have been popular in the aerospace sector for a long time. Nevertheless, the transition into the transportation sector, especially regarding metal sheet parts, is rather limited. One main reason is the challenging silicothermic production process of magnesium.¹¹ In the present work, deep drawing FEA of twin-roll-casted and hot-rolled strips of magnesium alloy AZ31 are focused. The analyzed magnesium sheets, which were developed and manufactured at the Institute of Metal Forming of Technische Universität Bergakademie Freiberg, are characterized by unique mechanical properties compared to other alloys due to the executed twin-roll-casting-process.¹² In this technology, the material is casted directly into the rolling process. The chemical composition of the alloy is given in Table 1.

TABLE 1 Chemical composition of the AZ31 magnesium alloy in wt.%

Al	Zn	Mn	Si	Cu	Fe	Ni	Others	Mg
2.90	1.08	0.375	0.022	<0.001	<0.003	<0.001	<0.01	Balance

Twin-roll-casting and hot-rolling was conducted using a horizontal twin-roll-caster and a reversing rolling mill for the production of magnesium thin strip on pilot scale (cf. Figure 1). Within this process, ingots of the AZ31 alloy are melted under protective gas atmosphere at 700°C. After melting, the melt passes through a casting system, consisting of a preheated casting channel and casting nozzle. The melt is transferred into the rolling gap between the two rolls. On first contact with the water-cooled rolls, the material solidifies quickly and the characteristic microstructure of twin-roll-casting develops.^12,13 Within this investigation, casting speed was 1.5 m/min. The 5.35 mm thick and 730 mm wide strip was coiled for further processing.

The twin-roll-casted strip was homogenized by a procedure adapted to coil heating (cf. Figure 2). In order to ensure a homogeneous temperature distribution and a uniform heating, heat treatment was performed in three steps: (1) heat up to 500°C in 1 h, holding time of 4 h, (2) cool down to 440°C for 2.5 h, holding time 6 h, and (3) cool down to rolling temperature of 370°C for 0.5 h, holding time of 6 h. Rough rolling was conducted in two rolling passes resulting in a strip thickness of 2.5 mm (degrees of deformation: φ₁ = 0.37 and φ₂ = 0.39, respectively).

Applied rolling speed was 100 m/min. An intermediate heat treatment step after the second rolling pass was used to eliminate hardening and to restore the rolling temperature. The treatment comprised three substeps with the following parameters: (1) heat up to 460°C in 1 h, holding time of 4 h, (2) cool down to 440°C for 2 h, holding time of 3 h, and (3) cool down to rolling temperature of 370°C for 0.25 h, holding time of 6 h. The duration of the second step was significantly decreased because of a high amount of dynamic recrystallization (DRX) after two rolling steps. The finish rolling pass to a final sheet thickness of 1.25 mm was performed in one pass with a deformation degree of φ₃ = 0.7 at a temperature of 370 °C and a rolling speed of 100 m/min. Due to the high strain in the finish rolling pass, the major part of the microstructure was recrystallized by DRX. However, in order to ensure a complete recrystallized microstructure, a final annealing at 330°C for 1 h holding time was carried out.

Plastic behavior of magnesium alloys

Choosing the proper material model depends on the material behavior, the demand for accuracy and the testing capabilities as well as the accepted testing effort. Magnesium alloys like the proposed twin-roll-casted AZ31 with its hexagonal closed-packed structure show a different behavior in comparison to other lattice structures. Due to their limited number of slip systems at room temperature, magnesium alloys exhibit a complex material behavior.¹⁴ Therefore, they require more effort in the characterization tests to map the material response during plastic deformation.¹⁵

Material behavior is described by flow criteria, which can be divided into three different groups. Isotropic, anisotropic symmetric, and anisotropic asymmetric yield criteria.¹⁶ Isotropic models, such as the best-known approaches of von-Mises¹⁷ and Tresca,¹⁸ represent the material behavior independently of the rolling direction. Anisotropic yield criteria include the dependence on the rolling direction, but do not distinguish between tension and compression direction. The classic representative is the model developed by Hill,¹⁹ which, in addition to the uniaxial stresses, also takes the perpendicular anisotropy in 0°, 45°, and 90° as well as the biaxial yield stress into account.²⁰ In addition to the direction-dependent material behavior, anisotropic asymmetric yield criteria, as the remaining category, also take the tension-compression asymmetry of the material into consideration. The tensile-compression asymmetry of the material results in a shifting or distortion of the initial yield locus.²¹ In the following Table 2 a short overview without a claim to completeness is given.

TABLE 2 Overview of anisotropic yield criteria

Anisotropic symmetric yield criteria	Anisotropic asymmetric yield criteria
Hill'9020	Rees22
Karafillis and Boyce23	Liu et al.24
Bron and Besson25	Vegter et al.26
Soare and Barlat27	Plunkett et al.28
Cazacu et al.29	Yoon et al.30
Banabic et al.31	Soare and Benzerga21
Banabic et al.32	Lee et al.33

Especially magnesium alloys with their complex structure and the tension-compression anisotropy require the use of an anisotropic and asymmetric yield criterion, in order to achieve an accurate modeling of the material behavior. The commonly used model for this application is the CPB06 yield surface formulation developed and improved by Cazacu et al.,¹⁵ which is based on the isotropic model of Drucker³⁴ and adapted by adding anisotropy coefficients. Yield criteria for hexagonal closed-packed materials hereby are usually based on this initial formulation and extended it for an enhanced accuracy by taking, for example, thermal effects into account.³⁵

The strain hardening behavior can be divided into three different types of yield locus evolution–isotropic strain hardening with uniform expansion, kinematic strain hardening with a translation, and distortion strain hardening with a distortion of the strain locus. In this context, especially with respect to the translation of the yield locus (which occurs in most metallic materials), the work of Bauschinger³⁶ makes a significant contribution. Complex material models can reproduce this behavior, but then require increased effort in terms of material characterization. But there are also existing solutions, for example, for orthotropic materials, that gained satisfying results just using uniaxial testing equipment.³⁷

This approach is investigated with the presented model in terms of suitability for fast, sufficiently accurate prediction of the forming behavior of magnesium alloy AZ31. It works with only two different characterization tests, tensile and plain strain specimen to gain the data for the criteria. The adapted yield criterion for describing the evolution of yield surfaces during a forming process was first presented by Küsters et al.³⁸ By using the adapted model, a better agreement with the experimentally produced and measured component was achieved. The approach was tested for the steel DC06 (1.0873) and DX54 (1.0306) and commonly used aluminum alloy EN-AA6016.³⁹ Figure 3 shows the results for DC06 as an example.

In the present article, the applicability of the criterion by Küsters et al. for HCP materials will be evaluated using the example of twin-roll-casted magnesium alloy AZ31. It is based on the well-known Yld2000-2d criterion,⁴⁰ which is shown in Equation (1). [Image Omitted. See PDF] The variables $$$ {X}_1^{\prime } $$$, $$$ {X}_2^{\prime } $$$ and $$$ {X}_2^{\prime \prime }+{X}_1^{\prime \prime } $$$ are linear transformed vectors from the Cauchy stress and are defined by the Equation (2). [Image Omitted. See PDF] It consists of nine different parameterseight α_i parameters and one exponent m (see Equations 1 and 2). In the initial yield function, all parameters are constant and determined in previously performed tests. The exponent m is chosen according to the structure of the material. Here, m = 6 for body-centered cubic and, m = 8 for face-centered cubic lattices are given as initial values. The authors are not aware of any application of this model for HCP materials, so no initial value for the exponent m is available. In the approach presented by Küsters et al.,³⁸ the exponent m is replaced by a strain dependent function which takes the r-value (also known as Lankford coefficient⁴¹) into account (cf. Figure 4A). A plane stress state and isotropic strain hardening behavior are assumed. A cubic Bézier curve is implemented by the coupling of the yield exponent and an internally defined corresponding accumulated plastic strain. The interpolation is described by four additional parameters m_i (cf. Figure 4B). The path of the curve is fixed by the four interpolation points of the curve. Due to the inclusion of the varying four m_i-exponents and constant α_i-values, a shape change of the yield surface occurs. After the initial parameter estimation for the yield locus, a half-analytical stress calculation is carried out based on the available experimental data and the strain curve. The residuals were calculated after the algorithm by Marquardt.⁴² The different parameters α_i and m_i were calculated until the minimum of the residual (least square error) from the internal section loads compared to the recorded forces is reached. The implemented subroutine used during the calculation is based on the cutting-plane algorithm based on Ortiz and Simo.⁴³ For additional information regarding this approach, please refer to the initial yield criterion⁴⁴ and to the specific publication provided by Küsters et al.³⁸

This shape variation influences the yield surface normal in the tensile stress state, applied on σ₁-axis in Figure 4C. Whereas the r-value is directly linked to the yield surface normal, and therefore changes the rotation, the yield exponent m can be used to take the r-value into account during the yielding. For this reason, the yield exponent evolution can be used for modeling the anisotropy development in the part. This leads to the applied distortion (red line) of the subsequent yield locus (cf. Figure 4C).

The determined parameters were implemented in LS-Dyna (R11.1.0) as a user defined material model by a subroutine developed for explicit LS-Dyna FE-Code (mpi 9.0.1-d / Intel FORTRAN Compiler 13.1 SSE2). With the inclusion of the different directional properties of the different materials via the adjustment of the m-value, an increase of the imaging accuracy could be demonstrated for different geometries.³⁹ In the following investigations, the adapted yield criterion was used for a HCP structured magnesium alloy to test whether the inclusion of the Lankford coefficient allows the model to be used in conjunction with an increase in imaging accuracy.

Material characterization and model parameter identification

Twin-roll-casted sheets of magnesium alloy AZ31 were characterized at a testing temperature of 225°C. At this temperature, additional slip systems are activated in magnesium alloys and a forming process is easier to conduct. The necessary model parameters were first determined by standardized testing methods. For this purpose, tensile tests and plane strain tests were performed according to ASTM E8⁴⁵ and EN ISO 6892-1,⁴⁶ respectively. The specimen dimensions are shown in Figure 5A. Using a twin-roll-casted magnesium sheet with a thickness t₀ = 1.25 mm, test samples were prepared in 0°, 45°, and 90° regarding the rolling direction (RD). The testing plan included 10 samples for each test configuration (specimen dimension and rolling direction).

The tests were performed on a Zwick 1475 material testing machine within a heating chamber (cf. Figure 5B). For the subsequent evaluation with the GOM^® Aramis system, the specimens were observed with two CCD-cameras throughout the test cycle, which were positioned in front of a window integrated on the side of the heating chamber. Additionally, a speckle pattern was applied to the surface of the samples for evaluation by the GOM^® Aramis system (cf. Figure 5C). For this purpose, the specimen's surface was cleaned and sprayed with a white primer before adding the black stochastic pattern manually. The specimens were placed inside the chamber for preheating, and the testing equipment and mechanically clamped specimen were held at test temperature for approx. 15 min to ensure a homogeneous temperature distribution. Throughout the tests, two temperature sensors close to the specimen monitored the temperatures of specimen and equipment, respectively.

With the prepared setup, the tests were performed with a strain rate of 0.001 s⁻¹ until the failure of the specimen. For accurate determination of the material characteristics, the transition point from elastic to plastic deformation is crucial, so the frequency of the image generation of the GOM^® software was set to 10 Hz up to R_p0.2 and to 4 Hz thereafter (see Table 3). This reduces the amount of data and the time for evaluation with a negligible impact on the accuracy of the experimental results.

TABLE 3 Summary of the testing parameters

Parameter	Value	Parameter	Value
Strain rate up to Rp0.2	0.001 s−1	Imaging frequency	10 Hz
Strain rate after Rp0.2	0.001 s−1	Imaging frequency	4 Hz

Reaction forces were detected by a standard load cell, deformation data was detected by the optical measurement system GOM^® 5 M and evaluated by the corresponding Aramis Software (version 2018). The evaluation in the GOM^® Aramis software was performed by using the cutting-line algorithm.⁴⁷ Accordingly, it was possible to gain additional values for the strain distribution across the specimen surface for every time step. The results are shown in Figure 6A with the stress–strain curves and the fitted solution for the flow curve in Figure 7A.

The results for the different rolling directions show a similar behavior. While there are only small deviations in the stress–strain curvesthe curves for 45° and 0° are slightly below the 90° curvethere are larger differences in the elongation at break. The elongation at break for the 45° and 0° specimens is significantly lower than for the 90° specimens. After the yield point R_p0.2 is reached, there is a minor decrease in the stress level. The yield strength R_m is slightly higher than the yield point.

Figure 6B shows the calculated Lankford coefficient r derived from the evaluated tensile tests for the three rolling directions. Usually, the r-value is an averaged value. Based on the illustrated development of the r-values, it can be assumed that the use of the averaged value r_m inevitably leads to deviations. In Figure 8A, it is visible that taking the evolution of the r-value into account results in a change of the yield locus shape during the calculated deformation. Whereas the common model shows an isotropic hardening development of the yield locus, the adapted model results in the mentioned change in the shape to a more oval form. The results of the performed tests are shown as dotted lines. They define the yield locus through the evaluated grid points gained from the experimental evaluation. The blue yield locus curve illustrates the change in shape with the help of the red tangent. While a constant m-value would only result in a uniform evolution of the yield locus curve, the shape variation through the r-dependent values m_i mentioned before (cf. Figure 3) becomes visible in Figure 8A illustrated by a rotated tangent in the tensile stress state. The calculated parameters for α_i and m_i for the adapted model are shown in Figure 8B. The approximation of the flow curve was calculated using the Swift approach.⁴⁸ The parameters, used in the simulation, are visible in Figure 7B.

NUMERICAL EVALUATION AND DISCUSSION

A T-cup was chosen as experimental geometry (cf. Figure 9A). The deep drawing tool used in the experiments was installed on a single acting press, which can be equipped with up to six gas pressure springs for applying the blank holder force. The exchange of the springs needs to be done in pairs, whereby a maximum blank holder force of 600 kN is achieved with the maximum number of springs. The tool system is modular and punches as well as drawing rings are changeable, which is favorable for an adaption of the tool for hot forming processes. In addition, the frame angle of the punch was about 5° (cf. Figure 9c). This is necessary in order to apply the required pressure in the area of the frame for the subsequent hybridization of the component with fiber-reinforced plastic in the consolidation process. The die had no defined bottom, which allows to vary the drawing depth. The implementation of heatable drawing rings and blank holder enabled the heating of the blanks.

For the simulation of the deep drawing step, the model was reduced to the essential parts with an overall punch size of 530 mm × 400 mm (cf. Figure 9B). Numerical analyzes incorporating the derived parameters were conducted in order to investigate the adapted yield function. Understandably, the approach will not reach the accuracy of the complex models due to the typical material properties, which is not the goal for the first dimensioning in the context of a process chain simulation.

The adapted yield function was implemented into LS-DYNA (11.1.0) via a user defined material subroutine (ls-dyna-usermat/9.0.1-d). The simulation was performed at the Center for Information Services and High-Performance Computing (ZIH). The setup was prepared and evaluated in LS-PrePost V4.7.9. The blank was meshed with an element length of 2 mm with adapted refinement. A fully integrated shell element was used (ELFORM16) with five integration points through the shell thickness. All parts, except the blank, were defined as rigid bodies. The movement of the punch was described by a predetermined velocity. The contact conditions are set by a one-way surface to surface definition. The calculation was performed explicit with mass scaling option. The blank holder force was chosen dependent on the gas pressure springs with an initial force of 200 kN, linear increasing to 250 kN during the forming. The velocity of the punch was set to v_punch = 2000 mm/s, accordingly the drawing depth s_D of 50 mm was reached after t = 0.025 s which is also the termination time. A comparison of the conventional approach (Yld2000-2d) and the adapted approach according to Küsters et al.³⁸ is shown in Figure 10 based on the differences visible by the illustration of the triaxiality.

The adapted criterion could not take the tension-compression anisotropy into account and calculates with a symmetric yield criterion with a shape shift due to the described evolution of the parameter m_i. The chosen T-cup with a moderate complexity is therefore a valid starting point for try-outs. Figure 10 shows the triaxiality with the different stress states between biaxial compression (η = −2/3) and biaxial tension (η = 2/3). The occurring stress states in the deep drawing process of this part are mainly located in the first quadrant of the yield locus with tension and biaxial tension, whereas areas with compression stress were only present in small areas. For magnesium, the compression area (η < 0) is particularly interesting, since the yield locus curve expands there in the compression region of the yield locus. Here, differences in the areas were identifiable in Figure 10 (0 < η < −2/3). The evolution of the yield locus shape leads to a better prediction of the parts stress states during the process. Due to the adjustment of the yield point by the adapted model, more realistic results in the bottom area with a bulge above the convex curvature were obtained. The significant area is therefore suitable for a first check of the results in the comparison of the simulation and a measurement of the experimentally manufactured component. A comparison between the experimental and calculated geometry of the deep-drawn T-cup was performed. Figure 11 shows an example of the results for the deep drawn T-cup regarding the z-displacement and the occurring bulge.

Striking similarities between the calculated and the deep-drawn part can be observed in the previously mentioned area above the concave curvature. While forming and the resulting stress superposition, a bulge occurs which can form freely due to the open design of the die. The adaptation of the model showed an improvement in the representation of the stress states especially in this area and took the tensions-compression anisotropy better into account. The experimentally produced cup was then measured with the GOM^® ATOS system and superimposed on the calculated solution via GOM^® inspect suite 2020 (cf. Figure 12A). The estimation in terms of a fast design approach is possible with compromises in accuracy. The wrinkles and bulges in the bottom area could also be reproduced quite well (cf. Figure 12B). In Figure 12A the wrinkling in the flange area is visible especially in the tip of the cup. Regarding changing and flexible process chains for the development of hybrid components independent from the chosen alloy, the model shows a sufficient match with the calculation.

The adapted criterion used the yield exponent and replaced it with an equation, which took the Lankford-coefficient in account for the description of the yield locus evolution during a forming process. This improves the prediction of distribution of the stress states by the shown triaxiality. Therefore, an improvement in the prediction of possible defects like thinning or wrinkling in deep drawn parts is possible. The stress conditions in the uniaxial tensile and biaxial tensile range, which mostly occur in deep drawing, can be reproduced well. With the characteristics of the criteria and the known properties of magnesium alloys, differences in the bottom area of the component are noticeable through the visible deviation due to the adaption of the yield point (cf. Figure 11). For a detailed analysis of the developed model, testing of more complex parts is planned. Nevertheless, it is visible that the mentioned criteria take the complex material behavior into account due to the inclusion of the anisotropy in the Yld2000-2d criterion. Regarding more complex geometries, it is not yet possible to make a statement within this short communication. Considering the modular process chain, the results show promising and improved results for different types of alloys with a moderate effort for the characterization tests. Therefore, the mentioned approach is a feasible option for the numerical simulation of the forming step of the metal part in a predesign stage, independent of the respective material structure.

SUMMARY AND OUTLOOK

Within this article, an adapted yield criterion for modeling the plastic material behavior of twin-roll-casted magnesium alloy AZ31 is investigated. Whereas other models require various tests and equipment to fully characterize the material, here the anisotropy was considered by an adaptation of the commonly used material model Yld2000-2d. The intent was to use a simple, versatile model which parameters can be collected in standardized tests with moderate testing effort. Compared to more complex models, such as the CPB06,¹⁵ the testing effort for the investigations carried out is significantly reduced and just a single tensile testing machine is needed.

The chosen modeling approach is described in detail and necessary tensile as well as plane strain tests for characterization purposes were performed and evaluated. Based on these results, the developed material model is configured and implemented into LS-Dyna. Finally, numerical simulations of a deep drawing step are performed and compared to experimental findings and the deep-drawn part via a geometrical comparison in GOM^®inspect. While the results for aluminum and steel alloys were already promising, it is shown within this article that the chosen approach is furthermore applicable for magnesium alloys within certain limits depending on the complexity of the deep drawn part. The consideration of the evolution of the r-value during deformation leads to a more accurate result with an easy applicable model even for the chosen HCP-structured material. Especially the performed simulation of a deep drawing process shows an improvement of the mapping of the stress states in the part along with a reduction of the performed material tests and therefore time in comparison to the conventional model. For a more precise interpretation, more complex models still must be used. Nevertheless, the presented approach can be a profitable contribution in the design of forming processes, as manufacturing technology attempts to push technological limits.

Thus, the examined approach is particularly suitable for a quick predimensioning at the beginning of a design process, where a first numerical estimation of the forming behavior must be made independently of the intrinsic material structure. By reducing the model to an isotropic-distorting locus evolution, the kinematic hardening cannot be represented and is therefore a potential reason for acceptable deviations in the calculation. Yet, it is an easy and fast forward option for a modular process chain and the design process of lightweight and resource efficient composite parts. The considered fast and versatile model for the simulation of deep drawing processes is also a useful option in the field of materials science as it enables a fast evaluation of novel alloys. Future investigations will cover additional load cases and more complex parts with different stress states in order to evaluate the model performance and its limits more deeply. Furthermore, the comparison to an established yield criteria will be done by expanding the performed experimental tests. Also, the AZ31 sheets will be deep drawn using the visioplasticity method in the presented T-cup tool in order to further validate the model by comparing it with detailed experimental results.

ACKNOWLEDGMENTS

The authors acknowledge the support of the project “Saxon Alliance for Material- and Resource-Efficient Technologies (AMARETO)” (Project No 100291445) that is funded by the European Union (European Regional Development Fund) and by the Free State of Saxony. Open Access funding enabled and organized by Projekt DEAL.

PEER REVIEW

The peer review history for this article is available at https://publons.com/publon/10.1002/eng2.12540.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CONFLICT OF INTEREST

The authors declare that there is no conflict of interest regarding the publication of this article.