Fig. 4b. Overall, there is a good agreement and only a small deviation of a maximum of 0.06 mm can be seen, which is particularly noticeable in the outer lower circumference (red region). Due to the good agreement between experiment and simulation, the FE model can be considered as validated.

<figure><img src="image_783.png" /><figcaption>Fig. 4. Comparison between experimental and numerical force-displacement curves (a) and geometric comparison (b) (10 mm/s; 1,000 °C).</figcaption></figure>

**Numerical parameter study.** Using the validated FE model, the influence of various process parameters was analysed. As shown in Fig. 5, at a press speed of 10 mm/s and a furnace temperature of 1,000 °C, the final Inconel distribution was significantly influenced by the choice of the initial Inconel layer thickness. With an initial Inconel thickness of 3 mm (Fig. 5a), the percentage deviations from the initial thickness are the highest compared to the other initial thicknesses, but the lowest upsetting to 3.2 mm (+6.7 %) of the Inconel can be observed in the lower radius (2). The strongest thinning to 0.6 mm (-80 %) can be observed in the area of the upper radius (3) and an initial thinning can already be recognised before complete forging. The highest value of plastic strain is also present at this point, which also extends into the tool steel at this initial layer thickness. Such a high value is not found in the tool steel for the other Inconel thicknesses. In contrast, the other Inconel thicknesses have a concentration of the higher plastic strain values on the Inconel layer, which is why the tool steel shows lower values. At the Inconel initial thickness of 5 mm (Fig. 5b), a kind of accumulation of the Inconel can be observed in the lower radius (2), resulting in an increase in Inconel up to a thickness of 5.6 mm (+12 %). In the area of the upper radius, a thinning to 1.6 mm (-68 %) can be seen (3). The accumulation of the Inconel in the lower radius (2) is even more clearly recognisable with an Inconel initial thickness of 7 mm (Fig. 5c). Here, the Inconel increases to a thickness of 8.3 mm (+18 %). During the forging process, it can be recognised that the Inconel is pushed towards the centre. For this reason, the smallest reduction to only 6.9 mm (-2 %) was calculated for this variant in the centre of the mandrel (1) at the end of the forging process. Comparison of relative changes show that an increase of the initial Inconel layer thickness leads to a stronger accumulation of Inconel in the lower region (2) and less reduction in the centre of the mandrel (1) and upper radius (3). Overall, the minimum Inconel thickness of 2.4 mm can be realised with each parameter variation investigated. With the lowest Inconel thickness, however, it is necessary to check how much material is lost through post-processing. From an ecological and cost point of view, the variant with the greatest Inconel thickness should not be favoured.
Fig. 4b. Overall, there is a good agreement and only a small deviation of a maximum of 0.06 mm can be seen, which is particularly noticeable in the outer lower circumference (red region). Due to the good agreement between experiment and simulation, the FE model can be considered as validated.

<figure><img src="image_791.png" /><figcaption>Fig. 4. Comparison between experimental and numerical force-displacement curves (a) and geometric comparison (b) (10 mm/s; 1,000 °C).</figcaption></figure>

**Numerical parameter study.** Using the validated FE model, the influence of various process parameters was analysed. As shown in Fig. 5, at a press speed of 10 mm/s and a furnace temperature of 1,000 °C, the final Inconel distribution was significantly influenced by the choice of the initial Inconel layer thickness. With an initial Inconel thickness of 3 mm (Fig. 5a), the percentage deviations from the initial thickness are the highest compared to the other initial thicknesses, but the lowest upsetting to 3.2 mm (+6.7 %) of the Inconel can be observed in the lower radius (2). The strongest thinning to 0.6 mm (-80 %) can be observed in the area of the upper radius (3) and an initial thinning can already be recognised before complete forging. The highest value of plastic strain is also present at this point, which also extends into the tool steel at this initial layer thickness. Such a high value is not found in the tool steel for the other Inconel thicknesses. In contrast, the other Inconel thicknesses have a concentration of the higher plastic strain values on the Inconel layer, which is why the tool steel shows lower values. At the Inconel initial thickness of 5 mm (Fig. 5b), a kind of accumulation of the Inconel can be observed in the lower radius (2), resulting in an increase in Inconel up to a thickness of 5.6 mm (+12 %). In the area of the upper radius, a thinning to 1.6 mm (-68 %) can be seen (3). The accumulation of the Inconel in the lower radius (2) is even more clearly recognisable with an Inconel initial thickness of 7 mm (Fig. 5c). Here, the Inconel increases to a thickness of 8.3 mm (+18 %). During the forging process, it can be recognised that the Inconel is pushed towards the centre. For this reason, the smallest reduction to only 6.9 mm (-2 %) was calculated for this variant in the centre of the mandrel (1) at the end of the forging process. Comparison of relative changes show that an increase of the initial Inconel layer thickness leads to a stronger accumulation of Inconel in the lower region (2) and less reduction in the centre of the mandrel (1) and upper radius (3). Overall, the minimum Inconel thickness of 2.4 mm can be realised with each parameter variation investigated. With the lowest Inconel thickness, however, it is necessary to check how much material is lost through post-processing. From an ecological and cost point of view, the variant with the greatest Inconel thickness should not be favoured.
<figure><img src="image_784.png" /><figcaption>Fig. 5. Final material distribution of Inconel and tool steel for an initial layer thickness of 3 mm (a), 5 mm (b) and 7 mm (c) as well as comparison between specific regions regarding final thickness and relative change of thickness for the Inconel layer (d) (10 mm/s; 1,000 °C).</figcaption></figure>

Fig. 6 shows the dependence of the required press force on the press speed and the selected furnace temperature for an initial Inconel layer thickness of 5 mm. As expected, the force requirement is strongly temperature-dependent and decreases with increasing semi-finished workpiece temperature. For the press speed, there is a slight increase in the press force with increasing speed, which can be attributed to the strain rate dependency of Inconel in particular. An increase in the press force with increasing layer thickness was observed for the variation of the layer thickness, as expected. Ultimately, all variants can be implemented with regard to the required press force. However, it should be noted that, on the one hand, the deformation capacity of the Inconel is reduced with decreasing temperature and, on the other hand, that the die load increases. Accordingly, the highest possible temperatures should be aimed for during forging. Also, from an economic point of view, only as much Inconel as necessary should be used.

<figure><img src="image_785.png" /><figcaption>Fig. 6. Results from the full factorial parameter study: The influence of temperature and press speed on the press force with an initial Inconel thickness of 5 mm.</figcaption></figure>

## Conclusion

In this work, the numerical process design for the production of hybrid dies was presented. The focus was on the final Inconel distribution to ensure sufficient protection for the thermal high loaded near surface die areas. First, the thermal load on the die was analysed using numerical
<figure><img src="image_792.png" /><figcaption>Fig. 5. Final material distribution of Inconel and tool steel for an initial layer thickness of 3 mm (a), 5 mm (b) and 7 mm (c) as well as comparison between specific regions regarding final thickness and relative change of thickness for the Inconel layer (d) (10 mm/s; 1,000 °C).</figcaption></figure>

Fig. 6 shows the dependence of the required press force on the press speed and the selected furnace temperature for an initial Inconel layer thickness of 5 mm. As expected, the force requirement is strongly temperature-dependent and decreases with increasing semi-finished workpiece temperature. For the press speed, there is a slight increase in the press force with increasing speed, which can be attributed to the strain rate dependency of Inconel in particular. An increase in the press force with increasing layer thickness was observed for the variation of the layer thickness, as expected. Ultimately, all variants can be implemented with regard to the required press force. However, it should be noted that, on the one hand, the deformation capacity of the Inconel is reduced with decreasing temperature and, on the other hand, that the die load increases. Accordingly, the highest possible temperatures should be aimed for during forging. Also, from an economic point of view, only as much Inconel as necessary should be used.

<figure><img src="image_793.png" /><figcaption>Fig. 6. Results from the full factorial parameter study: The influence of temperature and press speed on the press force with an initial Inconel thickness of 5 mm.</figcaption></figure>

## Conclusion

In this work, the numerical process design for the production of hybrid dies was presented. The focus was on the final Inconel distribution to ensure sufficient protection for the thermal high loaded near surface die areas. First, the thermal load on the die was analysed using numerical
simulation in order to define a minimum layer thickness for the Inconel. The temperature distribution indicates that the die requires a coating thickness of at least approx. 2.4 mm to 3.0 mm. Subsequently the hybrid forging process was designed by FE-simulation. The simulation showed that equivalent stresses are above the mechanical properties like yield strength of the material selected for the component. By placing a reinforcement ring around the shoulder insert, plastic deformation of the material can be prevented. A reduction in the load can be achieved, for example, by reducing the thickness of the Inconel. Experimental tests were carried out and the FE model was validated by comparing experiment and simulation. Finally, the required Inconel distribution in the hybrid die was successfully achieved by adjusting the Inconel layer thickness.

After successful validation of the FE model, a numerical parameter study was performed on the influence of the forging temperature, the initial Inconel thickness and the selected press speed on the resulting material distribution as well as the required press force. The initial layer thickness influences clearly the final Inconel distribution. The layer thickness distribution is only influenced by the initial layer thickness and not by the investigated process parameters temperature as well as press speed. In order to achieve the minimum required Inconel thickness of 2.4 mm in thermally highly stressed area, an initial thickness of 3 mm is required. As the formed hybrid die must then be reworked, the Inconel thickness at the end of the forging process should be greater than 2.4 mm. Accordingly, a slightly greater initial Inconel thickness should be selected. An initial Inconel thickness of 7 mm leads to a layer distribution that fits the requirements. However, this results in higher die loads and also from an economic point of view, this initial Inconel thickness should not be selected. Overall, the initial thickness of 5 mm can therefore be recommended for the process. As expected, a reduced temperature leads to an increase in press force. Furthermore, required press force can be reduced by low press speeds. The conclusion for the tests was that a furnace temperature of 1,000 °C or 1,100 °C should be aimed for. At the same time, a medium to slow press speed should be aimed for during forging the hybrid semi-finished workpiece.

In the future, the experimentally produced dies should be tested in forging tests regarding their lifetime potential. The die life analysis in series forging tests should determine whether the hybrid dies have a longer service life than conventional dies due to the adapted material distribution. Fatigue phenomena such as crack formation or abrasive wear play a particularly important role here. On the basis of these further findings, the conclusion can be drawn as to whether the higher die manufacturing costs due to the more complex manufacturing process and the higher material can be compensated by a longer service life of the dies. In addition, further simulations and tests should be carried out regarding the transfer to larger cross-sections. Further investigations may include local tensile tests on hybrid friction-welded specimens to determine the properties of the joining zone and a cooling simulation with analysis of the stress relaxation in the hybrid forging die. In the cooling simulations, the influence of the different thermal expansion coefficients on the stresses in the joining zone is of interest.

## Acknowledgment

The results presented were obtained in the research project "High-temperature-resistant tool edge layer by applying the Tailored Forming technology to hot forging tools" (T03) funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Collaborative Research Centre 1153 "Process chain to produce hybrid high performance components by Tailored Forming" - 252662854. The authors would like to thank the German Research Foundation for the financial support.

## References

[1] K. Vollrath, Simulation in the Forging Industry, Forging Information Service - Special Edition, Hagen (2013).
simulation in order to define a minimum layer thickness for the Inconel. The temperature distribution indicates that the die requires a coating thickness of at least approx. 2.4 mm to 3.0 mm. Subsequently the hybrid forging process was designed by FE-simulation. The simulation showed that equivalent stresses are above the mechanical properties like yield strength of the material selected for the component. By placing a reinforcement ring around the shoulder insert, plastic deformation of the material can be prevented. A reduction in the load can be achieved, for example, by reducing the thickness of the Inconel. Experimental tests were carried out and the FE model was validated by comparing experiment and simulation. Finally, the required Inconel distribution in the hybrid die was successfully achieved by adjusting the Inconel layer thickness.

After successful validation of the FE model, a numerical parameter study was performed on the influence of the forging temperature, the initial Inconel thickness and the selected press speed on the resulting material distribution as well as the required press force. The initial layer thickness influences clearly the final Inconel distribution. The layer thickness distribution is only influenced by the initial layer thickness and not by the investigated process parameters temperature as well as press speed. In order to achieve the minimum required Inconel thickness of 2.4 mm in thermally highly stressed area, an initial thickness of 3 mm is required. As the formed hybrid die must then be reworked, the Inconel thickness at the end of the forging process should be greater than 2.4 mm. Accordingly, a slightly greater initial Inconel thickness should be selected. An initial Inconel thickness of 7 mm leads to a layer distribution that fits the requirements. However, this results in higher die loads and also from an economic point of view, this initial Inconel thickness should not be selected. Overall, the initial thickness of 5 mm can therefore be recommended for the process. As expected, a reduced temperature leads to an increase in press force. Furthermore, required press force can be reduced by low press speeds. The conclusion for the tests was that a furnace temperature of 1,000 °C or 1,100 °C should be aimed for. At the same time, a medium to slow press speed should be aimed for during forging the hybrid semi-finished workpiece.

In the future, the experimentally produced dies should be tested in forging tests regarding their lifetime potential. The die life analysis in series forging tests should determine whether the hybrid dies have a longer service life than conventional dies due to the adapted material distribution. Fatigue phenomena such as crack formation or abrasive wear play a particularly important role here. On the basis of these further findings, the conclusion can be drawn as to whether the higher die manufacturing costs due to the more complex manufacturing process and the higher material can be compensated by a longer service life of the dies. In addition, further simulations and tests should be carried out regarding the transfer to larger cross-sections. Further investigations may include local tensile tests on hybrid friction-welded specimens to determine the properties of the joining zone and a cooling simulation with analysis of the stress relaxation in the hybrid forging die. In the cooling simulations, the influence of the different thermal expansion coefficients on the stresses in the joining zone is of interest.

## Acknowledgment

The results presented were obtained in the research project "High-temperature-resistant tool edge layer by applying the Tailored Forming technology to hot forging tools" (T03) funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Collaborative Research Centre 1153 "Process chain to produce hybrid high performance components by Tailored Forming" - 252662854. The authors would like to thank the German Research Foundation for the financial support.

## References

[1] K. Vollrath, Simulation in the Forging Industry, Forging Information Service - Special Edition, Hagen (2013).
[2] B.-A. Behrens, D. Rosenbusch, H. Wester, J. Siring, Numerical investigations on stresses and temperature development of tool dies during hot forging, in: Key Engineering Materials, 926 (2022) 559-568. https://doi.org/10.4028/p-sf68jl

[3] H. Prinzhorn, J. Richter, C. Böning, P. Nyhuis, Lot Depending Tool Wear, in: Zeitschrift für wirtschaftlichen Fabrikbetrieb, 111(7-8) (2016) 425-429. http://dx.doi.org/10.3139/104.111565

[4] F. Klocke, D. Heinen, F. Schongen, K. Arntz, Y. Liu, V. Bäcker, B. Feldhaus, Wear Protection of Deep Drawing Tools by Systematic Optimization of Highly Stressed Surfaces, in: Advanced Materials Research, 907 (2014) 439-453. https://doi.org/10.4028/www.scientific.net/AMR.907.439

[5] L. Renhof, Mikrostruktur und mechanische Eigenschaften der Nickellegierung IN718 (2007).

[6] J.R. Davis, ASM Speciality Handbook Heat-Resistant Materials, in: ASM International (1997).

[7] B.-A. Behrens, J. Uhe, Introduction to tailored forming, in: Production Engineering, 14(2) (2021) 133-136. https://doi.org/10.1007/s11740-021-01022-w

[8] D. Landgrebe, L. Krüger, N. Schubert, E. Jentsch, T. Lehnert, Resource-efficient development of thermally highly resistant engine components of hybrid metal composites – experiments and numerical analysis, in: Procedia Engineering 207 (2017) 884-889. https://doi.org/10.1016/j.proeng.2017.10.846

[9] J. Kruse, M. Mildebrath, L. Budde, T. Coors, M.Y. Faqiri, A. Barroi, M. Stonis, T. Hassel, F. Pape, M. Lammers, J. Hermsdorf, S. Kaierle, L. Overmeyer, G. Poll, Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Corss-Wedge Rolling, in: metals, 10 (2020) 1336. https://doi.org/10.3390/met10101336

[10] B.-A. Behrens, K. Brunotte, T. Petersen, R. Relge, M. Till, Transfer of ausforming parameters to scaled forging tools, in: Metal 2021 Conference Proceedings (2021). https://doi.org/10.37904/metal.2021.4118

[11] J. Siring, M. Till, H. Wester, J. Uhe, K. Brunotte, Characterisation and qualification of hot working tool steels and Inconel for the production of a hybrid forging die, Bauernhansl, T., Verl, A., Liewald, M., Möhring, HC. (eds) Production at the Leading Edge of Technology. WGP 2023. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-47394-4_62

[12] B.-A. Behrens, A. Huskic, D. Rosenbusch, J. Peddinghaus, H. Wester, M. Siegmund, J. Giedenbacher, J. Siring, Design, Characterisation and Numerical Investigations of Additively Manufactured H10 Hybrid-Forging Dies with Conformal Cooling Channels, in: metals, 12 (2022) 1063. https://doi.org/10.3390/met12071063

[13] A.K. Drexler, Microstructural based simulation of the residual stress field in heat treated turbine discs from INCONEL718 (2018). https://doi.org/10.34901/mul.pub.2023.103

[14] A.S. Agazhanov, D.A. Samoshkin, Y.M. Kozlovski, Thermophysical properties of Inconel 718 alloy, J. of Physicy: Conference Series, 1382(1) (2019) 1742-6596. http://dx.doi.org/10.1088/1742-6596/1382/1/012175

[15] D. Dye, K.T. Conlon, R.C. Reed, Characterization and modeling of quenching-induced residual stresses in the nickel-based superalloy IN718, in: Metallurgical and materials Transactions A, 35 (2004) 1543-1940. http://dx.doi.org/10.1007/s11661-004-0079-7
[2] B.-A. Behrens, D. Rosenbusch, H. Wester, J. Siring, Numerical investigations on stresses and temperature development of tool dies during hot forging, in: Key Engineering Materials, 926 (2022) 559-568. https://doi.org/10.4028/p-sf68jl

[3] H. Prinzhorn, J. Richter, C. Böning, P. Nyhuis, Lot Depending Tool Wear, in: Zeitschrift für wirtschaftlichen Fabrikbetrieb, 111(7-8) (2016) 425-429. http://dx.doi.org/10.3139/104.111565

[4] F. Klocke, D. Heinen, F. Schongen, K. Arntz, Y. Liu, V. Bäcker, B. Feldhaus, Wear Protection of Deep Drawing Tools by Systematic Optimization of Highly Stressed Surfaces, in: Advanced Materials Research, 907 (2014) 439-453. https://doi.org/10.4028/www.scientific.net/AMR.907.439

[5] L. Renhof, Mikrostruktur und mechanische Eigenschaften der Nickellegierung IN718 (2007).

[6] J.R. Davis, ASM Speciality Handbook Heat-Resistant Materials, in: ASM International (1997).

[7] B.-A. Behrens, J. Uhe, Introduction to tailored forming, in: Production Engineering, 14(2) (2021) 133-136. https://doi.org/10.1007/s11740-021-01022-w

[8] D. Landgrebe, L. Krüger, N. Schubert, E. Jentsch, T. Lehnert, Resource-efficient development of thermally highly resistant engine components of hybrid metal composites – experiments and numerical analysis, in: Procedia Engineering 207 (2017) 884-889. https://doi.org/10.1016/j.proeng.2017.10.846

[9] J. Kruse, M. Mildebrath, L. Budde, T. Coors, M.Y. Faqiri, A. Barroi, M. Stonis, T. Hassel, F. Pape, M. Lammers, J. Hermsdorf, S. Kaierle, L. Overmeyer, G. Poll, Numerical Simulation and Experimental Validation of the Cladding Material Distribution of Hybrid Semi-Finished Products Produced by Deposition Welding and Corss-Wedge Rolling, in: metals, 10 (2020) 1336. https://doi.org/10.3390/met10101336

[10] B.-A. Behrens, K. Brunotte, T. Petersen, R. Relge, M. Till, Transfer of ausforming parameters to scaled forging tools, in: Metal 2021 Conference Proceedings (2021). https://doi.org/10.37904/metal.2021.4118

[11] J. Siring, M. Till, H. Wester, J. Uhe, K. Brunotte, Characterisation and qualification of hot working tool steels and Inconel for the production of a hybrid forging die, Bauernhansl, T., Verl, A., Liewald, M., Möhring, HC. (eds) Production at the Leading Edge of Technology. WGP 2023. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-47394-4_62

[12] B.-A. Behrens, A. Huskic, D. Rosenbusch, J. Peddinghaus, H. Wester, M. Siegmund, J. Giedenbacher, J. Siring, Design, Characterisation and Numerical Investigations of Additively Manufactured H10 Hybrid-Forging Dies with Conformal Cooling Channels, in: metals, 12 (2022) 1063. https://doi.org/10.3390/met12071063

[13] A.K. Drexler, Microstructural based simulation of the residual stress field in heat treated turbine discs from INCONEL718 (2018). https://doi.org/10.34901/mul.pub.2023.103

[14] A.S. Agazhanov, D.A. Samoshkin, Y.M. Kozlovski, Thermophysical properties of Inconel 718 alloy, J. of Physicy: Conference Series, 1382(1) (2019) 1742-6596. http://dx.doi.org/10.1088/1742-6596/1382/1/012175

[15] D. Dye, K.T. Conlon, R.C. Reed, Characterization and modeling of quenching-induced residual stresses in the nickel-based superalloy IN718, in: Metallurgical and materials Transactions A, 35 (2004) 1543-1940. http://dx.doi.org/10.1007/s11661-004-0079-7
[16] Dörrenberg Edelstahl, Material data sheet X38CrMoV5-3 (2020), Information on https://www.doerrenberg.de/wp-content/uploads/2020/05/1.2367_en.pdf

[17] T. Lindner, A. Grünen, G. Töberling, S. Vogt, M.S. Karakas, M. Löbel, T. Lampke, Boriding of Laser-Clad Inconel 718 Coatings for Enhanced Wear Resistance, in: Applied Sciences, 11(24) (2021) 11935. http://dx.doi.org/10.3390/app112411935

[18] Lucefin, Material data sheet X37CrMoV5-1 (2020), Information on https://www.lucefin.com/wp-content/files_mf/15236074671.2343X37CrMoV51.pdf
[16] Dörrenberg Edelstahl, Material data sheet X38CrMoV5-3 (2020), Information on https://www.doerrenberg.de/wp-content/uploads/2020/05/1.2367_en.pdf

[17] T. Lindner, A. Grünen, G. Töberling, S. Vogt, M.S. Karakas, M. Löbel, T. Lampke, Boriding of Laser-Clad Inconel 718 Coatings for Enhanced Wear Resistance, in: Applied Sciences, 11(24) (2021) 11935. http://dx.doi.org/10.3390/app112411935

[18] Lucefin, Material data sheet X37CrMoV5-1 (2020), Information on https://www.lucefin.com/wp-content/files_mf/15236074671.2343X37CrMoV51.pdf
# Longitudinal buckling behavior in temper rolling of thin steel strips with delivery angle

OKAZAKI Toshiro<sup>1,a*</sup>, KIMURA Yukio<sup>2,b</sup>, KATSUMURA Tatsuro<sup>1,c</sup> and
UEOKA Satoshi<sup>1,d</sup>

<sup>1</sup>Steel Research Laboratory, JFE Steel Corporation, Kawasaki-cho 1, Handa, Aichi 475-8611, Japan

<sup>2</sup>Steel Research Laboratory, JFE Steel Corporation, Kawasaki-cho 1, Chuo-ku, Chiba 260-0835, Japan

<sup>a</sup>t-okazaki@jfe-steel.co.jp, <sup>b</sup>yu-kimura@jfe-steel.co.jp, <sup>c</sup>t-katsumura@jfe-steel.co.jp,

<sup>d</sup>s-ueoka@jfe-steel.co.jp

**Keywords:** Rolling, Temper Rolling, Skin Pass, Model Simulation, Buckling, Longitudinal Buckle

**Abstract.** The shape defect referred to as "longitudinal buckling" or "longitudinal buckle" tends to occur in temper rolling of double-reduced thin strips. In our previous study, we carried out an experiment to investigate the effect of the delivery angle on longitudinal buckling, and showed that longitudinal buckle completely disappears when the delivery angle exceeds a certain angle. The change of the buckling mode (number of longitudinal buckles) depending on the delivery angle calculated with a buckling model of a flat plate with curvature agreed with the experimental results under the condition of a delivery angle over 10°, but not under the condition of 10°. In this paper, it was found that the experimental results for the delivery angle of 0° could be explained by the Komori model, which assumes flat plate buckling of a length corresponding to the roll bite length. A FEM analysis of the limit buckling stress assuming constraint by the work roll proved that the limit buckling stress was larger than the estimated widthwise stress, indicating that initiation of buckling did not occur in the winding part on the work roll. On the other hand, a rolling experiment revealed that the buckling shape of many micro-waves generated near the roll bite could change in the winding part. These results suggest that longitudinal buckling begins around the roll gap and varies with the shape of the sheet wrapped around the work roll.

**Introduction**

Surface patterns called cross buckles or longitudinal buckles may occur during temper rolling of thin steel sheets. In particular, longitudinal buckles appear as a waveform parallel to the longitudinal (rolling) direction, and are considered to occur easily in sheets subjected to cold rolling and annealing followed by secondary cold rolling. Sheets with this type of surface defect often require additional processing such as a correction process.

Longitudinal buckling of steel sheets is considered to be a buckling phenomenon generated on the delivery side of a rolling mill due to the residual stress of the sheets caused by rolling [1]. Various studies have investigated the buckling phenomena of thin plates. Abdelkhalek et al. proposed a FEM model of flatness defects that appear during rolling of thin sheets [2]. Abdelkhalek et al. also used a FEM model to study the flatness behavior that may occur when rolling tension is released [3]. Fischer et al. and Friedl et al. used analytical buckling calculations to predict the buckling modes of thin plates related to rolling and leveling [4, 5], and Coman used an analytical buckling model to estimate the critical loads and buckling modes with a linear distribution of residual stresses [6]. Liu et al. proposed buckling model replacing the elastic modulus constant with the distribution function of tangent modulus in order to consider the effect of uneven

<figure><img src="image_786.png" /></figure>
# Longitudinal buckling behavior in temper rolling of thin steel strips with delivery angle

OKAZAKI Toshiro<sup>1,a*</sup>, KIMURA Yukio<sup>2,b</sup>, KATSUMURA Tatsuro<sup>1,c</sup> and
UEOKA Satoshi<sup>1,d</sup>

<sup>1</sup>Steel Research Laboratory, JFE Steel Corporation, Kawasaki-cho 1, Handa, Aichi 475-8611, Japan

<sup>2</sup>Steel Research Laboratory, JFE Steel Corporation, Kawasaki-cho 1, Chuo-ku, Chiba 260-0835, Japan

<sup>a</sup>t-okazaki@jfe-steel.co.jp, <sup>b</sup>yu-kimura@jfe-steel.co.jp, <sup>c</sup>t-katsumura@jfe-steel.co.jp,

<sup>d</sup>s-ueoka@jfe-steel.co.jp

**Keywords:** Rolling, Temper Rolling, Skin Pass, Model Simulation, Buckling, Longitudinal Buckle

**Abstract.** The shape defect referred to as "longitudinal buckling" or "longitudinal buckle" tends to occur in temper rolling of double-reduced thin strips. In our previous study, we carried out an experiment to investigate the effect of the delivery angle on longitudinal buckling, and showed that longitudinal buckle completely disappears when the delivery angle exceeds a certain angle. The change of the buckling mode (number of longitudinal buckles) depending on the delivery angle calculated with a buckling model of a flat plate with curvature agreed with the experimental results under the condition of a delivery angle over 10°, but not under the condition of 10°. In this paper, it was found that the experimental results for the delivery angle of 0° could be explained by the Komori model, which assumes flat plate buckling of a length corresponding to the roll bite length. A FEM analysis of the limit buckling stress assuming constraint by the work roll proved that the limit buckling stress was larger than the estimated widthwise stress, indicating that initiation of buckling did not occur in the winding part on the work roll. On the other hand, a rolling experiment revealed that the buckling shape of many micro-waves generated near the roll bite could change in the winding part. These results suggest that longitudinal buckling begins around the roll gap and varies with the shape of the sheet wrapped around the work roll.

**Introduction**

Surface patterns called cross buckles or longitudinal buckles may occur during temper rolling of thin steel sheets. In particular, longitudinal buckles appear as a waveform parallel to the longitudinal (rolling) direction, and are considered to occur easily in sheets subjected to cold rolling and annealing followed by secondary cold rolling. Sheets with this type of surface defect often require additional processing such as a correction process.

Longitudinal buckling of steel sheets is considered to be a buckling phenomenon generated on the delivery side of a rolling mill due to the residual stress of the sheets caused by rolling [1]. Various studies have investigated the buckling phenomena of thin plates. Abdelkhalek et al. proposed a FEM model of flatness defects that appear during rolling of thin sheets [2]. Abdelkhalek et al. also used a FEM model to study the flatness behavior that may occur when rolling tension is released [3]. Fischer et al. and Friedl et al. used analytical buckling calculations to predict the buckling modes of thin plates related to rolling and leveling [4, 5], and Coman used an analytical buckling model to estimate the critical loads and buckling modes with a linear distribution of residual stresses [6]. Liu et al. proposed buckling model replacing the elastic modulus constant with the distribution function of tangent modulus in order to consider the effect of uneven

<figure><img src="image_794.png" /></figure>
distribution of material property in hot rolled strip [7]. Tran et al. conducted an experiment to simulate the flatness defect of a thin plate using thermal stress, and the behavior showed good agreement with the FEM results [8, 9].

On the other hand, few studies have investigated longitudinal buckling. Kijima et al. conducted an experimental investigation of the effect of rolling conditions on the occurrence of longitudinal buckles, which revealed the following trends [10]:

* As the rolling load decreases, the wave height decreases.

* Longitudinal buckles occur regardless of the rolling tension.

* The wave height can be reduced by reducing the work roll roughness.

* The wave height increases with an increase in the delivery angle at the outlet side of the rolling mill.

Komori obtained the wavelength of waves formed by longitudinal buckling under a condition in which no delivery angle was given by an elementary analysis of buckling, and showed that the wavelength of the longitudinal buckles obtained by the analysis was in good agreement with the trend of the experimental value [11]. The analytical results also showed that buckling is less likely to occur when the arithmetic mean roughness of the temper roll is low, which is also consistent with the experimental results.

Changing the rolling load and/or work roll roughness is a possible approach to prevent longitudinal buckling. However, in many cases, these changes have a significant impact on product characteristics and are difficult to implement in practice. Therefore, in order to prevent longitudinal buckling, it is important to change the delivery angle, which has relatively little effect on product characteristics. In a typical temper mill, auxiliary rolls are provided on the exit side for screw stabilization, tension measurement, etc., and these rolls can also be used to give the strip a delivery angle relative to the horizontal pass line at the exit side of the mill.

In a previous study, Kijima et al. investigated the effect of the delivery angle in laboratory experiments with delivery angles ranging from 0° to 4° [10]. The present authors [12] conducted an experiment in which strips were given a delivery angle, and showed that longitudinal buckle completely disappeared when the delivery angle exceeded a certain angle. However, the change of the buckling mode (number of longitudinal buckles) depending on the delivery angle calculated by a buckling model of a flat plate with curvature agreed with the experimental results under the condition of delivery angles over 10°, but not under the condition of 10°.

On the other hand, the wavelength of the longitudinal buckle when a delivery angle is not given (i.e., delivery angle = 0°), which Komori obtained by the elementary analysis of buckling, agrees well with the trend of the experimental value. This paper reports the results of an investigation of the effect of the exit side delivery angle on the buckling generation behavior when a delivery angle is given, which was clarified experimentally in our previous study, by comparison with the elementary analysis model of buckling by Komori [11].

Moreover, in the above-mentioned study by the authors [12], we conjectured that the longitudinal buckling phenomenon could be divided into buckling generation behavior in which many micro-waves were generated near the roll bite and buckling generation behavior in which the buckling shape changed as rolling progressed and disappeared in some cases. In order to verify this hypothesis, this paper describes the results of a FEM buckling mode analysis and experimental observation to verify whether the buckling mode can occur or change in the winding part, where the rolled material is wrapped around the roll.

## Buckling analysis model

The change of longitudinal buckling in the experiment with the delivery angle was compared with the buckling mode obtained by the elementary analysis. As mentioned above, the results of the
distribution of material property in hot rolled strip [7]. Tran et al. conducted an experiment to simulate the flatness defect of a thin plate using thermal stress, and the behavior showed good agreement with the FEM results [8, 9].

On the other hand, few studies have investigated longitudinal buckling. Kijima et al. conducted an experimental investigation of the effect of rolling conditions on the occurrence of longitudinal buckles, which revealed the following trends [10]:

* As the rolling load decreases, the wave height decreases.

* Longitudinal buckles occur regardless of the rolling tension.

* The wave height can be reduced by reducing the work roll roughness.

* The wave height increases with an increase in the delivery angle at the outlet side of the rolling mill.

Komori obtained the wavelength of waves formed by longitudinal buckling under a condition in which no delivery angle was given by an elementary analysis of buckling, and showed that the wavelength of the longitudinal buckles obtained by the analysis was in good agreement with the trend of the experimental value [11]. The analytical results also showed that buckling is less likely to occur when the arithmetic mean roughness of the temper roll is low, which is also consistent with the experimental results.

Changing the rolling load and/or work roll roughness is a possible approach to prevent longitudinal buckling. However, in many cases, these changes have a significant impact on product characteristics and are difficult to implement in practice. Therefore, in order to prevent longitudinal buckling, it is important to change the delivery angle, which has relatively little effect on product characteristics. In a typical temper mill, auxiliary rolls are provided on the exit side for screw stabilization, tension measurement, etc., and these rolls can also be used to give the strip a delivery angle relative to the horizontal pass line at the exit side of the mill.

In a previous study, Kijima et al. investigated the effect of the delivery angle in laboratory experiments with delivery angles ranging from 0° to 4° [10]. The present authors [12] conducted an experiment in which strips were given a delivery angle, and showed that longitudinal buckle completely disappeared when the delivery angle exceeded a certain angle. However, the change of the buckling mode (number of longitudinal buckles) depending on the delivery angle calculated by a buckling model of a flat plate with curvature agreed with the experimental results under the condition of delivery angles over 10°, but not under the condition of 10°.

On the other hand, the wavelength of the longitudinal buckle when a delivery angle is not given (i.e., delivery angle = 0°), which Komori obtained by the elementary analysis of buckling, agrees well with the trend of the experimental value. This paper reports the results of an investigation of the effect of the exit side delivery angle on the buckling generation behavior when a delivery angle is given, which was clarified experimentally in our previous study, by comparison with the elementary analysis model of buckling by Komori [11].

Moreover, in the above-mentioned study by the authors [12], we conjectured that the longitudinal buckling phenomenon could be divided into buckling generation behavior in which many micro-waves were generated near the roll bite and buckling generation behavior in which the buckling shape changed as rolling progressed and disappeared in some cases. In order to verify this hypothesis, this paper describes the results of a FEM buckling mode analysis and experimental observation to verify whether the buckling mode can occur or change in the winding part, where the rolled material is wrapped around the roll.

## Buckling analysis model

The change of longitudinal buckling in the experiment with the delivery angle was compared with the buckling mode obtained by the elementary analysis. As mentioned above, the results of the
buckling model of a plate with curvature [12] agreed with the experimental values under high delivery angle conditions (>10°), but not under low delivery angle conditions.

The buckling model of a plate with curvature [12] calculates the critical buckling stress for each buckling mode from the thickness, width, curvature, delivery angle, Young's modulus, and Poisson's ratio of the flat plate. Komori's model [11] calculates the buckling mode from the plate thickness, material yield stress, rolling load per unit width and parameters about roll surface roughness.

Komori's model [11] and its assumptions for calculating the buckling mode in the buckling model of a plate with curvature are described below. Table 1 shows the assumptions of both models. In both models, the boundary condition of the plate edge, the stress distribution in the rolling direction, the number of waves in the longitudinal direction (wavenumber), and the assumption of contact with the roll are the same. However, the modeling area and the plate shape are different. Figure 1 and Figure 2 show the area in which the buckling mode is modeled as a flat plate. Komori's model assumes that buckling occurs during rolling, and the rolling direction length of the roll bite is assumed to be the plate length in the buckling mode derivation. In the buckling model of a plate with curvature, the length of the plate in determining the buckling mode is defined as the area where the rolled material is wrapped around the roll from just below the roll center.

<table><caption>Table 1 Comparison of analysis conditions</caption><thead><tr><th></th><th>Komori's model [11]</th><th>Flat plate model with curvature [12]</th></tr></thead><tbody><tr><td>Modeling area</td><td>Rolling direction: Range of contact length with roll (equivalent to roll bite)<br>Width direction: Calculable regardless of the plate width</td><td>Rolling direction: Range where the plate is wrapped around the roll, beginning from the bottom dead center of the roll<br>Width direction: Plate width</td></tr><tr><td>Plate shape</td><td>Plate without curvature</td><td>Plate with curvature</td></tr><tr><td>Boundary condition of plate ends</td><td>Rotating end</td><td></td></tr><tr><td>Material deformation</td><td>Elastic deformation</td><td></td></tr><tr><td>Stress distribution</td><td>Constant regardless of rolling direction position</td><td></td></tr><tr><td>Longitudinal wave number</td><td>1</td><td></td></tr><tr><td>Contact with roll</td><td>Neglected for buckling cycle calculations in elementary analysis</td><td></td></tr></tbody></table>
buckling model of a plate with curvature [12] agreed with the experimental values under high delivery angle conditions (>10°), but not under low delivery angle conditions.

The buckling model of a plate with curvature [12] calculates the critical buckling stress for each buckling mode from the thickness, width, curvature, delivery angle, Young's modulus, and Poisson's ratio of the flat plate. Komori's model [11] calculates the buckling mode from the plate thickness, material yield stress, rolling load per unit width and parameters about roll surface roughness.

Komori's model [11] and its assumptions for calculating the buckling mode in the buckling model of a plate with curvature are described below. Table 1 shows the assumptions of both models. In both models, the boundary condition of the plate edge, the stress distribution in the rolling direction, the number of waves in the longitudinal direction (wavenumber), and the assumption of contact with the roll are the same. However, the modeling area and the plate shape are different. Figure 1 and Figure 2 show the area in which the buckling mode is modeled as a flat plate. Komori's model assumes that buckling occurs during rolling, and the rolling direction length of the roll bite is assumed to be the plate length in the buckling mode derivation. In the buckling model of a plate with curvature, the length of the plate in determining the buckling mode is defined as the area where the rolled material is wrapped around the roll from just below the roll center.

<table><caption>Table 1 Comparison of analysis conditions</caption><thead><tr><th></th><th>Komori's model [11]</th><th>Flat plate model with curvature [12]</th></tr></thead><tbody><tr><td>Modeling area</td><td>Rolling direction: Range of contact length with roll (equivalent to roll bite)<br>Width direction: Calculable regardless of the plate width</td><td>Rolling direction: Range where the plate is wrapped around the roll, beginning from the bottom dead center of the roll<br>Width direction: Plate width</td></tr><tr><td>Plate shape</td><td>Plate without curvature</td><td>Plate with curvature</td></tr><tr><td>Boundary condition of plate ends</td><td>Rotating end</td><td></td></tr><tr><td>Material deformation</td><td>Elastic deformation</td><td></td></tr><tr><td>Stress distribution</td><td>Constant regardless of rolling direction position</td><td></td></tr><tr><td>Longitudinal wave number</td><td>1</td><td></td></tr><tr><td>Contact with roll</td><td>Neglected for buckling cycle calculations in elementary analysis</td><td></td></tr></tbody></table>
<figure><img src="image_787.png" /><figcaption>Figure 1 Modeling area in Komori's model</figcaption></figure>

<figure><img src="image_788.png" /><figcaption>Figure 2 Modeling area in buckling model of flat plate with curvature</figcaption></figure>

<table><caption>Table 2 Conditions of elementary analysis of buckling</caption><tr><td>Rolling load per unit width [kN/mm]</td><td>5.3</td></tr><tr><td>Thickness at entry side [mm]</td><td>0.15</td></tr><tr><td>Roughness of work roll surface Ra [µm]</td><td>1.3</td></tr><tr><td>Roughness of work roll surface RSm [µm]</td><td>90</td></tr><tr><td>Delivery angle [°]</td><td>0</td></tr><tr><td>Young's modulus [GPa]</td><td>200</td></tr><tr><td>Poisson's ratio [-]</td><td>0.3</td></tr><tr><td>Yield stress [MPa]</td><td>657</td></tr></table>

It has been shown that the wavelength obtained by the elementary analytical model of buckling proposed by Komori agrees with the experimental value under the condition in which no delivery angle is given (delivery angle = 0°) [11]. Using Komori's model, the wave cycle for the delivery angle of 0° was calculated under the conditions in the experiment [12]. The conditions are as shown in Table 2. The rolling conditions were a rolling load of 5.3 kN/mm, roughness of work roll surface Ra of 1.3 µm and roughness of work roll surface RSm of 90 µm. The rolled material had a thickness of 0.15 mm and a yield stress of 657 MPa, Young's modulus was 200 GPa and Poisson's ratio was 0.3.

As a result, the wave cycle calculated by Komori's model was 14 mm. However, according to the experimental results [12], the wave cycle of longitudinal buckle was relatively close to 22 mm when the delivery angle was 0°.

In addition, the length of the flat plate used in determining the buckling mode is considered. As mentioned above, Komori's model assumes that buckling occurs during rolling, and the rolling
<figure><img src="image_795.png" /><figcaption>Figure 1 Modeling area in Komori's model</figcaption></figure>

<figure><img src="image_796.png" /><figcaption>Figure 2 Modeling area in buckling model of flat plate with curvature</figcaption></figure>

<table><caption>Table 2 Conditions of elementary analysis of buckling</caption><tr><td>Rolling load per unit width [kN/mm]</td><td>5.3</td></tr><tr><td>Thickness at entry side [mm]</td><td>0.15</td></tr><tr><td>Roughness of work roll surface Ra [µm]</td><td>1.3</td></tr><tr><td>Roughness of work roll surface RSm [µm]</td><td>90</td></tr><tr><td>Delivery angle [°]</td><td>0</td></tr><tr><td>Young's modulus [GPa]</td><td>200</td></tr><tr><td>Poisson's ratio [-]</td><td>0.3</td></tr><tr><td>Yield stress [MPa]</td><td>657</td></tr></table>

It has been shown that the wavelength obtained by the elementary analytical model of buckling proposed by Komori agrees with the experimental value under the condition in which no delivery angle is given (delivery angle = 0°) [11]. Using Komori's model, the wave cycle for the delivery angle of 0° was calculated under the conditions in the experiment [12]. The conditions are as shown in Table 2. The rolling conditions were a rolling load of 5.3 kN/mm, roughness of work roll surface Ra of 1.3 µm and roughness of work roll surface RSm of 90 µm. The rolled material had a thickness of 0.15 mm and a yield stress of 657 MPa, Young's modulus was 200 GPa and Poisson's ratio was 0.3.

As a result, the wave cycle calculated by Komori's model was 14 mm. However, according to the experimental results [12], the wave cycle of longitudinal buckle was relatively close to 22 mm when the delivery angle was 0°.

In addition, the length of the flat plate used in determining the buckling mode is considered. As mentioned above, Komori's model assumes that buckling occurs during rolling, and the rolling
direction length of the roll bite is taken as the plate length in the buckling mode derivation. The roll bite length is calculated to be 26.9 mm by the method of Komori's model under the rolling conditions in the experiment [12]. In the buckling model of a plate with curvature, the length of the plate is proportional to the delivery angle. Figure 3 shows the winding length with respect to the delivery angle in the buckling model of a plate with curvature. At the delivery angle of 9.3°, the length of the plate is equivalent to the roll bite length of 26.9 mm calculated by the Komori model.

<figure><img src="image_789.png" /><figcaption>Figure 3 Winding length in buckling model of plate with curvature</figcaption></figure>

Based on the above examination, the effect of the delivery angle on the number of longitudinal buckles is considered. The experimental results can be explained by the Komori model under the condition of the delivery angle of 0°, and it is considered that the phenomenon which occurs is close to the buckling of a flat plate with a length corresponding to the roll bite length assumed in the model. As shown in Figure 3, under the condition that the delivery angle is less than 9.3°, the winding length is calculated to be smaller than the roll bite length calculated by the Komori model. Therefore, it is considered that the buckling mode diverges from the actual phenomenon because the buckling mode is calculated for a narrower range than the roll bite.

Regarding the behavior when the delivery angle is increased, the change in the number of longitudinal buckles can be explained from the buckling behavior of the plate with curvature, and the shape of the winding part is considered to have a large influence on the buckling behavior.

## FEM analysis

In the preceding section, it was considered that the shape of the part wrapped around the work roll affected the buckling behavior when the delivery angle was increased. However, as a real phenomenon, tension is applied to the rolled material, and the rolled material is pressed against the work roll in the winding part. The buckling model of the flat plate with curvature does not consider the constraint received from the work roll, but in practice, this constraint is expected to make the occurrence of buckling difficult.

To verify this point, the buckling limit stress was calculated by FEM, and the difference between the behavior of the material with and without constraint by the work roll was investigated. Abaqus/Standard Ver. 6.12 was used as the solver. As shown in Figure 4, the part corresponding to the winding part was modeled. The material was 0.15 mm in thickness and 300 mm width. Other conditions included a WR diameter of 330 mm, Young's modulus of 21,000 kg/mm² and Poisson's ratio of 0.3. The conditions under which the delivery angle β was 4° were analyzed. In the previous study, the FEM analysis for the delivery angle β = 4° confirmed that there is a region where the
direction length of the roll bite is taken as the plate length in the buckling mode derivation. The roll bite length is calculated to be 26.9 mm by the method of Komori's model under the rolling conditions in the experiment [12]. In the buckling model of a plate with curvature, the length of the plate is proportional to the delivery angle. Figure 3 shows the winding length with respect to the delivery angle in the buckling model of a plate with curvature. At the delivery angle of 9.3°, the length of the plate is equivalent to the roll bite length of 26.9 mm calculated by the Komori model.

<figure><img src="image_797.png" /><figcaption>Figure 3 Winding length in buckling model of plate with curvature</figcaption></figure>

Based on the above examination, the effect of the delivery angle on the number of longitudinal buckles is considered. The experimental results can be explained by the Komori model under the condition of the delivery angle of 0°, and it is considered that the phenomenon which occurs is close to the buckling of a flat plate with a length corresponding to the roll bite length assumed in the model. As shown in Figure 3, under the condition that the delivery angle is less than 9.3°, the winding length is calculated to be smaller than the roll bite length calculated by the Komori model. Therefore, it is considered that the buckling mode diverges from the actual phenomenon because the buckling mode is calculated for a narrower range than the roll bite.

Regarding the behavior when the delivery angle is increased, the change in the number of longitudinal buckles can be explained from the buckling behavior of the plate with curvature, and the shape of the winding part is considered to have a large influence on the buckling behavior.

## FEM analysis

In the preceding section, it was considered that the shape of the part wrapped around the work roll affected the buckling behavior when the delivery angle was increased. However, as a real phenomenon, tension is applied to the rolled material, and the rolled material is pressed against the work roll in the winding part. The buckling model of the flat plate with curvature does not consider the constraint received from the work roll, but in practice, this constraint is expected to make the occurrence of buckling difficult.

To verify this point, the buckling limit stress was calculated by FEM, and the difference between the behavior of the material with and without constraint by the work roll was investigated. Abaqus/Standard Ver. 6.12 was used as the solver. As shown in Figure 4, the part corresponding to the winding part was modeled. The material was 0.15 mm in thickness and 300 mm width. Other conditions included a WR diameter of 330 mm, Young's modulus of 21,000 kg/mm² and Poisson's ratio of 0.3. The conditions under which the delivery angle β was 4° were analyzed. In the previous study, the FEM analysis for the delivery angle β = 4° confirmed that there is a region where the
rolled material and the roll are in contact [12]. Therefore, the critical buckling stress when stress is applied in the width direction to the part corresponding to the winding part was calculated.

As shown in Figure 4, the analysis was carried out for Case 1 without constraint by the work roll and Case 2 with constraint by the work roll. In Case 2, the modeled portion is pressed against the work roll with a uniform surface pressure of 0.0909 MPa, which corresponds to the pressure on the work roll when the longitudinal tension is 100 MPa. Longitudinal tension is not applied in the analysis, but is applied as the pressure on the work roll. The friction coefficient of the contact surface was 0.05 [13-15].

The results are shown in Figure 5. This paper also shows the widthwise stress (173 MPa) generated in the rolled material at the roll bite side estimated in the previous study [12]. In Case 1 without constraint by the work roll, the critical buckling stress is smaller than the estimated widthwise stress regardless of the buckling mode, indicating that buckling can occur. However, in Case 2 with constraint by the work roll, the limit buckling stress is larger than the estimated widthwise stress regardless of the mode, which means that buckling cannot occur.

This result suggests that initiation of buckling is unlikely to occur in the winding part, even in the real phenomenon. Therefore, it is presumed that buckling is not initiated in the winding part, but occurs in the vicinity of the roll bite, and the buckling shape then changes in the winding part and disappears when the delivery angle is over a certain value.

<figure><img src="image_790.png" /><figcaption>Figure 4 Modeling area in FEM buckling analysis</figcaption></figure>
rolled material and the roll are in contact [12]. Therefore, the critical buckling stress when stress is applied in the width direction to the part corresponding to the winding part was calculated.

As shown in Figure 4, the analysis was carried out for Case 1 without constraint by the work roll and Case 2 with constraint by the work roll. In Case 2, the modeled portion is pressed against the work roll with a uniform surface pressure of 0.0909 MPa, which corresponds to the pressure on the work roll when the longitudinal tension is 100 MPa. Longitudinal tension is not applied in the analysis, but is applied as the pressure on the work roll. The friction coefficient of the contact surface was 0.05 [13-15].

The results are shown in Figure 5. This paper also shows the widthwise stress (173 MPa) generated in the rolled material at the roll bite side estimated in the previous study [12]. In Case 1 without constraint by the work roll, the critical buckling stress is smaller than the estimated widthwise stress regardless of the buckling mode, indicating that buckling can occur. However, in Case 2 with constraint by the work roll, the limit buckling stress is larger than the estimated widthwise stress regardless of the mode, which means that buckling cannot occur.

This result suggests that initiation of buckling is unlikely to occur in the winding part, even in the real phenomenon. Therefore, it is presumed that buckling is not initiated in the winding part, but occurs in the vicinity of the roll bite, and the buckling shape then changes in the winding part and disappears when the delivery angle is over a certain value.

<figure><img src="image_798.png" /><figcaption>Figure 4 Modeling area in FEM buckling analysis</figcaption></figure>
<figure><img src="image_791.png" /><figcaption>Figure 5 Modeling area in FEM buckling analysis</figcaption></figure>

Experiment

From the examination in the preceding paragraph, it was hypothesized that buckling which generates many micro-waves in the vicinity of the roll bite occurs, and the buckling shape changes in the winding part and disappears when the delivery angle is over a certain value. To establish this hypothesis, it is assumed that the change in the buckling shape occurs in the winding part. For verification, the buckling shape of the winding part was observed in a rolling experiment.

Figure 6 shows a schematic diagram of the laboratory rolling mill used in the experiment. An auxiliary roll was installed on the rolling stand exit side of the 2Hi mill, and the delivery angle was set to 27.6°.

The rolling conditions are shown in Table 3. The work roll diameter was 330 mm, the test material was 0.05 mm in thickness and 300 mm in width, and 50 % cold rolling was applied to the material after annealing. A thin material was used to prevent the waves from disappearing under the conditions with the delivery angle [16].

The roll gap of the work roll in the unrotated state was reduced to the position where the widthwise load was 0.4 tonf/mm for the full length of the unrolled rolled material. From this state, the work roll was rotated with the lowering position fixed, and rolling and observation were started. The inlet and outlet tensions were 120 MPa, and the lubrication condition was dry.

A video camera was installed on the rolling outlet side to observe the winding part. In the photographed image shown in Figure 7, it can be confirmed that the winding part and the noncontact area where the rolled material has left the work roll are in the field of view. As can be seen in Figure 7, there are many fine waves in the width direction at 3.2 seconds after the start of rolling, but as rolling progresses, the wave number decreases at 6.0 seconds, and the wave which existed at 6.0 seconds disappears at 6.4 seconds after the start of rolling.

These observation results confirmed that a change of the wavenumber, that is, a change of buckling shape, can occur in the winding part. Based on this fact, as mentioned above, there is a possibility that buckling which generates a large number of micro-waves in the vicinity of the roll bite occurs, and the buckling shape then changes in the winding part and disappears when the delivery angle is over a certain value. However, it is not obvious that the wavenumber change in the winding part coincides with the wavenumber expected in the buckling model of the plate with curvature. Therefore, the reason for this difference requires further examination.
<figure><img src="image_799.png" /><figcaption>Figure 5 Modeling area in FEM buckling analysis</figcaption></figure>

Experiment

From the examination in the preceding paragraph, it was hypothesized that buckling which generates many micro-waves in the vicinity of the roll bite occurs, and the buckling shape changes in the winding part and disappears when the delivery angle is over a certain value. To establish this hypothesis, it is assumed that the change in the buckling shape occurs in the winding part. For verification, the buckling shape of the winding part was observed in a rolling experiment.

Figure 6 shows a schematic diagram of the laboratory rolling mill used in the experiment. An auxiliary roll was installed on the rolling stand exit side of the 2Hi mill, and the delivery angle was set to 27.6°.

The rolling conditions are shown in Table 3. The work roll diameter was 330 mm, the test material was 0.05 mm in thickness and 300 mm in width, and 50 % cold rolling was applied to the material after annealing. A thin material was used to prevent the waves from disappearing under the conditions with the delivery angle [16].

The roll gap of the work roll in the unrotated state was reduced to the position where the widthwise load was 0.4 tonf/mm for the full length of the unrolled rolled material. From this state, the work roll was rotated with the lowering position fixed, and rolling and observation were started. The inlet and outlet tensions were 120 MPa, and the lubrication condition was dry.

A video camera was installed on the rolling outlet side to observe the winding part. In the photographed image shown in Figure 7, it can be confirmed that the winding part and the noncontact area where the rolled material has left the work roll are in the field of view. As can be seen in Figure 7, there are many fine waves in the width direction at 3.2 seconds after the start of rolling, but as rolling progresses, the wave number decreases at 6.0 seconds, and the wave which existed at 6.0 seconds disappears at 6.4 seconds after the start of rolling.

These observation results confirmed that a change of the wavenumber, that is, a change of buckling shape, can occur in the winding part. Based on this fact, as mentioned above, there is a possibility that buckling which generates a large number of micro-waves in the vicinity of the roll bite occurs, and the buckling shape then changes in the winding part and disappears when the delivery angle is over a certain value. However, it is not obvious that the wavenumber change in the winding part coincides with the wavenumber expected in the buckling model of the plate with curvature. Therefore, the reason for this difference requires further examination.
<table><caption>Table 3 Experimental conditions</caption><tr><td>Rolling load per unit width [kN/mm]</td><td>0.4</td></tr><tr><td>Thickness at entry side [mm]</td><td>0.05</td></tr><tr><td>Width [mm]</td><td>300</td></tr><tr><td>Unit tension at entry side [MPa]</td><td>120</td></tr><tr><td>Unit tension at delivery side [MPa]</td><td>120</td></tr><tr><td>Work roll diameter [mm]</td><td>330</td></tr><tr><td>Delivery angle [°]</td><td>27.6</td></tr><tr><td>Lubrication</td><td>Dry</td></tr></table>

<figure><img src="image_792.png" /><figcaption>Figure 6 Outline of experimental apparatus</figcaption></figure>

<figure><img src="image_793.png" /></figure>

<figure><img src="image_794.png" /></figure>
<table><caption>Table 3 Experimental conditions</caption><tr><td>Rolling load per unit width [kN/mm]</td><td>0.4</td></tr><tr><td>Thickness at entry side [mm]</td><td>0.05</td></tr><tr><td>Width [mm]</td><td>300</td></tr><tr><td>Unit tension at entry side [MPa]</td><td>120</td></tr><tr><td>Unit tension at delivery side [MPa]</td><td>120</td></tr><tr><td>Work roll diameter [mm]</td><td>330</td></tr><tr><td>Delivery angle [°]</td><td>27.6</td></tr><tr><td>Lubrication</td><td>Dry</td></tr></table>

<figure><img src="image_800.png" /><figcaption>Figure 6 Outline of experimental apparatus</figcaption></figure>

<figure><img src="image_801.png" /></figure>

<figure><img src="image_802.png" /></figure>
6.4 seconds from start of rolling

<figure><img src="image_795.png" /><figcaption>Figure 7 Appearance of winding part during rolling</figcaption></figure>

**Summary**

This paper investigates the effect of the delivery angle on the longitudinal buckle generation behavior in temper rolling of secondary cold-rolled steel sheets by comparison with an elementary analysis model of buckling. The existence of a change in the buckling mode in the winding part was verified by a laboratory experiment. The following findings were obtained.

1) When the delivery angle is 0°, the experimental results can be explained by the Komori model assuming flat plate buckling with a length corresponding to the roll bite length.

2) In the buckling model of a flat plate with curvature, the winding length is calculated to be smaller than the roll bite length under the condition of a delivery angle of less than 9.3°, and this is considered to be different from the actual phenomenon. When the delivery angle is increased, the change of the wavenumber can be explained from the buckling behavior of the plate with curvature, and the shape of the winding part appears to have a large influence on the buckling behavior.

3) The results of a FEM analysis suggested that buckling cannot occur under a condition of constraint by the work roll. Therefore, it is presumed that initiation of buckling does not occur in the winding part, where the material is in contact with the work roll, but occurs in the vicinity of the roll bite.

4) The results of verification by a rolling experiment confirmed that a change in the wavenumber occurred in the winding part. Based on this fact, it is presumed that buckling occurs in the vicinity of the roll bite, and the buckling shape then changes in the winding part.

**References**

[1] Komori K (1995) Analysis of cross and longitudinal buckle in sheet metal rolling. J. Jpn. Soc. Technol. Plast. 36(410):211-217

[2] Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P (2011) Coupled approach for flatness prediction in cold rolling of thin strip. International Journal of Mechanical Sciences. (53):661-675. https://doi.org/10.1016/j.ijmecsci.2011.04.001

[3] Abdelkhalek S, Zahrouni H, Legrand N, Potier-Ferry M (2015) Post-buckling modeling for strips under tension and residual stresses using asymptotic numerical method. International Journal of Mechanical Sciences. (104):126-137. https://doi.org/10.1016/j.ijmecsci.2015.10.011

[4] Fischer F.D., Rammerstorfer F.G., Friedl N, Wieser W (2000) Buckling phenomena related to rolling and levelling of sheet metal. International Journal of Mechanical Sciences. (42):1887-1910. https://doi.org/10.1016/S0020-7403(99)00079-X
6.4 seconds from start of rolling

<figure><img src="image_803.png" /><figcaption>Figure 7 Appearance of winding part during rolling</figcaption></figure>

## Summary

This paper investigates the effect of the delivery angle on the longitudinal buckle generation behavior in temper rolling of secondary cold-rolled steel sheets by comparison with an elementary analysis model of buckling. The existence of a change in the buckling mode in the winding part was verified by a laboratory experiment. The following findings were obtained.

1. When the delivery angle is 0°, the experimental results can be explained by the Komori model assuming flat plate buckling with a length corresponding to the roll bite length.

2. In the buckling model of a flat plate with curvature, the winding length is calculated to be smaller than the roll bite length under the condition of a delivery angle of less than 9.3°, and this is considered to be different from the actual phenomenon. When the delivery angle is increased, the change of the wavenumber can be explained from the buckling behavior of the plate with curvature, and the shape of the winding part appears to have a large influence on the buckling behavior.

3. The results of a FEM analysis suggested that buckling cannot occur under a condition of constraint by the work roll. Therefore, it is presumed that initiation of buckling does not occur in the winding part, where the material is in contact with the work roll, but occurs in the vicinity of the roll bite.

4. The results of verification by a rolling experiment confirmed that a change in the wavenumber occurred in the winding part. Based on this fact, it is presumed that buckling occurs in the vicinity of the roll bite, and the buckling shape then changes in the winding part.

## References

[1] Komori K (1995) Analysis of cross and longitudinal buckle in sheet metal rolling. J. Jpn. Soc. Technol. Plast. 36(410):211-217

[2] Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P (2011) Coupled approach for flatness prediction in cold rolling of thin strip. International Journal of Mechanical Sciences. (53):661-675. https://doi.org/10.1016/j.ijmecsci.2011.04.001

[3] Abdelkhalek S, Zahrouni H, Legrand N, Potier-Ferry M (2015) Post-buckling modeling for strips under tension and residual stresses using asymptotic numerical method. International Journal of Mechanical Sciences. (104):126-137. https://doi.org/10.1016/j.ijmecsci.2015.10.011

[4] Fischer F.D., Rammerstorfer F.G., Friedl N, Wieser W (2000) Buckling phenomena related to rolling and levelling of sheet metal. International Journal of Mechanical Sciences. (42):1887-1910. https://doi.org/10.1016/S0020-7403(99)00079-X
[5] Friedl N, Rammerstorfer F.G., Fischer F.D. (2000) Buckling of stretched strips. Computers and Structures. (78):185-190. https://doi.org/10.1016/S0045-7949(00)00072-9

[6] Coman C.D. (2009) The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips. Mechanics Research Communications. (36):826-832. https://doi.org/10.1016/j.mechrescom.2009.05.008

[7] Liu C, Wu H, He A, Jing F, Sun W, Shao J, Yao C (2023) Effect of Uneven Distribution of Material Property on Buckling Behavior of Strip during Hot Finishing Rolling. ISIJ Int. 63(1):102-110. https://doi.org/10.2355/isijinternational.ISIJINT-2022-221

[8] Tran D.C., Tardif N, Khaloui H.E., Limam A (2017) Thermal buckling of thin sheet related to cold rolling: Latent flatness defects modeling. Thin-Walled Structures. (113):129-135. https://doi.org/10.1016/j.tws.2016.12.010

[9] Tran D.C., Tardif N, Limam A (2015) Experimental and numerical modeling of flatness defects in strip cold rolling. International Journal of Solids and Structures. 69(70):343-349. https://doi.org/10.1016/j.ijsolstr.2015.05.017

[10] Kijima H, Kitahama M (2002) Longitudinal buckle in temper rolling of double reduced ultrathin strips. J. Jpn. Soc. Technol. Plast. 43(493):150-154

[11] Komori K (2008) Analysis of longitudinal buckling in temper rolling. Tetsu-to-Hagané. 94(10):70-77. https://doi.org/10.2355/tetsutohagane.94.452

[12] Okazaki T, Kimura Y, Kijima H, Miyake M (2020) Effect of Delivery Angle to Longitudinal Buckling in Temper Rolling of Thin Steel Strips. J. Jpn. Soc. Technol. Plast. 61(708):7-11. https://doi.org/10.9773/sosei.61.7

[13] Kijima H (2013) Influence of roll radius on contact condition and material deformation in skin-pass rolling of steel strip. J. Mater. Process. Technol. 10(213):1764-1771. https://doi.org/10.1016/j.jmatprotec.2013.04.011

[14] Domanti SA, Edwards WJ, Thomas PJ, Chefneux DIL (1994) Application of foil rolling models to thin steel strip and temper rolling. Proceedings of the Sixth International Rolling Conference. Dusseldorf:1764-1771

[15] Kijima H, Bay N (2007) Contact conditions in skin-pass rolling. Annals of CIRP 57. 1(56):301-306. https://doi.org/10.1016/j.cirp.2007.05.070

[16] Okazaki T, Kimura Y, Katsumura T, Miyake M (2022) Effect of Delivery Angle on Longitudinal Buckling in Temper Rolling of Thin Steel Strips. The Proceedings of Japanese Joint Conference for the Technology of Plasticity (128):37-38
[5] Friedl N, Rammerstorfer F.G., Fischer F.D. (2000) Buckling of stretched strips. Computers and Structures. (78):185-190. https://doi.org/10.1016/S0045-7949(00)00072-9

[6] Coman C.D. (2009) The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips. Mechanics Research Communications. (36):826-832. https://doi.org/10.1016/j.mechrescom.2009.05.008

[7] Liu C, Wu H, He A, Jing F, Sun W, Shao J, Yao C (2023) Effect of Uneven Distribution of Material Property on Buckling Behavior of Strip during Hot Finishing Rolling. ISIJ Int. 63(1):102-110. https://doi.org/10.2355/isijinternational.ISIJINT-2022-221

[8] Tran D.C., Tardif N, Khaloui H.E., Limam A (2017) Thermal buckling of thin sheet related to cold rolling: Latent flatness defects modeling. Thin-Walled Structures. (113):129-135. https://doi.org/10.1016/j.tws.2016.12.010

[9] Tran D.C., Tardif N, Limam A (2015) Experimental and numerical modeling of flatness defects in strip cold rolling. International Journal of Solids and Structures. 69(70):343-349. https://doi.org/10.1016/j.ijsolstr.2015.05.017

[10] Kijima H, Kitahama M (2002) Longitudinal buckle in temper rolling of double reduced ultrathin strips. J. Jpn. Soc. Technol. Plast. 43(493):150-154

[11] Komori K (2008) Analysis of longitudinal buckling in temper rolling. Tetsu-to-Hagané. 94(10):70-77. https://doi.org/10.2355/tetsutohagane.94.452

[12] Okazaki T, Kimura Y, Kijima H, Miyake M (2020) Effect of Delivery Angle to Longitudinal Buckling in Temper Rolling of Thin Steel Strips. J. Jpn. Soc. Technol. Plast. 61(708):7-11. https://doi.org/10.9773/sosei.61.7

[13] Kijima H (2013) Influence of roll radius on contact condition and material deformation in skin-pass rolling of steel strip. J. Mater. Process. Technol. 10(213):1764-1771. https://doi.org/10.1016/j.jmatprotec.2013.04.011

[14] Domanti SA, Edwards WJ, Thomas PJ, Chefneux DIL (1994) Application of foil rolling models to thin steel strip and temper rolling. Proceedings of the Sixth International Rolling Conference. Dusseldorf:1764-1771

[15] Kijima H, Bay N (2007) Contact conditions in skin-pass rolling. Annals of CIRP 57. 1(56):301-306. https://doi.org/10.1016/j.cirp.2007.05.070

[16] Okazaki T, Kimura Y, Katsumura T, Miyake M (2022) Effect of Delivery Angle on Longitudinal Buckling in Temper Rolling of Thin Steel Strips. The Proceedings of Japanese Joint Conference for the Technology of Plasticity (128):37-38
# Design of an experimental simulator of void closure during hot rolling process

GOPAKUMAR Akhil¹,²,a*, LANGLOIS Laurent²,b,
PONDAVEN Corentin¹,c and BIGOT Régis²,d

¹ABS Centre Métallurgique, 10 rue Pierre Simon de Laplace 57070 Metz, France

²Laboratoire de conception fabrication Commande (EA 4495), Arts et Métiers Institute of Technology, Université de Lorraine, HESAM université, 4 rue Augustin Fresnel 57070 Metz, France

a.a.gopakumar@absacciai.com, b.laurent.langlois@ensam.eu, c.c.pondaven@absacciai.com,

d.regis.bigot@ensam.eu

**Keywords:** Open Die Forging, Experimental Simulation, Finite Element Simulation, Porosity Closure

**Abstract.** The shrinkage porosities produced during the casting of steel blooms has to be fixed by the subsequent hot rolling process. To design the rolling route, finite element simulations integrating void closure models are necessary. However, these models have to be validated by experimental results. Because experiments under industrial conditions are hardly achievable, experimental simulations at lower scale can be considered. However, the experiment must be designed so as to reproduce industrial like conditions concerning the thermomechanical loading and microstructure with respect to void closure. Among the main parameters driving void closure are the equivalent plastic strain and the mean triaxiality. This paper is dedicated to the design of an experimental simulator of void closure during hot rolling. The simulator consists of several strokes performed on a sample containing a real shrinkage porosity, between shaped anvils and with alternations of the forming direction.

## Introduction

Hot rolling process is employed after the casting of blooms to have the proper metallurgical properties for the desired application. Moreover, during the rolling process the closure of shrinkage porosities is aimed. The study of the void closure can be substantial in optimizing the rolling process and increasing the efficiency of the process. The void closure has two stages, geometric closure and healing, as highlighted by Park and Young [1]. In the present study, only the geometric closure is considered. The parameters that govern void closure are the thermomechanical loading parameters and the geometry of the pore. The thermomechanical loadings concern mainly the plastic strain, the stress triaxiality with a fundamental effect of the change in the loading direction. The influential geometric parameters of the pore are its global shape (sphere, ellipsoid...) and its tortuosity corresponding to the local irregularities. To study the evolution of the void, the numerical simulation is commonly used integrating full field or mean field models as in Saby's [2] or Pondaven et al. [3] works. The full-field model considers an explicit pore to accurately predict its closure. This approach has limitations concerning the number of pores than can be considered and the high computation time. The mean field is used to bypass these limitations as it uses analytical or phenomenological formulation describing geometrical parameter fields such as the volume or the aspect ratio of the pores whose evolutions are governed by equation involving the thermomechanical loading parameters, mainly the equivalent plastic strain and the stress triaxiality. The pores are thus considered through parameter fields characterizing their geometry. The Cicaporo 2 model is a mean-field model developed by Saby et al. [4] that was identified using

<figure><img src="image_796.png" /></figure>
# Design of an experimental simulator of void closure during hot rolling process

GOPAKUMAR Akhil¹,²,a*, LANGLOIS Laurent²,b,
PONDAVEN Corentin¹,c and BIGOT Régis²,d

¹ABS Centre Métallurgique, 10 rue Pierre Simon de Laplace 57070 Metz, France

²Laboratoire de conception fabrication Commande (EA 4495), Arts et Métiers Institute of Technology, Université de Lorraine, HESAM université, 4 rue Augustin Fresnel 57070 Metz, France

a.a.gopakumar@absacciai.com, b.laurent.langlois@ensam.eu, c.c.pondaven@absacciai.com,

d.regis.bigot@ensam.eu

**Keywords:** Open Die Forging, Experimental Simulation, Finite Element Simulation, Porosity Closure

**Abstract.** The shrinkage porosities produced during the casting of steel blooms has to be fixed by the subsequent hot rolling process. To design the rolling route, finite element simulations integrating void closure models are necessary. However, these models have to be validated by experimental results. Because experiments under industrial conditions are hardly achievable, experimental simulations at lower scale can be considered. However, the experiment must be designed so as to reproduce industrial like conditions concerning the thermomechanical loading and microstructure with respect to void closure. Among the main parameters driving void closure are the equivalent plastic strain and the mean triaxiality. This paper is dedicated to the design of an experimental simulator of void closure during hot rolling. The simulator consists of several strokes performed on a sample containing a real shrinkage porosity, between shaped anvils and with alternations of the forming direction.

## Introduction

Hot rolling process is employed after the casting of blooms to have the proper metallurgical properties for the desired application. Moreover, during the rolling process the closure of shrinkage porosities is aimed. The study of the void closure can be substantial in optimizing the rolling process and increasing the efficiency of the process. The void closure has two stages, geometric closure and healing, as highlighted by Park and Young [1]. In the present study, only the geometric closure is considered. The parameters that govern void closure are the thermomechanical loading parameters and the geometry of the pore. The thermomechanical loadings concern mainly the plastic strain, the stress triaxiality with a fundamental effect of the change in the loading direction. The influential geometric parameters of the pore are its global shape (sphere, ellipsoid...) and its tortuosity corresponding to the local irregularities. To study the evolution of the void, the numerical simulation is commonly used integrating full field or mean field models as in Saby's [2] or Pondaven et al. [3] works. The full-field model considers an explicit pore to accurately predict its closure. This approach has limitations concerning the number of pores than can be considered and the high computation time. The mean field is used to bypass these limitations as it uses analytical or phenomenological formulation describing geometrical parameter fields such as the volume or the aspect ratio of the pores whose evolutions are governed by equation involving the thermomechanical loading parameters, mainly the equivalent plastic strain and the stress triaxiality. The pores are thus considered through parameter fields characterizing their geometry. The Cicaporo 2 model is a mean-field model developed by Saby et al. [4] that was identified using

<figure><img src="image_804.png" /></figure>
a numerical design of experiments performed with a full-field model. This model has limitations when applied to multi-stroke forming processes with alternations of loading direction. The model was later modified by Hibbe et al. [5] to overcome this limit and validated for ellipsoidal pores. Nevertheless, the current mean field models do not consider a description of the ‘tortuosity’ of the pore in their formulation which can lead to inadequate prediction of closure.

New approaches involving additional parameters characterizing the tortuosity or based on data learning method can be considered. These approaches need numerical design of experiments with a full-field model able to consider the fine geometrical details of the pores. Such models have to be validated by comparison with experiments for real ‘tortuous’ pores and thermomechanical paths including change of the loading direction. The actual paper presents the development of an experimental simulator of shrinkage porosity closure during multi-stroke hot forming process with alternations of the forming direction. This simulator consists in forging radially, between V and flat dies, a cylindrical billet containing a real shrinkage porosity. V shape anvils are chosen accordingly to their ability to apply quite a large range of triaxiality and strain [6],[7] representative of cogging or rolling processes.

The next part of the article is dedicated to the experimental simulator design. A second part is devoted to the design of forming routes for the study of void closure during hot rolling. Finally, a first application with drilled samples is presented to show the ability of the simulator to capture the effect of a change of the loading direction.

## Design of the Experimental Device

The experimental device, shown in Fig.1, consists of successive strokes performed between V-shaped and flat anvils to apply the triaxiality and equivalent strain ranges representative of an industrial hot rolling process. The sample implemented in the experimental simulator is a cylindrical billet containing a real naturally generated shrinkage porosity as in Pondaven et al. [3]. The zone of the sample containing the pore undergoes radial compression. Between two successive strokes, the sample, handled by a gripper mounted on a 6-axes robot, is rotated of 90° to reproduce the typical alternation of the forming direction of hot rolling.

The initial position and orientation of the pores within the sample is determined by X-Ray tomography control. One of the main challenges is the mastering of the position and orientation of the pore through the complete forming route. During the strokes, the sample undergoes elongation with respect to its axis and transverse widening. The gripper must accommodate the deformation of the sample during the stroke, but the system must be able to calculate the theoretical position of the porosity after deformation to reposition the sample before the following stroke. To do that, the displacement of both faces of the billet is measured using a laser system on the free side of the sample and by the gripper system itself on the robot side. The total elongation and the corresponding theoretical position of the pore in the sample are then calculated. This last calculation is performed directly by the robot controller for the achievement of the route to be completely automatized.

The pore closure is followed through X-ray tomography at different stages of the forging route. The initial diameter of the sample is fixed to 30 mm achieving a compromise between the X-Ray tomography capability and the minimum admissible ratio between the diameter of the pore and the diameter of the sample. A maximum void to billet ratio of 1/10 is recommended to reduce the disturbance of the macroscopic thermomechanical fields by the presence of the pore as used by Feng et Cui [8] (void to billet ratio of 0.07) to confront numerical full field and mean field model with experiment results. The next part is devoted to the anvil design.
a numerical design of experiments performed with a full-field model. This model has limitations when applied to multi-stroke forming processes with alternations of loading direction. The model was later modified by Hibbe et al. [5] to overcome this limit and validated for ellipsoidal pores. Nevertheless, the current mean field models do not consider a description of the ‘tortuosity’ of the pore in their formulation which can lead to inadequate prediction of closure.

New approaches involving additional parameters characterizing the tortuosity or based on data learning method can be considered. These approaches need numerical design of experiments with a full-field model able to consider the fine geometrical details of the pores. Such models have to be validated by comparison with experiments for real ‘tortuous’ pores and thermomechanical paths including change of the loading direction. The actual paper presents the development of an experimental simulator of shrinkage porosity closure during multi-stroke hot forming process with alternations of the forming direction. This simulator consists in forging radially, between V and flat dies, a cylindrical billet containing a real shrinkage porosity. V shape anvils are chosen accordingly to their ability to apply quite a large range of triaxiality and strain [6],[7] representative of cogging or rolling processes.

The next part of the article is dedicated to the experimental simulator design. A second part is devoted to the design of forming routes for the study of void closure during hot rolling. Finally, a first application with drilled samples is presented to show the ability of the simulator to capture the effect of a change of the loading direction.

## Design of the Experimental Device

The experimental device, shown in Fig.1, consists of successive strokes performed between V-shaped and flat anvils to apply the triaxiality and equivalent strain ranges representative of an industrial hot rolling process. The sample implemented in the experimental simulator is a cylindrical billet containing a real naturally generated shrinkage porosity as in Pondaven et al. [3]. The zone of the sample containing the pore undergoes radial compression. Between two successive strokes, the sample, handled by a gripper mounted on a 6-axes robot, is rotated of 90° to reproduce the typical alternation of the forming direction of hot rolling.

The initial position and orientation of the pores within the sample is determined by X-Ray tomography control. One of the main challenges is the mastering of the position and orientation of the pore through the complete forming route. During the strokes, the sample undergoes elongation with respect to its axis and transverse widening. The gripper must accommodate the deformation of the sample during the stroke, but the system must be able to calculate the theoretical position of the porosity after deformation to reposition the sample before the following stroke. To do that, the displacement of both faces of the billet is measured using a laser system on the free side of the sample and by the gripper system itself on the robot side. The total elongation and the corresponding theoretical position of the pore in the sample are then calculated. This last calculation is performed directly by the robot controller for the achievement of the route to be completely automatized.

The pore closure is followed through X-ray tomography at different stages of the forging route. The initial diameter of the sample is fixed to 30 mm achieving a compromise between the X-Ray tomography capability and the minimum admissible ratio between the diameter of the pore and the diameter of the sample. A maximum void to billet ratio of 1/10 is recommended to reduce the disturbance of the macroscopic thermomechanical fields by the presence of the pore as used by Feng et Cui [8] (void to billet ratio of 0.07) to confront numerical full field and mean field model with experiment results. The next part is devoted to the anvil design.
<figure><img src="image_797.png" /><figcaption>Fig.1 Experimental device, a) Set of V-Shaped anvils, b) The complete device with the instrumented gripper.</figcaption></figure>

Anvil design validation.

The first step is to find the required anvil dimensions to ensure that the proper thermomechanical properties are achieved at the centre of the sample during forging. The design profile of the die is shown in Fig.2. Using this profile, a parametrized 3D CAD model of the dies is constructed. The anvil width $W_a$ and depth, $H$, need to be optimized to have the proper distribution of the equivalent strain and stress triaxiality. The entry and exit radius are fixed at 2 mm. $L_f$ is taken as zero and $\alpha = 60^{\circ}$ for V120, 45^{\circ} for V90 and 0^{\circ}$ for flat die. To determine the depth, $H$, and width, $W_a$, design criteria are defined.

<figure><img src="image_798.png" /><figcaption>Fig.2 General profile of the V dies used to design the anvils.</figcaption></figure>
<figure><img src="image_805.png" /><figcaption>Fig.1 Experimental device, a) Set of V-Shaped anvils, b) The complete device with the instrumented gripper.</figcaption></figure>

Anvil design validation.

The first step is to find the required anvil dimensions to ensure that the proper thermomechanical properties are achieved at the centre of the sample during forging. The design profile of the die is shown in Fig.2. Using this profile, a parametrized 3D CAD model of the dies is constructed. The anvil width $W_a$ and depth, $H$, need to be optimized to have the proper distribution of the equivalent strain and stress triaxiality. The entry and exit radius are fixed at 2 mm. $L_f$ is taken as zero and $\alpha = 60^{\circ}$ for V120, $45^{\circ}$ for V90 and $0^{\circ}$ for flat die. To determine the depth, $H$, and width, $W_a$, design criteria are defined.

<figure><img src="image_806.png" /><figcaption>Fig.2 General profile of the V dies used to design the anvils.</figcaption></figure>
Criteria for the design of anvils.

The aimed equivalent plastic strain and stress triaxiality must be achieved before the lower and upper anvils get into contact with each other and without the formation of flash (see Fig.3.a). The second criterion concerns the homogeneity of the thermomechanical fields (equivalent strain and stress triaxiality) in the deformed zone. The size of this zone must be large enough compared to the volume of the pore (Fig.3.b) and to ensure a greater tolerance with respect to the pore position offset inevitably introduced by the experimental set-up (Fig.3.c). The homogeneity is linked to the anvil width where larger width increases the axial length of the homogenous zone. Therefore, an optimization of the anvil width is necessary, since the anvil width is likely to influence the applied thermomechanical fields and particularly the repartition between the elongation and the widening of the sample during its forming.

<figure><img src="image_799.png" /><figcaption>Fig.3 a) Contact between dies before reaching the aimed deformation and flash formation at the end of the forming b) Homogeneity of thermomechanical parameters (equivalent strain) c) Tolerance to the positioning of pore using robot.</figcaption></figure>

The different criteria are checked by FE simulation performed using Forge®NxT4.0. For the first two criteria, a conventional FE model is sufficient while the third criterion is validated using the full-field model developed in the next section.

Full-field numerical modelling of the experimental simulator.

A simulation model with a spherical pore of diameter 3 mm was used to model the forging of a sample using the designed anvils. The first two criteria, validated by conventional FE simulations, have led to an anvil width of 30 mm. Here, the material taken as reference is the 25MnCrS4 steel, corresponding experimentally to that of the container where the pore was inserted in [3]. It can be noted that the designed set of anvils should be applicable for any other low alloyed steel grades.

The full-field simulation is performed to ensure that the sample positioning variability introduced by the robot gripper does not significantly modify the void closure evolution. Mesh boxes were assigned to mesh the billet as shown in the figure 4. The mesh size is set up to 0.0625 mm in the vicinity of the pore and 1 mm far from it. To ensure a regular progression of the mesh size, four concentric mesh boxes are implemented. The mesh sizes in the different boxes are given in Fig.4. The sample free extremity is at a distance of 30 mm from the center of the tools (Fig.4) same as that of the experiment set up.
Criteria for the design of anvils.

The aimed equivalent plastic strain and stress triaxiality must be achieved before the lower and upper anvils get into contact with each other and without the formation of flash (see Fig.3.a). The second criterion concerns the homogeneity of the thermomechanical fields (equivalent strain and stress triaxiality) in the deformed zone. The size of this zone must be large enough compared to the volume of the pore (Fig.3.b) and to ensure a greater tolerance with respect to the pore position offset inevitably introduced by the experimental set-up (Fig.3.c). The homogeneity is linked to the anvil width where larger width increases the axial length of the homogenous zone. Therefore, an optimization of the anvil width is necessary, since the anvil width is likely to influence the applied thermomechanical fields and particularly the repartition between the elongation and the widening of the sample during its forming.

<figure><img src="image_807.png" /><figcaption>Fig.3 a) Contact between dies before reaching the aimed deformation and flash formation at the end of the forming b) Homogeneity of thermomechanical parameters (equivalent strain) c) Tolerance to the positioning of pore using robot.</figcaption></figure>

The different criteria are checked by FE simulation performed using Forge®NxT4.0. For the first two criteria, a conventional FE model is sufficient while the third criterion is validated using the full-field model developed in the next section.

Full-field numerical modelling of the experimental simulator.

A simulation model with a spherical pore of diameter 3 mm was used to model the forging of a sample using the designed anvils. The first two criteria, validated by conventional FE simulations, have led to an anvil width of 30 mm. Here, the material taken as reference is the 25MnCrS4 steel, corresponding experimentally to that of the container where the pore was inserted in [3]. It can be noted that the designed set of anvils should be applicable for any other low alloyed steel grades.

The full-field simulation is performed to ensure that the sample positioning variability introduced by the robot gripper does not significantly modify the void closure evolution. Mesh boxes were assigned to mesh the billet as shown in the figure 4. The mesh size is set up to 0.0625 mm in the vicinity of the pore and 1 mm far from it. To ensure a regular progression of the mesh size, four concentric mesh boxes are implemented. The mesh sizes in the different boxes are given in Fig.4. The sample free extremity is at a distance of 30 mm from the center of the tools (Fig.4) same as that of the experiment set up.
<figure><img src="image_800.png" /><figcaption>Fig.4 Mesh around the pore using mesh boxes.</figcaption></figure>

The flow stress σ0 is modelled using the Hansel-Spittel law (Equation 1) where ε, ε' and T are the equivalent plastic strain, the equivalent plastic strain rate and the temperature respectively.

$$ \sigma_0 = A_1 e^{m_1 T} \varepsilon^{m_2 T} \dot{\varepsilon}^{m_3 T} e^{\frac{m_4}{\varepsilon}} \quad (1) $$

The material coefficients given in the table 2 are taken from [3].

<table><caption>Table 1 Hansel-Spittel coefficients 25MnCrS4.</caption><thead><tr><th>A<sub>1</sub></th><th>m<sub>1</sub></th><th>m<sub>2</sub></th><th>m<sub>3</sub></th><th>m<sub>4</sub></th></tr></thead><tbody><tr><td>1 321.900</td><td>-0.002 570</td><td>-0.194 100</td><td>0.146 800</td><td>-0.065 210</td></tr></tbody></table>

The friction between the anvils and billet is modelled using the Tresca limited Coulomb law and the thermal interaction between the dies and the billet is modelled in the simulation to calculate the temperature of the billet during the forging process. The coefficients are shown in table 3 [3].

<table><caption>Table 2 Friction and thermal exchange modelling coefficients.</caption><thead><tr><th>Coulomb μ</th><th>Tresca m</th><th>Emissivity</th><th>Thermal exchange environment (W.m<sup>-2</sup>. K<sup>-1</sup>)</th><th>Thermal exchange anvils (W.m<sup>-2</sup>. K<sup>-1</sup>)</th></tr></thead><tbody><tr><td>0.4</td><td>0.8</td><td>0.88</td><td>10</td><td>2 000</td></tr></tbody></table>

The billet along with the pore is forged at 1 200 °C. The pore after forging is extracted from the billet mesh using GOM® Inspect 2019 software, and the dimensions and shape factors are calculated using python script (numpy-stl) to post-process the billet mesh after the forming simulation. The remeshing megamaf (function of Forge®NxT4.0) is used to suppress the remeshing when the internal self-contact of the pores is occurring. To observe the impact of the offset, centered and shifted pores with an offset of 0.7 and 1 mm are compared after forging, both cases to a final gap between the upper and lower anvil top surface of 3.7 mm.

In the Fig.5, the cross-section of the pores after forging for the two cases of offset is compared using GOM® Inspect 2019. Here, the maximum deviation is found to be 0.08 mm and 0.04 mm for 1 mm and 0.7 mm offset respectively. The positioning accuracy of the experimental set-up being about 0.5 mm the anvil width of 30 mm is validated.
<figure><img src="image_808.png" /><figcaption>Fig.4 Mesh around the pore using mesh boxes.</figcaption></figure>

The flow stress σ0 is modelled using the Hansel-Spittel law (Equation 1) where ε, ε' and T are the equivalent plastic strain, the equivalent plastic strain rate and the temperature respectively.

$$ \sigma_0 = A_1 e^{m_1 T} \varepsilon^{m_2 T} \dot{\varepsilon}^{m_3 T} e^{\frac{m_4}{\varepsilon}} \quad (1) $$

The material coefficients given in the table 2 are taken from [3].

<table><caption>Table 1 Hansel-Spittel coefficients 25MnCrS4.</caption><thead><tr><th>A<sub>1</sub></th><th>m<sub>1</sub></th><th>m<sub>2</sub></th><th>m<sub>3</sub></th><th>m<sub>4</sub></th></tr></thead><tbody><tr><td>1 321.900</td><td>-0.002 570</td><td>-0.194 100</td><td>0.146 800</td><td>-0.065 210</td></tr></tbody></table>

The friction between the anvils and billet is modelled using the Tresca limited Coulomb law and the thermal interaction between the dies and the billet is modelled in the simulation to calculate the temperature of the billet during the forging process. The coefficients are shown in table 3 [3].

<table><caption>Table 2 Friction and thermal exchange modelling coefficients.</caption><thead><tr><th>Coulomb μ</th><th>Tresca m</th><th>Emissivity</th><th>Thermal exchange environment (W.m<sup>-2</sup>. K<sup>-1</sup>)</th><th>Thermal exchange anvils (W.m<sup>-2</sup>. K<sup>-1</sup>)</th></tr></thead><tbody><tr><td>0.4</td><td>0.8</td><td>0.88</td><td>10</td><td>2 000</td></tr></tbody></table>

The billet along with the pore is forged at 1 200 °C. The pore after forging is extracted from the billet mesh using GOM® Inspect 2019 software, and the dimensions and shape factors are calculated using python script (numpy-stl) to post-process the billet mesh after the forming simulation. The remeshing megamaf (function of Forge®NxT4.0) is used to suppress the remeshing when the internal self-contact of the pores is occurring. To observe the impact of the offset, centered and shifted pores with an offset of 0.7 and 1 mm are compared after forging, both cases to a final gap between the upper and lower anvil top surface of 3.7 mm.

In the Fig.5, the cross-section of the pores after forging for the two cases of offset is compared using GOM® Inspect 2019. Here, the maximum deviation is found to be 0.08 mm and 0.04 mm for 1 mm and 0.7 mm offset respectively. The positioning accuracy of the experimental set-up being about 0.5 mm the anvil width of 30 mm is validated.
<figure><img src="image_801.png" /><figcaption>Fig. 5 a) Comparison of pore between centered pore and pore at an offset of a) 0.7 mm and b) 1 mm.</figcaption></figure>

The next section is dedicated to the design of different forming routes to study the effect of the change in the deformation direction on void closure.

## Design of Forging Route

Using the validated V and flat anvils, forging routes need to be proposed by analysing the equivalent strain and triaxiality for each stroke. To fix the gaps for each stroke, the equivalent strain, $ε_{reference}$, determined by the FE simulation of the industrial rolling process is considered as a reference [9]. The proposed route is shown in Fig.6.

<figure><img src="image_802.png" /><figcaption>Fig. 6 The proposed route with the aimed reference equivalent plastic strain of each stroke.</figcaption></figure>

The proposed methodology consists in analyzing the stress triaxiality and the mean stress triaxiality with respect to the equivalent strain at the center of the deformed zone of the sample. The driving parameter of a stroke is the final gap between the upper and the lower anvils. A route is thus defined by a set of four gaps, one per stroke. To determine the selected gaps, each stroke is simulated until the equivalent strain at the center of the sample reaches its reference value (Fig.6). The billet obtained at the end of a stroke is used for the simulation of the following stroke after a rotation of 90° to alternate of the forming direction.

The simulated evolution of the stress triaxiality and mean stress triaxiality during the first stroke of the first route is shown in Fig.7.
<figure><img src="image_809.png" /><figcaption>Fig.5 a) Comparison of pore between centered pore and pore at an offset of a) 0.7 mm and b) 1 mm.</figcaption></figure>

The next section is dedicated to the design of different forming routes to study the effect of the change in the deformation direction on void closure.

## Design of Forging Route

Using the validated V and flat anvils, forging routes need to be proposed by analysing the equivalent strain and triaxiality for each stroke. To fix the gaps for each stroke, the equivalent strain, $ε_{reference}$, determined by the FE simulation of the industrial rolling process is considered as a reference [9]. The proposed route is shown in Fig.6.

<figure><img src="image_810.png" /><figcaption>Fig.6 The proposed route with the aimed reference equivalent plastic strain of each stroke.</figcaption></figure>

The proposed methodology consists in analyzing the stress triaxiality and the mean stress triaxiality with respect to the equivalent strain at the center of the deformed zone of the sample. The driving parameter of a stroke is the final gap between the upper and the lower anvils. A route is thus defined by a set of four gaps, one per stroke. To determine the selected gaps, each stroke is simulated until the equivalent strain at the center of the sample reaches its reference value (Fig.6). The billet obtained at the end of a stroke is used for the simulation of the following stroke after a rotation of 90° to alternate of the forming direction.

The simulated evolution of the stress triaxiality and mean stress triaxiality during the first stroke of the first route is shown in Fig.7.
<figure><img src="image_803.png" /><figcaption>Fig. 7 Triaxiality vs equivalent strain for the first stroke (V120) for route 1 with cross-section extraction for three different final gaps.</figcaption></figure>

A gap of 5.7 mm is needed to obtain at the center of the sample the aimed equivalent strain ($ε_{reference}$). For V120 the stress triaxiality value becomes nearly constant from a strain of 0.2 (figure 7). The strain ranges from 0.2-0.45 provides a constant stress triaxiality. Using the deformed billet for a gap of 4 mm the second stroke is done after rotating the deformed billet at 90°. Then the process continues till the end of the forging routes. The cumulated strain is calculated by summing the strains achieved individually by each stroke that is 1.51 for the studied route.

By modifying the gaps of the route, it is possible to apply different levels of equivalent plastic strain under quite constant stress triaxiality. The designed anvils also allow the application of different routes. These degrees of freedom are useful for the study of the influence of the thermomechanical loading on void closure.

## Results and Discussion.

The forming test is conducted for samples made of 41Cr4. The material selected is different from that used for the design of the anvils for a first validation of the extension of the forging test to other low alloyed steel grades. To observe pore closure, billets with a drilled hole of 3.2 mm diameter and 47 mm length are used. The billets are forged according to first two strokes of the forming route of figure 6. The robot-gripper system is used to position the billet on the tool and rotates the sample by 90° for each forging stage. The trials are run multiple times to check the repeatability of the test. The samples are heated to 1,200°C in an electric furnace and placed into the gripper manually after the removal of the oxide scales. No lubrication is applied on the anvils and the samples are air-cooled after forging. The samples are then sand blasted and 3D-scanned for comparison with the FE results. The samples are finally cut for the cross-section observation of the drilled hole evolution after forging.

In parallel, the numerical simulation of the forging test is performed with Forge®NxT4.0 according to the full field modelling procedures described in section 2.3 (except for the Hansel-Spittel law) with a sample (41Cr4) containing a cylindrical hole instead of a sphere. The applied time cycle of the simulation corresponds to that individually measured during each trial. Concerning the material behaviour, the simulation are performed using the Hansel-
<figure><img src="image_811.png" /><figcaption>Fig. 7 Triaxiality vs equivalent strain for the first stroke (V120) for route 1 with cross-section extraction for three different final gaps.</figcaption></figure>

A gap of 5.7 mm is needed to obtain at the center of the sample the aimed equivalent strain ($ε_{reference}$). For V120 the stress triaxiality value becomes nearly constant from a strain of 0.2 (figure 7). The strain ranges from 0.2-0.45 provides a constant stress triaxiality. Using the deformed billet for a gap of 4 mm the second stroke is done after rotating the deformed billet at 90°. Then the process continues till the end of the forging routes. The cumulated strain is calculated by summing the strains achieved individually by each stroke that is 1.51 for the studied route.

By modifying the gaps of the route, it is possible to apply different levels of equivalent plastic strain under quite constant stress triaxiality. The designed anvils also allow the application of different routes. These degrees of freedom are useful for the study of the influence of the thermomechanical loading on void closure.

## Results and Discussion.

The forming test is conducted for samples made of 41Cr4. The material selected is different from that used for the design of the anvils for a first validation of the extension of the forging test to other low alloyed steel grades. To observe pore closure, billets with a drilled hole of 3.2 mm diameter and 47 mm length are used. The billets are forged according to first two strokes of the forming route of figure 6. The robot-gripper system is used to position the billet on the tool and rotates the sample by 90° for each forging stage. The trials are run multiple times to check the repeatability of the test. The samples are heated to 1,200°C in an electric furnace and placed into the gripper manually after the removal of the oxide scales. No lubrication is applied on the anvils and the samples are air-cooled after forging. The samples are then sand blasted and 3D-scanned for comparison with the FE results. The samples are finally cut for the cross-section observation of the drilled hole evolution after forging.

In parallel, the numerical simulation of the forging test is performed with Forge®NxT4.0 according to the full field modelling procedures described in section 2.3 (except for the Hansel-Spittel law) with a sample (41Cr4) containing a cylindrical hole instead of a sphere. The applied time cycle of the simulation corresponds to that individually measured during each trial. Concerning the material behaviour, the simulation are performed using the Hansel-
Spittel parameters of 41Cr4 from the Forge®NxT4.0 database using the coefficients given in table 3.

<table><caption>Table 3 Hansel-Spittel coefficients 41Cr4 (Forge®NxT4.0 database).</caption><thead><tr><th>A<sub>1</sub></th><th>m<sub>1</sub></th><th>m<sub>2</sub></th><th>m<sub>3</sub></th><th>m<sub>4</sub></th></tr></thead><tbody><tr><td>1 620.466</td><td>-0.002 770</td><td>-0.174 240</td><td>0.154 100</td><td>-0.064 970</td></tr></tbody></table>

The global analysis of the 3D-scan geometry of the sample highlights a slight bending in the deformed zone of the sample (illustrated in Fig.8). The geometry of the section in the deformed zone is not centered on the axis of the not deformed cylindrical zone of the sample. This dissymmetry can come from a difference in friction between the upper and the lower dies or a parallelism defect between the initial sample axis and that of the V anvils. It can be noted that this defect is not constant from one trial to the other and is a source of non-repeatability of the experiments.

<figure><img src="image_804.png" /><figcaption>Fig.8 Geometry of an experimentally forged sample and schematic emphasised representation of the bending defect.</figcaption></figure>

On Fig.9, are presented the micrographs of the drilled samples that have undergone the first stroke and first two strokes of the forming route.

<figure><img src="image_805.png" /><figcaption>Fig.9 Micrography of the cross section of the drilled sample forged in two stages a) V120 b) V120-V90 with alternations of forging direction.</figcaption></figure>

After the first stroke (V120), the closure was observed. The extremities exhibit contact lines but, because of the presence of an oxide layer, no healing is observed. After the second stroke (V90), mainly due to the alternation of load direction, the reopening of the hole was observed. The
Spittel parameters of 41Cr4 from the Forge®NxT4.0 database using the coefficients given in table 3.

<table><caption>Table 3 Hansel-Spittel coefficients 41Cr4 (Forge®NxT4.0 database).</caption><thead><tr><th>A<sub>1</sub></th><th>m<sub>1</sub></th><th>m<sub>2</sub></th><th>m<sub>3</sub></th><th>m<sub>4</sub></th></tr></thead><tbody><tr><td>1 620.466</td><td>-0.002 770</td><td>-0.174 240</td><td>0.154 100</td><td>-0.064 970</td></tr></tbody></table>

The global analysis of the 3D-scan geometry of the sample highlights a slight bending in the deformed zone of the sample (illustrated in Fig.8). The geometry of the section in the deformed zone is not centered on the axis of the not deformed cylindrical zone of the sample. This dissymmetry can come from a difference in friction between the upper and the lower dies or a parallelism defect between the initial sample axis and that of the V anvils. It can be noted that this defect is not constant from one trial to the other and is a source of non-repeatability of the experiments.

<figure><img src="image_812.png" /><figcaption>Fig.8 Geometry of an experimentally forged sample and schematic emphasised representation of the bending defect.</figcaption></figure>

On Fig.9, are presented the micrographs of the drilled samples that have undergone the first stroke and first two strokes of the forming route.

<figure><img src="image_813.png" /><figcaption>Fig.9 Micrography of the cross section of the drilled sample forged in two stages a) V120 b) V120-V90 with alternations of forging direction.</figcaption></figure>

After the first stroke (V120), the closure was observed. The extremities exhibit contact lines but, because of the presence of an oxide layer, no healing is observed. After the second stroke (V90), mainly due to the alternation of load direction, the reopening of the hole was observed. The
dimensions of the hole were measured from the micrography and are compared with the simulation (see Fig.10).

A cross-section analysis of the simulated geometry of the hole is performed at the center of the deformed zone. The dimensions D1 and D2 are respectively the dimensions of the hole parallel and perpendicularly to the forming direction of the first stroke. The evolution of D1 and D2 and their ratios are plotted according to the equivalent strain along with experimental results as shown in Fig.10. It is observed that for the first stroke (V120) the value of D1 and D2 decreases. The dimension parallel to the forming direction, D1, decreases faster. For the next stroke, because of the alternation of the forging direction, the hole is initially elongated and flat according to a plane containing the new forming direction. This leads to the reopening of the hole.

<figure><img src="image_806.png" /><figcaption>Fig.10 Evolution of geometries of hole with respect to the equivalent strain for two strokes a) D1 and D2 b) D1/D2.</figcaption></figure>

In Fig.10, it can be seen that the void closure is overestimated by the simulation. This can be due to numerical difficulties to simulate the contact line during the closure. The mesh size, the use of the megamaf function or the hole self-contact friction coefficients can be considered in a numerical study to optimize the prediction.

## Conclusions

This article presents a set-up for the experimental simulation of void closure under thermomechanical conditions representative of industrial hot rolling. This set-up consists in a succession of free forging strokes applied radially by shaped anvils on a cylindrical sample containing a porosity. The designed set of V-shaped (90° and 120°) and flat anvils allows reproducing the main characteristics of the hot rolling thermomechanical fields with respect to void closure, namely, the equivalent plastic strain, the mean stress triaxiality and the alternation of the forging direction between two successive stages.

One of the main difficulties of the experiment lie in the in-situ measurement of the deformed sample geometry to control the repositioning of the sample between two strokes. To solve partially this problem, the gripper was instrumented, and a laser sensor was implemented so as to measure the total elongation of the sample and to allow the calculation of the actual position of the porosity.

The first experiments performed with drilled samples demonstrated the key influence of the alternation of the forming direction. They also highlighted numerical difficulties to simulate the void closure when the internal contact gets into contact with itself.

The future work will first concern the optimization of the FE simulation of the simulator and especially the simulation of the void closure. The simulator will be applied to samples containing real shrinkage porosities as in Pondaven et al. work [3] with the objective to validate a full-field
dimensions of the hole were measured from the micrography and are compared with the simulation (see Fig.10).

A cross-section analysis of the simulated geometry of the hole is performed at the center of the deformed zone. The dimensions D1 and D2 are respectively the dimensions of the hole parallel and perpendicularly to the forming direction of the first stroke. The evolution of D1 and D2 and their ratios are plotted according to the equivalent strain along with experimental results as shown in Fig.10. It is observed that for the first stroke (V120) the value of D1 and D2 decreases. The dimension parallel to the forming direction, D1, decreases faster. For the next stroke, because of the alternation of the forging direction, the hole is initially elongated and flat according to a plane containing the new forming direction. This leads to the reopening of the hole.

<figure><img src="image_814.png" /><figcaption>Fig. 10 Evolution of geometries of hole with respect to the equivalent strain for two strokes a) D1 and D2 b) D1/D2.</figcaption></figure>

In Fig.10, it can be seen that the void closure is overestimated by the simulation. This can be due to numerical difficulties to simulate the contact line during the closure. The mesh size, the use of the megamaf function or the hole self-contact friction coefficients can be considered in a numerical study to optimize the prediction.

## Conclusions

This article presents a set-up for the experimental simulation of void closure under thermomechanical conditions representative of industrial hot rolling. This set-up consists in a succession of free forging strokes applied radially by shaped anvils on a cylindrical sample containing a porosity. The designed set of V-shaped (90° and 120°) and flat anvils allows reproducing the main characteristics of the hot rolling thermomechanical fields with respect to void closure, namely, the equivalent plastic strain, the mean stress triaxiality and the alternation of the forging direction between two successive stages.

One of the main difficulties of the experiment lie in the in-situ measurement of the deformed sample geometry to control the repositioning of the sample between two strokes. To solve partially this problem, the gripper was instrumented, and a laser sensor was implemented so as to measure the total elongation of the sample and to allow the calculation of the actual position of the porosity.

The first experiments performed with drilled samples demonstrated the key influence of the alternation of the forming direction. They also highlighted numerical difficulties to simulate the void closure when the internal contact gets into contact with itself.

The future work will first concern the optimization of the FE simulation of the simulator and especially the simulation of the void closure. The simulator will be applied to samples containing real shrinkage porosities as in Pondaven et al. work [3] with the objective to validate a full-field
model of void closure. A longer-term objective is the use of the validated model in the frame of numerical design of experiments to characterize the influence of the void geometry and tortuosity on its closure during hot rolling.

## Acknowledgements

The authors are grateful to Alexandre Fendler for his technical contribution during the experiments. The authors express their thanks to ISEETECH for the provision of the VULCAIN Platform facilities.

## References

[1] C. Y. Park et D. Y. Yang, « Modelling of void crushing for large-ingot hot forging », *J. Mater. Process. Technol.*, vol. 67, n° 1-3, p. 195-200, mai 1997. https://doi.org/10.1016/S0924-0136(96)02843-9

[2] M. Saby, « Understanding and modeling of void closure mechanisms in hot metal forming processes », 2013.

[3] C. Pondaven, L. Langlois, B. Erzar, et R. Bigot, « Numerical and experimental simulation of shrinkage porosity closure during hot rolling of bars », *ESAFORM 2021*, avr. 2021. https://doi.org/10.25518/esaform21.1896

[4] M. Saby, P.-O. Bouchard, et M. Bernacki, « Void closure criteria for hot metal forming: A review », *J. Manuf. Process.*, vol. 19, p. 239-250, août 2015. https://doi.org/10.1016/j.jmapro.2014.05.006

[5] P. Hibbe, M. Wolfgarten, et G. Hirt, « Investigation of void closure in open-die forging considering changing load directions », *Prod. Eng.*, vol. 13, n° 6, p. 703-711, déc. 2019. https://doi.org/10.1007/s11740-019-00924-0

[6] M. Kukuryk, « Experimental and FEM Analysis of Void Closure in the Hot Cogging Process of Tool Steel », *Metals*, vol. 9, n° 5, Art. n° 5, mai 2019. https://doi.org/10.3390/met9050538

[7] G. Banaszek, K. Ozhmegov, A. Kawalek, S. Sawicki, M. Magzhanov, et A. Arbuz, « Investigation of the Influence of Hot Forging Parameters on the Closing Conditions of Internal Metallurgical Defects in Zirconium Alloy Ingots », *Materials*, vol. 16, n° 4, Art. n° 4, janv. 2023. https://doi.org/10.3390/ma16041427

[8] C. Feng et Z. Cui, « A 3-D model for void evolution in viscous materials under large compressive deformation », *Int. J. Plast.*, vol. 74, p. 192-212, nov. 2015. https://doi.org/10.1016/j.ijplas.2015.06.012

[9] C. Pondaven, L. Langlois, R. Bigot, et D. Chevalier, « FEM-Based Methodology for the Design of Reduced Scale Representative Experimental Testing Allowing the Characterization of Defect Evolution during Hot Rolling of Bars », *Metals*, vol. 10, n° 8, Art. n° 8, août 2020. https://doi.org/10.3390/met10081035
model of void closure. A longer-term objective is the use of the validated model in the frame of numerical design of experiments to characterize the influence of the void geometry and tortuosity on its closure during hot rolling.

## Acknowledgements

The authors are grateful to Alexandre Fendler for his technical contribution during the experiments. The authors express their thanks to ISEETECH for the provision of the VULCAIN Platform facilities.

## References

[1] C. Y. Park et D. Y. Yang, « Modelling of void crushing for large-ingot hot forging », *J. Mater. Process. Technol.*, vol. 67, n° 1-3, p. 195-200, mai 1997. https://doi.org/10.1016/S0924-0136(96)02843-9

[2] M. Saby, « Understanding and modeling of void closure mechanisms in hot metal forming processes », 2013.

[3] C. Pondaven, L. Langlois, B. Erzar, et R. Bigot, « Numerical and experimental simulation of shrinkage porosity closure during hot rolling of bars », *ESAFORM 2021*, avr. 2021. https://doi.org/10.25518/esaform21.1896

[4] M. Saby, P.-O. Bouchard, et M. Bernacki, « Void closure criteria for hot metal forming: A review », *J. Manuf. Process.*, vol. 19, p. 239-250, août 2015. https://doi.org/10.1016/j.jmapro.2014.05.006

[5] P. Hibbe, M. Wolfgarten, et G. Hirt, « Investigation of void closure in open-die forging considering changing load directions », *Prod. Eng.*, vol. 13, n° 6, p. 703-711, déc. 2019. https://doi.org/10.1007/s11740-019-00924-0

[6] M. Kukuryk, « Experimental and FEM Analysis of Void Closure in the Hot Cogging Process of Tool Steel », *Metals*, vol. 9, n° 5, Art. n° 5, mai 2019. https://doi.org/10.3390/met9050538

[7] G. Banaszek, K. Ozhmegov, A. Kawalek, S. Sawicki, M. Magzhanov, et A. Arbuz, « Investigation of the Influence of Hot Forging Parameters on the Closing Conditions of Internal Metallurgical Defects in Zirconium Alloy Ingots », *Materials*, vol. 16, n° 4, Art. n° 4, janv. 2023. https://doi.org/10.3390/ma16041427

[8] C. Feng et Z. Cui, « A 3-D model for void evolution in viscous materials under large compressive deformation », *Int. J. Plast.*, vol. 74, p. 192-212, nov. 2015. https://doi.org/10.1016/j.ijplas.2015.06.012

[9] C. Pondaven, L. Langlois, R. Bigot, et D. Chevalier, « FEM-Based Methodology for the Design of Reduced Scale Representative Experimental Testing Allowing the Characterization of Defect Evolution during Hot Rolling of Bars », *Metals*, vol. 10, n° 8, Art. n° 8, août 2020. https://doi.org/10.3390/met10081035
# Advanced functionalisation and numerical simulation of the boundary layer by deformation-induced martensite on bearing rings through bulk metal forming

PEDDINGHAUS Simon¹,*, TILL Michael¹, WESTER Hendrik¹, PEDDINGHAUS Julius¹, BRUNOTTE Kai¹ and BEHRENS Bernd-Arno¹,†

¹Institute of Forming Technology and Machines, Leibniz Universität Hannover, Germany

a:s.peddinghaus@ifum.uni-hannover.de, bbehrens@ifum.uni-hannover.de

**Keywords:** Bulk Metal Forming, Phase Transformation, Local Martensite Formation, Cryogenic Forming

**Abstract.** The phase transformation of metastable austenitic steels caused by externally superimposed strains during cold forming increases the material strength in addition to strain hardening. Although numerous research papers have described the basic effects of the phase transformation from metastable austenite to martensite, it is not yet applied in the dimensions of common bulk formed components. Thereby the functionalisation of deformation-induced martensite to increase the material strength specifically at heavily loaded surfaces bears potential. However, the amount of deformation-induced martensite formation within a forming process is limited through the occurring strain hardening. In this paper an approach for an advanced functionalisation of this transformation through an adaption of the process is presented. The setup of a forming process is adapted, forming experiments are carried out at low temperatures and the specimens are investigated through hardness measurements (HV1), magnetic inductive testing (Feritscope MP3C) and microstructure analysis. The results were compared to distributions of plastic strain determined through FE simulations and showed a good correlation. It can be shown, that at cryogenic temperatures a significant increase of martensite formation is achieved.

**Introduction**

For applications with high mechanical and tribological loads bulk formed components with tailored heat treatments such as hardening or tempering are required because of their superior mechanical properties [1]. However, this does not apply for austenitic stainless steels, since they cannot be hardened conventionally and therefore don't reach sufficient properties such as hardness or yield strength [2]. As Stainless steels are usually applied in corrosive environments due to their strong resistance to corrosion, increasing their mechanical and tribological properties expands their field of applications. In the context of ball bearings, a suitable approach to enhance the service life is increasing the material strength specifically at heavily loaded surfaces, such as the contact areas of a rolling element to the rings. For example, Coors et al. demonstrated the positive effects of an increased material strength at the bearing surface on the service life through a hybrid material approach [3]. As the most common stainless steels are austenitic and have a metastable austenitic state at room temperature, they allow deformation-induced martensite transformation [4]. The functionalisation of this deformation-induced martensite transformation at heavily loaded surfaces bears considerable potential.

In principle, a crystal structure can be described through its current specific Gibbs free energy, whereby a low amount of free energy is strived for. In a so-called metastable state, the amount of free energy is higher, until additional energy is brought in, a threshold is surpassed and the structure can transform into a more stable state with less free energy. For austenitic stainless steels, the austenitic structure is metastable and can transform to the stable martensitic structure. For this

<figure><img src="image_807.png" /></figure>
# Advanced functionalisation and numerical simulation of the boundary layer by deformation-induced martensite on bearing rings through bulk metal forming

PEDDINGHAUS Simon¹,*, TILL Michael¹, WESTER Hendrik¹, PEDDINGHAUS Julius¹, BRUNOTTE Kai¹ and BEHRENS Bernd-Arno¹,†

¹Institute of Forming Technology and Machines, Leibniz Universität Hannover, Germany

a:s.peddinghaus@ifum.uni-hannover.de, bbehrens@ifum.uni-hannover.de

**Keywords:** Bulk Metal Forming, Phase Transformation, Local Martensite Formation, Cryogenic Forming

**Abstract.** The phase transformation of metastable austenitic steels caused by externally superimposed strains during cold forming increases the material strength in addition to strain hardening. Although numerous research papers have described the basic effects of the phase transformation from metastable austenite to martensite, it is not yet applied in the dimensions of common bulk formed components. Thereby the functionalisation of deformation-induced martensite to increase the material strength specifically at heavily loaded surfaces bears potential. However, the amount of deformation-induced martensite formation within a forming process is limited through the occurring strain hardening. In this paper an approach for an advanced functionalisation of this transformation through an adaption of the process is presented. The setup of a forming process is adapted, forming experiments are carried out at low temperatures and the specimens are investigated through hardness measurements (HV1), magnetic inductive testing (Feritscope MP3C) and microstructure analysis. The results were compared to distributions of plastic strain determined through FE simulations and showed a good correlation. It can be shown, that at cryogenic temperatures a significant increase of martensite formation is achieved.

**Introduction**

For applications with high mechanical and tribological loads bulk formed components with tailored heat treatments such as hardening or tempering are required because of their superior mechanical properties [1]. However, this does not apply for austenitic stainless steels, since they cannot be hardened conventionally and therefore don't reach sufficient properties such as hardness or yield strength [2]. As Stainless steels are usually applied in corrosive environments due to their strong resistance to corrosion, increasing their mechanical and tribological properties expands their field of applications. In the context of ball bearings, a suitable approach to enhance the service life is increasing the material strength specifically at heavily loaded surfaces, such as the contact areas of a rolling element to the rings. For example, Coors et al. demonstrated the positive effects of an increased material strength at the bearing surface on the service life through a hybrid material approach [3]. As the most common stainless steels are austenitic and have a metastable austenitic state at room temperature, they allow deformation-induced martensite transformation [4]. The functionalisation of this deformation-induced martensite transformation at heavily loaded surfaces bears considerable potential.

In principle, a crystal structure can be described through its current specific Gibbs free energy, whereby a low amount of free energy is strived for. In a so-called metastable state, the amount of free energy is higher, until additional energy is brought in, a threshold is surpassed and the structure can transform into a more stable state with less free energy. For austenitic stainless steels, the austenitic structure is metastable and can transform to the stable martensitic structure. For this

<figure><img src="image_815.png" /></figure>
transformation, a specific minimum amount of energy, shown as $ΔG$ in Fig. 1a, has to be brought into the microstructure. This can be achieved when the required amount of energy $ΔG$ is brought in thermally through strong cooling as $ΔG_{chem}$, mechanically, through induced deformation as $ΔG_{mech}$, or through a combination of both. The transformation can occur thermally for every amount of deformation if the so-called martensite start temperature $M_s$ is reached, but not at all, if the temperature rises above a critical threshold $T_0$, as shown schematically in Fig. 1b. The specific values of these limit temperatures depend on the alloy elements in the investigated material [5].

<figure><img src="image_808.png" /><figcaption>Figure 1: The metastable and stable states (a) and the thermodynamical description of the martensite transformation (b) according to [2]</figcaption></figure>

Martensite formation from γ-austenite can occur in different forms. As shown in Fig. 2, the austenite can either transform directly to α-martensite or to ε-martensite, which then can also transform into α-martensite. For the direct transformation from austenite to α-martensite the volume increases by 2.1 % and the material strength is enhanced. The volume decreases by 0.8 % for the transformation to ε-martensite which results in a slight increase of the strength but a strong increase of ductility. Although the transformation from austenite first to ε-martensite and then to α-martensite leads to the same volume behaviour, the material strength is increased less than for the direct transformation [2]. As the different transformations lead to different mechanical properties, the resulting properties are a result of the totality of the occurred transformations. These three transformations all take place simultaneously, whereby their specific distribution depends on the forming parameters such as the temperature, the strain rate and the resulting stress. In general, lower temperatures, slower forming rates and tensile stresses (rather than compressive) lead to higher amounts of α-martensite [7].

In the context of sheet metal forming, Behrens et al. researched the effects of deformation induced martensite transformation and developed a material model for FE simulations to determine the resulting amount of martensite as well as consider the change of flow stress. For bulk forming the material model was transferred and applied to simplified forming processes such as uniaxial compression tests [8]. Behrens et al. also presented a first functionalisation of the deformation induced martensite for bulk forming, whereby two forming processes were numerically designed and carried out [9]. The following research [10] showed increased hardness values and microstructures images, which indicated deformation induced martensite transformation.

This paper is dedicated to the advanced functionalisation for bulk forming. The forming processes of Behrens et al. [10] are revisited, the martensite contents of the specimens are determined and compared to numerically determined distributions of plastic strain, as well as to previous results of hardness measurements and microstructure analysis. Additionally, to enable a stronger martensite formation as in the previous studies, the process with the higher degree of plastic strain was carried out at cryogenic temperatures of -196 °C. The formed specimens were analysed and compared to the results of forming at -17 °C.
transformation, a specific minimum amount of energy, shown as $\Delta G$ in Fig. 1a, has to be brought into the microstructure. This can be achieved when the required amount of energy $\Delta G$ is brought in thermally through strong cooling as $\Delta G_{chem}$, mechanically, through induced deformation as $\Delta G_{mech}$, or through a combination of both. The transformation can occur thermally for every amount of deformation if the so-called martensite start temperature $M_s$ is reached, but not at all, if the temperature rises above a critical threshold $T_0$, as shown schematically in Fig. 1b. The specific values of these limit temperatures depend on the alloy elements in the investigated material [5].

<figure><img src="image_816.png" /><figcaption>Figure 1: The metastable and stable states (a) and the thermodynamical description of the martensite transformation (b) according to [2]</figcaption></figure>

Martensite formation from $\gamma$-austenite can occur in different forms. As shown in Fig. 2, the austenite can either transform directly to $\alpha$-martensite or to $\varepsilon$-martensite, which then can also transform into $\alpha$-martensite. For the direct transformation from austenite to $\alpha$-martensite the volume increases by 2.1 % and the material strength is enhanced. The volume decreases by 0.8 % for the transformation to $\varepsilon$-martensite which results in a slight increase of the strength but a strong increase of ductility. Although the transformation from austenite first to $\varepsilon$-martensite and then to $\alpha$-martensite leads to the same volume behaviour, the material strength is increased less than for the direct transformation [2]. As the different transformations lead to different mechanical properties, the resulting properties are a result of the totality of the occurred transformations. These three transformations all take place simultaneously, whereby their specific distribution depends on the forming parameters such as the temperature, the strain rate and the resulting stress. In general, lower temperatures, slower forming rates and tensile stresses (rather than compressive) lead to higher amounts of $\alpha$- martensite [7].

In the context of sheet metal forming, Behrens et al. researched the effects of deformation induced martensite transformation and developed a material model for FE simulations to determine the resulting amount of martensite as well as consider the change of flow stress. For bulk forming the material model was transferred and applied to simplified forming processes such as uniaxial compression tests [8]. Behrens et al. also presented a first functionalisation of the deformation induced martensite for bulk forming, whereby two forming processes were numerically designed and carried out [9]. The following research [10] showed increased hardness values and microstructures images, which indicated deformation induced martensite transformation.

This paper is dedicated to the advanced functionalisation for bulk forming. The forming processes of Behrens et al. [10] are revisited, the martensite contents of the specimens are determined and compared to numerically determined distributions of plastic strain, as well as to previous results of hardness measurements and microstructure analysis. Additionally, to enable a stronger martensite formation as in the previous studies, the process with the higher degree of plastic strain was carried out at cryogenic temperatures of -196 °C. The formed specimens were analysed and compared to the results of forming at -17 °C.
<figure><img src="image_809.png" /><figcaption>Figure 2: The effects of deformation induced martensite transformation (a) and the possible transformation paths (b) [7]</figcaption></figure>

## Material and Methods

As testing material, the stainless steel AISI 304 (EN 1.4301) was chosen. It was already used in previous studies and thereby showed strong hardening through deformation-induced martensite transformation. To recreate the forming processes of ball bearing rings with different diameters, two processes with different material flows were designed. This was an upsetting process for smaller diameters and a full forward extrusion for larger diameters. As shown in Fig. 3 schematically, the forming processes were both carried out with the same set of dies and only the dimensions of the cylindrical semi-finished product were varied. The dimensions were a diameter of 35 mm and a height of 22 mm for the upsetting process and for the full forward extrusion a diameter of 49 mm and a height of 11.7 mm. The lower die was additionally devided into two sections to reduce the stresses in the buttom radius. The die setup is designed as a transportable system with an additional thermal container to reduce the heat exchange with the enviroment. Through this, the complete die system can be cooled as whole and mounted quickly into the press. Before the cooling, all functional surfaces of the die and the specimen are lubricated with molybdenum disulfide and the complete setup is assemlied after the lubricant has dried. The forming tests were carried out on a Schirmer & Plate hydraulic press with an adjustable ram speed. On the one hand, a low ram speed and therefore a low strain rate as well as a longer process time would lead to a stronger heating of the die system (including the specimen) and result in a reduced martensite transformation. On the other hand, a high ram speed and therefore higher strain rate would lead to higher press forces, higher mechanical loads on the dies and also less martensite transformation. Because the work of [9] showed a strong temperature dependency and comparatively low strain rate dependency, in the work of [10] a ram speed of 10 mm/s was chosen as it leads to realtively low strain rates whilst still being in the range of industrial processes. To ensure the comparability of the results to [10], for this study the ram speed of 10 mm/s was kept.
<figure><img src="image_817.png" /><figcaption>Figure 2: The effects of deformation induced martensite transformation (a) and the possible transformation paths (b) [7]</figcaption></figure>

## Material and Methods

As testing material, the stainless steel AISI 304 (EN 1.4301) was chosen. It was already used in previous studies and thereby showed strong hardening through deformation-induced martensite transformation. To recreate the forming processes of ball bearing rings with different diameters, two processes with different material flows were designed. This was an upsetting process for smaller diameters and a full forward extrusion for larger diameters. As shown in Fig. 3 schematically, the forming processes were both carried out with the same set of dies and only the dimensions of the cylindrical semi-finished product were varied. The dimensions were a diameter of 35 mm and a height of 22 mm for the upsetting process and for the full forward extrusion a diameter of 49 mm and a height of 11.7 mm. The lower die was additionally divided into two sections to reduce the stresses in the bottom radius. The die setup is designed as a transportable system with an additional thermal container to reduce the heat exchange with the environment. Through this, the complete die system can be cooled as whole and mounted quickly into the press. Before the cooling, all functional surfaces of the die and the specimen are lubricated with molybdenum disulfide and the complete setup is assembled after the lubricant has dried. The forming tests were carried out on a Schirmer & Plate hydraulic press with an adjustable ram speed. On the one hand, a low ram speed and therefore a low strain rate as well as a longer process time would lead to a stronger heating of the die system (including the specimen) and result in a reduced martensite transformation. On the other hand, a high ram speed and therefore higher strain rate would lead to higher press forces, higher mechanical loads on the dies and also less martensite transformation. Because the work of [9] showed a strong temperature dependency and comparatively low strain rate dependency, in the work of [10] a ram speed of 10 mm/s was chosen as it leads to relatively low strain rates whilst still being in the range of industrial processes. To ensure the comparability of the results to [10], for this study the ram speed of 10 mm/s was kept.
<figure><img src="image_810.png" /><figcaption>Figure 3: The investigated forming processes: a.) upsetting, b.) full forward extrusion</figcaption></figure>

First, the flow curves at -17 °C from previous work of the authors of [9] were applied to the processes of [10] to determine the distribution of plastic strain numerically through a 2D simulation with the Finite Element (FE) software Simufact Forming v16.0. The dies were assumed as rigid and for the discretisation the element type “quads” was used with an element size of 0.2 mm. Additionally, the martensite contents of the specimens of the former forming experiments at -17 °C were measured. The martensite contents and the numerically determined plastic strain distributions were compared to the results of [10]. As fundamental research, such as Olson [5] and Angel [11], showed the potential of an increased martensite transformation at even lower temperatures, additionally a cryogenic temperature was investigated experimentally. For this, the experimental forming process with higher degrees of plastic strain and therefore a higher potential for martensite transformation was carried out at -196 °C. The specimens were analysed through magnetic inductive testing (Feritscope MP3C), microstructure analysis and hardness measurements (HV1) as shown in Fig. 4.

The content of α-martensite was determined through magnetic inductive analysis for each formed specimen. Thereby, the α-martensite content $f^α$ was calculated through the approach of the work of Talonen [7] from the mass percentage of ferrite $f^F$, as shown in Eq. 1. The ferrite percentage was measured at the surface at six separate locations, as schematically shown in Fig. 4b, at the surface of the contact area to the bearing ball.

$$f^α=0.261 + 1.714 \cdot f^F \qquad (1)$$

The hardness measurements were taken out on cross-sections of the formed bearings in two directions as shown schematically in Fig. 4a. Along the radius, the hardness was measured every 0.2 mm and perpendicular to the surface at the middle of the contact area, it was tested up to a depth of 5 mm into the specimen. The measurements were carried out with a Qness Q10 A+ micro hardness testing device.

<figure><img src="image_811.png" /><figcaption>Figure 4: Measuring points for hardness(a) and martensite content(b)</figcaption></figure>

To analyse the microstructure, cross sections of the formed specimens were taken from the area where the contact to the bearing ball shall be. Therefore, cross-sections were cut out of the
<figure><img src="image_818.png" /><figcaption>Figure 3: The investigated forming processes: a.) upsetting, b.) full forward extrusion</figcaption></figure>

First, the flow curves at -17 °C from previous work of the authors of [9] were applied to the processes of [10] to determine the distribution of plastic strain numerically through a 2D simulation with the Finite Element (FE) software Simufact Forming v16.0. The dies were assumed as rigid and for the discretisation the element type “quads” was used with an element size of 0.2 mm. Additionally, the martensite contents of the specimens of the former forming experiments at -17 °C were measured. The martensite contents and the numerically determined plastic strain distributions were compared to the results of [10]. As fundamental research, such as Olson [5] and Angel [11], showed the potential of an increased martensite transformation at even lower temperatures, additionally a cryogenic temperature was investigated experimentally. For this, the experimental forming process with higher degrees of plastic strain and therefore a higher potential for martensite transformation was carried out at -196 °C. The specimens were analysed through magnetic inductive testing (Feritscope MP3C), microstructure analysis and hardness measurements (HV1) as shown in Fig. 4.

The content of α-martensite was determined through magnetic inductive analysis for each formed specimen. Thereby, the α-martensite content $f^α$ was calculated through the approach of the work of Talonen [7] from the mass percentage of ferrite $f^F$, as shown in Eq. 1. The ferrite percentage was measured at the surface at six separate locations, as schematically shown in Fig. 4b, at the surface of the contact area to the bearing ball.

$$f^α=0.261 + 1.714 \cdot f^F \quad (1)$$

The hardness measurements were taken out on cross-sections of the formed bearings in two directions as shown schematically in Fig. 4a. Along the radius, the hardness was measured every 0.2 mm and perpendicular to the surface at the middle of the contact area, it was tested up to a depth of 5 mm into the specimen. The measurements were carried out with a Qness Q10 A+ micro hardness testing device.

<figure><img src="image_819.png" /><figcaption>Figure 4: Measuring points for hardness(a) and martensite content(b)</figcaption></figure>

To analyse the microstructure, cross sections of the formed specimens were taken from the area where the contact to the bearing ball shall be. Therefore, cross-sections were cut out of the
specimen and cold embedded. Afterwards the samples were grinded, polished, etched with Beraha I and metallographic images were taken.

## Results and Discussion

As shown in Fig. 5, the hardness along the radius shows a nearly linear increase for the upsetting and a decrease for the full forward extrusion at -17 °C. This is consistent to the simulations where a similar increase and decrease of plastic strain along the radius can be observed. The hardness values at the beginning of the radius were higher for the full forward extrusion than the upsetting, which changed around the measuring point 20. From there on, higher values were measured for the upsetting process. These hardness profiles are in accordance to the calculated distributions of plastic strain from the simulations. The measurements perpendicular to the radius show a linear decrease in depth for both processes. Thereby, for both processes comparable hardness values as well as similar decreases can be seen. The decrease itself is consistent to the numerically determined distributions of plastic strain, but the low difference between the both processes does not fit to the high differences of plastic strain that could be observed in the simulations.

For forming at -196 °C, an increased hardness can be observed along the radius whilst showing a decrease with a similar gradient as for the forming at -17 °C. In the depth, the hardness is also increased overall, whilst only a low decrease can be seen. In comparison to the hardness of conventional AISI 304 (without strain hardening), which is roughly about 220 HV to 240 HV, both forming processes lead to a strong increase of hardness at -17 °C. This effect is enhanced for forming at -196 °C.

<figure><img src="image_812.png" /><figcaption>Figure 5: Results of the hardness measurements along the edge (a) and perpendicular to the surface (b) with the numerically determined distributions of plastic strain(c)</figcaption></figure>

The determined martensite contents at the surface of the testing points, as schematically shown in Fig. 4b, are presented in Table 1. As substantial contents of α-martensite could be measured for
specimen and cold embedded. Afterwards the samples were grinded, polished, etched with Beraha I and metallographic images were taken.

## Results and Discussion

As shown in Fig. 5, the hardness along the radius shows a nearly linear increase for the upsetting and a decrease for the full forward extrusion at -17 °C. This is consistent to the simulations where a similar increase and decrease of plastic strain along the radius can be observed. The hardness values at the beginning of the radius were higher for the full forward extrusion than the upsetting, which changed around the measuring point 20. From there on, higher values were measured for the upsetting process. These hardness profiles are in accordance to the calculated distributions of plastic strain from the simulations. The measurements perpendicular to the radius show a linear decrease in depth for both processes. Thereby, for both processes comparable hardness values as well as similar decreases can be seen. The decrease itself is consistent to the numerically determined distributions of plastic strain, but the low difference between the both processes does not fit to the high differences of plastic strain that could be observed in the simulations.

For forming at -196 °C, an increased hardness can be observed along the radius whilst showing a decrease with a similar gradient as for the forming at -17 °C. In the depth, the hardness is also increased overall, whilst only a low decrease can be seen. In comparison to the hardness of conventional AISI 304 (without strain hardening), which is roughly about 220 HV to 240 HV, both forming processes lead to a strong increase of hardness at -17 °C. This effect is enhanced for forming at -196 °C.

<figure><img src="image_820.png" /><figcaption>Figure 5: Results of the hardness measurements along the edge (a) and perpendicular to the surface (b) with the numerically determined distributions of plastic strain(c)</figcaption></figure>

The determined martensite contents at the surface of the testing points, as schematically shown in Fig. 4b, are presented in Table 1. As substantial contents of α-martensite could be measured for
each specimen, the increase in hardness can be related to deformation induced martensite transformation and not solely to strain hardening. For the full forward extrusion, the martensite content is higher than for the upsetting process, which is in accordance to the numerically calculated higher plastic strain. The low difference in transformed martensite of only 2 Ma.-%, is a possible explanation for the low difference of the hardness values in depth between the two processes (compared to the high differences of calculated plastic strains).

In general, the measured martensite contents were considerably lower than contents that fundamental research, such as [11], have reached for the same forming temperatures and degrees of strain. This can be explained through the inhomogeneous and higher strain rates, thereby higher amount of dissipated heat, as well as possible heat exchange with the surrounding environment. The full forward extrusion at -196 °C reached higher martensite contents of approximately 81 % at the contact surface of the ball bearing. Other researchers, such as Angel [11] or Nebel [12], have identified the maximum amount of achievable martensite content at approximately 80 - 90 % for higher temperatures and lower degrees of strain. Therefore, it is likely that the maximum martensite content achievable for the presented forming process in the area of interest, with its comparatively high strain rate, has been reached at the investigated surface and a further increase is not possible.

<table><caption>Table 1: Determined martensite contents for the formed bearing rings</caption><thead><tr><th>Forming temperature [°C]</th><th>Forming process [-]</th><th>Martensite content [Ma.-%]</th><th>Standard deviation [Ma.-%]</th></tr></thead><tbody><tr><td rowspan="2">-17 °C</td><td>Upsetting</td><td>2.66</td><td>0.38</td></tr><tr><td>Full forward extrusion</td><td>4.55</td><td>0.25</td></tr><tr><td>-196 °C</td><td>Full forward extrusion</td><td>81.68</td><td>1.87</td></tr></tbody></table>

As presented in Fig. 6, at -17 °C both processes showed inhomogeneous microstructures with noticeable line formations of martensite. These lines indicate twin planes and thereby a deformation induced transformation. The concentration of these lines is higher towards the surface of the contact area than in the depth for both processes. Thereby it is not possible to distinguish clearly between α-martensite and ε-martensite. For the full forward extrusion, the overall concentration is higher than for the upsetting process. Additionally, the microstructures show dark patterns, which are in accordance to the distribution of plastic strain determined through the simulations. This indicates deformation-induced martensite formation and grain refinement. At -196 °C the area of martensite transformation is significantly enlarged and the grain structure is more refined, but it still shows the same schematic pattern as for -17 °C. This pattern is also schematically in agreement to the distribution of plastic strain determined in the simulations. The low decrease of the hardness values in depth as well as the microstructure indicate that martensite was transformed in such a big area of the specimen, and not specifically at the surface. This might be disadvantageous for the mechanical properties of a component in question.
each specimen, the increase in hardness can be related to deformation induced martensite transformation and not solely to strain hardening. For the full forward extrusion, the martensite content is higher than for the upsetting process, which is in accordance to the numerically calculated higher plastic strain. The low difference in transformed martensite of only 2 Ma.-%, is a possible explanation for the low difference of the hardness values in depth between the two processes (compared to the high differences of calculated plastic strains).

In general, the measured martensite contents were considerably lower than contents that fundamental research, such as [11], have reached for the same forming temperatures and degrees of strain. This can be explained through the inhomogeneous and higher strain rates, thereby higher amount of dissipated heat, as well as possible heat exchange with the surrounding environment. The full forward extrusion at -196 °C reached higher martensite contents of approximately 81 % at the contact surface of the ball bearing. Other researchers, such as Angel [11] or Nebel [12], have identified the maximum amount of achievable martensite content at approximately 80 - 90 % for higher temperatures and lower degrees of strain. Therefore, it is likely that the maximum martensite content achievable for the presented forming process in the area of interest, with its comparatively high strain rate, has been reached at the investigated surface and a further increase is not possible.

<table><caption>Table 1: Determined martensite contents for the formed bearing rings</caption><thead><tr><th>Forming temperature [°C]</th><th>Forming process [-]</th><th>Martensite content [Ma.-%]</th><th>Standard deviation [Ma.-%]</th></tr></thead><tbody><tr><td rowspan="2">-17 °C</td><td>Upsetting</td><td>2.66</td><td>0.38</td></tr><tr><td>Full forward extrusion</td><td>4.55</td><td>0.25</td></tr><tr><td>-196 °C</td><td>Full forward extrusion</td><td>81.68</td><td>1.87</td></tr></tbody></table>

As presented in Fig. 6, at -17 °C both processes showed inhomogeneous microstructures with noticeable line formations of martensite. These lines indicate twin planes and thereby a deformation induced transformation. The concentration of these lines is higher towards the surface of the contact area than in the depth for both processes. Thereby it is not possible to distinguish clearly between α-martensite and ε-martensite. For the full forward extrusion, the overall concentration is higher than for the upsetting process. Additionally, the microstructures show dark patterns, which are in accordance to the distribution of plastic strain determined through the simulations. This indicates deformation-induced martensite formation and grain refinement. At -196 °C the area of martensite transformation is significantly enlarged and the grain structure is more refined, but it still shows the same schematic pattern as for -17 °C. This pattern is also schematically in agreement to the distribution of plastic strain determined in the simulations. The low decrease of the hardness values in depth as well as the microstructure indicate that martensite was transformed in such a big area of the specimen, and not specifically at the surface. This might be disadvantageous for the mechanical properties of a component in question.
<figure><img src="image_813.png" /><figcaption>Figure 6: Metallographic images of the formed specimens of the upsetting (a) and full forward extrusion (b) forming process</figcaption></figure>

## Conclusion and Outlook

Through a thorough investigation the fundamental knowledge of deformation induced martensite transformation was functionalised for the application in the field of bulk forming. In previous studies two forming processes were numerically designed to show high plastic strains, and thus martensite transformation, at specific surfaces of the workpiece, which are expected to be heavily loaded. In this study specimens formed at -17 °C were investigated through magnetic inductive testing as well as through FE simulations and compared to hardness measurements and microstructure analysis. To study the possibilities of a further increase of hardness through martensite transformation, the full forward extrusion was additionally carried out at -196 °C. At -17 °C both processes showed increased hardness values at the surfaces of interest. The values were in agreement of the microstructure images as well as the magnetic inductive testing which showed an increased martensite content at these surfaces. The full forward extrusion process showed higher contents of martensite and a more refined microstructure. This can be explained through the higher degrees of plastic strain, which were calculated through the simulations. The forming at -196 °C led to a further increase in hardness with a more homogeneous distribution. The microstructure showed an expansion of the area of the martensite transformation as well as a greater grain refinement. As a martensite content of approximately 81 % was reached specifically at the heavily loaded surface and fundamental researchers identify the limits of deformation induced martensite transformation at 80 to 90 % for processes with higher temperatures and lower degrees of deformation, it is assumed that this limit was reached for the presented process.

Throughout this series of studies, the numerically determined distribution of plastic strain was in good agreement with the occurring martensite transformation. Therefore, the simulation of the plastic strain can be considered as suitable simplified approach to estimate an approximate distribution of the deformation induced martensite transformation for a preliminary process design. This approach does not require additional models nor extended material data.
<figure><img src="image_821.png" /><figcaption>Figure 6: Metallographic images of the formed specimens of the upsetting (a) and full forward extrusion (b) forming process</figcaption></figure>

## Conclusion and Outlook

Through a thorough investigation the fundamental knowledge of deformation induced martensite transformation was functionalised for the application in the field of bulk forming. In previous studies two forming processes were numerically designed to show high plastic strains, and thus martensite transformation, at specific surfaces of the workpiece, which are expected to be heavily loaded. In this study specimens formed at -17 °C were investigated through magnetic inductive testing as well as through FE simulations and compared to hardness measurements and microstructure analysis. To study the possibilities of a further increase of hardness through martensite transformation, the full forward extrusion was additionally carried out at -196 °C. At -17 °C both processes showed increased hardness values at the surfaces of interest. The values were in agreement of the microstructure images as well as the magnetic inductive testing which showed an increased martensite content at these surfaces. The full forward extrusion process showed higher contents of martensite and a more refined microstructure. This can be explained through the higher degrees of plastic strain, which were calculated through the simulations. The forming at -196 °C led to a further increase in hardness with a more homogeneous distribution. The microstructure showed an expansion of the area of the martensite transformation as well as a greater grain refinement. As a martensite content of approximately 81 % was reached specifically at the heavily loaded surface and fundamental researchers identify the limits of deformation induced martensite transformation at 80 to 90 % for processes with higher temperatures and lower degrees of deformation, it is assumed that this limit was reached for the presented process.

Throughout this series of studies, the numerically determined distribution of plastic strain was in good agreement with the occurring martensite transformation. Therefore, the simulation of the plastic strain can be considered as a suitable simplified approach to estimate an approximate distribution of the deformation induced martensite transformation for a preliminary process design. This approach does not require additional models nor extended material data.
In following studies, the resulting residual stresses will be investigated. Although the full forward extrusion showed higher amounts of deformation and therefore reached higher amounts of α-martensite, the resulting residual stresses might have a negative influence on the service life. Also, a high martensite content will weaken the resistance to corrosion. Therefore, service life tests will be carried out for the specimens of this study to evaluate the influence of the martensite content, the hardness distribution and the resulting residual stresses.

As the cooling, as well as the handling of the complete die system was challenging, applying the presented approach industrially would require a high amount of effort and resources per workpiece. The results of the service life tests will allow to evaluate which forming process is more suitable and if the benefits of the functionalisation of deformation-induced martensite transformation are enough to consider an industrial application.

## Acknowledgements

The results presented were obtained in the research project "Surface layer treatment using martensite formation of formed stainless steel" financed under project number 423160066 by the German Research Foundation (DFG). The authors would like to thank the German Research Foundation for the financial support.

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[5] G. B. Olson, M. Cohen, Kinetics of strain-induced martensitic nucleation, Metallurgical Transactions A., vol. 6, no. 4 (1975) 791-795. https://doi.org/10.1007/BF02672301

[6] H. U. Lindenberg, O. Kazmierski, A. Otto, Kaltgewalztes Band aus nichtrostenden Edelstählen und die Anwendungspotentiale, Stahl und Eisen, vol. 120, no. 5 (2000) 37-42.

[7] J. Talonen, Effect of Strain-Induced α'-Martensite Transformation on Mechanical Properties of Metastable Austenitic Stainless Steels, Espoo, 2007

[8] B.-A. Behrens, S. Hubner, J. Knigge, K. Voges-Schwieger, K. Weilandt, Local Strain-Hardening in Sheet Metal and Forging Components, Steel Research International, vol. 79, no. 3 (2008) 165-171. https://doi.org/10.1002/srin.200806335

[9] B.-A. Behrens, K. Brunotte, H. Wester, J. Peddinghaus, M. Till, Functionalisation of the boundary Layer by Deformation-Induced Martensite on Bearing Rings by Means of Bulk Metal Forming Processes, METAL 2022 Conference Proceedings (2022) 250-255 https://doi.org/10.37904/metal.2022.4394

[10] M. Till, S. Kuhlmann, J. Peddinghaus, H. Wester, D. Rosenbusch, B.-A. Behrens, Deformation-Induced Strength Increase in a Functional Surface of Angular Ball Bearing Rings
In following studies, the resulting residual stresses will be investigated. Although the full forward extrusion showed higher amounts of deformation and therefore reached higher amounts of α-martensite, the resulting residual stresses might have a negative influence on the service life. Also, a high martensite content will weaken the resistance to corrosion. Therefore, service life tests will be carried out for the specimens of this study to evaluate the influence of the martensite content, the hardness distribution and the resulting residual stresses.

As the cooling, as well as the handling of the complete die system was challenging, applying the presented approach industrially would require a high amount of effort and resources per workpiece. The results of the service life tests will allow to evaluate which forming process is more suitable and if the benefits of the functionalisation of deformation-induced martensite transformation are enough to consider an industrial application.

## Acknowledgements

The results presented were obtained in the research project "Surface layer treatment using martensite formation of formed stainless steel" financed under project number 423160066 by the German Research Foundation (DFG). The authors would like to thank the German Research Foundation for the financial support.

## References

[1] T. Altan, G. Ngaile, G. Shen, Cold and hot forging: fundamentals and applications, ASM International, Materials Park, OH; 2004, https://doi.org/10.31399/asm.tb.chffa.9781627083003

[2] J. Knigge, Lokale Martensitbildung in metastabilen austenitischen Stählen durch Verfahren der Massivumformung, Hannover, 2015

[3] T. Coors, M. Mildebrath, C. Büdenbender, F. Saure, M. Y Faqiri, C. Kahra, V. Prasanthan, A. Chugreeva, T. Matthias, L. Budde, F. Pape, F. Nürnberger, T. Hassel, J. Hermsdorf, L. Overmeyer, B. Breidenstein, B. Denkena, B.-A. Behrens, H. J. Maier, G. Poll, Investigations on Tailored Forming of AISI 52100 as Rolling Bearing Raceway, Metals, 10, no. 10 (2020), 1363. https://doi.org/10.3390/met10101363

[4] M. Okayasu, H. Fukui, H. Ohfuji, T. Shiraishi, Strain-induced martensite formation in austenitic stainless steel, J Mater Sci 48 (2013) 6157-6166. https://doi.org/10.1007/s10853-013-7412-8

[5] G. B. Olson, M. Cohen, Kinetics of strain-induced martensitic nucleation, Metallurgical Transactions A., vol. 6, no. 4 (1975) 791-795. https://doi.org/10.1007/BF02672301

[6] H. U. Lindenberg, O. Kazmierski, A. Otto, Kaltgewalztes Band aus nichtrostenden Edelstählen und die Anwendungspotentiale, Stahl und Eisen, vol. 120, no. 5 (2000) 37-42.

[7] J. Talonen, Effect of Strain-Induced α'-Martensite Transformation on Mechanical Properties of Metastable Austenitic Stainless Steels, Espoo, 2007

[8] B.-A. Behrens, S. Hubner, J. Knigge, K. Voges-Schwieger, K. Weilandt, Local Strain-Hardening in Sheet Metal and Forging Components, Steel Research International, vol. 79, no. 3 (2008) 165-171. https://doi.org/10.1002/srin.200806335

[9] B.-A. Behrens, K. Brunotte, H. Wester, J. Peddinghaus, M. Till, Functionalisation of the boundary Layer by Deformation-Induced Martensite on Bearing Rings by Means of Bulk Metal Forming Processes, METAL 2022 Conference Proceedings (2022) 250-255 https://doi.org/10.37904/metal.2022.4394

[10] M. Till, S. Kuhlmann, J. Peddinghaus, H. Wester, D. Rosenbusch, B.-A. Behrens, Deformation-Induced Strength Increase in a Functional Surface of Angular Ball Bearing Rings
Made of X5CrNi18-10 (AISI 304), METAL 2023 Conference Proceedings (2023) 170-174
https://doi.org/10.37904/metal.2023.4634

[11] T. Angel, Formation of Martensite in Austenitic Stainless Steels Journal of the Iron and Steel Institute, Nr. 177 (1954) 165-174

[12] T. Nebel, Deformation Behavior and Microstructure of Metastable Austenitic Stainless Steels Under Cyclic Loading, Kaiserslautern, 2002
Made of X5CrNi18-10 (AISI 304), METAL 2023 Conference Proceedings (2023) 170-174
https://doi.org/10.37904/metal.2023.4634

[11] T. Angel, Formation of Martensite in Austenitic Stainless Steels Journal of the Iron and Steel Institute, Nr. 177 (1954) 165-174

[12] T. Nebel, Deformation Behavior and Microstructure of Metastable Austenitic Stainless Steels Under Cyclic Loading, Kaiserslautern, 2002
# Necking of invar layer in copper-invar laminates during roll-bonding

MKINSI Ismaïl¹,ᵃ*, BERDIN Clotilde¹,ᵇ*, HELBERT Anne-Laure¹,ᶜ,
BAUDIN Thierry¹,ᵈ, SOLAS Denis¹,ᵉ, ATEBA BETANDA Yanick²,ᵉ and
WACKERLE Thierry²,⁹

¹ Université Paris-Saclay, CNRS, Institut de chimie moléculaire et des matériaux d'Orsay,
91405, Orsay, France

² APERAM Alloys Imphy, BP1, Centre de recherche Pierre Chevenard, 58160 Imphy, France

ᵃ ismail.mkinsi@universite-paris-saclay.fr, ᵇ clotilde.berdin@universite-paris-saclay.fr,

ᶜ anne-laure.helbert@universite-paris-saclay.fr, ᵈ thierry.baudin@universite-paris-saclay.fr,

ᵉ denis.solas@universite-paris-saclay.fr, ᶜ yanick.ateba-betanda@aperam.com

and ⁹ thierry.waeckerle@aperam.com

**Keywords:** Roll-Bonding, Necking, Metal Composites, FE Simulation

**Abstract.** Sheets of Fe-36%Ni (Invar) and copper alloys are bonded by roll-bonding process to produce metallic composites with a low thermal expansion coefficient and large conductivity. To boost the thermal conductivity of the composite, the Invar layers must be fragmented. For a given volume fraction of Invar, the necking/fragmentation depends on the spatial distribution of the Invar layers, meaning their number and thickness. Hence, different configurations of copper/Invar composites are processed to determine the effect of each parameter on the necking/fragmentation. The materials are then mechanically characterised to use the results as input data to the simulation of the process. Finally, to obtain a realistic simulation, a multi-step roll-bonding simulation using a remeshing solution is carried out for each cycle. The occurrence of necking during the cold-roll bonding of copper and Invar layers is both numerically and experimentally studied. In all cases, the experimental and simulation results are in good agreement. Invar layer thickness is of major importance to facilitate the fragmentation.

**Introduction**

Power modules are increasingly utilized and in demand for applications in energy management or onboard systems [1,2]. They need constant improvement to enhance efficiency and reliability. The development of metallic composites that could serve as substrates or leadframes for electronic components is therefore of major importance. High transverse thermal conductivity and low thermal expansion in the plane of those components are mandatory to mitigate thermal stresses. The combination of copper and Invar sheets is a promising option to achieve optimal properties as proposed in the literature [1]. This work aims to use roll-bonding of copper and Invar simple sheets for manufacturing Invar-copper composites.

The roll-bonding is a solid-state welding process to assemble sheets of different physical and/or mechanical properties and obtain composites with optimized properties [3–5]. When materials of different hardness are rolled together, the hardest material can exhibit, under certain conditions, areas of necking leading to the fragmentation of the hard layer in the soft matrix. This fragmentation is necessary for the application in this work. Indeed, the fragmentation of Invar layers (hard material) inside the copper matrix (soft material) will induce thermal bridges of copper, thereby enhancing the thermal conductivity of the composite. Nonetheless, as it could affect the thermal expansion along the length: the fragmentation has to be optimized. Therefore, roll-bonding process has to be studied in order to control the structure of the final product.

Necking of hard layers during roll-bonding has been studied in the literature. A link between necking of hard layers and yield strength or hardness mismatch between soft and hard materials

<figure><img src="image_814.png" /></figure>
# Necking of invar layer in copper-invar laminates during roll-bonding

MKINSI Ismaïl¹,ᵃ*, BERDIN Clotilde¹,ᵇ*, HELBERT Anne-Laure¹,ᶜ,
BAUDIN Thierry¹,ᵈ, SOLAS Denis¹,ᵉ, ATEBA BETANDA Yanick²,ᵉ and
WACKERLE Thierry²,⁹

¹ Université Paris-Saclay, CNRS, Institut de chimie moléculaire et des matériaux d'Orsay,
91405, Orsay, France

² APERAM Alloys Imphy, BP1, Centre de recherche Pierre Chevenard, 58160 Imphy, France

ᵃ ismail.mkinsi@universite-paris-saclay.fr, ᵇ clotilde.berdin@universite-paris-saclay.fr,

ᶜ anne-laure.helbert@universite-paris-saclay.fr, ᵈ thierry.baudin@universite-paris-saclay.fr,

ᵉ denis.solas@universite-paris-saclay.fr, Ṡ yanick.ateba-betanda@aperam.com

and ⁹ thierry.waeckerle@aperam.com

**Keywords:** Roll-Bonding, Necking, Metal Composites, FE Simulation

**Abstract.** Sheets of Fe-36%Ni (Invar) and copper alloys are bonded by roll-bonding process to produce metallic composites with a low thermal expansion coefficient and large conductivity. To boost the thermal conductivity of the composite, the Invar layers must be fragmented. For a given volume fraction of Invar, the necking/fragmentation depends on the spatial distribution of the Invar layers, meaning their number and thickness. Hence, different configurations of copper/Invar composites are processed to determine the effect of each parameter on the necking/fragmentation. The materials are then mechanically characterised to use the results as input data to the simulation of the process. Finally, to obtain a realistic simulation, a multi-step roll-bonding simulation using a remeshing solution is carried out for each cycle. The occurrence of necking during the cold-roll bonding of copper and Invar layers is both numerically and experimentally studied. In all cases, the experimental and simulation results are in good agreement. Invar layer thickness is of major importance to facilitate the fragmentation.

**Introduction**

Power modules are increasingly utilized and in demand for applications in energy management or onboard systems [1,2]. They need constant improvement to enhance efficiency and reliability. The development of metallic composites that could serve as substrates or leadframes for electronic components is therefore of major importance. High transverse thermal conductivity and low thermal expansion in the plane of those components are mandatory to mitigate thermal stresses. The combination of copper and Invar sheets is a promising option to achieve optimal properties as proposed in the literature [1]. This work aims to use roll-bonding of copper and Invar simple sheets for manufacturing Invar-copper composites.

The roll-bonding is a solid-state welding process to assemble sheets of different physical and/or mechanical properties and obtain composites with optimized properties [3–5]. When materials of different hardness are rolled together, the hardest material can exhibit, under certain conditions, areas of necking leading to the fragmentation of the hard layer in the soft matrix. This fragmentation is necessary for the application in this work. Indeed, the fragmentation of Invar layers (hard material) inside the copper matrix (soft material) will induce thermal bridges of copper, thereby enhancing the thermal conductivity of the composite. Nonetheless, as it could affect the thermal expansion along the length: the fragmentation has to be optimized. Therefore, roll-bonding process has to be studied in order to control the structure of the final product.

Necking of hard layers during roll-bonding has been studied in the literature. A link between necking of hard layers and yield strength or hardness mismatch between soft and hard materials

<figure><img src="image_822.png" /></figure>
was demonstrated [5–7]. However, the understanding of necking occurrence during roll-bonding is only partially mastered. Criteria for predicting necking in hard layers are typically based on the maximal load criterion, as a generalization of the Considere criterion [4,8,9]. Nevertheless, these criteria underestimate the required reduction ratio to observe this plastic instability [4,10].

In this work, the influence of stacking geometry on Invar layers necking is studied through an experimental approach completed by simulations with the finite element method. For that purpose, stackings with different Invar volume fractions and spatial distribution, meaning the number and thickness of Invar layers, have been considered aiming to optimize their physical properties. The materials behaviour laws were identified to obtain input data for the simulation. The numerical simulation of multi-cycle roll-bonding was then developed and results were compared to the experimental ones.

## Experiment

Rolling process:

The Invar and copper sheets were kindly provided by APERAM Alloys Imphy. The copper plate in a strain-hardened state is composed of 99.99% Cu (traces of Pb and Bi) and exhibits a 1.06 mm initial thickness. The Invar sheets (Fe-36%Ni) are received in an annealed state and have an initial thickness of either 1.0 or 2.2 mm.

In order to produce the stackings, a rolling apparatus equipped with a 33.5 mm roll radius is used to roll the copper and Invar sheets to a specific thickness. The rolling machine exhibits an electrical power of 2.2 kW. The rolling speed is set to 48 mm/s for the whole process. Three stackings were studied. They initially measure 75 by 20 mm² in length/width and are composed of rolled sheets of copper and Invar with thicknesses (before roll-bonding) as follows:

- Configuration A: Cu 700 µm / Invar 200 µm / Cu 700 µm

- Configuration B: Cu 600 µm / Invar 400 µm / Cu 600 µm

- Configuration C: Cu 400 µm / Invar 200 µm / Cu 400 µm / Invar 200 µm / Cu 400 µm

Therefore, the stackings have an initial thickness of 1.6 mm and they are rolled down to 180 µm thickness. The volume fraction of Invar is equal to 12.5% for stacking A and 25% for stackings B and C. For the two last configurations with the same Invar volume fraction, configuration B consisted of one 400 µm thick Invar layer embedded between two copper layers, while configuration C consisted of two 200 µm thick Invar layers sandwiched between three copper layers.

As said above, copper sheets were derived from a 1.06 mm thick sheet, which underwent cold rolling to produce sheets of various thicknesses used in configurations A, B, and C. These sheets were then annealed at 550 °C for 1h30 before the stacking. This heat treatment allows copper softening after cold reduction. Hence, the annealing treatment makes thickness reduction easier and likely promotes necking by increasing the yield strength ratio between hard and soft layers.

Invar sheets for configurations A and C were obtained from cold rolling of a plate 1.0 mm thick, while for configuration B, the 400 µm thick sheet was manufactured by cold rolling of a 2.2 mm thick sheet. As the reduction ratio applied to the initial sheets of Invar is approximately the same and they are in a close initial state, 200 µm sheets (from 1.0 mm) and 400 µm (from 2.2 mm) have identical mechanical properties. This was verified with hardness measurements. Thus, the Invar sheets used in the configurations A, B and C, are considered equivalents.

Before the roll-bonding, to have better welding, the sheets are cleaned with acetone, and then mechanically brushed. The sheets are then stacked and held together using iron wires. The roll-bonding is done at 200 °C. After the roll-bonding, each cycle is composed of a heat treatment at 350 °C for 1h30 followed by rolling.

The full thickness reduction of the composite from 1.6 mm to 180 µm is therefore achieved through multiple annealing-rolling cycles: the composite is extracted from the oven at the end of the treatment and directly rolled. The elapsed time of a few seconds between the output of the oven
was demonstrated [5-7]. However, the understanding of necking occurrence during roll-bonding is only partially mastered. Criteria for predicting necking in hard layers are typically based on the maximal load criterion, as a generalization of the Considere criterion [4,8,9]. Nevertheless, these criteria underestimate the required reduction ratio to observe this plastic instability [4,10].

In this work, the influence of stacking geometry on Invar layers necking is studied through an experimental approach completed by simulations with the finite element method. For that purpose, stackings with different Invar volume fractions and spatial distribution, meaning the number and thickness of Invar layers, have been considered aiming to optimize their physical properties. The materials behaviour laws were identified to obtain input data for the simulation. The numerical simulation of multi-cycle roll-bonding was then developed and results were compared to the experimental ones.

## Experiment

Rolling process:

The Invar and copper sheets were kindly provided by APERAM Alloys Imphy. The copper plate in a strain-hardened state is composed of 99.99% Cu (traces of Pb and Bi) and exhibits a 1.06 mm initial thickness. The Invar sheets (Fe-36%Ni) are received in an annealed state and have an initial thickness of either 1.0 or 2.2 mm.

In order to produce the stackings, a rolling apparatus equipped with a 33.5 mm roll radius is used to roll the copper and Invar sheets to a specific thickness. The rolling machine exhibits an electrical power of 2.2 kW. The rolling speed is set to 48 mm/s for the whole process. Three stackings were studied. They initially measure 75 by 20 mm² in length/width and are composed of rolled sheets of copper and Invar with thicknesses (before roll-bonding) as follows:

- Configuration A: Cu 700 µm / Invar 200 µm / Cu 700 µm

- Configuration B: Cu 600 µm / Invar 400 µm / Cu 600 µm

- Configuration C: Cu 400 µm / Invar 200 µm / Cu 400 µm / Invar 200 µm / Cu 400 µm

Therefore, the stackings have an initial thickness of 1.6 mm and they are rolled down to 180 µm thickness. The volume fraction of Invar is equal to 12.5% for stacking A and 25% for stackings B and C. For the two last configurations with the same Invar volume fraction, configuration B consisted of one 400 µm thick Invar layer embedded between two copper layers, while configuration C consisted of two 200 µm thick Invar layers sandwiched between three copper layers.

As said above, copper sheets were derived from a 1.06 mm thick sheet, which underwent cold rolling to produce sheets of various thicknesses used in configurations A, B, and C. These sheets were then annealed at 550 °C for 1h30 before the stacking. This heat treatment allows copper softening after cold reduction. Hence, the annealing treatment makes thickness reduction easier and likely promotes necking by increasing the yield strength ratio between hard and soft layers.

Invar sheets for configurations A and C were obtained from cold rolling of a plate 1.0 mm thick, while for configuration B, the 400 µm thick sheet was manufactured by cold rolling of a 2.2 mm thick sheet. As the reduction ratio applied to the initial sheets of Invar is approximately the same and they are in a close initial state, 200 µm sheets (from 1.0 mm) and 400 µm (from 2.2 mm) have identical mechanical properties. This was verified with hardness measurements. Thus, the Invar sheets used in the configurations A, B and C, are considered equivalents.

Before the roll-bonding, to have better welding, the sheets are cleaned with acetone, and then mechanically brushed. The sheets are then stacked and held together using iron wires. The roll-bonding is done at 200 °C. After the roll-bonding, each cycle is composed of a heat treatment at 350 °C for 1h30 followed by rolling.

The full thickness reduction of the composite from 1.6 mm to 180 µm is therefore achieved through multiple annealing-rolling cycles: the composite is extracted from the oven at the end of the treatment and directly rolled. The elapsed time of a few seconds between the output of the oven
and the entry under the rolls induces a temperature drop of the composite: indeed, the rolling temperature has been measured at 200 °C by infrared camera and thermocouple.

The roll-bonding is performed at the first cycle up to 45% thickness reduction. Each composite is rolled 4 additional times until a thickness of 180 µm is achieved. The experimental setup and procedure are illustrated in Figure 1. The cumulative roll reduction ratio is defined as follow for each cycle *j*:

$$r_j = \frac{(h_t - h_j)}{h_t} \qquad (1)$$

$h_j$ is the height of the stacking after the cycle *j* and $h_t$ is the initial thickness of the stacking (1.6 mm). The cycles are detailed later for the configuration C (see Table 3).

<figure><img src="image_815.png" /><figcaption>Figure 1: Experimental setup for roll-bonding (3 layers case)</figcaption></figure>

The annealing treatment is used to enable the apparition of necking by softening the Copper, whereas this heat treatment does not modify the Invar mechanical properties. This statement has been verified: the hardness of copper and Invar was measured in a hardened and annealed state. The sheets initial thicknesses of configuration A were chosen (700 µm for copper and 200 µm for Invar) and reduced by 45% (corresponding to the first roll-bonding reduction). The measurements are thus carried out on 110 µm thick sheet of Invar and 385 µm thick sheet of copper sheets in both hardened and annealed state after 350°C for 1h30. As it can be seen in Table 1, the copper hardness is significantly higher in the hardened state than the hardness in annealing state, which means that the annealing permits the recovery and recrystallization of the copper sheets after rolling. For Invar, the hardness is similar in both states, thus Invar is insensitive to the applied annealing.

<table><caption>Table 1: HV₀.₂ hardness measurements of copper and Invar sheets</caption><thead><tr><td>State</td><td>Hardened</td><td>Annealed</td></tr></thead><tbody><tr><td>Copper hardness [HV₀.₂]</td><td>135 ± 5</td><td>50 ± 5</td></tr><tr><td>Invar hardness [HV₀.₂]</td><td>257 ± 5</td><td>254 ± 3</td></tr></tbody></table>

### Structure of composites:

After each cycle, longitudinal cuts (RD/ND plane) of composites were polished and observed with optical microscopy. The structural evolution and in particular, the necking of Invar layers was quantified with the maximal degree of necking calculated as follows:

$$Z_{max} = \frac{t_{max} - t_{min}}{t_{max}} \qquad (2)$$
and the entry under the rolls induces a temperature drop of the composite: indeed, the rolling temperature has been measured at 200 °C by infrared camera and thermocouple.

The roll-bonding is performed at the first cycle up to 45% thickness reduction. Each composite is rolled 4 additional times until a thickness of 180 µm is achieved. The experimental setup and procedure are illustrated in Figure 1. The cumulative roll reduction ratio is defined as follow for each cycle *j*:

$$r_j = \frac{(h_t - h_j)}{h_t} \qquad (1)$$

$h_j$ is the height of the stacking after the cycle *j* and $h_t$ is the initial thickness of the stacking (1.6 mm). The cycles are detailed later for the configuration C (see Table 3).

<figure><img src="image_823.png" /><figcaption>Figure 1: Experimental setup for roll-bonding (3 layers case)</figcaption></figure>

The annealing treatment is used to enable the apparition of necking by softening the Copper, whereas this heat treatment does not modify the Invar mechanical properties. This statement has been verified: the hardness of copper and Invar was measured in a hardened and annealed state. The sheets initial thicknesses of configuration A were chosen (700 µm for copper and 200 µm for Invar) and reduced by 45% (corresponding to the first roll-bonding reduction). The measurements are thus carried out on 110 µm thick sheet of Invar and 385 µm thick sheet of copper sheets in both hardened and annealed state after 350°C for 1h30. As it can be seen in Table 1, the copper hardness is significantly higher in the hardened state than the hardness in annealing state, which means that the annealing permits the recovery and recrystallization of the copper sheets after rolling. For Invar, the hardness is similar in both states, thus Invar is insensitive to the applied annealing.

<table><caption>Table 1: HV₀.₂ hardness measurements of copper and Invar sheets</caption><thead><tr><td>State</td><td>Hardened</td><td>Annealed</td></tr></thead><tbody><tr><td>Copper hardness [HV₀.₂]</td><td>135 ± 5</td><td>50 ± 5</td></tr><tr><td>Invar hardness [HV₀.₂]</td><td>257 ± 5</td><td>254 ± 3</td></tr></tbody></table>

### Structure of composites:

After each cycle, longitudinal cuts (RD/ND plane) of composites were polished and observed with optical microscopy. The structural evolution and in particular, the necking of Invar layers was quantified with the maximal degree of necking calculated as follows:

$$Z_{max} = \frac{t_{max} - t_{min}}{t_{max}} \qquad (2)$$
$t_{min}$ and $t_{max}$ are the maximal and minimal thickness of the Invar layer respectively. If there is no necking, $Z_{max} = 0$ whereas fragmentation is characterized by $Z_{max} = 1$

The micrographs obtained after 89 % reduction ratio are presented in Figure 2. The micrographs reveal three different advancements in necking:

- Configuration A: Invar layer has a large degree of necking ($Z_{max} = 0.8$)

- Configuration B: There is almost no necking ($Z_{max} = 0.1$)

- Configuration C: Invar layers are fragmented in the copper matrix ($Z_{max} = 1$)

<figure><img src="image_816.png" /><figcaption>Figure 2: Experimental results of the stackings at a rolling reduction of 89%</figcaption></figure>

Comparing configurations A and B, it is evident that as the volume fraction of Invar increases, necking is delayed ($Z_{max} = 0.8$ for A and $Z_{max} = 0.1$ for B). The comparison of A and C highlights the effect of the number of Invar layers on the apparition of necking: configuration C exhibits a fragmentation pattern ($Z_{max} = 1$), while configuration A is highly necked ($Z_{max} = 0.8$). Configurations B and C present the same volume fraction of Invar (25%), but different number of layers. Bilayer configuration C shows a higher degree of necking compared to the monolayer configuration B. The effect of Invar layer thickness on necking occurrence is consistent with the literature [4,5,11]. Hard layer volume fraction is widely used in the literature as an indicator to predict necking, as the maximal force-based criterion for necking varies linearly with this fraction [4,5,11]. This parameter is not sufficient to predict the necking of hard layers as necking occurrence depends also on the layer thickness.

Geometrical effects on necking occurrence have been identified, but they are combined with mechanical effects, such as hardness mismatch between soft and hard layers. As there is no reliable criterion to predict the necking of hard layers, finite element simulation of the process is a viable approach to optimize the manufacturing of composites with the expected structure. To model the process accurately, the mechanical behaviour of copper and Invar has to be determined, and this point is studied in the following section.

## Characterization of materials mechanical behaviour

### Approach:

Copper and Invar sheets used in the composite are obtained from rolling. This can induce crystallographic texture and mechanical anisotropy. Therefore, the mechanical behaviours of copper and Invar are determined as follows:

1) The strain hardening is obtained through tensile tests carried out at 200 °C (rolling temperature) along the rolling direction in quasi-static conditions;