<figure><img src="image_1472.png" /><figcaption>Fig. 9. (a) 3D view of the strain distribution during the forming process and (b) effective plastic strain profiles for the three step size cases</figcaption></figure>

**Summary**

The work presented in this study highlights the effect of step size in incremental forming of polycarbonate material. Experiments took place where the wall angle of 20° and the feed rate of 2000 mm/min were kept constant throughout the experiments. The spindle of the CNC machine was unlocked and was free to rotate as the forming tool was in contact with the workpiece. Three step sizes were investigated, namely 0.1, 0.5, and 1.0 mm. It was found that the change in step size did not have a significant effect on springback. However, it was generally observed that the smaller step size the more sheet thinning, or thickness reduction, was observed. This was attributed to the multiple passes the material had to go through to achieve the desired height.

Additionally, a commercial finite element code was utilized to simulate the process parameters investigated experimentally. The model was first validated against profile height and thickness distribution, and then used to investigate the effective plastic strain distribution along a cross section of the cone, for the different step size values considered. This analysis highlighted the larger deformation occurring when small step size values are implemented (i.e. 0.1 mm) resulting in a slightly thinner final part.

Future work will focus on extending the investigation to include more process parameters, for example, additional values for the step size as well as various wall angles.
<figure><img src="image_1476.png" /><figcaption>Fig. 9. (a) 3D view of the strain distribution during the forming process and (b) effective plastic strain profiles for the three step size cases</figcaption></figure>

**Summary**

The work presented in this study highlights the effect of step size in incremental forming of polycarbonate material. Experiments took place where the wall angle of 20° and the feed rate of 2000 mm/min were kept constant throughout the experiments. The spindle of the CNC machine was unlocked and was free to rotate as the forming tool was in contact with the workpiece. Three step sizes were investigated, namely 0.1, 0.5, and 1.0 mm. It was found that the change in step size did not have a significant effect on springback. However, it was generally observed that the smaller step size the more sheet thinning, or thickness reduction, was observed. This was attributed to the multiple passes the material had to go through to achieve the desired height.

Additionally, a commercial finite element code was utilized to simulate the process parameters investigated experimentally. The model was first validated against profile height and thickness distribution, and then used to investigate the effective plastic strain distribution along a cross section of the cone, for the different step size values considered. This analysis highlighted the larger deformation occurring when small step size values are implemented (i.e. 0.1 mm) resulting in a slightly thinner final part.

Future work will focus on extending the investigation to include more process parameters, for example, additional values for the step size as well as various wall angles.
## References

[1] I. Ragai, J. Goldstein, C. Meyer, and C. Upcraft, Effect of Tool Material and Process Parameters on Surface Conditions in SPIF of Polymeric Materials, Proc. of the ASME 2022 Int Mech Eng Cong and Expo (2022), Columbus, OH, USA. https://doi.org/10.1115/IMECE2022-95951

[2] G. Palumbo and M. Brandizzi, Experimental investigations on the single point incremental forming of a titanium alloy component combining static heating with high tool rotation speed, Materials & Design, 2012, pp. 43-51. https://doi.org/10.1016/j.matdes.2012.03.031

[3] P. E. Romero, O. Rodriguez-Albanda, E. Molero, and G. Guerrero-Vaca, Use of the Support Vector Machine (SVM) algorithm to predict the geometrical accuracy in the manufacture of molds via single point incremental forming (SPIF) using aluminized steel sheets, Journal of Materials Research and Technology, 2021, pp. 1562-1571. https://doi.org/10.1016/j.jmrt.2021.08.155

[4] M. Milutinović, R. Lendjel, S. Balos, D. L. Zlatanovic, L. Sevsek, and T. Pepelnjak, Characterization of geometrical and physical properties of a stainless-steel denture framework manufactured by single-point incremental forming, Journal of Materials and Research Technology, 2021, pp. 605-623. https://doi.org/10.1016/j.jmrt.2020.12.014

[5] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, and J. Allwood, Asymmetric single point incremental forming of sheet metal, CIRP Annals, 2005, pp.88-114. https://doi.org/10.1016/S0007-8506(07)60021-3

[6] B. J. Ruszkiewicz, S. S. Dodds, Z. C. Reese, J. T. Roth, and I. Ragai, Incrementally Formed Stiffeners Effect on the Reduction of Springback in 2024-T3 Aluminum after Single Point Incremental Forming, ASME International Manufacturing Science and Engineering Conference (2015), Charlotte, NC, USA. https://doi.org/10.1115/MSEC2015-9437

[7] T. J. Grimm, I. Ragai, and J. T. Roth, Utilization of wavy toolpath in single-point incremental forming, ASME 2018 Int Mech Eng Cong and Expo (2018), Pittsburgh, PA, USA. https://doi.org/10.1115/IMECE2018-86885

[8] H. Zhu, H. Ou, and A. Popov, Incremental sheet forming of thermoplastics: a review, Int J Adv Manuf Technol 111 (2020) 565-587. https://doi.org/10.1007/s00170-020-06056-5

[9] M. A. Davarpanah, and R. Malhotra, Formability and Failure Modes in SPIF of Metal-Polymer Laminates, Proc. Manuf. 26 (2018), 343-348. https://doi.org/10.1016/j.promfg.2018.07.042

[10] V. Franzen, L. Kwiatkowski, J. Neves, P. A. F. Martins, A. E. Tekkaya, On the capability of single point incremental forming for manufacturing polymer sheet parts, Proceedings of the 9th ICTP-International Conference on Technology of Plasticity (2008), Gyeongju, Korea.

[11] V. Franzen, L. Kwiatkowski, P. A. F. Martins, A. E. Tekkaya, Single point incremental forming of PVC, Journal of Materials and Processing Technology, 2009, pp. 462-469. https://doi.org/10.1016/j.jmatprotec.2008.02.013

[12] P. Martins, L. Kwiatkowski, V. Franzen, A. Tekkaya and M. Kleiner, Single point incremental forming of polymers, CIRP Annals, 2009, pp.229-232. https://doi.org/10.1016/j.cirp.2009.03.095

[13] Y. Li, Z. Liu, W.J.T. Daniel, P.A. Meehan, Simulation and experimental observations of effect of different contact interfaces on the incremental sheet forming process. Mater. Manuf. Process. 29 (2014) 121-128. https://doi.org/10.1080/10426914.2013.822977
## References

[1] I. Ragai, J. Goldstein, C. Meyer, and C. Upcraft, Effect of Tool Material and Process Parameters on Surface Conditions in SPIF of Polymeric Materials, Proc. of the ASME 2022 Int Mech Eng Cong and Expo (2022), Columbus, OH, USA. https://doi.org/10.1115/IMECE2022-95951

[2] G. Palumbo and M. Brandizzi, Experimental investigations on the single point incremental forming of a titanium alloy component combining static heating with high tool rotation speed, Materials & Design, 2012, pp. 43-51. https://doi.org/10.1016/j.matdes.2012.03.031

[3] P. E. Romero, O. Rodriguez-Albanda, E. Molero, and G. Guerrero-Vaca, Use of the Support Vector Machine (SVM) algorithm to predict the geometrical accuracy in the manufacture of molds via single point incremental forming (SPIF) using aluminized steel sheets, Journal of Materials Research and Technology, 2021, pp. 1562-1571. https://doi.org/10.1016/j.jmrt.2021.08.155

[4] M. Milutinović, R. Lendjel, S. Balos, D. L. Zlatanovic, L. Sevsek, and T. Pepelnjak, Characterization of geometrical and physical properties of a stainless-steel denture framework manufactured by single-point incremental forming, Journal of Materials and Research Technology, 2021, pp. 605-623. https://doi.org/10.1016/j.jmrt.2020.12.014

[5] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, and J. Allwood, Asymmetric single point incremental forming of sheet metal, CIRP Annals, 2005, pp.88-114. https://doi.org/10.1016/S0007-8506(07)60021-3

[6] B. J. Ruszkiewicz, S. S. Dodds, Z. C. Reese, J. T. Roth, and I. Ragai, Incrementally Formed Stiffeners Effect on the Reduction of Springback in 2024-T3 Aluminum after Single Point Incremental Forming, ASME International Manufacturing Science and Engineering Conference (2015), Charlotte, NC, USA. https://doi.org/10.1115/MSEC2015-9437

[7] T. J. Grimm, I. Ragai, and J. T. Roth, Utilization of wavy toolpath in single-point incremental forming, ASME 2018 Int Mech Eng Cong and Expo (2018), Pittsburgh, PA, USA. https://doi.org/10.1115/IMECE2018-86885

[8] H. Zhu, H. Ou, and A. Popov, Incremental sheet forming of thermoplastics: a review, Int J Adv Manuf Technol 111 (2020) 565-587. https://doi.org/10.1007/s00170-020-06056-5

[9] M. A. Davarpanah, and R. Malhotra, Formability and Failure Modes in SPIF of Metal-Polymer Laminates, Proc. Manuf. 26 (2018), 343-348. https://doi.org/10.1016/j.promfg.2018.07.042

[10] V. Franzen, L. Kwiatkowski, J. Neves, P. A. F. Martins, A. E. Tekkaya, On the capability of single point incremental forming for manufacturing polymer sheet parts, Proceedings of the 9th ICTP-International Conference on Technology of Plasticity (2008), Gyeongju, Korea.

[11] V. Franzen, L. Kwiatkowski, P. A. F. Martins, A. E. Tekkaya, Single point incremental forming of PVC, Journal of Materials and Processing Technology, 2009, pp. 462-469. https://doi.org/10.1016/j.jmatprotec.2008.02.013

[12] P. Martins, L. Kwiatkowski, V. Franzen, A. Tekkaya and M. Kleiner, Single point incremental forming of polymers, CIRP Annals, 2009, pp.229-232. https://doi.org/10.1016/j.cirp.2009.03.095

[13] Y. Li, Z. Liu, W.J.T. Daniel, P.A. Meehan, Simulation and experimental observations of effect of different contact interfaces on the incremental sheet forming process. Mater. Manuf. Process. 29 (2014) 121-128. https://doi.org/10.1080/10426914.2013.822977
[14] B. Lu, Y. Fang, D.K. Xu, J. Chen, H. Ou, N.H. Moser, J. Cao, Mechanism investigation of friction-related effects in single point incremental forming using a developed oblique roller-ball tool. Int. J. Mach. Tools Manuf. 85 (2014) 14-29.
https://doi.org/10.1016/j.ijmachtools.2014.04.007

[15] M. Vahdati, R. Mahdavinejad, S. Amini, Investigation of the ultrasonic vibration effect in incremental sheet metal forming process. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 231 (2017) 971-982.
https://doi.org/10.1177/0954405415578579

[16] G.P. Cai, C.W. Xing, Z.H. Jiang, Z.K. Zhang, Sheet Single point vibration incremental forming process simulation and analysis of process parameters. Advanced Materials Research. 430 (2012) 74-78.
https://doi.org/10.4028/www.scientific.net/AMR.430-432.74

[17] T.J. Grimm, I. Ragai, J.T. Roth, A Novel Modification to the Incremental Forming Process, Part 1: Multi-directional Tooling. Procedia Manuf. 10 (2017) 510-519.
https://doi.org/10.1016/j.promfg.2017.07.035

[18] T.J. Grimm, I. Ragai, J.T. Roth, A Novel Modification to the Incremental Forming Process, Part 2: Validation of the Multidirectional Tooling Method. Procedia Manuf. 10 (2017) 520-530.
https://doi.org/10.1016/j.promfg.2017.07.036

[19] D. Young, J. Jeswiet, Wall thickness variations in single-point incremental forming. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2018 (2004) 218, 1453-1459.
https://doi.org/10.1243/0954405042418400

[20] Z. Liu, W.J.T. Daniel, Y. Li, S. Liu, P.A. Meehan, Multi-pass deformation design for incremental sheet forming: analytical modeling, finite element analysis and experimental validation. J. Mater. Process. Technol. 214 (2014) 620-634.
https://doi.org/10.1016/j.jmatprotec.2013.11.010

[21] I. Bagudanch, G. Centeno, C. Vallellano and M. Garcia-Romeu, Revisiting formability and failure of polymeric sheets deformed by single point Incremental Forming, Polymer and Degradation Stability, (2017) 366-377.
https://doi.org/10.1016/j.polymdegradstab.2017.08.021

[22] C. Upcraft, R. Diefenderfer, C. Vanderwiel and I. Ragai, Toward Better Formability of Polymeric Materials in Single Point Incremental Forming: Effect of Process Parameters, Proc. of the ASME 2023 Int Mech Eng Cong and Expo (2023), New Orleans, LA, USA.
https://doi.org/10.1115/IMECE2023-112000

[23] https://www.professionalplastics.com/professionalplastics/content/downloads/MakrolonGP
V_Specs.pdf

[24] https://materion.com/-/media/files/alloy/datasheets/moldmax/moldmax-hh-alloy-data-sheet.pdf
[14] B. Lu, Y. Fang, D.K. Xu, J. Chen, H. Ou, N.H. Moser, J. Cao, Mechanism investigation of friction-related effects in single point incremental forming using a developed oblique roller-ball tool. Int. J. Mach. Tools Manuf. 85 (2014) 14-29.
https://doi.org/10.1016/j.ijmachtools.2014.04.007

[15] M. Vahdati, R. Mahdavinejad, S. Amini, Investigation of the ultrasonic vibration effect in incremental sheet metal forming process. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 231 (2017) 971-982.
https://doi.org/10.1177/0954405415578579

[16] G.P. Cai, C.W. Xing, Z.H. Jiang, Z.K. Zhang, Sheet Single point vibration incremental forming process simulation and analysis of process parameters. Advanced Materials Research. 430 (2012) 74-78.
https://doi.org/10.4028/www.scientific.net/AMR.430-432.74

[17] T.J. Grimm, I. Ragai, J.T. Roth, A Novel Modification to the Incremental Forming Process, Part 1: Multi-directional Tooling. Procedia Manuf. 10 (2017) 510-519.
https://doi.org/10.1016/j.promfg.2017.07.035

[18] T.J. Grimm, I. Ragai, J.T. Roth, A Novel Modification to the Incremental Forming Process, Part 2: Validation of the Multidirectional Tooling Method. Procedia Manuf. 10 (2017) 520-530.
https://doi.org/10.1016/j.promfg.2017.07.036

[19] D. Young, J. Jeswiet, Wall thickness variations in single-point incremental forming. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2018 (2004) 218, 1453-1459.
https://doi.org/10.1243/0954405042418400

[20] Z. Liu, W.J.T. Daniel, Y. Li, S. Liu, P.A. Meehan, Multi-pass deformation design for incremental sheet forming: analytical modeling, finite element analysis and experimental validation. J. Mater. Process. Technol. 214 (2014) 620-634.
https://doi.org/10.1016/j.jmatprotec.2013.11.010

[21] I. Bagudanch, G. Centeno, C. Vallellano and M. Garcia-Romeu, Revisiting formability and failure of polymeric sheets deformed by single point Incremental Forming, Polymer and Degradation Stability, (2017) 366-377.
https://doi.org/10.1016/j.polymdegradstab.2017.08.021

[22] C. Upcraft, R. Diefenderfer, C. Vanderwiel and I. Ragai, Toward Better Formability of Polymeric Materials in Single Point Incremental Forming: Effect of Process Parameters, Proc. of the ASME 2023 Int Mech Eng Cong and Expo (2023), New Orleans, LA, USA.
https://doi.org/10.1115/IMECE2023-112000

[23] https://www.professionalplastics.com/professionalplastics/content/downloads/MakrolonGP
V_Specs.pdf

[24] https://materion.com/-/media/files/alloy/datasheets/moldmax/moldmax-hh-alloy-data-sheet.pdf
# Strain rates in high velocity forming of foils

LANGSTÄDTLER Lasse¹,²,³,*, BECKSCHWARTE Björn¹,²,ᵇ, VALENTINO Tobias⁴,ᶜ and RADEL Tim⁴,ᵈ

¹University of Bremen, Bibliothekstraße 1, 28359 Bremen, Germany

²BIME - Bremen Institute for Mechanical Engineering, Badgasteiner Straße 1, 28359 Bremen, Germany

³MAPEX - Center for Materials and Processes, 28334 Bremen, Germany

⁴BIAS - Bremer Institut für angew. Strahltechnik GmbH, Klagenfurter Str. 5, 28359 Bremen, Germany

ªlangstaedtler@bime.de, ᵇbeckschwarte@bime.de, ᶜmikrofertigung@bias.de, ᵈradel@bias.de

**Keywords:** Forming, In-Process Measurement, Electromagnetic Forming, Laser Shock Forming

**Abstract.** Energy- and working media based high velocity forming processes show various advantages forming metal foils. However, due to different process characteristics, differences in workpiece response by impulse transfer for different high velocity forming processes are expected. Free forming experiments with 50 µm metallic foils were carried out to identify the process influence, using electromagnetic forming and laser shock forming. For these two forming methods the response of the workpiece was described. The description was done by in-situ measurement of the strain and the strain rate over time and determination of workpiece velocities.

**Introduction**

High velocity forming technologies show the ability for shaping complex parts. Therefore, they are a key means of reducing a component's weight. Förster described in 1883 the advantages of high velocity forming. He used the detonation of explosives over a stamping die for engraving metal sheets [1]. Starting from these early experiments, further process advantages could be identified. Thus, the high forming velocity was described to increase formability of various materials [2]. Further, it was shown that the formation of winkles [3] and springback [4] is reducible due to high strain rates. In addition to these advantages, using inertial locking mechanisms in the design of the tools allows the use of smaller and therefore less expensive equipment [5]. High velocity forming was tested in a wide variety of objectives, workpieces and geometries to be produced around these processes. One field was the forming of thin foils, which brings with them the fundamental challenges of micro forming [6]. Energy- and working media-based high velocity forming processes enable to overcome these challenges.

One possibility to obtain is laser shock forming (LSF). The high repetition rate of lasers and the rapidly expanding shock wave offers the possibility of mass production of micro parts. Different laser-based high velocity forming process variants, such as deep drawing, bending, stretch drawing, and joining with a TEA-CO2-laser have been studied [7].

A further way of foil processing is electromagnetic forming (EMF). Here, volume dependent electromagnetic forces act onto the foils to be processed, whereby solutions for production and integration into the process chain already exist [8]. Different process variants of electromagnetic forming such as forming [9], embossing [10], cutting [11] and joining [12] metal foils were investigated.

The primary difference between the two forming techniques, which are capable to forming metal foils, is the difference in the energy transmission to the workpiece. During laser shock

<figure><img src="image_1473.png" /></figure>
# Strain rates in high velocity forming of foils

LANGSTÄDTLER Lasse¹,²,³,*, BECKSCHWARTE Björn¹,²,ᵇ, VALENTINO Tobias⁴,ᶜ and RADEL Tim⁴,ᵈ

¹University of Bremen, Bibliothekstraße 1, 28359 Bremen, Germany

²BIME - Bremen Institute for Mechanical Engineering, Badgasteiner Straße 1, 28359 Bremen, Germany

³MAPEX - Center for Materials and Processes, 28334 Bremen, Germany

⁴BIAS - Bremer Institut für angew. Strahltechnik GmbH, Klagenfurter Str. 5, 28359 Bremen, Germany

ªlangstaedtler@bime.de, ᵇbeckschwarte@bime.de, ᶜmikrofertigung@bias.de, ᵈradel@bias.de

**Keywords:** Forming, In-Process Measurement, Electromagnetic Forming, Laser Shock Forming

**Abstract.** Energy- and working media based high velocity forming processes show various advantages forming metal foils. However, due to different process characteristics, differences in workpiece response by impulse transfer for different high velocity forming processes are expected. Free forming experiments with 50 µm metallic foils were carried out to identify the process influence, using electromagnetic forming and laser shock forming. For these two forming methods the response of the workpiece was described. The description was done by in-situ measurement of the strain and the strain rate over time and determination of workpiece velocities.

**Introduction**

High velocity forming technologies show the ability for shaping complex parts. Therefore, they are a key means of reducing a component's weight. Förster described in 1883 the advantages of high velocity forming. He used the detonation of explosives over a stamping die for engraving metal sheets [1]. Starting from these early experiments, further process advantages could be identified. Thus, the high forming velocity was described to increase formability of various materials [2]. Further, it was shown that the formation of winkles [3] and springback [4] is reducible due to high strain rates. In addition to these advantages, using inertial locking mechanisms in the design of the tools allows the use of smaller and therefore less expensive equipment [5]. High velocity forming was tested in a wide variety of objectives, workpieces and geometries to be produced around these processes. One field was the forming of thin foils, which brings with them the fundamental challenges of micro forming [6]. Energy- and working media-based high velocity forming processes enable to overcome these challenges.

One possibility to obtain is laser shock forming (LSF). The high repetition rate of lasers and the rapidly expanding shock wave offers the possibility of mass production of micro parts. Different laser-based high velocity forming process variants, such as deep drawing, bending, stretch drawing, and joining with a TEA-CO2-laser have been studied [7].

A further way of foil processing is electromagnetic forming (EMF). Here, volume dependent electromagnetic forces act onto the foils to be processed, whereby solutions for production and integration into the process chain already exist [8]. Different process variants of electromagnetic forming such as forming [9], embossing [10], cutting [11] and joining [12] metal foils were investigated.

The primary difference between the two forming techniques, which are capable to forming metal foils, is the difference in the energy transmission to the workpiece. During laser shock

<figure><img src="image_1477.png" /></figure>
forming laser radiation causes thermo- and field emission of electrons, which irradiate out of the target surface. Collision processes between these highly energetic electrons and the atmosphere molecules produce ions. They absorb the ongoing laser radiation. Miziolek et al. described that these free ions absorb energy on the principle of inverse bremsstrahlung [13]. This sets an avalanche ionization in motion, which leads to plasma and subsequently, to shock wave formation and pressure increase, which is responsible for the forming of the foils. The expansion of the shock wave and therefore the pressure distribution can be influenced e.g., by pressure cells [14]. In contrast, in electromagnetic forming, forces are applied by the interaction of the workpiece with an electromagnetic field introduced by a transient current through a tool coil. Based on the penetration depth of the electromagnetic field and the sheet thickness, volume forces occur in the workpiece [15]. These volume forces and their distribution are directly related to the current density distribution and time series in the tool coil as well as in the workpiece. Further for insufficient shielding of the electromagnetic field by the thin workpiece, the inducted current in the surrounding parts can influence the workpiece during electromagnetic forming [16].

Both processes promote the advantages of high velocity forming for foils, but produce different energy transfer to the workpiece. The fundamental difference is the transient action of pressure in laser shock forming compared to the transient volume force in electromagnetic forming. Within this work the process effect on foil displacement was investigated experimentally. The resulting strain and strain rates over time were determined on the base of a free forming experiments and compared between both forming methods. Furthermore, reached velocities of the foils were calculated.

## Materials and Methods

To investigate the impact of the impulse transfer during high velocity forming of thin foils, a free forming operation was used. Foils of Al99.5 (EN AW-1050), cut to a 50×50 mm² sheet, with a thickness $s_0$ of 50 µm were used as workpiece. The milled die was made of 90MnCrV8 as shown in Fig. 1 (a). The free forming operation was based on a rectangular cut-out of 8×16 mm² within the die. Furthermore, the cut-out was rounded with a 3 mm radius. For better accessibility, a cut-out was made on the unused die side. The installation of the die depended on the specific boundary conditions of the used forming processes. For the benefit of comparability, no distance between the workpiece and the die was used, so that the workpiece was in full contact with the die. Specific to the installation in electromagnetic forming was the contact of the tool coils 195 µm thick polyimide insulation with the workpiece (see Fig. 1 (b)). To avoid the influence of air, an additional gap of 135 µm in the middle section between the insulation and the workpiece was set. In the case of laser shock forming, on the other hand, a round blank holder with a diameter of 15 mm was used, which simultaneously defined the maximum effective area of the TEA-CO2 laser (see Fig. 1 (c)).
forming laser radiation causes thermo- and field emission of electrons, which irradiate out of the
target surface. Collision processes between these highly energetic electrons and the atmosphere
molecules produce ions. They absorb the ongoing laser radiation. Miziolek et al. described that
these free ions absorb energy on the principle of inverse bremsstrahlung [13]. This sets an
avalanche ionization in motion, which leads to plasma and subsequently, to shock wave formation
and pressure increase, which is responsible for the forming of the foils. The expansion of the shock
wave and therefore the pressure distribution can be influenced e.g., by pressure cells [14]. In
contrast, in electromagnetic forming, forces are applied by the interaction of the workpiece with
an electromagnetic field introduced by a transient current through a tool coil. Based on the
penetration depth of the electromagnetic field and the sheet thickness, volume forces occur in the
workpiece [15]. These volume forces and their distribution are directly related to the current
density distribution and time series in the tool coil as well as in the workpiece. Further for
insufficient shielding of the electromagnetic field by the thin workpiece, the inducted current in
the surrounding parts can influence the workpiece during electromagnetic forming [16].

Both processes promote the advantages of high velocity forming for foils, but produce different
energy transfer to the workpiece. The fundamental difference is the transient action of pressure in
laser shock forming compared to the transient volume force in electromagnetic forming. Within
this work the process effect on foil displacement was investigated experimentally. The resulting
strain and strain rates over time were determined on the base of a free forming experiments and
compared between both forming methods. Furthermore, reached velocities of the foils were
calculated.

Materials and Methods

To investigate the impact of the impulse transfer during high velocity forming of thin foils, a free
forming operation was used. Foils of Al99.5 (EN AW-1050), cut to a 50×50 mm² sheet, with a
thickness s₀ of 50 µm were used as workpiece. The milled die was made of 90MnCrV8 as shown
in Fig. 1 (a). The free forming operation was based on a rectangular cut-out of 8×16 mm² within
the die. Furthermore, the cut-out was rounded with a 3 mm radius. For better accessibility, a cut-
out was made on the unused die side. The installation of the die depended on the specific boundary
conditions of the used forming processes. For the benefit of comparability, no distance between
the workpiece and the die was used, so that the workpiece was in full contact with the die. Specific
to the installation in electromagnetic forming was the contact of the tool coils 195 µm thick
polyimide insulation with the workpiece (see Fig. 1 (b)). To avoid the influence of air, an
additional gap of 135 µm in the middle section between the insulation and the workpiece was set.
In the case of laser shock forming, on the other hand, a round blank holder with a diameter of 15
mm was used, which simultaneously defined the maximum effective area of the TEA-CO₂ laser
(see Fig. 1 (c)).
<figure><img src="image_1474.png" /></figure>

<figure><img src="image_1475.png" /></figure>

<figure><img src="image_1476.png" /></figure>

<figure><img src="image_1477.png" /><figcaption>Fig. 1: Die geometry and installation: (a) sketch of the die geometry, (b) installation for LSF, (c) installation for EMF</figcaption></figure>

The experiments were conducted with a TEA-CO2 laser (TEA = Transverse Excitation at Atmospheric Pressure). The pulse energy EP was emitted with a wavelength of λ of 10.6 µm with a pulse duration of tₚ of 100 ns. The pulse duration refers to the full width at half maximum. The beam quality factor was M² of 28.4 and the spatial energy distribution was best approximated as homogeneous (flat-top). The pulse energy EP was set to 4.5 J. The laser beam was focused on a sheet via a concave focusing mirror with a focal length f of 200 mm. The focus was shifted 30 mm below the surface, resulting in a beam area of AF of 32 mm² on the sheet. A frequency of 50 Hz was used in the experiments with double pulse. Hence, the forming process of the first pulse was fully finished before the second starts. Further details about the basic laser system can be taken from Valentino [17].

Electromagnetic forming experiments were carried out with a pulsed power generator (see Fig. 2 (a)) with a total capacitor capacity C of 100 μF. During experiments a charge voltage U₀ of 2.82 kV and 4 kV was used, which results in a charge energy E_C of 800 J. Besides single discharges, multiple discharges were performed without changing the workpiece. As tool coil a single-conductor made of copper with a cross-section of 5×5 mm² was used (see Fig. 1 (c)). The charge energy E_C was switched by an ignitron (NL8900, National Electronics, LaFox, Il, USA), and resulted in a ≈ 700 µs long current oscillation with an oscillation frequency f₀ of ≈10 kHz (see Fig. 2 (b)). As a result of the resistances R_m, R tc and R_c and inductances L_m, L tc and L_c of the pulsed power generator, the tool coil current I tc shown in Fig. 2 (b) was generated.
<figure><img src="image_1478.png" /></figure>

<figure><img src="image_1479.png" /></figure>

<figure><img src="image_1480.png" /></figure>

<figure><img src="image_1481.png" /><figcaption>Fig. 1: Die geometry and installation: (a) sketch of the die geometry, (b) installation for LSF, (c) installation for EMF</figcaption></figure>

The experiments were conducted with a TEA-CO2 laser (TEA = Transverse Excitation at Atmospheric Pressure). The pulse energy EP was emitted with a wavelength of λ of 10.6 µm with a pulse duration of tₚ of 100 ns. The pulse duration refers to the full width at half maximum. The beam quality factor was M² of 28.4 and the spatial energy distribution was best approximated as homogeneous (flat-top). The pulse energy EP was set to 4.5 J. The laser beam was focused on a sheet via a concave focusing mirror with a focal length f of 200 mm. The focus was shifted 30 mm below the surface, resulting in a beam area of AF of 32 mm² on the sheet. A frequency of 50 Hz was used in the experiments with double pulse. Hence, the forming process of the first pulse was fully finished before the second starts. Further details about the basic laser system can be taken from Valentino [17].

Electromagnetic forming experiments were carried out with a pulsed power generator (see Fig. 2 (a)) with a total capacitor capacity C of 100 µF. During experiments a charge voltage U₀ of 2.82 kV and 4 kV was used, which results in a charge energy E_C of 800 J. Besides single discharges, multiple discharges were performed without changing the workpiece. As tool coil a single-conductor made of copper with a cross-section of 5×5 mm² was used (see Fig. 1 (c)). The charge energy E_C was switched by an ignitron (NL8900, National Electronics, LaFox, Il, USA), and resulted in a ≈ 700 µs long current oscillation with an oscillation frequency f₀ of ≈10 kHz (see Fig. 2 (b)). As a result of the resistances R_m, R tc and R_c and inductances L_m, L tc and L_c of the pulsed power generator, the tool coil current I tc shown in Fig. 2 (b) was generated.
<figure><img src="image_1478.png" /></figure>

<figure><img src="image_1479.png" /><figcaption>Fig. 2: Electromagnetic forming setup: (a) simplified electric circuit diagram, (b) resulting tool coil current $I_{tc}$ over time t</figcaption></figure>

A photoelectric sensor (LK-H157, Keyence, Osaka, Japan) was used to observe the displacement h of the workpiece sampled every 2.55 µs (see Fig. 3 (c)). The sensor was installed in the centre of the formed geometry (see Fig. 3 (a)) and its laser line was aligned transverse to the rolling orientation of the foils.

The resulting signal of the displacement h was filtered with a low-pass filter of 50 kHz. In connection with the circular shape in the X-Y-plane (see Fig. 3 (b)), the length of the arc segment L₁ was calculated from the displacement h (see Eq. 1).

<figure><img src="image_1480.png" /><figcaption>Fig. 3: Strain measurement: (a) sketch of the setup, (b) displacement h over time and (c) strain calculation</figcaption></figure>

To calculate the strain over the formed geometry εg, the length L₁ was set in relation to the initial length L₀ (see Eq. 2). Further, the strain rate ε̇g was determined by differentiate the strain εg over time t (see Eq. 3).

$$L_1 = \frac{\tan^{-1} \frac{2 * h}{L_0} * (4 * h^2 + L_0^2)}{2 * h} \quad (1)$$
<figure><img src="image_1482.png" /></figure>

<figure><img src="image_1483.png" /><figcaption>Fig. 2: Electromagnetic forming setup: (a) simplified electric circuit diagram, (b) resulting tool coil current $I_{tc}$ over time t</figcaption></figure>

A photoelectric sensor (LK-H157, Keyence, Osaka, Japan) was used to observe the displacement h of the workpiece sampled every 2.55 µs (see Fig. 3 (c)). The sensor was installed in the centre of the formed geometry (see Fig. 3 (a)) and its laser line was aligned transverse to the rolling orientation of the foils.

The resulting signal of the displacement h was filtered with a low-pass filter of 50 kHz. In connection with the circular shape in the X-Y-plane (see Fig. 3 (b)), the length of the arc segment L₁ was calculated from the displacement h (see Eq. 1).

<figure><img src="image_1484.png" /><figcaption>Fig. 3: Strain measurement: (a) sketch of the setup, (b) displacement h over time and (c) strain calculation</figcaption></figure>

To calculate the strain over the formed geometry εg, the length L₁ was set in relation to the initial length L₀ (see Eq. 2). Further, the strain rate ε̇g was determined by differentiate the strain εg over time t (see Eq. 3).

$$L_1 = \frac{\tan^{-1} \frac{2 * h}{L_0} * (4 * h^2 + L_0^2)}{2 * h} \quad (1)$$
$$ \epsilon_g = \frac{L_1 - L_0}{L_0} \qquad (2) $$

$$ \dot{\epsilon}_g = \frac{\Delta\epsilon_g}{\Delta t} \qquad (3) $$

For comparison of the measuring system used, the deformation velocity $v_d$ was calculated according to Veenas et al. [7]. Furthermore, the present workpiece velocity $v_w$ hence the maximum workpiece velocity $v_{w,m}$ was obtained by derivation of the displacement h (see Eq. 4).

$$ v_w = \frac{\Delta h}{\Delta t} \qquad (4) $$

## Results

Fig. 4 compares the measured average velocity with the results determined by Veenaas et al. [7]. Minor differences were expected in this comparison due to the deviation of the die geometry, Fig. 4 (a). The results determined with the position sensor were comparable with the ones determined via the light barrier by Veenaas et al, which validated the suitability of the position sensor in high velocity foil forming, Fig. 4 (b). Based on the definition of the deformation velocity $v_d$, there was found a deviation to the present workpiece velocity $v_w$. Fig. 4 (c) shows the maximum reached workpiece velocity $v_{w,m}$.

<figure><img src="image_1481.png" /><figcaption>Fig. 4: Measurement system: (a) formed foils for different tests methods, (b) comparison of measured velocities $v_d$ for position sensor and light barrier, (c) workpiece velocities $v_{w,m}$ determined for LSF and EMF</figcaption></figure>

Higher maximum workpiece velocity $v_{w,m}$ were measured - using the current settings - for laser shock forming compared to electromagnetic forming. Nevertheless, both processes exceed the workpiece velocity limit of 15 m/s for high velocity forming processes defined by Bruno et al. [18].

In laser shock forming, three phases of forming were identified (see Fig. 5). The first phase preceded the actual forming, where a small alternating strain $\epsilon_g$ occurred. This phase could be a result of the plasma initiation. After this phase, the main deformation occurred up to the maximum of the strain. Here, a strain rate $\epsilon_g$ of 10000 1/s was calculated based on the displacement measurement (see Fig. 5 (b)). Following this phase, a phase of springback of the workpiece arose, which ended with a remaining strain of approx. 0.074 (see Fig. 5 (a)). After this, a variation in
$$ \epsilon_g = \frac{L_1 - L_0}{L_0} \qquad (2) $$

$$ \dot{\epsilon}_g = \frac{\Delta\epsilon_g}{\Delta t} \qquad (3) $$

For comparison of the measuring system used, the deformation velocity $v_d$ was calculated according to Veenas et al. [7]. Furthermore, the present workpiece velocity $v_w$ hence the maximum workpiece velocity $v_{w,m}$ was obtained by derivation of the displacement h (see Eq. 4).

$$ v_w = \frac{\Delta h}{\Delta t} \qquad (4) $$

## Results

Fig. 4 compares the measured average velocity with the results determined by Veenas et al. [7]. Minor differences were expected in this comparison due to the deviation of the die geometry, Fig. 4 (a). The results determined with the position sensor were comparable with the ones determined via the light barrier by Veenas et al, which validated the suitability of the position sensor in high velocity foil forming, Fig. 4 (b). Based on the definition of the deformation velocity $v_d$, there was found a deviation to the present workpiece velocity $v_w$. Fig. 4 (c) shows the maximum reached workpiece velocity $v_{w,m}$.

<figure><img src="image_1485.png" /><figcaption>Fig. 4: Measurement system: (a) formed foils for different tests methods, (b) comparison of measured velocities $v_d$ for position sensor and light barrier, (c) workpiece velocities $v_{w,m}$ determined for LSF and EMF</figcaption></figure>

Higher maximum workpiece velocity $v_{w,m}$ were measured - using the current settings - for laser shock forming compared to electromagnetic forming. Nevertheless, both processes exceed the workpiece velocity limit of 15 m/s for high velocity forming processes defined by Bruno et al. [18].

In laser shock forming, three phases of forming were identified (see Fig. 5). The first phase preceded the actual forming, where a small alternating strain $\epsilon_g$ occurred. This phase could be a result of the plasma initiation. After this phase, the main deformation occurred up to the maximum of the strain. Here, a strain rate $\epsilon_g$ of 10000 1/s was calculated based on the displacement measurement (see Fig. 5 (b)). Following this phase, a phase of springback of the workpiece arose, which ended with a remaining strain of approx. 0.074 (see Fig. 5 (a)). After this, a variation in
strain and strain rate was determined due to the process-induced vibration and noise of the measurement system.

<figure><img src="image_1482.png" /><figcaption>Fig. 5: Laser shock forming: (a) strain $\epsilon_g$ over time t, (b) strain rate $\dot{\epsilon}_g$ over time t</figcaption></figure>

Free electromagnetic forming could be divided into two phases (see Fig. 6). The first phase consisted of the elongation of the workpiece up to the first reach of the remaining strain $\epsilon_g$.
strain and strain rate was determined due to the process-induced vibration and noise of the measurement system.

<figure><img src="image_1486.png" /><figcaption>Fig. 5: Laser shock forming: (a) strain $\dot{\varepsilon}_g$ over time t, (b) strain rate $\dot{\varepsilon}_g^*$ over time t</figcaption></figure>

Free electromagnetic forming could be divided into two phases (see Fig. 6). The first phase consisted of the elongation of the workpiece up to the first reach of the remaining strain $\varepsilon_g$.
<figure><img src="image_1483.png" /><figcaption>Fig. 6: Electromagnetic forming; (a) strain $\varepsilon_g$ over time t (b) strain rate $\dot{\varepsilon}_g$ over time t</figcaption></figure>

Based on the oscillation of the electromagnetic force indicated by the oscillation of the tool coil current $I_{tc}$, a discontinuous straining takes place. Within this phase, the highest strain rate $\dot{\varepsilon}_g$ of approx. 2100 1/s occurred (see Fig. 6 (b)). Following to this phase, a workpiece vibration around the remaining strain $\varepsilon_g$ arose with a maximum strain rate $\dot{\varepsilon}_g$ of approx. 1000 1/s with no springback. As the amplitude of the workpiece vibration decays, a strain $\varepsilon_g$ of approx. 0.044 remained. Again, due to the vibration of the measuring system and noise, a variation of the strain $\varepsilon_g$ and strain rate $\dot{\varepsilon}_g$ appeared.

## Discussion

Both forming processes fulfil the high-velocity criteria established by Bruno et al. [18]. Nevertheless, both differ in their process effect, so that different characteristics occurred during the forming process. During laser shock forming, a surface force acted which had its origin above the surface. On the other hand, volume forces acted during electromagnetic forming. As a result of the different force application, different time sequences of the forming occurred. As a reaction to the pressure wave during laser shock forming, a single movement occurred. The actual forming motion was preceded by a workpiece motion, which could be a result of the plasma or shockwave initiation. In electromagnetic forming, a movement occurred as a function of the tool coil current, which was divided into the actual forming and vibration for the tool coil current used [19].
<figure><img src="image_1487.png" /><figcaption>Fig. 6: Electromagnetic forming; (a) strain $\varepsilon_g$ over time t (b) strain rate $\dot{\varepsilon}_g$ over time t</figcaption></figure>

Based on the oscillation of the electromagnetic force indicated by the oscillation of the tool coil current $I_{tc}$, a discontinuous straining takes place. Within this phase, the highest strain rate $\dot{\varepsilon}_g$ of approx. 2100 1/s occurred (see Fig. 6 (b)). Following to this phase, a workpiece vibration around the remaining strain $\varepsilon_g$ arose with a maximum strain rate $\dot{\varepsilon}_g$ of approx. 1000 1/s with no springback. As the amplitude of the workpiece vibration decays, a strain $\varepsilon_g$ of approx. 0.044 remained. Again, due to the vibration of the measuring system and noise, a variation of the strain $\varepsilon_g$ and strain rate $\dot{\varepsilon}_g$ appeared.

## Discussion

Both forming processes fulfil the high-velocity criteria established by Bruno et al. [18]. Nevertheless, both differ in their process effect, so that different characteristics occurred during the forming process. During laser shock forming, a surface force acted which had its origin above the surface. On the other hand, volume forces acted during electromagnetic forming. As a result of the different force application, different time sequences of the forming occurred. As a reaction to the pressure wave during laser shock forming, a single movement occurred. The actual forming motion was preceded by a workpiece motion, which could be a result of the plasma or shockwave initiation. In electromagnetic forming, a movement occurred as a function of the tool coil current, which was divided into the actual forming and vibration for the tool coil current used [19].
## Conclusion

A new measurement set up for investigation of different high velocity forming processes was introduced in this paper. The comparison with a light barrier-based measurement system showed the useability as well as advantages of the new system for investigation of energy transmission in high velocity forming processes.

Based on the first experiments comparing laser shock forming and electromagnetic forming with 50 µm thin Al99.5 foils following conclusion can be drawn:

* LSF and EMF are characterized as high-speed forming processes with maximum workpiece velocity over 15 m/s

* The reached maximum velocity of LSF ≈135 m/s was higher than for EMF with ≈50 m/s

* Differences in strain and strain rate over time were observed

* EMF showed reduction of springback which was explained by force oscillation

## Future work

The method used made it possible to determine the deformation at one point on the sheet metal. Since impulse forming processes such as electrohydraulic forming are based on the effect of transient pressure fields, the aim is to extend the method for future investigations of energy transfer, e.g. by adding further distance sensors and pressure sensors in the pressure-transmitting fluid.

## References

[1] D.R. Kennedy, History of the shaped charge effect: The first 100 years, (1983).

[2] G. Avrillaud et al., Examples of How Increased Formability through High Strain Rates Can Be Used in Electro-Hydraulic Forming and Electromagnetic Forming Industrial Applications, J. of Man. and Mat. Pro. 5 (3), (2021) 96. https://doi.org/10.3390/jmmp5030096

[3] H.-G. Noh et al., Two-step electromagnetic forming process using spiral forming coils to deform sheet metal in a middle-block die, Int J Adv Man. Technol., 76 (9-12), (2015) 1691-1703. https://doi.org/10.1007/s00170-014-6392-4

[4] X. Cui et al., Springback Calibration of a U-Shaped Electromagnetic Impulse Forming Process, Metals 9 (5) 603. https://doi.org/10.3390/met9050603

[5] Z Lai et al., Application of Electromagnetic Forming as a Light-Weight Manufacturing Method for Large-Scale Sheet Metal Parts, (2018).

[6] M. Geiger et al., Microforming, CIRP Annals 50 (2), (2001) 445-462. https://doi.org/10.1016/S0007-8506(07)62991-6

[7] S. Veenaas et al., Determination of forming speed at a laser shock stretch drawing process, Proceedings of the 7th ICHSF, (2016) 105-114.

[8] B. Kuhfuss et al., Electromagnetic Linked Micro Parts Processing, Proc. Eng. 81, (2014) 2135-2140. https://doi.org/10.1016/j.proeng.2014.10.298

[9] Z. Long et al., Electromagnetic micro-forming using flat spiral coil, Int. J. Adv. Manuf. Technol. 121 (1-2), (2022) 1161-1171. https://doi.org/10.1007/s00170-022-09363-1

[10] Z. Zimniak, Plastic Deformation Zone in Electromagnetic Cutting, Archives of Metallurgy and Materials 62 (4), (2017) 2303-2308. https://doi.org/10.1515/amm-2017-0339
## Conclusion

A new measurement set up for investigation of different high velocity forming processes was introduced in this paper. The comparison with a light barrier-based measurement system showed the useability as well as advantages of the new system for investigation of energy transmission in high velocity forming processes.

Based on the first experiments comparing laser shock forming and electromagnetic forming with 50 µm thin Al99.5 foils following conclusion can be drawn:

* LSF and EMF are characterized as high-speed forming processes with maximum workpiece velocity over 15 m/s

* The reached maximum velocity of LSF ≈135 m/s was higher than for EMF with ≈50 m/s

* Differences in strain and strain rate over time were observed

* EMF showed reduction of springback which was explained by force oscillation

## Future work

The method used made it possible to determine the deformation at one point on the sheet metal. Since impulse forming processes such as electrohydraulic forming are based on the effect of transient pressure fields, the aim is to extend the method for future investigations of energy transfer, e.g. by adding further distance sensors and pressure sensors in the pressure-transmitting fluid.

## References

[1] D.R. Kennedy, History of the shaped charge effect: The first 100 years, (1983).

[2] G. Avrillaud et al., Examples of How Increased Formability through High Strain Rates Can Be Used in Electro-Hydraulic Forming and Electromagnetic Forming Industrial Applications, J. of Man. and Mat. Pro. 5 (3), (2021) 96. https://doi.org/10.3390/jmmp5030096

[3] H.-G. Noh et al., Two-step electromagnetic forming process using spiral forming coils to deform sheet metal in a middle-block die, Int J Adv Man. Technol., 76 (9-12), (2015) 1691-1703. https://doi.org/10.1007/s00170-014-6392-4

[4] X. Cui et al., Springback Calibration of a U-Shaped Electromagnetic Impulse Forming Process, Metals 9 (5) 603. https://doi.org/10.3390/met9050603

[5] Z Lai et al., Application of Electromagnetic Forming as a Light-Weight Manufacturing Method for Large-Scale Sheet Metal Parts, (2018).

[6] M. Geiger et al., Microforming, CIRP Annals 50 (2), (2001) 445-462. https://doi.org/10.1016/S0007-8506(07)62991-6

[7] S. Veenaas et al., Determination of forming speed at a laser shock stretch drawing process, Proceedings of the 7th ICHSF, (2016) 105-114.

[8] B. Kuhfuss et al., Electromagnetic Linked Micro Parts Processing, Proc. Eng. 81, (2014) 2135-2140. https://doi.org/10.1016/j.proeng.2014.10.298

[9] Z. Long et al., Electromagnetic micro-forming using flat spiral coil, Int. J. Adv. Manuf. Technol. 121 (1-2), (2022) 1161-1171. https://doi.org/10.1007/s00170-022-09363-1

[10] Z. Zimniak, Plastic Deformation Zone in Electromagnetic Cutting, Archives of Metallurgy and Materials 62 (4), (2017) 2303-2308. https://doi.org/10.1515/amm-2017-0339
[11] M. Kamal et al., Agile manufacturing of a micro-embossed case by a two-step electromagnetic forming process, J. of Mat. Pro. Tec. 190, (2007) 41-50.
https://doi.org/10.1016/j.jmatprotec.2007.03.114

[12] L. Langstädtler et al., Electromagnetic Joining of Thin Sheets by Adapted Pulses, KEM 767, (2018) 439-446. https://doi.org/10.4028/www.scientific.net/KEM.767.439

[13] A. W. Miziolek et al., Laser Induced Breakdown Spectroscopy, Cambridge University Press, (2006). https://doi.org/10.1017/CBO9780511541261

[14] H. Fenske et al., Tailoring the Pressure Profile of TEA-CO2 Laser-Induced Shock Waves for Mechanical Forming and Separation Processes, Lasers Manuf. Mater. Process. 7 (1), (2020) 1-14.
https://doi.org/10.1007/s40516-019-00105-y

[15] H. Bühler et al., Ein Beitrag zur Magnetumformung rohrförmiger Werkstücke, Werkstatt und Betrieb 110.9, (1968) 513-516.

[16] B. Beckschwarte et al., Numerical and Experimental Investigation of the Impact of the Electromagnetic Properties of the Die Materials in Electromagnetic Forming of Thin Sheet Metal, J. manuf. mater. process. 5 (1), (2021) 18ff. https://doi.org/10.3390/jmmp5010018

[17] T. Valentino, Nutzung laserinduzierter Stoßwellen zur Hochdurchsatz-Werkstoffprüfung, (2021).

[18] E. J. Bruno, High-velocity forming of metals, American Society of Tool and Manufacturing Engineers, (1968).

[19] B. Beckschwarte et al., Response of Thin Sheet Metal on the Excitation in Electromagnetic Forming, Eng. Proc. 26 (1), (2022) 4. https://doi.org/10.3390/engproc2022026004
[11] M. Kamal et al., Agile manufacturing of a micro-embossed case by a two-step electromagnetic forming process, J. of Mat. Pro. Tec. 190, (2007) 41-50.
https://doi.org/10.1016/j.jmatprotec.2007.03.114

[12] L. Langstädtler et al., Electromagnetic Joining of Thin Sheets by Adapted Pulses, KEM 767, (2018) 439-446. https://doi.org/10.4028/www.scientific.net/KEM.767.439

[13] A. W. Miziolek et al., Laser Induced Breakdown Spectroscopy, Cambridge University Press, (2006). https://doi.org/10.1017/CBO9780511541261

[14] H. Fenske et al., Tailoring the Pressure Profile of TEA-CO2 Laser-Induced Shock Waves for Mechanical Forming and Separation Processes, Lasers Manuf. Mater. Process. 7 (1), (2020) 1-14.
https://doi.org/10.1007/s40516-019-00105-y

[15] H. Bühler et al., Ein Beitrag zur Magnetumformung rohrförmiger Werkstücke, Werkstatt und Betrieb 110.9, (1968) 513-516.

[16] B. Beckschwarte et al., Numerical and Experimental Investigation of the Impact of the Electromagnetic Properties of the Die Materials in Electromagnetic Forming of Thin Sheet Metal, J. manuf. mater. process. 5 (1), (2021) 18ff. https://doi.org/10.3390/jmmp5010018

[17] T. Valentino, Nutzung laserinduzierter Stoßwellen zur Hochdurchsatz-Werkstoffprüfung, (2021).

[18] E. J. Bruno, High-velocity forming of metals, American Society of Tool and Manufacturing Engineers, (1968).

[19] B. Beckschwarte et al., Response of Thin Sheet Metal on the Excitation in Electromagnetic Forming, Eng. Proc. 26 (1), (2022) 4. https://doi.org/10.3390/engproc2022026004
# Processing of sheets made of long fibers reinforced plastics by SPIF

AMBROGIO Giuseppina¹,ª*, BORDA Francesco¹,ᵇ*, CONTE Romina¹,ᶜ, FILICE Luigino¹,ᵈ, GAGLIARDI Francesco¹,ᵉ

¹University of Calabria, Ponte P. Bucci - Cubo 45C, 87036 Arcavacata di Rende (CS) - Italy

ªgiuseppina.ambrogio@unical.it, ᵇfrancesco.borda@unical.it, ᶜromina.conte@unical.it,

ᵈluigino.filice@unical.it, ᶜfrancesco.gagliardi@unical.it

**Keywords:** SPIF, Incremental Forming, Composite Material, Thermoplastic, Long Fiber, Carbon Fiber, Glass Fiber

**Abstract.** The flexibility of the Single Point Incremental Forming (SPIF) has been exploited in processing of sheets made by fiber reinforced polymers. Indeed, polymer-based sheets are always more employed in product planning, meeting the increasing demand of lightweight structures. However, considering the SPIF features, especially the need to totally clamp the formed sheet along its edges, processing of long-fiber reinforced sheets is critical owing to the brittleness of the fibers, whose length must be preserved. The SPIF dynamics of a customized process solution to be used for long fibers reinforced thermoplastics (LFRTPs) were already proposed and analyzed by FE simulations. Herein, the design of the equipment that allows the process to be executed was proposed detailing it in each part. In particular, the idea was based on assembling a working room that was designed to be able to control both: a) the desired process temperature maintaining it constant during the whole forming step looking at the glass and melting point of the polymeric matrix; b) a hydrostatic pressure on the bottom side of the sheet to guarantee its proper shaping. Moreover, numerical simulations were also executed to locally analyze the forming behavior of the sheet at changing of some specific properties.

## Introduction

In the pursuit of lightweight design, high-strength materials, long fiber composites have emerged as a promising candidate for various engineering applications. These materials, characterized by the incorporation of continuous fibers within a polymer matrix, offer exceptional mechanical properties and design flexibility. Specifically, long fiber composites, characterized by extended and continuous fibers embedded within a polymer matrix, exhibit remarkable strength, stiffness, and fatigue resistance compared to traditional materials. However, the manufacturing of long fiber reinforced thermoplastic sheets (LFRTPs) presents a myriad of challenges that necessitate careful examination to fully unlock the potential of these advanced materials. The integration of long fiber composites in various industries has been a revolutionary stride towards achieving lightweight structures with enhanced mechanical properties. Long fiber composites have found applications in industries ranging from automotive to aerospace, where the demand for lightweight yet durable components is paramount. The intrinsic advantages of LFRTPs, such as enhanced tensile strength and impact resistance, position them as a preferred choice for structural elements. Despite these advantages, challenges arise during the manufacturing processes due to the inherent anisotropic nature of the material. Conventional manufacturing technologies, such as injection molding and compression molding, struggle to seamlessly shape LFRTPs without compromising their mechanical properties. In this perspective, as with any cutting-edge technology, the implementation of long fiber composites is not without any challenges. Several technologies are commonly used for shaping long fiber thermoplastic composites, as summarized in Table 1 [1,2].

<figure><img src="image_1484.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
# Processing of sheets made of long fibers reinforced plastics by SPIF

AMBROGIO Giuseppina¹,ª*, BORDA Francesco¹,ᵇ*, CONTE Romina¹,ᶜ, FILICE Luigino¹,ᵈ, GAGLIARDI Francesco¹,ᵉ

¹University of Calabria, Ponte P. Bucci - Cubo 45C, 87036 Arcavacata di Rende (CS) - Italy

ªgiuseppina.ambrogio@unical.it, ᵇfrancesco.borda@unical.it, ᶜromina.conte@unical.it,

ᵈluigino.filice@unical.it, ᶜfrancesco.gagliardi@unical.it

**Keywords:** SPIF, Incremental Forming, Composite Material, Thermoplastic, Long Fiber, Carbon Fiber, Glass Fiber

**Abstract.** The flexibility of the Single Point Incremental Forming (SPIF) has been exploited in processing of sheets made by fiber reinforced polymers. Indeed, polymer-based sheets are always more employed in product planning, meeting the increasing demand of lightweight structures. However, considering the SPIF features, especially the need to totally clamp the formed sheet along its edges, processing of long-fiber reinforced sheets is critical owing to the brittleness of the fibers, whose length must be preserved. The SPIF dynamics of a customized process solution to be used for long fibers reinforced thermoplastics (LFRTPs) were already proposed and analyzed by FE simulations. Herein, the design of the equipment that allows the process to be executed was proposed detailing it in each part. In particular, the idea was based on assembling a working room that was designed to be able to control both: a) the desired process temperature maintaining it constant during the whole forming step looking at the glass and melting point of the polymeric matrix; b) a hydrostatic pressure on the bottom side of the sheet to guarantee its proper shaping. Moreover, numerical simulations were also executed to locally analyze the forming behavior of the sheet at changing of some specific properties.

## Introduction

In the pursuit of lightweight design, high-strength materials, long fiber composites have emerged as a promising candidate for various engineering applications. These materials, characterized by the incorporation of continuous fibers within a polymer matrix, offer exceptional mechanical properties and design flexibility. Specifically, long fiber composites, characterized by extended and continuous fibers embedded within a polymer matrix, exhibit remarkable strength, stiffness, and fatigue resistance compared to traditional materials. However, the manufacturing of long fiber reinforced thermoplastic sheets (LFRTPs) presents a myriad of challenges that necessitate careful examination to fully unlock the potential of these advanced materials. The integration of long fiber composites in various industries has been a revolutionary stride towards achieving lightweight structures with enhanced mechanical properties. Long fiber composites have found applications in industries ranging from automotive to aerospace, where the demand for lightweight yet durable components is paramount. The intrinsic advantages of LFRTPs, such as enhanced tensile strength and impact resistance, position them as a preferred choice for structural elements. Despite these advantages, challenges arise during the manufacturing processes due to the inherent anisotropic nature of the material. Conventional manufacturing technologies, such as injection molding and compression molding, struggle to seamlessly shape LFRTPs without compromising their mechanical properties. In this perspective, as with any cutting-edge technology, the implementation of long fiber composites is not without any challenges. Several technologies are commonly used for shaping long fiber thermoplastic composites, as summarized in Table 1 [1,2].

<figure><img src="image_1488.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
<table><caption>Table 1 - Manufacturing process adopted for long fiber composites</caption><thead><tr><td>Process</td><td>Description</td><td>Weakness</td></tr></thead><tbody><tr><td>Injection molding</td><td>Molten thermoplastic material is injected into a mold cavity, where it solidifies into the desired shape</td><td>Tooling costs can be high, and it may be challenging to achieve uniform fiber orientation in complex parts</td></tr><tr><td>Thermoforming</td><td>This process involves heating a pre-consolidated thermoplastic sheet until it becomes pliable, and then forming it into a specific shape using a mold</td><td>Limited to simple shapes, may not be suitable for high-strength applications</td></tr><tr><td>Pultrusion</td><td>Continuous process where fibers (usually glass or carbon) are impregnated with a thermoplastic resin and pulled through a heated die to shape the composite</td><td>Limited to linear shapes, may not be suitable for complex three-dimensional parts</td></tr><tr><td>Stamping</td><td>Composite sheet are pressed between dies</td><td>Limited to specific and simple shapes and may have higher tooling costs</td></tr></tbody></table>

In recent years, the field of materials science and manufacturing has witnessed a paradigm shift with the advent of Single Point Incremental Forming (SPIF). This innovative manufacturing technique has garnered substantial attention for its potential to revolutionize the production processes [3], particularly in the domain of unconventional materials [4,5]. This paper explores the innovation prosecutable by the intersection of SPIF and long fiber thermoplastics use, aiming to shed light on the synergies that can propel advancements in both application fields. In contrast with the conventional manufacturing techniques, SPIF stands out as a promising alternative, offering a more agile and cost-effective approach to shaping intricate geometries with reduced material waste. By exploring the synergy between this innovative forming technique and long fiber composites materials, we aim to uncover novel pathways for enhancing manufacturing efficiency, material properties, and ultimately fostering a new era of design possibilities.

## The designed Equipment

An equipment was designed pointing out each component required to perform the forming phase of SPIF on sheets made by LFRTPs. A scheme of the whole experimental equipment is reported in Fig. 1.
<table><caption>Table 1 - Manufacturing process adopted for long fiber composites</caption><thead><tr><td>Process</td><td>Description</td><td>Weakness</td></tr></thead><tbody><tr><td>Injection molding</td><td>Molten thermoplastic material is injected into a mold cavity, where it solidifies into the desired shape</td><td>Tooling costs can be high, and it may be challenging to achieve uniform fiber orientation in complex parts</td></tr><tr><td>Thermoforming</td><td>This process involves heating a pre-consolidated thermoplastic sheet until it becomes pliable, and then forming it into a specific shape using a mold</td><td>Limited to simple shapes, may not be suitable for high-strength applications</td></tr><tr><td>Pultrusion</td><td>Continuous process where fibers (usually glass or carbon) are impregnated with a thermoplastic resin and pulled through a heated die to shape the composite</td><td>Limited to linear shapes, may not be suitable for complex three-dimensional parts</td></tr><tr><td>Stamping</td><td>Composite sheet are pressed between dies</td><td>Limited to specific and simple shapes and may have higher tooling costs</td></tr></tbody></table>

In recent years, the field of materials science and manufacturing has witnessed a paradigm shift with the advent of Single Point Incremental Forming (SPIF). This innovative manufacturing technique has garnered substantial attention for its potential to revolutionize the production processes [3], particularly in the domain of unconventional materials [4,5]. This paper explores the innovation prosecutable by the intersection of SPIF and long fiber thermoplastics use, aiming to shed light on the synergies that can propel advancements in both application fields. In contrast with the conventional manufacturing techniques, SPIF stands out as a promising alternative, offering a more agile and cost-effective approach to shaping intricate geometries with reduced material waste. By exploring the synergy between this innovative forming technique and long fiber composites materials, we aim to uncover novel pathways for enhancing manufacturing efficiency, material properties, and ultimately fostering a new era of design possibilities.

## The designed Equipment

An equipment was designed pointing out each component required to perform the forming phase of SPIF on sheets made by LFRTPs. A scheme of the whole experimental equipment is reported in Fig. 1.
<figure><img src="image_1485.png" /><figcaption>Fig. 1 – Scheme of the designed equipment</figcaption></figure>

Specifically, the equipment was conceived with the aim to be able to control working temperature and back hydrostatic pressure, continuously, in the working phase. The SPIF of LFRTPs is executed by using a metallic sheet in between the rigid tool and the composite sheet to be processed [4,5]. Both the metal and the composite blanks have to be totally blocked along their perimeter on the upper part of the processing tank covering and sealing, as a lid, the working area.

It has to be highlighted that the long fibers, both carbon and glass fibers, that are commonly used to reinforce polymeric matrices, can not be blocked being characterized by really high breakability and absolutely no plastic deformation. Taking that into account, the idea was to divide the polymer-based blank in two portions leaving the external frame, used for its clamping, without reinforcements (Fig. 2).

<figure><img src="image_1486.png" /><figcaption>Fig. 2 – A sketch of the working composite sheet</figcaption></figure>

By doing so, the composite sheet, at the working temperature, chosen taking into account the glass and melting temperature of the processed thermoplastic matrix and depending on its level of crystallinity, is sagging affecting the dimensional accuracy in the forming phase. For that reason, the composite sheet has to adhere to the metallic blank up to both forming and cooling phases are completed.

For that reason, a specific fluid, for example a thermal oil, is pressurized inside the processing tank resulting in a hydrostatic force that pushes the composite sheet to the metallic one. This
<figure><img src="image_1489.png" /><figcaption>Fig. 1 – Scheme of the designed equipment</figcaption></figure>

Specifically, the equipment was conceived with the aim to be able to control working temperature and back hydrostatic pressure, continuously, in the working phase. The SPIF of LFRTPs is executed by using a metallic sheet in between the rigid tool and the composite sheet to be processed [4,5]. Both the metal and the composite blanks have to be totally blocked along their perimeter on the upper part of the processing tank covering and sealing, as a lid, the working area.

It has to be highlighted that the long fibers, both carbon and glass fibers, that are commonly used to reinforce polymeric matrices, can not be blocked being characterized by really high breakability and absolutely no plastic deformation. Taking that into account, the idea was to divide the polymer-based blank in two portions leaving the external frame, used for its clamping, without reinforcements (Fig. 2).

<figure><img src="image_1490.png" /><figcaption>Fig. 2 – A sketch of the working composite sheet</figcaption></figure>

By doing so, the composite sheet, at the working temperature, chosen taking into account the glass and melting temperature of the processed thermoplastic matrix and depending on its level of crystallinity, is sagging affecting the dimensional accuracy in the forming phase. For that reason, the composite sheet has to adhere to the metallic blank up to both forming and cooling phases are completed.

For that reason, a specific fluid, for example a thermal oil, is pressurized inside the processing tank resulting in a hydrostatic force that pushes the composite sheet to the metallic one. This
pressurized fluid allows the contact between the two sheets to be obtained, exactly. In detail, before the SPIF starts, the processing tank is filled up to the clamping plane by this oil. Two relief tubes are utilized to ensure the complete filling of the working volume avoiding air pockets under the sheets.

The pressurized fluid is further utilized to control the working temperature of the plastic material avoiding thermal fluctuation that can affect the formability of the sheet. An electrical resistance is inserted in the oil, in the processing tank's volume, to heat the system and control the temperature, remotely, by a thermometric probe. Furthermore, the processing tank is isolated by the basis of the equipment by placing on its bottom a thick plate of ceramic material acting as thermal insulator (Fig. 3).

<figure><img src="image_1487.png" /><figcaption>Fig. 3 – A section of the designed processing tank</figcaption></figure>

Summing up, the fluid inside the processing is employed for controlling both pressure and temperature during the SPIF's steps. The process monitoring has to take into account that, while the forming phase proceeds, the formed sheets go in the chamber of the processing tank reducing the volume taken by the oil. For that reason, in order to be able to make independent the hydrostatic pressure history from the rigid tool's position, an expansion vessel was introduced in the equipment working as an outlet for the fluid. The pressure in the working zone is, therefore, controlled, by setting with a control panel the desired pressure trend inside the expansion vessel.

For this purpose, a pneumatic regulator is employed with the aim to take an inlet air pressure, adjusting it automatically to follow the desired output pressure, namely the working pressure, and guaranteeing a stable functioning of the system by also using a vent valve.

A stratified thermal separator was, finally, placed at the exit of the processing tank, with the aim of reducing the temperature of the fluid before it reaches the expansion vessel. For safety reasons, indeed, the temperature of the pressurized oil has to be reduced before reaching the expansion vessel. This control was provided by monitoring the temperature by an additional thermometer placed in the thermal separator.

Finally, the control panel allows pressure and temperature to be regulated by the highlighted equipment relating these variables to the SPIF's specific phases.

## Designed process solution investigated by FEM

Numerical simulations were set to investigate the mechanical behavior of the LFRTs sheets processed by SPIF using the highlighted process peculiarities. The aim is to gain through the numerical study a deeper understanding of the sheet deformation allowing the equipment
pressurized fluid allows the contact between the two sheets to be obtained, exactly. In detail, before the SPIF starts, the processing tank is filled up to the clamping plane by this oil. Two relief tubes are utilized to ensure the complete filling of the working volume avoiding air pockets under the sheets.

The pressurized fluid is further utilized to control the working temperature of the plastic material avoiding thermal fluctuation that can affect the formability of the sheet. An electrical resistance is inserted in the oil, in the processing tank's volume, to heat the system and control the temperature, remotely, by a thermometric probe. Furthermore, the processing tank is isolated by the basis of the equipment by placing on its bottom a thick plate of ceramic material acting as thermal insulator (Fig.3).

<figure><img src="image_1491.png" /><figcaption>Fig. 3 – A section of the designed processing tank</figcaption></figure>

Summing up, the fluid inside the processing is employed for controlling both pressure and temperature during the SPIF's steps. The process monitoring has to take into account that, while the forming phase proceeds, the formed sheets go in the chamber of the processing tank reducing the volume taken by the oil. For that reason, in order to be able to make independent the hydrostatic pressure history from the rigid tool's position, an expansion vessel was introduced in the equipment working as an outlet for the fluid. The pressure in the working zone is, therefore, controlled, by setting with a control panel the desired pressure trend inside the expansion vessel.

For this purpose, a pneumatic regulator is employed with the aim to take an inlet air pressure, adjusting it automatically to follow the desired output pressure, namely the working pressure, and guaranteeing a stable functioning of the system by also using a vent valve.

A stratified thermal separator was, finally, placed at the exit of the processing tank, with the aim of reducing the temperature of the fluid before it reaches the expansion vessel. For safety reasons, indeed, the temperature of the pressurized oil has to be reduced before reaching the expansion vessel. This control was provided by monitoring the temperature by an additional thermometer placed in the thermal separator.

Finally, the control panel allows pressure and temperature to be regulated by the highlighted equipment relating these variables to the SPIF's specific phases.

## Designed process solution investigated by FEM

Numerical simulations were set to investigate the mechanical behavior of the LFRTs sheets processed by SPIF using the highlighted process peculiarities. The aim is to gain through the numerical study a deeper understanding of the sheet deformation allowing the equipment
construction to be validated. A single-point incremental forming (SPIF) process was proposed on LFRTPs blank consisting of a thermoplastic polypropylene (PP) matrix and a long glass fiber (GF) reinforcement. Specifically, the [0/45/-45/90]s or quasi-isotropic configuration was analyzed. In the simulation process, the possibility of applying the single-point incremental forming process (SPIF) assisted by a pressurized fluid was evaluated. The pressurized fluid could creep between the aluminum blank, which acts as a membrane, interposed between the composite blank and the tool, used in the incremental forming process. In order to avoid this problem, the implementation of a polymeric frame, of the same material as the matrix (PP), properly realized around the composite laminate (GFRP), has been proposed, which has the function of guaranteeing an optimal seal between the rigid support and the laminate and thus avoiding fluid leakage.

The FE numerical model was created by modeling four bodies: the deformation tool, the rigid support, the aluminum blank and the composite laminate blank, the latter made of GFRP and an external PP frame. A diagram of the assembly used in the simulation is shown in Fig. 4.

<figure><img src="image_1488.png" /><figcaption>Fig. 4 - Cross-section view of the FE model assembly</figcaption></figure>

The FE model was developed from a specific material model to be implemented for the definition of the virtual composite sheet. This sheet is made of GFRP and a part entirely of PP. In addition, PP, whose forming temperature is approximately 220 °C, was chosen as the matrix, considering its hygroscopic characteristics to carry out future experimental validation tests using the proposed process technology (Fig.1). Long glass fibers, not stitched into the pre-impregnated foils, are the reinforcement type. The volume fraction of fibers in each lamina is 60%. The virtual composite sheet was built considering an overlapping of laminas, under quasi-isotropic conditions, as described in Table 2. The mechanical properties of the lamina at working temperature are given in Table 3.

<table><caption>Table 2 - Configuration of GFRP panel</caption><thead><tr><td>Laminate sequence</td><td>Diameter (mm)</td><td>Lamina Thickness (mm)</td><td>Laminate Thickness (mm)</td></tr></thead><tbody><tr><td>[0/45/-45/0]s</td><td>160</td><td>0.25</td><td>2</td></tr></tbody></table>

The mechanical properties of the lamina at working temperature are given in Table 2.
construction to be validated. A single-point incremental forming (SPIF) process was proposed on LFRTPs blank consisting of a thermoplastic polypropylene (PP) matrix and a long glass fiber (GF) reinforcement. Specifically, the [0/45/-45/90]s or quasi-isotropic configuration was analyzed. In the simulation process, the possibility of applying the single-point incremental forming process (SPIF) assisted by a pressurized fluid was evaluated. The pressurized fluid could creep between the aluminum blank, which acts as a membrane, interposed between the composite blank and the tool, used in the incremental forming process. In order to avoid this problem, the implementation of a polymeric frame, of the same material as the matrix (PP), properly realized around the composite laminate (GFRP), has been proposed, which has the function of guaranteeing an optimal seal between the rigid support and the laminate and thus avoiding fluid leakage.

The FE numerical model was created by modeling four bodies: the deformation tool, the rigid support, the aluminum blank and the composite laminate blank, the latter made of GFRP and an external PP frame. A diagram of the assembly used in the simulation is shown in Fig. 4.

<figure><img src="image_1492.png" /><figcaption>Fig. 4 - Cross-section view of the FE model assembly</figcaption></figure>

The FE model was developed from a specific material model to be implemented for the definition of the virtual composite sheet. This sheet is made of GFRP and a part entirely of PP. In addition, PP, whose forming temperature is approximately 220 °C, was chosen as the matrix, considering its hygroscopic characteristics to carry out future experimental validation tests using the proposed process technology (Fig.1). Long glass fibers, not stitched into the pre-impregnated foils, are the reinforcement type. The volume fraction of fibers in each lamina is 60%. The virtual composite sheet was built considering an overlapping of laminas, under quasi-isotropic conditions, as described in Table 2. The mechanical properties of the lamina at working temperature are given in Table 3.

<table><caption>Table 2 - Configuration of GFRP panel</caption><thead><tr><td>Laminate sequence</td><td>Diameter (mm)</td><td>Lamina Thickness (mm)</td><td>Laminate Thickness (mm)</td></tr></thead><tbody><tr><td>[0/45/-45/0]s</td><td>160</td><td>0.25</td><td>2</td></tr></tbody></table>

The mechanical properties of the lamina at working temperature are given in Table 2.
<table><caption>Table 3 - Mechanical properties of the utilized prepreg [6]</caption><thead><tr><th>Parameters 220°C</th><th>E11</th><th>E22</th><th>μ12</th><th>G12</th><th>G23</th></tr></thead><tbody><tr><th>Value</th><td>2.5 GPa</td><td>0.5 MPa</td><td>0.35</td><td>0.2 MPa</td><td>0.2 MPa</td></tr></tbody></table>

The laminas are set by taking into account their linear elastic properties and implementing Hashin's damage model [7] to study matrix and fiber failures. The parameters of the sheet constitutive model were set according to [5]. The dummy sheet used as a cover is a 2 mm thick aluminum alloy (AA-6056). The plastic behavior of sheet AA-6056 was modeled according to [5].

## Numerical model

The finite element model of the proposed SPIF process was run with the FE Abaqus/CAE commercial code. Fig. 4 shows the cross-section of the FE model assembly based on the previously described process strategy. In detail, the rotational molding tool, modeled as a rigid body, is in contact with a square aluminum blank characterized by a 200 mm side and fixed in the periphery on a steel frame, modeled as a rigid body. A Coulomb friction coefficient of 0.1 between the tool and the metal plate was set [8, 5]. The outer edge of the panel is made of PP, which is melted under the chosen process conditions, while the remaining part is made of GFRP and is subjected to hydrostatic pressure simulating the presence of pressurized fluid. A constant pressure is set under the GFRP and PP sheet, as shown in Fig. 4. A friction-free approach was used between the two slabs, which were modeled as deformable bodies using shell elements (S4R). Simpson's integration rule with 5 integration points was modeled along the thickness direction, and approximately 3000 elements for the aluminum blank and 3500 elements for the GFRP and PP sheet were used. An explicit solver, with time and mass scaling, was used to accelerate the simulation. In particular, semi-automatic mass scaling with a target time increment of 2e-6 s was implemented. The tool path was defined by three tabular amplitudes and the total simulation time was set equal to 6 s.

## Investigated process variables

A truncated cone was numerically formed. The cone is characterized by an inclination angle of 30°, a final height of 25 mm, and a base diameter of 100 mm. The effects on the quality of the formed parts, focusing on the surface quality, shape accuracy and/or local thinning of the sheet formed from GFRP and PP, were assessed by changing the pressure value on the back face of the GFRP and PP panel. Constant values of 0.01, 0.05, 0.1 and 0.2 MPa were assessed during the entire forming phase.

## FE model results

This section focuses on the analysis of the numerical results obtained from the simulations carried out on the SPIF process. Specifically, the results of the model were evaluated both in the section realized in GFRP and in the frame realized in PP. The results were evaluated in terms of formability, thickness distribution and accuracy of the shape as the pressure exerted by the fluid during the SPIF process varied, as shown in Fig. 5. In detail, in Fig. 5a is shown the back side of the GFRP plates for the four configurations studied. These analyses were performed by setting different back pressure levels, from a low back pressure of 0.01 MPa to a high back pressure of 0.2 MPa. The quasi-isotropic configuration, i.e. [0/45/-45/90]s, is characterized by a uniform deformation along the main directions that preserves the circular shape of the section as a trajectory imposed on the tool. With regard to surface defects, the wrinkles appear along the conical side with an out-of-plane deformation that has to be taken into account. Furthermore, looking at Fig. 5a, the presence of the PP frame allows for a constant thickness of the laminate with a variation in thickness, only in the portion made of PP, correlated to the imposed back pressure. In Fig. 5b, on
<table><caption>Table 3 - Mechanical properties of the utilized prepreg [6]</caption><thead><tr><th>Parameters 220°C</th><th>E11</th><th>E22</th><th>μ12</th><th>G12</th><th>G23</th></tr></thead><tbody><tr><th>Value</th><td>2.5 GPa</td><td>0.5 MPa</td><td>0.35</td><td>0.2 MPa</td><td>0.2 MPa</td></tr></tbody></table>

The laminas are set by taking into account their linear elastic properties and implementing Hashin's damage model [7] to study matrix and fiber failures. The parameters of the sheet constitutive model were set according to [5]. The dummy sheet used as a cover is a 2 mm thick aluminum alloy (AA-6056). The plastic behavior of sheet AA-6056 was modeled according to [5].

## Numerical model

The finite element model of the proposed SPIF process was run with the FE Abaqus/CAE commercial code. Fig. 4 shows the cross-section of the FE model assembly based on the previously described process strategy. In detail, the rotational molding tool, modeled as a rigid body, is in contact with a square aluminum blank characterized by a 200 mm side and fixed in the periphery on a steel frame, modeled as a rigid body. A Coulomb friction coefficient of 0.1 between the tool and the metal plate was set [8, 5]. The outer edge of the panel is made of PP, which is melted under the chosen process conditions, while the remaining part is made of GFRP and is subjected to hydrostatic pressure simulating the presence of pressurized fluid. A constant pressure is set under the GFRP and PP sheet, as shown in Fig. 4. A friction-free approach was used between the two slabs, which were modeled as deformable bodies using shell elements (S4R). Simpson's integration rule with 5 integration points was modeled along the thickness direction, and approximately 3000 elements for the aluminum blank and 3500 elements for the GFRP and PP sheet were used. An explicit solver, with time and mass scaling, was used to accelerate the simulation. In particular, semi-automatic mass scaling with a target time increment of 2e-6 s was implemented. The tool path was defined by three tabular amplitudes and the total simulation time was set equal to 6 s.

## Investigated process variables

A truncated cone was numerically formed. The cone is characterized by an inclination angle of 30°, a final height of 25 mm, and a base diameter of 100 mm. The effects on the quality of the formed parts, focusing on the surface quality, shape accuracy and/or local thinning of the sheet formed from GFRP and PP, were assessed by changing the pressure value on the back face of the GFRP and PP panel. Constant values of 0.01, 0.05, 0.1 and 0.2 MPa were assessed during the entire forming phase.

## FE model results

This section focuses on the analysis of the numerical results obtained from the simulations carried out on the SPIF process. Specifically, the results of the model were evaluated both in the section realized in GFRP and in the frame realized in PP. The results were evaluated in terms of formability, thickness distribution and accuracy of the shape as the pressure exerted by the fluid during the SPIF process varied, as shown in Fig. 5. In detail, in Fig. 5a is shown the back side of the GFRP plates for the four configurations studied. These analyses were performed by setting different back pressure levels, from a low back pressure of 0.01 MPa to a high back pressure of 0.2 MPa. The quasi-isotropic configuration, i.e. [0/45/-45/90]s, is characterized by a uniform deformation along the main directions that preserves the circular shape of the section as a trajectory imposed on the tool. With regard to surface defects, the wrinkles appear along the conical side with an out-of-plane deformation that has to be taken into account. Furthermore, looking at Fig. 5a, the presence of the PP frame allows for a constant thickness of the laminate with a variation in thickness, only in the portion made of PP, correlated to the imposed back pressure. In Fig. 5b, on
the other hand, the cross-section profiles, extracted from the composite and the metal plate, have been superimposed for all the back pressure configurations studied. These profiles were related to the ideal profile of the truncated cone, which is considered a reference with respect to the imposed tool path. A consistent overlap was observed for each configuration, leading to the conclusion that the low back pressure of 0.01 MPa provides adequate support to allow the composite to adhere to the metal. This can be justified considering the very low mechanical properties of GFRP at the imposed operating temperature, as previously reported in Table 2.

<figure><img src="image_1489.png" /><figcaption>Fig. 5 - Comparison of (a) thickness distribution and (b) shape accuracy for an imposed back pressure for the panel configuration studied. Looking at the Fig. from the top, the back pressure is set at 0.01 MPa to 0.2 MPa at the bottom.</figcaption></figure>

## Conclusions

CFRTPs are high strength, low density and stiffness materials. These properties make them for a wide range of applications. Even if CFRTPs are characterized by many advantages, some drawbacks have to be faced. Firstly, CFRTPs are costly to be produced and manufactured. Flexibility in CFRTPs manufacturing can result in a decrease in cost for customized applications. The SPIF is a process far to be applicable if the sheet to be formed is reinforced by long and brittle fibers. Anyway, the process peculiarities can strengthen the flexibility needed for rapid prototyping and small-scale production, opening new possibilities for the CFRTPs manufacturing industry. For that reason, in the proposed research paper, the design of a specific equipment was detailed. This equipment allows the SPIF to be employed in forming sheets made by CFRTPs with the aid of a pressurized fluid that is also used to heat the polymers maintaining a preset working temperature for the whole forming phase. The process feasibility was verified by numerical simulations for
the other hand, the cross-section profiles, extracted from the composite and the metal plate, have been superimposed for all the back pressure configurations studied. These profiles were related to the ideal profile of the truncated cone, which is considered a reference with respect to the imposed tool path. A consistent overlap was observed for each configuration, leading to the conclusion that the low back pressure of 0.01 MPa provides adequate support to allow the composite to adhere to the metal. This can be justified considering the very low mechanical properties of GFRP at the imposed operating temperature, as previously reported in Table 2.

<figure><img src="image_1493.png" /><figcaption>Fig. 5 - Comparison of (a) thickness distribution and (b) shape accuracy for an imposed back pressure for the panel configuration studied. Looking at the Fig. from the top, the back pressure is set at 0.01 MPa to 0.2 MPa at the bottom.</figcaption></figure>

## Conclusions

CFRTPs are high strength, low density and stiffness materials. These properties make them for a wide range of applications. Even if CFRTPs are characterized by many advantages, some drawbacks have to be faced. Firstly, CFRTPs are costly to be produced and manufactured. Flexibility in CFRTPs manufacturing can result in a decrease in cost for customized applications. The SPIF is a process far to be applicable if the sheet to be formed is reinforced by long and brittle fibers. Anyway, the process peculiarities can strengthen the flexibility needed for rapid prototyping and small-scale production, opening new possibilities for the CFRTPs manufacturing industry. For that reason, in the proposed research paper, the design of a specific equipment was detailed. This equipment allows the SPIF to be employed in forming sheets made by CFRTPs with the aid of a pressurized fluid that is also used to heat the polymers maintaining a preset working temperature for the whole forming phase. The process feasibility was verified by numerical simulations for
different laminate configurations. The next step of the research will be the construction of the equipment comparing the experimental results with those obtained in a simulation environment extracting useful data to improve the model as well as to optimize the process of changing the properties of the CFRTPs to be manufactured.

References

[1] S. Alwekar, R. Ogle, S. Kim, U. Vaidya, Manufacturing and characterization of continuous fiber-reinforced thermoplastic tape overmolded long fiber thermoplastic, Composites Part B: Engineering (2021) 207, 15 https://doi.org/10.1016/j.compositesb.2020.108597

[2] J. Wu, K. Zhang, D. Yang, Material extrusion additive manufacturing of recycled discontinuous carbon fibre reinforced thermoplastic composites with different fibre lengths: Through-process microstructural evolution and mechanical property loss, Additive Manufacturing (2023) 78, 25 https://doi.org/10.1016/j.addma.2023.103839

[3] G. Kajal, M.R. Tyagi, G. Kumar, A review on the effect of residual stresses in incremental sheet metal forming used in automotive and medical sectors, Mat Today Proc (2023) 78/3, 524-534 https://doi.org/10.1016/j.matpr.2022.11.235

[4] A. AL-Obaidi, A. Kunke, V. Kräusel, Hot single-point incremental forming of glass-fiber-reinforced polymer (PA6GF47) supported by hot air, J. Manuf. Proc. 43 (2019) 17-25. https://doi.org/10.1016/j.jmapro.2019.04.036

[5] R. Conte, G. Serratore, G. Ambrogio, F. Gagliardi, Numerical analyses of long fiber-reinforced polymeric sheets processed by Single Point Incremental Forming, Int. J. Adv. Manuf. Tech. 123 (2022) 1203-1214. https://doi.org/10.1007/s00170-022-10212-4

[6] Liu K, Zhang B, Xu X et al (2019) Simulation and analysis of process-induced distortions in hemispherical thermostamping for unidirectional thermoplastic composites. Polym Compos 40:1786-1800. https://doi.org/10.1002/pc.24936

[7] Hashin Z (1980) Failure criteria for unidirectional fiber composites. J Appl Mech 47:329-334. https://doi.org/10.1115/1.3153664

[8] Tayebi P, Fazli A, Asadi P, Soltanpour M (2019) Formability analysis of dissimilar friction stir welded AA 6061 and AA 5083 blanks by SPIF process. CIRP J Manuf Sci Technol 25:50-68. https://doi.org/10.1016/j.cirpj.2019.02.002
different laminate configurations. The next step of the research will be the construction of the equipment comparing the experimental results with those obtained in a simulation environment extracting useful data to improve the model as well as to optimize the process of changing the properties of the CFRTPs to be manufactured.

## References

[1] S. Alwekar, R. Ogle, S. Kim, U. Vaidya, Manufacturing and characterization of continuous fiber-reinforced thermoplastic tape overmolded long fiber thermoplastic, Composites Part B: Engineering (2021) 207, 15 https://doi.org/10.1016/j.compositesb.2020.108597

[2] J. Wu, K. Zhang, D. Yang, Material extrusion additive manufacturing of recycled discontinuous carbon fibre reinforced thermoplastic composites with different fibre lengths: Through-process microstructural evolution and mechanical property loss, Additive Manufacturing (2023) 78, 25 https://doi.org/10.1016/j.addma.2023.103839

[3] G. Kajal, M.R. Tyagi, G. Kumar, A review on the effect of residual stresses in incremental sheet metal forming used in automotive and medical sectors, Mat Today Proc (2023) 78/3, 524-534 https://doi.org/10.1016/j.matpr.2022.11.235

[4] A. AL-Obaidi, A. Kunke, V. Kräusel, Hot single-point incremental forming of glass-fiber-reinforced polymer (PA6GF47) supported by hot air, J. Manuf. Proc. 43 (2019) 17-25. https://doi.org/10.1016/j.jmapro.2019.04.036

[5] R. Conte, G. Serratore, G. Ambrogio, F. Gagliardi, Numerical analyses of long fiber-reinforced polymeric sheets processed by Single Point Incremental Forming, Int. J. Adv. Manuf. Tech. 123 (2022) 1203-1214. https://doi.org/10.1007/s00170-022-10212-4

[6] Liu K, Zhang B, Xu X et al (2019) Simulation and analysis of process-induced distortions in hemispherical thermostamping for unidirectional thermoplastic composites. Polym Compos 40:1786-1800. https://doi.org/10.1002/pc.24936

[7] Hashin Z (1980) Failure criteria for unidirectional fiber composites. J Appl Mech 47:329-334. https://doi.org/10.1115/1.3153664

[8] Tayebi P, Fazli A, Asadi P, Soltanpour M (2019) Formability analysis of dissimilar friction stir welded AA 6061 and AA 5083 blanks by SPIF process. CIRP J Manuf Sci Technol 25:50-68. https://doi.org/10.1016/j.cirpj.2019.02.002
# Formability analysis of incrementally hole-flanged parts using different tool sizes

BORREGO-PUCHE Marcos¹,ª, PALOMO-VÁZQUEZ David¹,ᵇ,
MORALES-PALMA Domingo¹,ᶜ, MARTÍNEZ-DONAIRE Andres Jesus¹,ᵈ*,
CENTENO Gabriel¹,ᵉ, VALLELLANO Carpoforo¹,ᵉ

¹Department of Mechanical and Manufacturing Engineering, University of Sevilla, Spain

ªmborrego@us.es, ᵇdpalomoi@us.es, ᶜdmpalma@us.es,

ᵈajmd@us.es, ᶜgaceba@us.es, ᶠcarpofor@us.es

**Keywords:** Sheet Metal Forming, SPIF, Flanging, Formability, Flangeability

**Abstract.** This contribution analyses the formability of incrementally hole flanged parts using different tool radii (10, 20 and 47.9 mm). The smallest radius (10 mm) can induce full incremental benefits in the hole-flanged specimen, whereas the biggest one generates a formability behaviour closer to a conventional press forming. In the first case, the necking process is clearly delayed, being the development of a fracture in the middle of the wall flange the mechanism that controls the failure of the specimen. In contrast, in the second case, failure is governed by the appearance and development of a neck at the edge of the flange, which ends in material fracture. The intermediate tool radius (20 mm) shows midway features between a conventional and a fully incrementally formed specimen. The location and fracture mode of the flanged parts with different tool sizes are experimentally analysed and discussed within the Forming Limit Diagram (FLD) using the optical strain measurement system ARGUS®.

**Introduction**

Hole flanges are commonly used in industry to provide stiffness or support for joining to other metallic parts. Usually performed by conventional press forming, it requires robust machinery and dedicated setups. For this reason, only a great number of operations justify the investment in this forming process. In recent decades, the use of incremental forming processes has been extended, particularly its simplest version, known as Single Point Incremental Forming (SPIF). This relative new forming process, whose first patents date back to 1967, not only addresses the disadvantages mentioned above, answering the increasing demand of flexible and cost-effective tooling, but also has a great advantage over conventional forming processes from the formability point of view. In this sense, the paper by Emmens and van den Boogaard [1] collects the most significant contributions that have been proposed to explain plastic deformation of incremental forming processes above the Forming Limit Curve (FLC) at necking. Among them, Silva et al. [2] proposed fracture as the key failure mechanism and, therefore, that localised necking typical of conventional sheet metal forming is inhibited in SPIF. Lately, new explanations for the increase of the FLC above the one obtained by conventional Nakazima tests have been suggested. Silva et al. [3] pointed out that it could be due to the stabilising effect of dynamic bending under tension. Authors carried out experimental work on AA1050-H111 with a series of truncated pyramidal and conical shapes under SPIF conditions for a range of tool sizes from 4 to 25 mm radius. Martínez-Donaire et al. [4] analysed the role of the level of average stress triaxiality attained in incremental processes, in the light of experimental and numerical results in hole flanging operations by single-stage SPIF on AA7075-O sheets.

In addition to the number of authors studying this phenomenon from the forces / stress point of view, many other authors maintain that the reason for the improvement in formability lies in the

<figure><img src="image_1490.png" /></figure>
# Formability analysis of incrementally hole-flanged parts using different tool sizes

BORREGO-PUCHE Marcos¹,ª, PALOMO-VÁZQUEZ David¹,ᵇ,
MORALES-PALMA Domingo¹,ᶜ, MARTÍNEZ-DONAIRE Andres Jesus¹,ᵈ*,
CENTENO Gabriel¹,ᵉ, VALLELLANO Carpoforo¹,ᵉ

¹Department of Mechanical and Manufacturing Engineering, University of Sevilla, Spain

ªmborrego@us.es, ᵇdpalomoi@us.es, ᶜdmpalma@us.es,

ᵈajmd@us.es, ᶜgaceba@us.es, ᶠcarpofor@us.es

**Keywords:** Sheet Metal Forming, SPIF, Flanging, Formability, Flangeability

**Abstract.** This contribution analyses the formability of incrementally hole flanged parts using different tool radii (10, 20 and 47.9 mm). The smallest radius (10 mm) can induce full incremental benefits in the hole-flanged specimen, whereas the biggest one generates a formability behaviour closer to a conventional press forming. In the first case, the necking process is clearly delayed, being the development of a fracture in the middle of the wall flange the mechanism that controls the failure of the specimen. In contrast, in the second case, failure is governed by the appearance and development of a neck at the edge of the flange, which ends in material fracture. The intermediate tool radius (20 mm) shows midway features between a conventional and a fully incrementally formed specimen. The location and fracture mode of the flanged parts with different tool sizes are experimentally analysed and discussed within the Forming Limit Diagram (FLD) using the optical strain measurement system ARGUS®.

**Introduction**

Hole flanges are commonly used in industry to provide stiffness or support for joining to other metallic parts. Usually performed by conventional press forming, it requires robust machinery and dedicated setups. For this reason, only a great number of operations justify the investment in this forming process. In recent decades, the use of incremental forming processes has been extended, particularly its simplest version, known as Single Point Incremental Forming (SPIF). This relative new forming process, whose first patents date back to 1967, not only addresses the disadvantages mentioned above, answering the increasing demand of flexible and cost-effective tooling, but also has a great advantage over conventional forming processes from the formability point of view. In this sense, the paper by Emmens and van den Boogaard [1] collects the most significant contributions that have been proposed to explain plastic deformation of incremental forming processes above the Forming Limit Curve (FLC) at necking. Among them, Silva et al. [2] proposed fracture as the key failure mechanism and, therefore, that localised necking typical of conventional sheet metal forming is inhibited in SPIF. Lately, new explanations for the increase of the FLC above the one obtained by conventional Nakazima tests have been suggested. Silva et al. [3] pointed out that it could be due to the stabilising effect of dynamic bending under tension. Authors carried out experimental work on AA1050-H111 with a series of truncated pyramidal and conical shapes under SPIF conditions for a range of tool sizes from 4 to 25 mm radius. Martínez-Donaire et al. [4] analysed the role of the level of average stress triaxiality attained in incremental processes, in the light of experimental and numerical results in hole flanging operations by single-stage SPIF on AA7075-O sheets.

In addition to the number of authors studying this phenomenon from the forces / stress point of view, many other authors maintain that the reason for the improvement in formability lies in the

<figure><img src="image_1494.png" /></figure>
microstructure [5-6]. Mosecker et al. [5] analysed the microstructural evolution with the increase in plastic strain under different parameters for Ti6Al4V sheet incremental forming of Ti6Al4V sheets. More recently, Chang et al. [6] characterised grain fragmentation, orientation, void deformation, and deformation dislocation by EBSD X-ray, SEM and TEM, concerning the incremental deformation of different regions around the contact area in truncated cone parts of AA5052-H32.

This paper presents an experimental investigation focused on analysing formability limits and failure mechanism in hole flanging by single-stage SPIF with hemispherical forming tools of increasing size (radii of 10, 20 and 47.9 mm) up to the target hole size (47.9 mm), where this limit situation corresponds in fact to a conventional press forming process. Results are analysed in terms of Limiting Forming Ratio (LFR) and fractographies of tested specimens to accurately assess the failure mechanism and strain distributions in the FLD.

## Experimental procedure

A series of experimental hole flanging tests by single-stage SPIF with different pre-cut holes (do) and the same predefined target geometry were carried out on AA7075-O sheets of 1.6 mm thickness using hemispherical tools of different radii. The conventional press forming test corresponds to a limiting case of SPIF when the tool diameter and the final flange hole diameter match.

<figure><img src="image_1491.png" /><figcaption>Fig. 1. Schema of hemispherical tools and setup used in the hole flanging experiments by SPIF.</figcaption></figure>

The backing plate radius was 50 mm. All tests were carried out to obtain flanges with an inner radius of 47.9 mm considering the backing plate radius, the sheet thickness and a sheet-to-die clearance of 0.5 mm. The selected tool radii were 10, 20 and 47.9 mm. Fig. 1 presents a schema of the 10 and 20 mm radius tools and the experimental setup for single-stage SPIF. Fig. 2 shows the Erichsen machine for conventional press forming along with a schematic of the conventional hole flanging operation using the 47.9 mm punch radius.

An Emco Umill 630 machine was the selected machine for hole flanging tests by SPIF. The tool trajectory was programmed with CATIA®, following a 0.2 mm pitch helix with a feed rate of 1000 mm/min. No spindle rotation was used. The sheet-tool contact was sufficiently lubricated during the tests. For conventional forming tests, the Erichsen machine was employed under the recommendation of the standard ISO 12004-2 in terms of punch speed and tribological conditions. It should be noted that the forces reached for the 47.9 mm radius punch, i.e., in conventional forming, were an order of magnitude greater than in SPIF, exceeding the maximum force in the Z direction allowed by the Emco CNC machine.
microstructure [5-6]. Mosecker et al. [5] analysed the microstructural evolution with the increase in plastic strain under different parameters for Ti6Al4V sheet incremental forming of Ti6Al4V sheets. More recently, Chang et al. [6] characterised grain fragmentation, orientation, void deformation, and deformation dislocation by EBSD X-ray, SEM and TEM, concerning the incremental deformation of different regions around the contact area in truncated cone parts of AA5052-H32.

This paper presents an experimental investigation focused on analysing formability limits and failure mechanism in hole flanging by single-stage SPIF with hemispherical forming tools of increasing size (radii of 10, 20 and 47.9 mm) up to the target hole size (47.9 mm), where this limit situation corresponds in fact to a conventional press forming process. Results are analysed in terms of Limiting Forming Ratio (LFR) and fractographies of tested specimens to accurately assess the failure mechanism and strain distributions in the FLD.

## Experimental procedure

A series of experimental hole flanging tests by single-stage SPIF with different pre-cut holes (do) and the same predefined target geometry were carried out on AA7075-O sheets of 1.6 mm thickness using hemispherical tools of different radii. The conventional press forming test corresponds to a limiting case of SPIF when the tool diameter and the final flange hole diameter match.

<figure><img src="image_1495.png" /><figcaption>Fig. 1. Schema of hemispherical tools and setup used in the hole flanging experiments by SPIF.</figcaption></figure>

The backing plate radius was 50 mm. All tests were carried out to obtain flanges with an inner radius of 47.9 mm considering the backing plate radius, the sheet thickness and a sheet-to-die clearance of 0.5 mm. The selected tool radii were 10, 20 and 47.9 mm. Fig. 1 presents a schema of the 10 and 20 mm radius tools and the experimental setup for single-stage SPIF. Fig. 2 shows the Erichsen machine for conventional press forming along with a schematic of the conventional hole flanging operation using the 47.9 mm punch radius.

An Emco Umill 630 machine was the selected machine for hole flanging tests by SPIF. The tool trajectory was programmed with CATIA®, following a 0.2 mm pitch helix with a feed rate of 1000 mm/min. No spindle rotation was used. The sheet-tool contact was sufficiently lubricated during the tests. For conventional forming tests, the Erichsen machine was employed under the recommendation of the standard ISO 12004-2 in terms of punch speed and tribological conditions. It should be noted that the forces reached for the 47.9 mm radius punch, i.e., in conventional forming, were an order of magnitude greater than in SPIF, exceeding the maximum force in the Z direction allowed by the Emco CNC machine.
<figure><img src="image_1492.png" /><figcaption>Fig. 2. Erichsen machine setup and schema of conventional hole-flanging process.</figcaption></figure>

## Results and discussion

This section presents and discusses the achieved Limiting Forming Ratio (LFR), fractographies of failed specimens, and strain analysis in the FLD.

Limiting Forming Ratio (LFR): In all tests where a failure-free flange was produced, the HER (Hole Expansion Ratio) was calculated as the $d_f/d_o$ ratio. Then, the measurement of formability was computed using the concept of LFR first introduced by Huang et al. [7,8], as the maximum HER attained by the material:

$$LFR \equiv HER_{max} \equiv \frac{d_f}{d_o}|_{max} \qquad (1)$$

where $d_f$ is the inner diameter of the produced hole-flanged part. A fixed value $d_f = 95.8$ mm has been used.

Table 1 summarises the results of the experimental campaign carried out for different pre-cut holes and tool radii. Table 2 presents LFR values achieved for each tool radius. It is worth noting that the value of the LFR for 20 mm tool radius is the highest achieved, although this tool size is in between the other two tests.

<table><caption>Table 1. Results of experimental hole flanging tests by single-stage SPIF and conventional press forming. 'X' stands for a failed flange and 'O' for a successful flange.</caption><thead><tr><th rowspan="2">Hole flanging</th><th rowspan="2">Tool radius [mm]</th><th colspan="9">Initial pre-cut hole diameter, d<sub>o</sub> [mm]</th></tr><tr><th>52</th><th>53</th><th>54</th><th>55</th><th>56</th><th>57</th><th>58</th><th>59</th><th>60</th><th>61</th></tr></thead><tbody><tr><td>SPIF</td><td>10</td><td></td><td></td><td></td><td>X</td><td>X</td><td>X</td><td>O</td><td></td><td></td><td></td></tr><tr><td>SPIF</td><td>20</td><td>X</td><td></td><td>X</td><td>O</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Press forming</td><td>47.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td>X</td><td>X</td><td>O</td><td></td></tr></tbody></table>

<table><caption>Table 2. LFR values in hole flanging by single-stage SPIF and conventional press forming.</caption><thead><tr><th>Hole flanging</th><th>Tool radius [mm]</th><th>d<sub>o,min</sub> [mm]</th><th>LFR</th></tr></thead><tbody><tr><td>SPIF</td><td>10</td><td>58</td><td>1.65</td></tr><tr><td>SPIF</td><td>20</td><td>55</td><td>1.72</td></tr><tr><td>Press forming</td><td>47.9</td><td>61</td><td>1.57</td></tr></tbody></table>
<figure><img src="image_1496.png" /><figcaption>Fig. 2. Erichsen machine setup and schema of conventional hole-flanging process.</figcaption></figure>

## Results and discussion

This section presents and discusses the achieved Limiting Forming Ratio (LFR), fractographies of failed specimens, and strain analysis in the FLD.

Limiting Forming Ratio (LFR): In all tests where a failure-free flange was produced, the HER (Hole Expansion Ratio) was calculated as the $d_f/d_o$ ratio. Then, the measurement of formability was computed using the concept of LFR first introduced by Huang et al. [7,8], as the maximum HER attained by the material:

$$LFR = HER_{max} = \frac{d_f}{d_o} \bigg|_{max} \qquad (1)$$

where $d_f$ is the inner diameter of the produced hole-flanged part. A fixed value $d_f = 95.8$ mm has been used.

Table 1 summarises the results of the experimental campaign carried out for different pre-cut holes and tool radii. Table 2 presents LFR values achieved for each tool radius. It is worth noting that the value of the LFR for 20 mm tool radius is the highest achieved, although this tool size is in between the other two tests.

<table><caption>Table 1. Results of experimental hole flanging tests by single-stage SPIF and conventional press forming. 'X' stands for a failed flange and 'O' for a successful flange.</caption><thead><tr><th rowspan="2">Hole flanging</th><th rowspan="2">Tool radius [mm]</th><th colspan="9">Initial pre-cut hole diameter, d<sub>o</sub> [mm]</th></tr><tr><th>52</th><th>53</th><th>54</th><th>55</th><th>56</th><th>57</th><th>58</th><th>59</th><th>60</th><th>61</th></tr></thead><tbody><tr><td>SPIF</td><td>10</td><td></td><td></td><td></td><td>X</td><td>X</td><td>X</td><td>O</td><td></td><td></td><td></td></tr><tr><td>SPIF</td><td>20</td><td>X</td><td></td><td>X</td><td>O</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Press forming</td><td>47.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td>X</td><td>X</td><td>O</td><td></td></tr></tbody></table>

<table><caption>Table 2. LFR values in hole flanging by single-stage SPIF and conventional press forming.</caption><thead><tr><th>Hole flanging</th><th>Tool radius [mm]</th><th>d<sub>o,min</sub> [mm]</th><th>LFR</th></tr></thead><tbody><tr><td>SPIF</td><td>10</td><td>58</td><td>1.65</td></tr><tr><td>SPIF</td><td>20</td><td>55</td><td>1.72</td></tr><tr><td>Press forming</td><td>47.9</td><td>61</td><td>1.57</td></tr></tbody></table>
**Fractographies:** The samples were carefully examined under the microscope and images of the failure were taken at x20 magnification to clearly see the failure mode. For the smallest tool radius (Fig. 3a), the failure occurred in the middle of the wall along the circumferential direction, while the others presented a failure at the flange edge. As expected, specimens tested by SPIF using the smallest tool radius presented fracture with a very incipient neck (i.e., almost inhibited necking), in contrast to specimens tested by conventional press forming, which showed fracture developed from previous necking (Fig. 3c). In the 20 mm radius tool test by SPIF, a fracture with previous necking was also observed (Fig. 3b).

<figure><img src="image_1493.png" /><figcaption>Fig. 3. Failed tested specimens and fractographies with x20 magnification: (a) SPIF with 10 mm tool radius, (b) SPIF with 20 mm tool radius, and (c) conventional press forming.</figcaption></figure>

**Strain analysis:** Deformations were measured using the ARGUS® 3D optical system from a pattern of circular dots previously electroetched at the outer surface of the specimen. This system is unable to provide information near the free boundaries, that is, in fractured areas or at the edge of the hole. In such a case, the strains must be calculated from direct measurement of thickness and circumferential strains and assuming material volume constancy.

Fig. 4 depicts the evolution of the major and minor strain distributions measured on the outer surface of the specimens within the Forming Limit Diagram (FLD). The FLC (Forming Limit Curve at necking) and FFL (Fracture Forming Limit) for the material obtained in previous research [9] are also shown. The FLC was obtained following the time-dependent methodology proposed by Martínez-Donaire et al. [10] and the FFL was estimated by the procedure proposed by Cristino et al. [11]. Fig. 4 shows the contour map of the failed specimens. The location of the highest major strains, where the failure appeared, is indicated.
**Fractographies:** The samples were carefully examined under the microscope and images of the failure were taken at x20 magnification to clearly see the failure mode. For the smallest tool radius (Fig. 3a), the failure occurred in the middle of the wall along the circumferential direction, while the others presented a failure at the flange edge. As expected, specimens tested by SPIF using the smallest tool radius presented fracture with a very incipient neck (i.e., almost inhibited necking), in contrast to specimens tested by conventional press forming, which showed fracture developed from previous necking (Fig. 3c). In the 20 mm radius tool test by SPIF, a fracture with previous necking was also observed (Fig. 3b).

<figure><img src="image_1497.png" /><figcaption>Fig. 3. Failed tested specimens and fractographies with x20 magnification: (a) SPIF with 10 mm tool radius, (b) SPIF with 20 mm tool radius, and (c) conventional press forming.</figcaption></figure>

**Strain analysis:** Deformations were measured using the ARGUS® 3D optical system from a pattern of circular dots previously electroetched at the outer surface of the specimen. This system is unable to provide information near the free boundaries, that is, in fractured areas or at the edge of the hole. In such a case, the strains must be calculated from direct measurement of thickness and circumferential strains and assuming material volume constancy.

Fig. 4 depicts the evolution of the major and minor strain distributions measured on the outer surface of the specimens within the Forming Limit Diagram (FLD). The FLC (Forming Limit Curve at necking) and FFL (Fracture Forming Limit) for the material obtained in previous research [9] are also shown. The FLC was obtained following the time-dependent methodology proposed by Martínez-Donaire et al. [10] and the FFL was estimated by the procedure proposed by Cristino et al. [11]. Fig. 4 shows the contour map of the failed specimens. The location of the highest major strains, where the failure appeared, is indicated.
<figure><img src="image_1494.png" /><figcaption>Fig. 4. Major-minor strain distribution of the outer surface of failed specimens for 10 mm, 20 mm, and 47.9 mm tool radii in the Forming Limit Diagram of AA7075-O, 1.6 mm thickness.</figcaption></figure>

As mentioned above, the failure location was completely different despite the incremental nature of the process using 10 and 20 mm tool radii. A fracture was observed after a delayed or even suppressed necking in the middle of the wall using 10 mm tool radius. Instead, a fracture after a more severe necking at the flange edge occurred with the 20 mm tool radius, which is the same failure mechanism as in conventional flanging by press forming.

Regarding the location of the fracture using 20 mm tool radius, a priori it could be thought that the SPIF test using this tool is very similar to the conventional press forming process. Moreover, the shape of the strain distribution in both cases is very similar, as can be seen in the FLD depicted in Fig. 4. Both strain distributions present values close to plane strain stretching in the middle part of the flange wall, clearly between the uniaxial stretching and the biaxial stretching observed in the other tests.

However, there are clear differences between both processes. On the one hand, as can be seen in Fig. 4, the strains obtained by SPIF with a tool radius of 20 mm far exceed not only those obtained by conventional forming with a 47.9 mm punch radius, but also the FLC curve. This means that the conventional FLC is not applicable for SPIF even if the failure mechanism is necking. On the other hand, it should be noted that the strains of specimens tested by conventional forming slightly exceed the FLC (see Fig. 4) because of the bending induced in the material with respect to the Nakazima tests and the inherent experimental scatter, as discussed in previous research [12].

The hole flanging process by SPIF was proposed to address the drawbacks of conventional press forming, the enormous forces involved in the process, and the dedicated tooling. Traditionally, SPIF processes use small size tools (under 10 mm radius), but probably to the particular geometry of the test, larger tool radius can be employed successfully, producing a combination of failure modes and strain distribution in between conventional press forming and SPIF.
<figure><img src="image_1498.png" /><figcaption>Fig. 4. Major-minor strain distribution of the outer surface of failed specimens for 10 mm, 20 mm, and 47.9 mm tool radii in the Forming Limit Diagram of AA7075-O, 1.6 mm thickness.</figcaption></figure>

As mentioned above, the failure location was completely different despite the incremental nature of the process using 10 and 20 mm tool radii. A fracture was observed after a delayed or even suppressed necking in the middle of the wall using 10 mm tool radius. Instead, a fracture after a more severe necking at the flange edge occurred with the 20 mm tool radius, which is the same failure mechanism as in conventional flanging by press forming.

Regarding the location of the fracture using 20 mm tool radius, a priori it could be thought that the SPIF test using this tool is very similar to the conventional press forming process. Moreover, the shape of the strain distribution in both cases is very similar, as can be seen in the FLD depicted in Fig. 4. Both strain distributions present values close to plane strain stretching in the middle part of the flange wall, clearly between the uniaxial stretching and the biaxial stretching observed in the other tests.

However, there are clear differences between both processes. On the one hand, as can be seen in Fig. 4, the strains obtained by SPIF with a tool radius of 20 mm far exceed not only those obtained by conventional forming with a 47.9 mm punch radius, but also the FLC curve. This means that the conventional FLC is not applicable for SPIF even if the failure mechanism is necking. On the other hand, it should be noted that the strains of specimens tested by conventional forming slightly exceed the FLC (see Fig. 4) because of the bending induced in the material with respect to the Nakazima tests and the inherent experimental scatter, as discussed in previous research [12].

The hole flanging process by SPIF was proposed to address the drawbacks of conventional press forming, the enormous forces involved in the process, and the dedicated tooling. Traditionally, SPIF processes use small size tools (under 10 mm radius), but probably to the particular geometry of the test, larger tool radius can be employed successfully, producing a combination of failure modes and strain distribution in between conventional press forming and SPIF.
## Conclusions and future works

A series of tests have been performed under SPIF conditions and conventional press forming to study the evolution of the strain distribution on the outer surface of the specimens and the location of the failure. The main conclusions can be summarised as follows:

* The LFR was higher in single-stage SPIF with a 20 mm tool radius than the one using a 10 mm tool radius and the conventional forming with a 47.9 mm punch radius. This suggests that a threshold tool radius must exist that maximises the LFR in the flanging process.

* The same failure mechanism (onset of necking and subsequent fracture) and the same location (flange edge) were found in both hole flanging operations by single-stage SPIF with a 20 mm tool radius and conventional flanging. Besides, the strain distributions of both processes have the same shape in the FLD.

* Nevertheless, the incremental effect of the SPIF process is clearly appreciated in the FLD by strains well above the FLC for necking. This indicates that the conventional FLC is not applicable for SPIF even if the failure mechanism is necking.

Next steps to complete this study are currently in progress:

* Development of a numerical model to accurately predict the stress and strain distribution during the flanging process.

* Analysis of formability limits and failure mechanism in the average stress triaxiality versus the equivalent plastic strain space in order to elucidate the transition from incremental to conventional forming of hole-flanged parts.

## Acknowledgements

The authors acknowledge the funding provided by Grant PID2021-125934OB-I00 financed by MCIN/AEI/10.13039/501100011033 and by ERDF 'A way of making Europe' (EU).

## References

[1] Emmens, WC, van den Boogaard, AH., An overview of stabilizing deformation mechanisms in incremental sheet forming. Journal of Materials Processing Technology 209 (2009)3688-3695.
https://doi.org/10.1016/j.jmatprotec.2008.10.003

[2] Silva MB, Skjoedt M, Atkins AG, Bay N, Martins PAF. Single point incremental forming & formability/failure diagrams. J Strain Anal Eng Des 43 (2008) 15-36.
https://doi.org/10.1243/03093247JSA340

[3] Silva, MB., Nielsen, PS., Bay, N., Martins, PAF., Failure mechanisms in single point incremental forming of metals. International Journal of Advanced Manufacturing Technology 56 (2011) 893-903.
https://doi.org/10.1007/s00170-011-3254-1

[4] Martínez-Donaire, A.J., Borrego, M., Morales-Palma, D., Centeno, G., Vallellano, C.: Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF. Int. J. Mech. Sci. 151, 76-84 (2019).
https://doi.org/10.1016/j.ijmecsci.2018.11.006

[5] Mosecker, L., Gottmann, A., Saeed-Akbari, A., Bleck, W., Bambach, M., Hirt, G., Deformation mechanisms of Ti6Al4V sheet material during the incremental sheet forming with laser heating. Key Eng. Mater. 549 (2013) 372-380.
https://doi.org/10.4028/www.scientific.net/KEM.549.372

[6] Chang, Z., Yang, M., Chen, J., 2. Experimental investigations on deformation characteristics in microstructure level during incremental forming of AA5052 sheet. J. Mater. Process. Technol. 291 (2001) 117006
## Conclusions and future works

A series of tests have been performed under SPIF conditions and conventional press forming to study the evolution of the strain distribution on the outer surface of the specimens and the location of the failure. The main conclusions can be summarised as follows:

* The LFR was higher in single-stage SPIF with a 20 mm tool radius than the one using a 10 mm tool radius and the conventional forming with a 47.9 mm punch radius. This suggests that a threshold tool radius must exist that maximises the LFR in the flanging process.

* The same failure mechanism (onset of necking and subsequent fracture) and the same location (flange edge) were found in both hole flanging operations by single-stage SPIF with a 20 mm tool radius and conventional flanging. Besides, the strain distributions of both processes have the same shape in the FLD.

* Nevertheless, the incremental effect of the SPIF process is clearly appreciated in the FLD by strains well above the FLC for necking. This indicates that the conventional FLC is not applicable for SPIF even if the failure mechanism is necking.

Next steps to complete this study are currently in progress:

* Development of a numerical model to accurately predict the stress and strain distribution during the flanging process.

* Analysis of formability limits and failure mechanism in the average stress triaxiality versus the equivalent plastic strain space in order to elucidate the transition from incremental to conventional forming of hole-flanged parts.

## Acknowledgements

The authors acknowledge the funding provided by Grant PID2021-125934OB-I00 financed by MCIN/AEI/10.13039/501100011033 and by ERDF 'A way of making Europe' (EU).

## References

[1] Emmens, WC, van den Boogaard, AH., An overview of stabilizing deformation mechanisms in incremental sheet forming. Journal of Materials Processing Technology 209 (2009)3688–3695.
https://doi.org/10.1016/j.jmatprotec.2008.10.003

[2] Silva MB, Skjoedt M, Atkins AG, Bay N, Martins PAF. Single point incremental forming & formability/failure diagrams. J Strain Anal Eng Des 43 (2008) 15–36.
https://doi.org/10.1243/03093247JSA340

[3] Silva, MB., Nielsen, PS., Bay, N., Martins, PAF., Failure mechanisms in single point incremental forming of metals. International Journal of Advanced Manufacturing Technology 56 (2011) 893-903.
https://doi.org/10.1007/s00170-011-3254-1

[4] Martínez-Donaire, A.J., Borrego, M., Morales-Palma, D., Centeno, G., Vallellano, C.: Analysis of the influence of stress triaxiality on formability of hole-flanging by single-stage SPIF. Int. J. Mech. Sci. 151, 76–84 (2019).
https://doi.org/10.1016/j.ijmecsci.2018.11.006

[5] Mosecker, L., Gottmann, A., Saeed-Akbari, A., Bleck, W., Bambach, M., Hirt, G., Deformation mechanisms of Ti6Al4V sheet material during the incremental sheet forming with laser heating. Key Eng. Mater. 549 (2013) 372–380.
https://doi.org/10.4028/www.scientific.net/KEM.549.372

[6] Chang, Z., Yang, M., Chen, J., 2. Experimental investigations on deformation characteristics in microstructure level during incremental forming of AA5052 sheet. J. Mater. Process. Technol. 291 (2001) 117006
[7] Huang, Y.M., Chien, K.H. Influence of the punch profile on the limitation of formability in the hole-flanging process. Journal of Materials Processing Technology 113 (2001) 720-724. https://doi.org/10.1016/S0924-0136(01)00597-0

[8] Huang, Y.M., Chien, K.H. The formability limitation of the hole-flanging process. Journal of Materials Processing Technology 117 (2001) 43-51. https://doi.org/10.1016/S0924-0136(01)01060-3

[9] Borrego, M., Morales-Palma, D., Martinez-Donaire, A.J., Centeno, G., Vallellano, C., Experimental study of hole-flanging by single-stage incremental sheet forming. Journal of Materials Processing Technology 237 (2016) pp. 320-330. https://doi.org/10.1016/j.jmatprotec.2016.06.026

[10] Martinez-Donaire, A.J., Garcia-Lomas, F.J., Vallellano, C., New approaches to detect the onset of localised necking in sheets under through thickness strain gradients. Materials and Design 57 (2014) 135-145. https://doi.org/10.1016/j.matdes.2014.01.012

[11] Cristino, V., Silva, M. B., Wong, P., Martins, P.A.F. Determining the fracture forming limits in sheet metal forming: A technical note. The Journal of Strain Analysis for Engineering Design. 52 (2017). https://doi.org/10.1177/0309324717727443

[12] Borrego, M., Morales-Palma, D., Martínez-Donaire, A.J., Centeno, G., Vallellano, C., Analysis of formability in conventional hole flanging of AA7075-O sheets: punch edge radius effect and limitations of the FLC. Int J Mater Form 13, 303-316 (2020). https://doi.org/10.1007/s12289-019-01487-2
[7] Huang, Y.M., Chien, K.H. Influence of the punch profile on the limitation of formability in the hole-flanging process. Journal of Materials Processing Technology 113 (2001) 720-724. https://doi.org/10.1016/S0924-0136(01)00597-0

[8] Huang, Y.M., Chien, K.H. The formability limitation of the hole-flanging process. Journal of Materials Processing Technology 117 (2001) 43-51. https://doi.org/10.1016/S0924-0136(01)01060-3

[9] Borrego, M., Morales-Palma, D., Martinez-Donaire, A.J., Centeno, G., Vallellano, C., Experimental study of hole-flanging by single-stage incremental sheet forming. Journal of Materials Processing Technology 237 (2016) pp. 320-330. https://doi.org/10.1016/j.jmatprotec.2016.06.026

[10] Martinez-Donaire, A.J., Garcia-Lomas, F.J., Vallellano, C., New approaches to detect the onset of localised necking in sheets under through thickness strain gradients. Materials and Design 57 (2014) 135-145. https://doi.org/10.1016/j.matdes.2014.01.012

[11] Cristino, V., Silva, M. B., Wong, P., Martins, P.A.F. Determining the fracture forming limits in sheet metal forming: A technical note. The Journal of Strain Analysis for Engineering Design. 52 (2017). https://doi.org/10.1177/0309324717727443

[12] Borrego, M., Morales-Palma, D., Martínez-Donaire, A.J., Centeno, G., Vallellano, C., Analysis of formability in conventional hole flanging of AA7075-O sheets: punch edge radius effect and limitations of the FLC. Int J Mater Form 13, 303-316 (2020). https://doi.org/10.1007/s12289-019-01487-2
# Numerical analysis of flanging using tailored rubber pad forming on AA7075-O sheets

BORREGO-PUCHE Marcos¹,ª, PALOMO-VÁZQUEZ David¹,ᵇ, MORALES-PALMA Domingo¹,ᶜ*, MARTÍNEZ-DONAIRE Andres Jesus¹,ᵈ, ROSA-SAINZ Ana¹,ᵉ, CENTENO Gabriel¹,ᵉ and VALLELLANO Carpoforo¹,ᵉ

¹Dpt. Mechanical and Manufacturing Engineering, University of Sevilla, Spain

ªmborrego@us.es, ᵇdpalomo1@us.es, ᶜdmpalma@us.es, ᵈajmd@us.es, ᵉarosa@us.es, ᵃgaceba@us.es, ᵇcarpofor@us.es

**Keywords:** Sheet Metal Forming, Rubber Pad Forming, Flanging, Flangeability

**Abstract.** The flanging of metal sheets is extensively used in the automotive and aeronautical industries to provide rigidity or support for subsequent assembly. Flanging by rubber pad forming is one of the most common processes for small and medium batch production. Flanges with non-linear bending lines are exposed to severe conditions that significantly hinder our comprehension of the geometrical, material, and process factors associated with flange formability (i.e., flangeability). This work presents a numerical study of the flanging process by a tailored rubber pad of hollow AA7075-O parts with continuous concave and convex flanges. The flangeability limits, the geometric capabilities of the forming process, and the deformation mechanisms of stretched and shrunk flanges as well as in the transition zone between them are analysed.

**Introduction**

The flanging process is widely established in the automotive and aeronautical industries to provide stiffness or support for further assembly in sheet metal parts. This consists of bending, usually at 90°, the perimeter of the part along a given line. Regarding the curvature of the bending line, three elemental types of flanges can be distinguished in: straight, concave, or convex flange. In concave flange, also referred to as stretch flange, the material is subjected to a combination of bending and stretching. The most likely mode of failure is localized necking and/or ductile fracture. And in convex flange, also named shrink flange, the material withstands bending and compression, being the appearance of wrinkling the expected mode of failure. Different combinations of these elemental flanges are also common in industrial practice.

Conventional flanging used in medium- or small-batch production, as usual in the aeronautical industry, is mainly performed by rubber pad forming and hydroforming. Despite their technical importance, the conventional flanging processes are subjected to strong restrictions that greatly limit the process. Thus, the interest of scientists and technicians in understanding the geometric, material and process parameters that limit the formability of the flange (i.e., flangeability) in industrial practice is not surprising [1-4].

This work presents a numerical study of flanging hollow 7075-O aluminium alloy sheet parts with continuous concave and convex flanges by rubber pad forming. The objective is to evaluate the forming capabilities of the process to manufacture combined stretch and shrink flanges. The preliminary numerical results show severe difficulties to form the flanges of the proposed specimen as well as excessive forces. The use of tailored rubber pads is required to better distribute pressure, improve flange deformation, and reduce overall forces. Flangeability limits, geometric capabilities of the forming process and deformation mechanisms of stretch and shrink flanges, as well as in the transition zone between them, are analysed.

<figure><img src="image_1495.png" /></figure>
# Numerical analysis of flanging using tailored rubber pad forming on AA7075-O sheets

BORREGO-PUCHE Marcos¹,ª, PALOMO-VÁZQUEZ David¹,ᵇ, MORALES-PALMA Domingo¹,ᶜ*, MARTÍNEZ-DONAIRE Andres Jesus¹,ᵈ, ROSA-SAINZ Ana¹,ᵉ, CENTENO Gabriel¹,ᵉ and VALLELLANO Carpoforo¹,ᵉ

¹Dpt. Mechanical and Manufacturing Engineering, University of Sevilla, Spain

ªmborrego@us.es, ᵇdpalomo1@us.es, ᶜdmpalma@us.es, ᵈajmd@us.es, ᵉarosa@us.es, ᵃgaceba@us.es, ᵇcarpofor@us.es

**Keywords:** Sheet Metal Forming, Rubber Pad Forming, Flanging, Flangeability

**Abstract.** The flanging of metal sheets is extensively used in the automotive and aeronautical industries to provide rigidity or support for subsequent assembly. Flanging by rubber pad forming is one of the most common processes for small and medium batch production. Flanges with non-linear bending lines are exposed to severe conditions that significantly hinder our comprehension of the geometrical, material, and process factors associated with flange formability (i.e., flangeability). This work presents a numerical study of the flanging process by a tailored rubber pad of hollow AA7075-O parts with continuous concave and convex flanges. The flangeability limits, the geometric capabilities of the forming process, and the deformation mechanisms of stretched and shrunk flanges as well as in the transition zone between them are analysed.

**Introduction**

The flanging process is widely established in the automotive and aeronautical industries to provide stiffness or support for further assembly in sheet metal parts. This consists of bending, usually at 90°, the perimeter of the part along a given line. Regarding the curvature of the bending line, three elemental types of flanges can be distinguished in: straight, concave, or convex flange. In concave flange, also referred to as stretch flange, the material is subjected to a combination of bending and stretching. The most likely mode of failure is localized necking and/or ductile fracture. And in convex flange, also named shrink flange, the material withstands bending and compression, being the appearance of wrinkling the expected mode of failure. Different combinations of these elemental flanges are also common in industrial practice.

Conventional flanging used in medium- or small-batch production, as usual in the aeronautical industry, is mainly performed by rubber pad forming and hydroforming. Despite their technical importance, the conventional flanging processes are subjected to strong restrictions that greatly limit the process. Thus, the interest of scientists and technicians in understanding the geometric, material and process parameters that limit the formability of the flange (i.e., flangeability) in industrial practice is not surprising [1-4].

This work presents a numerical study of flanging hollow 7075-O aluminium alloy sheet parts with continuous concave and convex flanges by rubber pad forming. The objective is to evaluate the forming capabilities of the process to manufacture combined stretch and shrink flanges. The preliminary numerical results show severe difficulties to form the flanges of the proposed specimen as well as excessive forces. The use of tailored rubber pads is required to better distribute pressure, improve flange deformation, and reduce overall forces. Flangeability limits, geometric capabilities of the forming process and deformation mechanisms of stretch and shrink flanges, as well as in the transition zone between them, are analysed.

<figure><img src="image_1499.png" /></figure>
Methodology

The proposed specimen of analysis is based on the work of Zhang et al. [5], consisting of a clover-shaped hole (see Fig. 1(a)) that allows forming 3 stretch flanges and 3 shrink flanges in a single sample. The flange height $h_0$ and radii $R_{stretch}$ and $R_{shrink}$ of the specimens were selected from typical values used in aeronautical ribs.

<figure><img src="image_1496.png" /><figcaption>Fig. 1: (a) Schema of the parametrized sheet blank; (b) FLD (Forming Limit Diagram) for AA7075-O sheets showing predicted localized necking at the flange edge (FLC is the Forming Limit Curve for localized necking and FFL is the Fracture Forming Limit).</figcaption></figure>

Different values of $R_{stretch}$ (25, 50 and 75 mm) and $R_{shrink}$ (0, 25, 50, 100 mm and $\infty$) have been tested by simulations to obtain flanged parts with different combinations of the characteristic failure modes of conventional sheet metal forming: localized necking prior to fracture, and wrinkling. This work presents the modelling and simulation of a selected specimen that allows to produce both types of failure simultaneously.

As a reference value for the flange width $h_0$, it has been considered the one that would produce localized necking just at the end of the flanging operation. Knowing that necking will occur at the edge of the hole, the reference value for $h_0$ can be estimated from the major principal strain at the flange edge by

$$ \epsilon_1 = \ln ( R_{stretch} / (R_{stretch} - h_0) ) \qquad (1) $$

and assuming uniaxial tension conditions.

Fig. 1(b) shows the FLD (Forming Limit Diagram) for the material under study: 1.6 mm thick 7075-O aluminium alloy sheets [6-7]. As represented in the FLD, necking will occur when the strain path at the edge reaches the FLC (Forming Limit Curve for localized necking), i.e. $\epsilon_1 = 0.5$ approximately (see Fig. 1(b)) [6]. Substituting in Eq. (1) for a radius $R_{stretch} = 50$ mm, the reference value is $h_0^* = 19.7$ mm. However, to ensure that failure occurs, a slightly larger flange width should be chosen. Thus, in this work, a specimen with the following dimensions has been considered: $R_{stretch} = R_{shrink} = 50$ mm and $h_0 = 21$ mm.
Methodology

The proposed specimen of analysis is based on the work of Zhang et al. [5], consisting of a clover-shaped hole (see Fig. 1(a)) that allows forming 3 stretch flanges and 3 shrink flanges in a single sample. The flange height $h_0$ and radii $R_{stretch}$ and $R_{shrink}$ of the specimens were selected from typical values used in aeronautical ribs.

<figure><img src="image_1500.png" /><figcaption>Fig. 1: (a) Schema of the parametrized sheet blank; (b) FLD (Forming Limit Diagram) for AA7075-O sheets showing predicted localized necking at the flange edge (FLC is the Forming Limit Curve for localized necking and FFL is the Fracture Forming Limit).</figcaption></figure>

Different values of $R_{stretch}$ (25, 50 and 75 mm) and $R_{shrink}$ (0, 25, 50, 100 mm and $\infty$) have been tested by simulations to obtain flanged parts with different combinations of the characteristic failure modes of conventional sheet metal forming: localized necking prior to fracture, and wrinkling. This work presents the modelling and simulation of a selected specimen that allows to produce both types of failure simultaneously.

As a reference value for the flange width $h_0$, it has been considered the one that would produce localized necking just at the end of the flanging operation. Knowing that necking will occur at the edge of the hole, the reference value for $h_0$ can be estimated from the major principal strain at the flange edge by

$$ \varepsilon_1 = \ln ( R_{stretch} / (R_{stretch} - h_0) ) \qquad (1) $$

and assuming uniaxial tension conditions.

Fig. 1(b) shows the FLD (Forming Limit Diagram) for the material under study: 1.6 mm thick 7075-O aluminium alloy sheets [6-7]. As represented in the FLD, necking will occur when the strain path at the edge reaches the FLC (Forming Limit Curve for localized necking), i.e. $\varepsilon_1 = 0.5$ approximately (see Fig. 1(b)) [6]. Substituting in Eq. (1) for a radius $R_{stretch} = 50$ mm, the reference value is $h_0^* = 19.7$ mm. However, to ensure that failure occurs, a slightly larger flange width should be chosen. Thus, in this work, a specimen with the following dimensions has been considered: $R_{stretch} = R_{shrink} = 50$ mm and $h_0 = 21$ mm.
<figure><img src="image_1497.png" /><figcaption>Fig. 2: Schema of rubber pad forming: (a) conventional process; and (b) tailored rubber pad forming.</figcaption></figure>

Specimens are to be tested by rubber pad forming. Fig. 2(a) shows a schema of this process. In general, a high-capacity press is required to form the sheet metal part from the rubber pad (or set of pads). The alternative process proposed in this work is shown schematically in Fig. 2(b). It basically consists of replacing the large rubber pads with a single rubber pad of tailored geometry to exert pressure only on the area of the part to be formed, avoiding redundant work and thus reducing the forming force. In order to keep the pressure of the rubber tool on the sheet metal part, a rigid dike must be carefully designed and integrated, as represented in Fig. 2(b).

## Numerical Simulations

Numerical simulations have been carried out to evaluate conventional and proposed tailored rubber pad forming, using the commercial finite element (FE) code Abaqus/Explicit. Fig. 3 shows schematically the design procedure of the FE models. Fig. 3(a,c) present the setup for the conventional rubber pad forming and tailored rubber pad forming, respectively. To reduce the computational cost of the simulations, the models have been reduced to a 60° section by two symmetry planes relative to the deformation of the sheet, see Fig. 3(b,d). All part modelling has been developed with CATIA V5. Fig. 3(e) presents the parts meshing with Abaqus of one of the FE models.

The rubber tooling is modelled as a deformable part of 3D elements. The sheet blank is modelled as a deformable part of 2D-shell elements with five integration points through the thickness. All the degrees of freedom of the nodes on the outer edge of the blank are fixed to simplify the clamping of the blank. The die and the dike are modelled as discrete rigid parts. An analytical rigid horizontal plane is used to press on the rubber pad. This plane is not shown in Fig. 3 for clarity.

The rubber material is a polyurethane rubber with Shore hardness 90 A. The Mooney-Rivlin theory ($C_1 = 2.824, C_2 = 0.706$) is used to model the hyperelastic behaviour of rubber [8]. The sheet material is 7075-O aluminium alloy sheet of 1.6 mm thickness. Its mechanical properties are $E = 70$ GPa, $v = 0.33$ and $YS = 109.5$ MPa. The von Mises yield criterion and a law $\sigma = 314 \epsilon^{0.13}$ are used to describe the plasticity behaviour and hardening of the metal sheet, respectively.
<figure><img src="image_1501.png" /><figcaption>Fig. 2: Schema of rubber pad forming: (a) conventional process; and (b) tailored rubber pad forming.</figcaption></figure>

Specimens are to be tested by rubber pad forming. Fig. 2(a) shows a schema of this process. In general, a high-capacity press is required to form the sheet metal part from the rubber pad (or set of pads). The alternative process proposed in this work is shown schematically in Fig. 2(b). It basically consists of replacing the large rubber pads with a single rubber pad of tailored geometry to exert pressure only on the area of the part to be formed, avoiding redundant work and thus reducing the forming force. In order to keep the pressure of the rubber tool on the sheet metal part, a rigid dike must be carefully designed and integrated, as represented in Fig. 2(b).

## Numerical Simulations

Numerical simulations have been carried out to evaluate conventional and proposed tailored rubber pad forming, using the commercial finite element (FE) code Abaqus/Explicit. Fig. 3 shows schematically the design procedure of the FE models. Fig. 3(a,c) present the setup for the conventional rubber pad forming and tailored rubber pad forming, respectively. To reduce the computational cost of the simulations, the models have been reduced to a 60° section by two symmetry planes relative to the deformation of the sheet, see Fig. 3(b,d). All part modelling has been developed with CATIA V5. Fig. 3(e) presents the parts meshing with Abaqus of one of the FE models.

The rubber tooling is modelled as a deformable part of 3D elements. The sheet blank is modelled as a deformable part of 2D-shell elements with five integration points through the thickness. All the degrees of freedom of the nodes on the outer edge of the blank are fixed to simplify the clamping of the blank. The die and the dike are modelled as discrete rigid parts. An analytical rigid horizontal plane is used to press on the rubber pad. This plane is not shown in Fig. 3 for clarity.

The rubber material is a polyurethane rubber with Shore hardness 90 A. The Mooney-Rivlin theory ($C_1 = 2.824$, $C_2 = 0.706$) is used to model the hyperelastic behaviour of rubber [8]. The sheet material is 7075-O aluminium alloy sheet of 1.6 mm thickness. Its mechanical properties are $E = 70$ GPa, $v = 0.33$ and $YS = 109.5$ MPa. The von Mises yield criterion and a law $\sigma = 314 \epsilon^{0.13}$ are used to describe the plasticity behaviour and hardening of the metal sheet, respectively.
<figure><img src="image_1498.png" /><figcaption>Fig. 3: Schema of the numerical models: (a) conventional rubber pad forming; (b) simplified model by using symmetry planes; (c) tailored rubber pad forming; (d) corresponding simplified model; and (e) meshing of parts.</figcaption></figure>

The rubber pad and flange area of the sheet blank are meshed with elements of size 0.8 mm approximately. For the rest, elements between 2 and 4 times larger are used to reduce the computational cost (see Fig. 3(e)). A surface-to-surface contact algorithm with the finite slip formulation is used. A Coulomb friction coefficient of 0.3 is assumed in all part contacts.

<figure><img src="image_1499.png" /><figcaption>Fig. 4: Simulation of the deformation of: (a) the tailored rubber pad; and (b) the flanged sheet metal specimen.</figcaption></figure>
<figure><img src="image_1502.png" /><figcaption>Fig. 3: Schema of the numerical models: (a) conventional rubber pad forming; (b) simplified model by using symmetry planes; (c) tailored rubber pad forming; (d) corresponding simplified model; and (e) meshing of parts.</figcaption></figure>

The rubber pad and flange area of the sheet blank are meshed with elements of size 0.8 mm approximately. For the rest, elements between 2 and 4 times larger are used to reduce the computational cost (see Fig. 3(e)). A surface-to-surface contact algorithm with the finite slip formulation is used. A Coulomb friction coefficient of 0.3 is assumed in all part contacts.

<figure><img src="image_1503.png" /><figcaption>Fig. 4: Simulation of the deformation of: (a) the tailored rubber pad; and (b) the flanged sheet metal specimen.</figcaption></figure>
Simulations of conventional rubber pad forming predicted a required press force greater than 3 MN for the specimen under study. Instead, for the tailored rubber pad forming simulations, forces in the range of 300-550 kN were obtained, i.e. 10 times less than the conventional process.

Fig. 4 shows the deformation of tailored rubber pad and sheet metal in the simulation of tailored rubber pad forming. As can be seen in Fig. 4(a), the rubber is compressed between the dike and the die and pushes the sheet against the die to finish the complete folding. Fig. 1(b) shows the formation of a small wrinkle in the compressed flange region at the end of the forming process.

Fig. 5 presents the major (ε₁) and minor (ε₂) in-plane principal plastic strain distributions in outer and inner sheet surfaces. Red elements in Fig. 5(a) indicate that the more stretched material is the edge in the stretched flange region. A maximum value of ε₁ = 0.547 was found at the edge, on the inner surface of the flange, a few centimetres from the symmetry plane in the stretched flange region (see Fig. 5(a) bottom). This is a very accurate prediction since, as described below, experimental tests show that localized necking and subsequent tearing of the flange occurs very close to this point.

<figure><img src="image_1500.png" /><figcaption>Fig. 5: (a) Major and (b) minor in-plane principal plastic strains on both surfaces of the metal sheet.</figcaption></figure>

As can be seen from the strain contours in Fig. 5, there are substantial differences in strains between the two sheet surfaces in some areas, especially along the fold and the wrinkle. This indicates a significant strain gradient through the sheet thickness. Such strain gradients can be better analysed in the FLD of Fig. 6. This Fig. depicts the strain distribution along the flange on both sheet surfaces in 3 different regions: (a) in the symmetry plane of the compressed flange region, (b) in the transition between compressed and stretched flange regions, and (c) in the symmetry plane of the stretched flange region. As can be seen, the strain gradient in the fold remains similar in all 3 regions. Regarding the edge, there is a noticeable strain gradient through the sheet thickness only in the compressed region of the flange due to the wrinkle (see Fig. 6(a)). Necking in the stretched flange region is also clearly predicted in Fig. 6(c), given that the strain at the edge exceeds the FLC on both sides of the sheet. It should be noted that although the strain at the outer surface of the fold exceeds the FLC in some regions (see Fig. 6(a,c)), this does not indicate necking due to the strain gradient through the sheet thickness [6].
Simulations of conventional rubber pad forming predicted a required press force greater than 3 MN for the specimen under study. Instead, for the tailored rubber pad forming simulations, forces in the range of 300-550 kN were obtained, i.e. 10 times less than the conventional process.

Fig. 4 shows the deformation of tailored rubber pad and sheet metal in the simulation of tailored rubber pad forming. As can be seen in Fig. 4(a), the rubber is compressed between the dike and the die and pushes the sheet against the die to finish the complete folding. Fig. 1(b) shows the formation of a small wrinkle in the compressed flange region at the end of the forming process.

Fig. 5 presents the major (ε₁) and minor (ε₂) in-plane principal plastic strain distributions in outer and inner sheet surfaces. Red elements in Fig. 5(a) indicate that the more stretched material is the edge in the stretched flange region. A maximum value of ε₁ = 0.547 was found at the edge, on the inner surface of the flange, a few centimetres from the symmetry plane in the stretched flange region (see Fig. 5(a) bottom). This is a very accurate prediction since, as described below, experimental tests show that localized necking and subsequent tearing of the flange occurs very close to this point.

<figure><img src="image_1504.png" /><figcaption>Fig. 5: (a) Major and (b) minor in-plane principal plastic strains on both surfaces of the metal sheet.</figcaption></figure>

As can be seen from the strain contours in Fig. 5, there are substantial differences in strains between the two sheet surfaces in some areas, especially along the fold and the wrinkle. This indicates a significant strain gradient through the sheet thickness. Such strain gradients can be better analysed in the FLD of Fig. 6. This Fig. depicts the strain distribution along the flange on both sheet surfaces in 3 different regions: (a) in the symmetry plane of the compressed flange region, (b) in the transition between compressed and stretched flange regions, and (c) in the symmetry plane of the stretched flange region. As can be seen, the strain gradient in the fold remains similar in all 3 regions. Regarding the edge, there is a noticeable strain gradient through the sheet thickness only in the compressed region of the flange due to the wrinkle (see Fig. 6(a)). Necking in the stretched flange region is also clearly predicted in Fig. 6(c), given that the strain at the edge exceeds the FLC on both sides of the sheet. It should be noted that although the strain at the outer surface of the fold exceeds the FLC in some regions (see Fig. 6(a,c)), this does not indicate necking due to the strain gradient through the sheet thickness [6].
<figure><img src="image_1501.png" /><figcaption>Fig. 6: Strain distributions along the flange: (a) compressed region; (b) transition; (c) stretched region.</figcaption></figure>

## Experimental Validation

Tailored rubber pad forming experimental tests were performed to validate the numerical analysis. The experiments were carried out using the setup depicted in Fig. 7(a,b). Die, dike, tailored rubber pad and blank metal sheets were designed and manufactured to meet the experimental plan and to be interchangeable. The rubber pad was lubricated with Vaseline. The testing machine has a capacity of 600 kN and a stroke speed of 1 mm/s was used. The forming load and travel were monitored during the tests.

The tailored rubber pad (Fig. 7(b)) was produced by moulding in a silicone mould for polyurethane. To fabricate the silicone mould, a PLA (PolyLactic Acid) pattern was manufactured on an FFF (Fused Filament Fabrication) 3D printer. Using the same procedure, cylindrical specimens were also fabricated to validate by compression testing that the hardness of the polyurethane rubber is around Shore 90 A.

The metal blanks were machined on an EMCO UMILL 630 CNC machining centre. The hole edges were subsequently ground with fine grit sandpaper to eliminate any burrs. Fig. 7(c,d) depicted a tested specimen viewed from both surfaces. As can be seen, the two types of failure predicted in the numerical simulation occurred very accurately. On the one hand, a small wrinkle was produced right in the middle of each shrink flange (i.e. in the plane of symmetry used in the numerical model). On the other hand, a localized necking occurred at the edge at a location very close to that predicted by the numerical simulation, which caused the crack propagation shown in Fig. 7(c,d).
<figure><img src="image_1505.png" /><figcaption>Fig. 6: Strain distributions along the flange: (a) compressed region; (b) transition; (c) stretched region.</figcaption></figure>

## Experimental Validation

Tailored rubber pad forming experimental tests were performed to validate the numerical analysis. The experiments were carried out using the setup depicted in Fig. 7(a,b). Die, dike, tailored rubber pad and blank metal sheets were designed and manufactured to meet the experimental plan and to be interchangeable. The rubber pad was lubricated with Vaseline. The testing machine has a capacity of 600 kN and a stroke speed of 1 mm/s was used. The forming load and travel were monitored during the tests.

The tailored rubber pad (Fig. 7(b)) was produced by moulding in a silicone mould for polyurethane. To fabricate the silicone mould, a PLA (PolyLactic Acid) pattern was manufactured on an FFF (Fused Filament Fabrication) 3D printer. Using the same procedure, cylindrical specimens were also fabricated to validate by compression testing that the hardness of the polyurethane rubber is around Shore 90 A.

The metal blanks were machined on an EMCO UMILL 630 CNC machining centre. The hole edges were subsequently ground with fine grit sandpaper to eliminate any burrs. Fig. 7(c,d) depicted a tested specimen viewed from both surfaces. As can be seen, the two types of failure predicted in the numerical simulation occurred very accurately. On the one hand, a small wrinkle was produced right in the middle of each shrink flange (i.e. in the plane of symmetry used in the numerical model). On the other hand, a localized necking occurred at the edge at a location very close to that predicted by the numerical simulation, which caused the crack propagation shown in Fig. 7(c,d).
<figure><img src="image_1502.png" /><figcaption>Fig. 7: Experimental setup showing (a) die, dike, (b) tailored rubber pad, sheet blank, and (c-d) the manufactured part.</figcaption></figure>

Conclusions and Further Work

Flanging by tailored rubber pads of hollow AA7075-O sheet parts with continuous stretch and shrink flanges has been designed and numerically analysed using FE simulations. The following conclusions can be drawn from this study:

* The FLD is a valuable tool for the design of sheet metal parts. In this work the FLC has been used to accurately estimate the flange size that would produce a failure by necking and/or fracture in the flange edge.

* The appearance of wrinkles can be predicted by FE simulations using different values of radius in shrink flanges ($R_{shrink}$). This provides a practical alternative to theoretical/analytical methods of predicting such instabilities.

* The results obtained allow establishing a robust specimen design methodology to address a flanging test campaign to elucidate safe conformability windows in terms of variables used in the literature such as $h/R$ and $R/t$.

* Tailored rubber pads are easy to manufacture, e.g. by liquid moulding, and provide a cost-effective alternative in the equipment for flanging complex parts. In this sense, simulation results facilitate the design of these flexible elements as well as of the specimens, dies and tools.
<figure><img src="image_1506.png" /><figcaption>Fig. 7: Experimental setup showing (a) die, dike, (b) tailored rubber pad, sheet blank, and (c-d) the manufactured part.</figcaption></figure>

## Conclusions and Further Work

Flanging by tailored rubber pads of hollow AA7075-O sheet parts with continuous stretch and shrink flanges has been designed and numerically analysed using FE simulations. The following conclusions can be drawn from this study:

* The FLD is a valuable tool for the design of sheet metal parts. In this work the FLC has been used to accurately estimate the flange size that would produce a failure by necking and/or fracture in the flange edge.

* The appearance of wrinkles can be predicted by FE simulations using different values of radius in shrink flanges ($R_{shrink}$). This provides a practical alternative to theoretical/analytical methods of predicting such instabilities.

* The results obtained allow establishing a robust specimen design methodology to address a flanging test campaign to elucidate safe conformability windows in terms of variables used in the literature such as $h/R$ and $R/t$.

* Tailored rubber pads are easy to manufacture, e.g. by liquid moulding, and provide a cost-effective alternative in the equipment for flanging complex parts. In this sense, simulation results facilitate the design of these flexible elements as well as of the specimens, dies and tools.
As mentioned above, the next step is to carry out a campaign of numerical and experimental flanging tests to elucidate the safe conformability windows of AA7075-O sheets and other aeronautical materials by tailored rubber forming. A comparative study using an incremental forming process (SPIF, Single-Point Incremental Forming) to perform the flange operations is also planned.

## Acknowledgements

The authors acknowledge the funding provided by Grant PID2021-125934OB-I00 financed by MCIN/AEI/10.13039/501100011033 and by ERDF “A way of making Europe” (EU).

## References

[1] N. Asnafi, On stretch and shrink flanging of sheet aluminium by fluid forming, J. Mat. Proc. Tech. 96 (1999) 198–214. https://doi.org/10.1016/S0924-0136(99)00352-0

[2] H. Livatyali, A. Müderrisoğlu, M.A. Ahmetoğlu, N. Akgerman, G.L. Kinzel, T. Altan, Improvement of hem quality by optimizing flanging and pre-hemming operations using computer aided die design, J. Mater. Proc. Tech. 98 (2000) 41-52. https://doi.org/10.1016/S0924-0136(99)00304-0

[3] L. Chen, H. Chen, Q. Wang, Z. Li, Studies on wrinkling and control method in rubber forming using aluminium sheet shrink flanging process, Mater. Des. 65 (2015) 505-510. https://doi.org/10.1016/j.matdes.2014.09.057

[4] S. Kumar, M. Ahmed, S.K. Panthi, Effect of punch profile on deformation behaviour of AA5052 sheet in stretch flanging process, Archiv. Civ. Mech. Eng 20 (2020) 18. https://doi.org/10.1007/s43452-020-00016-2

[5] H. Zhang, Z. Zhang, H. Ren, J. Cao, J. Chen, Deformation mechanics and failure mode in stretch and shrink flanging by double-sided incremental forming, Int. J. Mech. Sci. 144 (2018) 216-222. https://doi.org/10.1016/j.ijmecsci.2018.06.002

[6] M. Borrego, D. Morales-Palma, A.J. Martínez-Donaire, G. Centeno, C. Vallellano, Analysis of formability in conventional hole flanging of AA7075-O sheets: punch edge radius effect and limitations of the FLC, Int. J. Mater. Form. 13 (2020) 303-316. https://doi.org/10.1007/s12289-019-01487-2

[7] M. Borrego, D. Morales-Palma, C. Vallellano, Analysis of Flangeability by Single-Stage SPIF and Press-Working in AA7075-O Sheet, J. Manuf. Sci. Eng. 143(1) (2020) 011005. https://doi.org/10.1115/1.4047997

[8] L. Belhassen, S. Koubaa, M. Wali, F. Dammak, Numerical prediction of springback and ductile damage in rubber-pad forming process of aluminum sheet metal, Int. J. Mech. Sci. 117 (2016) 218-226. https://doi.org/10.1016/j.ijmecsci.2016.08.015
As mentioned above, the next step is to carry out a campaign of numerical and experimental flanging tests to elucidate the safe conformability windows of AA7075-O sheets and other aeronautical materials by tailored rubber forming. A comparative study using an incremental forming process (SPIF, Single-Point Incremental Forming) to perform the flange operations is also planned.

## Acknowledgements

The authors acknowledge the funding provided by Grant PID2021-125934OB-I00 financed by MCIN/AEI/10.13039/501100011033 and by ERDF “A way of making Europe” (EU).

## References

[1] N. Asnafi, On stretch and shrink flanging of sheet aluminium by fluid forming, J. Mat. Proc. Tech. 96 (1999) 198–214. https://doi.org/10.1016/S0924-0136(99)00352-0

[2] H. Livatyali, A. Müderrisoğlu, M.A. Ahmetoğlu, N. Akgerman, G.L. Kinzel, T. Altan, Improvement of hem quality by optimizing flanging and pre-hemming operations using computer aided die design, J. Mater. Proc. Tech. 98 (2000) 41-52. https://doi.org/10.1016/S0924-0136(99)00304-0

[3] L. Chen, H. Chen, Q. Wang, Z. Li, Studies on wrinkling and control method in rubber forming using aluminium sheet shrink flanging process, Mater. Des. 65 (2015) 505-510. https://doi.org/10.1016/j.matdes.2014.09.057

[4] S. Kumar, M. Ahmed, S.K. Panthi, Effect of punch profile on deformation behaviour of AA5052 sheet in stretch flanging process, Archiv. Civ. Mech. Eng 20 (2020) 18. https://doi.org/10.1007/s43452-020-00016-2

[5] H. Zhang, Z. Zhang, H. Ren, J. Cao, J. Chen, Deformation mechanics and failure mode in stretch and shrink flanging by double-sided incremental forming, Int. J. Mech. Sci. 144 (2018) 216-222. https://doi.org/10.1016/j.ijmecsci.2018.06.002

[6] M. Borrego, D. Morales-Palma, A.J. Martínez-Donaire, G. Centeno, C. Vallellano, Analysis of formability in conventional hole flanging of AA7075-O sheets: punch edge radius effect and limitations of the FLC, Int. J. Mater. Form. 13 (2020) 303-316. https://doi.org/10.1007/s12289-019-01487-2

[7] M. Borrego, D. Morales-Palma, C. Vallellano, Analysis of Flangeability by Single-Stage SPIF and Press-Working in AA7075-O Sheet, J. Manuf. Sci. Eng. 143(1) (2020) 011005. https://doi.org/10.1115/1.4047997

[8] L. Belhassen, S. Koubaa, M. Wali, F. Dammak, Numerical prediction of springback and ductile damage in rubber-pad forming process of aluminum sheet metal, Int. J. Mech. Sci. 117 (2016) 218-226. https://doi.org/10.1016/j.ijmecsci.2016.08.015
# Effect of vibration frequency and amplitude on formability in rotational vibration-assisted incremental sheet forming (RV-ISF)

ZHU Hui¹,ᵃ, PENG Wenxuan¹,ᵇ and LONG Hui¹,ᶜ*

¹Department of Mechanical Engineering, The University of Sheffield, Sheffield S1 3JD, UK

ᵃhui.zhu@sheffield.ac.uk, ᵇwx.dusk.peng@gmail.com, ᶜh.long@sheffield.ac.uk

**Keywords:** Incremental Sheet Forming, Rotational Vibration, Material Formability

**Abstract.** Incremental sheet forming (ISF) is a flexible manufacturing process, potentially for producing small-batched and customized sheet products. To improve formability of hard-to-form materials, part surface finish and forming accuracy, the rotational vibration-assisted ISF (RV-ISF) has been developed by the University of Sheffield with the use of novel tool designs with either offsets or grooves on the tool surface to introduce both mechanical vibration and localized heating into the conventional ISF process (C-ISF). With the use of double-offset (T2) and four-groove (T4) tools in the experiments, this work studies the effects of tool design and tool rotational speed on sheet vibration amplitude and frequency, as well as their effects on forming temperature and force reduction and formability improvement. Results show that the sheet vibration amplitude is mainly influenced by the tool design, while the vibration frequency is affected by both tool design and rotational speed. RV-ISF with T4 shows greater material formability improvement of AA3003-O due to greater temperature rise and low-frequency-low-amplitude vibration. RV-ISF with T2 results in greater reduction of forming force because of the higher sheet vibration amplitude.

**Introduction**

Incremental sheet forming (ISF) is a flexible forming technology, with potentials for manufacturing small-batch or customized sheet parts to achieve considerable cost and time savings [1]. The advantages of the conventional ISF (C-ISF) include process flexibility, improved formability, reduced equipment requirements, short production cycle, low cost, and high material utilization. However, there are still some aspects requiring improvement to broaden the ISF application prospective, for instance, further enhancement of formability of hard-to-form materials for processing high-strength materials, improving part surface finish and forming accuracy.

To improve the material formability for manufacture of more complicated geometries, heat-assisted ISF (HA-ISF) processes were developed. As one variant of heat-assisted ISF processes, friction stir-ISF (FS-ISF) provided localized temperature rise without the need of using external heating devices, which led to the formability improvement, as reported by Otsu [2]. As the friction between forming tool and sheet material affected the surface roughness, Wang et al. [3] proposed a process window to achieve increased formability and maintain the surface quality of low-ductility aluminium alloys AA2024-T3 and AA5052-H31. Zhan et al. [4] developed a novel two-stage FS-ISF process for AA2024-T3 and AA6061-T4, and found that this process helped to improve the geometric accuracy, material ductility and strength because of forming the uniform grains, homogeneous and fine precipitates.

Efforts have also been made to develop ultrasonic vibration-assisted ISF (UV-ISF) for the reduction of forming force, improvement of surface finish and formability. Due to the effect of ultrasonic softening, Long et al. [5] found that materials with higher yield stress had greater forming force reduction because of greater stress superimposition and higher absorption of ultrasonic energy. Amini et al. [6] reported that the significant improvement of material formability of AA1050 sheets under ultrasonic assistance in ISF process. The results of Amini et al. [7] also

<figure><img src="image_1503.png" /></figure>
# Effect of vibration frequency and amplitude on formability in rotational vibration-assisted incremental sheet forming (RV-ISF)

ZHU Hui¹,ᵃ, PENG Wenxuan¹,ᵇ and LONG Hui¹,ᶜ*

¹Department of Mechanical Engineering, The University of Sheffield, Sheffield S1 3JD, UK

ᵃhui.zhu@sheffield.ac.uk, ᵇwx.dusk.peng@gmail.com, ᶜh.long@sheffield.ac.uk

**Keywords:** Incremental Sheet Forming, Rotational Vibration, Material Formability

**Abstract.** Incremental sheet forming (ISF) is a flexible manufacturing process, potentially for producing small-batched and customized sheet products. To improve formability of hard-to-form materials, part surface finish and forming accuracy, the rotational vibration-assisted ISF (RV-ISF) has been developed by the University of Sheffield with the use of novel tool designs with either offsets or grooves on the tool surface to introduce both mechanical vibration and localized heating into the conventional ISF process (C-ISF). With the use of double-offset (T2) and four-groove (T4) tools in the experiments, this work studies the effects of tool design and tool rotational speed on sheet vibration amplitude and frequency, as well as their effects on forming temperature and force reduction and formability improvement. Results show that the sheet vibration amplitude is mainly influenced by the tool design, while the vibration frequency is affected by both tool design and rotational speed. RV-ISF with T4 shows greater material formability improvement of AA3003-O due to greater temperature rise and low-frequency-low-amplitude vibration. RV-ISF with T2 results in greater reduction of forming force because of the higher sheet vibration amplitude.

**Introduction**

Incremental sheet forming (ISF) is a flexible forming technology, with potentials for manufacturing small-batch or customized sheet parts to achieve considerable cost and time savings [1]. The advantages of the conventional ISF (C-ISF) include process flexibility, improved formability, reduced equipment requirements, short production cycle, low cost, and high material utilization. However, there are still some aspects requiring improvement to broaden the ISF application prospective, for instance, further enhancement of formability of hard-to-form materials for processing high-strength materials, improving part surface finish and forming accuracy.

To improve the material formability for manufacture of more complicated geometries, heat-assisted ISF (HA-ISF) processes were developed. As one variant of heat-assisted ISF processes, friction stir-ISF (FS-ISF) provided localized temperature rise without the need of using external heating devices, which led to the formability improvement, as reported by Otsu [2]. As the friction between forming tool and sheet material affected the surface roughness, Wang et al. [3] proposed a process window to achieve increased formability and maintain the surface quality of low-ductility aluminium alloys AA2024-T3 and AA5052-H31. Zhan et al. [4] developed a novel two-stage FS-ISF process for AA2024-T3 and AA6061-T4, and found that this process helped to improve the geometric accuracy, material ductility and strength because of forming the uniform grains, homogeneous and fine precipitates.

Efforts have also been made to develop ultrasonic vibration-assisted ISF (UV-ISF) for the reduction of forming force, improvement of surface finish and formability. Due to the effect of ultrasonic softening, Long et al. [5] found that materials with higher yield stress had greater forming force reduction because of greater stress superimposition and higher absorption of ultrasonic energy. Amini et al. [6] reported that the significant improvement of material formability of AA1050 sheets under ultrasonic assistance in ISF process. The results of Amini et al. [7] also

<figure><img src="image_1507.png" /></figure>
revealed that applying ultrasonic vibration together with tool rotation reduced the surface roughness significantly.

As concluded from literature, both FS-ISF and UV-ISF have some limitations. The parts formed by the FS-ISF usually have poor surface finish because of the friction effect between the tool and sheet at high temperatures. The limitation of the UV-ISF lies in the requirement of an ultrasonic generator for forming high-strength materials. By combining the features of FS-ISF and UV-ISF, the rotational vibration-assisted ISF (RV-ISF) has been proposed by the University of Sheffield [8] to take both advantages and avoid limitations of FS-ISF and UV-ISF by introducing friction heating and mechanical vibration with simple process setup and new tool designs. Long et al. [8] firstly proposed a novel type of rosette tools with three-grooves or four-grooves for developing a new ISF process of the RV-ISF to improve the material formability of a hard-to-form material of magnesium alloy AZ31B significantly. Lu et al. [9] firstly developed single-offset (T1) and double-offset (T2) vibration tools for generating both friction heating effect and mechanical vibration effect, which induced microstructure refinement of AZ31B magnesium alloy. Peng et al. [10] revealed that under the effect of low frequency and low amplitude vibrations by using the novel four-groove rosette tool (T4) design, the developed RV-ISF can improve the surface quality by reducing the formation of fish-scale surface texture.

Following the design of the double-offset tool T2 and the new four-groove rosette tool T4 for RV-ISF developed [8], this work analyses the vibration amplitude and frequency when employing different tool designs and rotational speeds. Experimental testing and finite element (FE) modelling are conducted to investigate the effect of the tool design and rotational speed on the forming temperature, forming force and formability of AA3003-O sheets.

## Methods

### RV-ISF tool designs

In this study, a hemispherical tool T0 was used in the C-ISF and FS-ISF to form sheet parts, while a double offset tool T2 and a four-groove rosette tool T4 were used in the RV-ISF, as shown in Fig. 1. In the C-ISF, the conventional tool T0 produces the localised material deformation at room temperature, and in the FS-ISF, localised temperature rise is produced by localised heat generation due to friction and plastic work. However, in the RV-ISF, the double offset tool T2 and four-groove rosette tool T4 introduce both localised temperature and sheet vibration because of the periodic contact and the loss of contact with the rotating tool. Different from T2, the advantages of T4 lie in greater contact area, frequent changes between contact and loss of contact status, with greater sheet vibration frequency and smaller vibration amplitude, and a possibility of producing higher temperature rise.

### Experimental methods

AA3003-O sheets of 0.9 mm thickness were used for C-ISF, FS-ISF and RV-ISF tests. The sheets were cut into squared blanks with size of 150 mm × 150 mm. To test the capability and formability of RV-ISF, a hyperbolic truncated cone shape with varying drawing angle from 21° to 85° was designed and the toolpath was generated as shown in Fig. 2(c) and (d). Identical feed rate of 1000 mm/min and step size of 0.3 mm were applied for all tests. The summary of the ISF tests can be found in Table 1. T0, T2 and T4 tools were tested with different rotational speeds. For all the tests, machine oil was used as lubricant. The ISF tests were performed on a 3-axis CNC milling machine (XYZ 1060 HS) as shown in Fig. 2(a). During the tests, forming forces were recorded by a 3-axis force transducer (Kistler 9367C), forming temperature were recorded by an infrared thermal camera (FLIR T650sc), and the fracture depth was recorded by the machine controller. Considering the deformation in plane strain condition for ISF of truncated cone parts, the
revealed that applying ultrasonic vibration together with tool rotation reduced the surface roughness significantly.

As concluded from literature, both FS-ISF and UV-ISF have some limitations. The parts formed by the FS-ISF usually have poor surface finish because of the friction effect between the tool and sheet at high temperatures. The limitation of the UV-ISF lies in the requirement of an ultrasonic generator for forming high-strength materials. By combining the features of FS-ISF and UV-ISF, the rotational vibration-assisted ISF (RV-ISF) has been proposed by the University of Sheffield [8] to take both advantages and avoid limitations of FS-ISF and UV-ISF by introducing friction heating and mechanical vibration with simple process setup and new tool designs. Long et al. [8] firstly proposed a novel type of rosette tools with three-grooves or four-grooves for developing a new ISF process of the RV-ISF to improve the material formability of a hard-to-form material of magnesium alloy AZ31B significantly. Lu et al. [9] firstly developed single-offset (T1) and double-offset (T2) vibration tools for generating both friction heating effect and mechanical vibration effect, which induced microstructure refinement of AZ31B magnesium alloy. Peng et al. [10] revealed that under the effect of low frequency and low amplitude vibrations by using the novel four-groove rosette tool (T4) design, the developed RV-ISF can improve the surface quality by reducing the formation of fish-scale surface texture.

Following the design of the double-offset tool T2 and the new four-groove rosette tool T4 for RV-ISF developed [8], this work analyses the vibration amplitude and frequency when employing different tool designs and rotational speeds. Experimental testing and finite element (FE) modelling are conducted to investigate the effect of the tool design and rotational speed on the forming temperature, forming force and formability of AA3003-O sheets.

## Methods

### RV-ISF tool designs

In this study, a hemispherical tool T0 was used in the C-ISF and FS-ISF to form sheet parts, while a double offset tool T2 and a four-groove rosette tool T4 were used in the RV-ISF, as shown in Fig. 1. In the C-ISF, the conventional tool T0 produces the localised material deformation at room temperature, and in the FS-ISF, localised temperature rise is produced by localised heat generation due to friction and plastic work. However, in the RV-ISF, the double offset tool T2 and four-groove rosette tool T4 introduce both localised temperature and sheet vibration because of the periodic contact and the loss of contact with the rotating tool. Different from T2, the advantages of T4 lie in greater contact area, frequent changes between contact and loss of contact status, with greater sheet vibration frequency and smaller vibration amplitude, and a possibility of producing higher temperature rise.

### Experimental methods

AA3003-O sheets of 0.9 mm thickness were used for C-ISF, FS-ISF and RV-ISF tests. The sheets were cut into squared blanks with size of 150 mm × 150 mm. To test the capability and formability of RV-ISF, a hyperbolic truncated cone shape with varying drawing angle from 21° to 85° was designed and the toolpath was generated as shown in Fig. 2(c) and (d). Identical feed rate of 1000 mm/min and step size of 0.3 mm were applied for all tests. The summary of the ISF tests can be found in Table 1. T0, T2 and T4 tools were tested with different rotational speeds. For all the tests, machine oil was used as lubricant. The ISF tests were performed on a 3-axis CNC milling machine (XYZ 1060 HS) as shown in Fig. 2(a). During the tests, forming forces were recorded by a 3-axis force transducer (Kistler 9367C), forming temperature were recorded by an infrared thermal camera (FLIR T650sc), and the fracture depth was recorded by the machine controller. Considering the deformation in plane strain condition for ISF of truncated cone parts, the
equivalent fracture strain $\bar{\varepsilon}_f$ were calculated by Eq. (1) with the initial sheet thickness $t_0$ and the thickness at fracture $t_f$ after tests.

$$ \bar{\varepsilon}_f = \frac{2}{\sqrt{3}} \ln \frac{t_0}{t_f} \qquad (1) $$

<figure><img src="image_1504.png" /></figure>

T0: hemispherical tool with diameter of 10 mm

T2: semielliptical tool with long axis of 10 mm and short axis of 8 mm

T4: rosette tool with groove length of 4.35 mm and width of 2.4 mm

<caption>Fig. 1. Tool design: conventional tool T0, double offset tool T2 and four-groove tool T4.</caption>

<table><caption>Table 1. Experimental test parameters of C-ISF, FS-ISF and RV-ISF of AA3003-O sheets with hyperbolic truncated cone shape.</caption><thead><tr><th>No.</th><th>Material</th><th>Sheet thickness [mm]</th><th>Tool design</th><th>Rotational speed [rpm]</th><th>Feed rate [mm/min]</th><th>Step size [mm]</th><th>Lubricant</th></tr></thead><tbody><tr><td>1</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>0</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>2</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>4000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>3</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>7000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>4</td><td>AA3003-O</td><td>0.9</td><td>T2</td><td>3000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>5</td><td>AA3003-O</td><td>0.9</td><td>T2</td><td>6000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>6</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>3000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>7</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>5000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>8</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>6000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>9</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>7000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr></tbody></table>
equivalent fracture strain $\bar{\varepsilon}_f$ were calculated by Eq. (1) with the initial sheet thickness $t_0$ and the thickness at fracture $t_f$ after tests.

$$ \bar{\varepsilon}_f = \frac{2}{\sqrt{3}} \ln \frac{t_0}{t_f} \qquad (1) $$

<figure><img src="image_1508.png" /></figure>

T0: hemispherical tool with diameter of 10 mm

T2: semielliptical tool with long axis of 10 mm and short axis of 8 mm

T4: rosette tool with groove length of 4.35 mm and width of 2.4 mm

<caption>Fig. 1. Tool design: conventional tool T0, double offset tool T2 and four-groove tool T4.</caption>

<table><caption>Table 1. Experimental test parameters of C-ISF, FS-ISF and RV-ISF of AA3003-O sheets with hyperbolic truncated cone shape.</caption><thead><tr><th>No.</th><th>Material</th><th>Sheet thickness [mm]</th><th>Tool design</th><th>Rotational speed [rpm]</th><th>Feed rate [mm/min]</th><th>Step size [mm]</th><th>Lubricant</th></tr></thead><tbody><tr><td>1</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>0</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>2</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>4000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>3</td><td>AA3003-O</td><td>0.9</td><td>T0</td><td>7000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>4</td><td>AA3003-O</td><td>0.9</td><td>T2</td><td>3000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>5</td><td>AA3003-O</td><td>0.9</td><td>T2</td><td>6000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>6</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>3000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>7</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>5000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>8</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>6000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr><tr><td>9</td><td>AA3003-O</td><td>0.9</td><td>T4</td><td>7000</td><td>1000</td><td>0.3</td><td>Machine oil</td></tr></tbody></table>
<figure><img src="image_1505.png" /><figcaption>Fig. 2. (a) RV-ISF test setup; (b) RV-ISF formed hyperbolic truncated cone parts; (c) Dimensions of the designed hyperbolic truncated cone; (d) Generated toolpath.</figcaption></figure>

Finite element (FE) modelling

FE simulation was conducted by using ABAQUS software to analyse the vibration frequency and amplitude of sheet material with the use of T2 and T4. Forming tools and a pre-shaped truncated cone part with a constant drawing angle of 50° and a forming depth of 30 mm were used in the FE model. After moving downwards for 0.3 mm, the forming tool T2 or T4 followed a circular toolpath, which was defined based on a fixed depth. The field output was requested at every $10^{-3}$ s to obtain the displacement data for calculation of vibration frequency and amplitude by fast Fourier transform (FFT). As the temperature effect was not considered in the vibration simulation, Johnson-Cook model without the temperature-related term was used for the material plasticity definition as given in Eq. (2):

$$ \bar{\sigma} = (A + B\bar{\epsilon}_p^n) (1 + C \ln \frac{\dot{\epsilon}}{\dot{\epsilon}_{ref}}) \quad (2) $$

where, $\bar{\sigma}$ is the equivalent stress, $\bar{\epsilon}_p$ is the equivalent plastic strain, $\dot{\epsilon}$ is the strain rate, $\dot{\epsilon}_{ref}$ is the reference strain rate, A, B, n and C are model parameters. Table 2 gives the parameters for Johnson-Cook model and other material parameters. The coefficient of friction was set as 0.15. The deforming sheet was meshed with 8-node brick elements with reduced integration (C3D8R) and the forming tool was meshed with 4-node tetrahedral elements (C3D4). To achieve a balance between simulation accuracy and efficiency, the mass scaling was used to request a minimum time increment of at $10^{-5}$ s.
<figure><img src="image_1509.png" /><figcaption>Fig. 2. (a) RV-ISF test setup; (b) RV-ISF formed hyperbolic truncated cone parts; (c) Dimensions of the designed hyperbolic truncated cone; (d) Generated toolpath.</figcaption></figure>

Finite element (FE) modelling

FE simulation was conducted by using ABAQUS software to analyse the vibration frequency and amplitude of sheet material with the use of T2 and T4. Forming tools and a pre-shaped truncated cone part with a constant drawing angle of 50° and a forming depth of 30 mm were used in the FE model. After moving downwards for 0.3 mm, the forming tool T2 or T4 followed a circular toolpath, which was defined based on a fixed depth. The field output was requested at every $10^{-3}$ s to obtain the displacement data for calculation of vibration frequency and amplitude by fast Fourier transform (FFT). As the temperature effect was not considered in the vibration simulation, Johnson-Cook model without the temperature-related term was used for the material plasticity definition as given in Eq. (2):

$$ \bar{\sigma} = (A + B\bar{\varepsilon}_p^n) (1 + C \ln \frac{\dot{\varepsilon}}{\dot{\varepsilon}_{ref}}) \quad (2) $$

where, $\bar{\sigma}$ is the equivalent stress, $\bar{\varepsilon}_p$ is the equivalent plastic strain, $\dot{\varepsilon}$ is the strain rate, $\dot{\varepsilon}_{ref}$ is the reference strain rate, A, B, n and C are model parameters. Table 2 gives the parameters for Johnson-Cook model and other material parameters. The coefficient of friction was set as 0.15. The deforming sheet was meshed with 8-node brick elements with reduced integration (C3D8R) and the forming tool was meshed with 4-node tetrahedral elements (C3D4). To achieve a balance between simulation accuracy and efficiency, the mass scaling was used to request a minimum time increment of at $10^{-5}$ s.
<table><caption>Table 2. Material parameters of AA3003-O [11] used in FE modelling of RV-ISF.</caption><tr><td>Johnson-Cook model</td><td>A (MPa)</td><td>B (MPa)</td><td>n</td><td>C</td></tr><tr><td>Value</td><td>42.97</td><td>180</td><td>0.21</td><td>0.00747</td></tr><tr><td>Other parameters</td><td>Density (kg/m³)</td><td>Young's modulus (MPa)</td><td>Poisson's ratio</td><td></td></tr><tr><td>Value</td><td>2790</td><td>72600</td><td>0.36</td><td></td></tr></table>

## Results and discussions

Analysis of vibration frequency and amplitude using FE simulation

In RV-ISF, the sheet vibration is resulted from the contact and loss of contact between forming tool and sheet surface. In theory, the reference vibration frequency can be calculated by the following equation:

$$f_{\text{ref}} = \frac{N \cdot S}{60} \qquad (3)$$

where N is the number of tool offsets or grooves and S is the tool rotational speed. The calculated reference frequencies for T2 and T4 with 3000 rpm and 6000 rpm are listed in Table 3.

<table><caption>Table 3. Reference frequencies, simulated frequencies and amplitudes for T2 and T4 in RV-ISF.</caption><thead><tr><th>Condition</th><th>Reference frequency</th><th>Simulated frequency</th><th>Simulated amplitude</th></tr></thead><tbody><tr><td rowspan="4">T2, 3000 rpm</td><td rowspan="4">100 Hz</td><td>100 Hz</td><td>17.34 µm</td></tr><tr><td>200 Hz</td><td>18.47 µm</td></tr><tr><td>300 Hz</td><td>8.48 µm</td></tr><tr><td>193.33 Hz</td><td>12.45 µm</td></tr><tr><td rowspan="3">T2, 6000 rpm</td><td rowspan="3">200 Hz</td><td>206.67 Hz</td><td>12.72 µm</td></tr><tr><td>406.67 Hz</td><td>4.33 µm</td></tr><tr><td>60 Hz</td><td>3.28 µm</td></tr><tr><td rowspan="2">T4, 3000 rpm</td><td rowspan="2">200 Hz</td><td>113.33 Hz</td><td>2.34 µm</td></tr><tr><td>200 Hz</td><td>4.92 µm</td></tr><tr><td rowspan="2">T4, 6000 rpm</td><td rowspan="2">400 Hz</td><td>66.67 Hz</td><td>2.55 µm</td></tr><tr><td>113.33 Hz</td><td>2.64 µm</td></tr></tbody></table>

The vibration frequency and amplitude of different tool designs at different tool rotational speeds were analysed by FE simulation. As shown in Fig. 3, the displacement data were obtained from the field output of the FE simulation. After adjusting the data with relative time and centralizing the displacement – relative time curve, the amplitude – frequency diagram was obtained by FFT as shown in Fig. 3(d).

Fig. 4 shows the simulated vibration frequencies and amplitudes of T2 and T4 with 3000 rpm and 6000 rpm, respectively. The peaks appearing in the amplitude – frequency diagrams are summarised in Table 3. For T2 tool, the simulated vibrations can be seen at 100 Hz and 200 Hz for 3000 rpm and 6000 rpm, respectively, which are the fundamental frequencies and are the same to the reference values. Harmonics can also be found at higher frequencies. For T4 tool with 3000 rpm, the simulated vibration can be seen at 200 Hz, the same as the reference frequency. However, the peak vibration by T4 tool with 6000 rpm from the FE simulation does not show the reference frequency, which should appear at 400 Hz. Both cases of using T4 with 3000 rpm and 6000 rpm predict small peaks at lower frequencies of around 66.67 Hz and 113.33 Hz, which may be resulted from the simulation error because mass scaling was used to reduce computational time.
<table><caption>Table 2. Material parameters of AA3003-O [11] used in FE modelling of RV-ISF.</caption><tr><th>Johnson-Cook model</th><th>A (MPa)</th><th>B (MPa)</th><th>n</th><th>C</th></tr><tr><td>Value</td><td>42.97</td><td>180</td><td>0.21</td><td>0.00747</td></tr><tr><th>Other parameters</th><th>Density (kg/m³)</th><th>Young's modulus (MPa)</th><th>Poisson's ratio</th><td></td></tr><tr><td>Value</td><td>2790</td><td>72600</td><td>0.36</td><td></td></tr></table>

## Results and discussions

Analysis of vibration frequency and amplitude using FE simulation

In RV-ISF, the sheet vibration is resulted from the contact and loss of contact between forming tool and sheet surface. In theory, the reference vibration frequency can be calculated by the following equation:

$$f_{\text{ref}} = \frac{N \cdot S}{60} \qquad (3)$$

where N is the number of tool offsets or grooves and S is the tool rotational speed. The calculated reference frequencies for T2 and T4 with 3000 rpm and 6000 rpm are listed in Table 3.

<table><caption>Table 3. Reference frequencies, simulated frequencies and amplitudes for T2 and T4 in RV-ISF.</caption><thead><tr><th>Condition</th><th>Reference frequency</th><th>Simulated frequency</th><th>Simulated amplitude</th></tr></thead><tbody><tr><td rowspan="4">T2, 3000 rpm</td><td rowspan="4">100 Hz</td><td>100 Hz</td><td>17.34 µm</td></tr><tr><td>200 Hz</td><td>18.47 µm</td></tr><tr><td>300 Hz</td><td>8.48 µm</td></tr><tr><td>193.33 Hz</td><td>12.45 µm</td></tr><tr><td rowspan="3">T2, 6000 rpm</td><td rowspan="3">200 Hz</td><td>206.67 Hz</td><td>12.72 µm</td></tr><tr><td>406.67 Hz</td><td>4.33 µm</td></tr><tr><td>60 Hz</td><td>3.28 µm</td></tr><tr><td rowspan="2">T4, 3000 rpm</td><td rowspan="2">200 Hz</td><td>113.33 Hz</td><td>2.34 µm</td></tr><tr><td>200 Hz</td><td>4.92 µm</td></tr><tr><td rowspan="2">T4, 6000 rpm</td><td rowspan="2">400 Hz</td><td>66.67 Hz</td><td>2.55 µm</td></tr><tr><td>113.33 Hz</td><td>2.64 µm</td></tr></tbody></table>

The vibration frequency and amplitude of different tool designs at different tool rotational speeds were analysed by FE simulation. As shown in Fig. 3, the displacement data were obtained from the field output of the FE simulation. After adjusting the data with relative time and centralizing the displacement – relative time curve, the amplitude – frequency diagram was obtained by FFT as shown in Fig. 3(d).

Fig. 4 shows the simulated vibration frequencies and amplitudes of T2 and T4 with 3000 rpm and 6000 rpm, respectively. The peaks appearing in the amplitude – frequency diagrams are summarised in Table 3. For T2 tool, the simulated vibrations can be seen at 100 Hz and 200 Hz for 3000 rpm and 6000 rpm, respectively, which are the fundamental frequencies and are the same to the reference values. Harmonics can also be found at higher frequencies. For T4 tool with 3000 rpm, the simulated vibration can be seen at 200 Hz, the same as the reference frequency. However, the peak vibration by T4 tool with 6000 rpm from the FE simulation does not show the reference frequency, which should appear at 400 Hz. Both cases of using T4 with 3000 rpm and 6000 rpm predict small peaks at lower frequencies of around 66.67 Hz and 113.33 Hz, which may be resulted from the simulation error because mass scaling was used to reduce computational time.
<figure><img src="image_1506.png" /><figcaption>Fig. 3. Calculation process of vibration frequency and amplitude in the RV-ISF FE simulation of AA3003-O using T4 with 3000 rpm: (a) Displacement map; (b) Displacement – relative time curve; (c) Centralized displacement – relative time curve; (d) Amplitude – frequency diagram.</figcaption></figure>

<figure><img src="image_1507.png" /><figcaption>Fig. 4. Vibration frequencies and amplitudes of T2 and T4 with 3000 rpm and 6000 rpm from FE simulation results</figcaption></figure>

Obviously, the increase of tool rotational speed leads to an increased sheet vibration frequency. It is also observed that for both T2 and T4, the increase of tool rotational speed results in the reduction of vibration amplitudes. Especially for T4, the higher frequency and amplitude from the FE simulation disappear at high rotational speed of 6000 rpm. The reason may be the insufficient
<figure><img src="image_1510.png" /><figcaption>Fig. 3. Calculation process of vibration frequency and amplitude in the RV-ISF FE simulation of AA3003-O using T4 with 3000 rpm: (a) Displacement map; (b) Displacement – relative time curve; (c) Centralized displacement – relative time curve; (d) Amplitude – frequency diagram.</figcaption></figure>

<figure><img src="image_1511.png" /><figcaption>Fig. 4. Vibration frequencies and amplitudes of T2 and T4 with 3000 rpm and 6000 rpm from FE simulation results</figcaption></figure>

Obviously, the increase of tool rotational speed leads to an increased sheet vibration frequency. It is also observed that for both T2 and T4, the increase of tool rotational speed results in the reduction of vibration amplitudes. Especially for T4, the higher frequency and amplitude from the FE simulation disappear at high rotational speed of 6000 rpm. The reason may be the insufficient