## References

[1] H.M. Ortner, P.Ettmayer, H. Kolaska, I.Smid, The history of the technological progress of hardmetals, International Journal of Refractory Metals and Hard Materials, 49 (2015) 3-8.
https://doi.org/10.1016/j.ijrmhm.2014.04.016

[2] J.García, V.C. Ciprés, A. Blomqvist, B. Kaplan, Cemented carbide microstructures: a review, International Journal of Refractory Metals and Hard Materials, 80 (2019) 40-68.
https://doi.org/10.1016/j.ijrmhm.2018.12.004

[3] B.Tanrikulu, R. Karakuzu, Fatigue life prediction model of WC-Co cold forging dies based on experimental and numerical studies, Engineering Failure Analysis, 118 (2020)
https://doi.org/10.1016/j.engfailanal.2020.104910

[4] T.Klünsner, S.Marsoner, R. Ebner, R. Pippan, J. Glätzle, A.Püschel, Effect of microstructure on fatigue properties of WC-Co hardmetals, Procedia Engineering 2 (2010) 2001-2010.
https://doi.org/10.1016/j.proeng.2010.03.215

[5] J.A.M. Ferreira, M.A. Pina Amaral, F.V. Antunes, J.D.M. Costa, A study on the mechanical behaviour of WC/Co hardmetals, International Journal of Refractory Metals and Hard Materials 27 (2009) 1-8.
https://doi.org/10.1016/j.ijrmhm.2008.01.013

[6] H. Mikado, S.Ishira, N. Oguma, K.Masuda, S. Kitawaga, S.Kawamura, Effect of stress ratio on fatigue lifetime and crack growth behavior of WC-Co cemented carbide, Transactions of Nonferrous Metals Society of China 24(2014) 14-19.
https://doi.org/10.1016/S1003-6326(14)63282-9

[7] Y.Torres, M. Anglada, L.Llanes. Fatigue mechanics of WC-Co cemented carbides, International Journal of Refractory Metals and Hard Materials, 19(2001) 341-348.
https://doi.org/10.1016/S0263-4368(01)00032-4

[8] A.Li, J.Zhao, D.Wang, X. Gao, H. Tang, Three-point bending fatigue behavior of WC-Co cemented carbides, Materials & Design 45(2013) 271-278.
https://doi.org/10.1016/j.matdes.2012.08.075

[9] *Hardmetals - Determination of transverse rupture strength*, ISO 3327:2009 (2009)
## References

[1] H.M. Ortner, P.Ettmayer, H. Kolaska, I.Smid, The history of the technological progress of hardmetals, International Journal of Refractory Metals and Hard Materials, 49 (2015) 3-8.
https://doi.org/10.1016/j.ijrmhm.2014.04.016

[2] J.García, V.C. Ciprés, A. Blomqvist, B. Kaplan, Cemented carbide microstructures: a review, International Journal of Refractory Metals and Hard Materials, 80 (2019) 40-68.
https://doi.org/10.1016/j.ijrmhm.2018.12.004

[3] B.Tanrikulu, R. Karakuzu, Fatigue life prediction model of WC-Co cold forging dies based on experimental and numerical studies, Engineering Failure Analysis, 118 (2020)
https://doi.org/10.1016/j.engfailanal.2020.104910

[4] T.Klünsner, S.Marsoner, R. Ebner, R. Pippan, J. Glätzle, A.Püschel, Effect of microstructure on fatigue properties of WC-Co hardmetals, Procedia Engineering 2 (2010) 2001-2010.
https://doi.org/10.1016/j.proeng.2010.03.215

[5] J.A.M. Ferreira, M.A. Pina Amaral, F.V. Antunes, J.D.M. Costa, A study on the mechanical behaviour of WC/Co hardmetals, International Journal of Refractory Metals and Hard Materials 27 (2009) 1-8.
https://doi.org/10.1016/j.ijrmhm.2008.01.013

[6] H. Mikado, S.Ishira, N. Oguma, K.Masuda, S. Kitawaga, S.Kawamura, Effect of stress ratio on fatigue lifetime and crack growth behavior of WC-Co cemented carbide, Transactions of Nonferrous Metals Society of China 24(2014) 14-19.
https://doi.org/10.1016/S1003-6326(14)63282-9

[7] Y.Torres, M. Anglada, L.Llanes. Fatigue mechanics of WC-Co cemented carbides, International Journal of Refractory Metals and Hard Materials, 19(2001) 341-348.
https://doi.org/10.1016/S0263-4368(01)00032-4

[8] A.Li, J.Zhao, D.Wang, X. Gao, H. Tang, Three-point bending fatigue behavior of WC-Co cemented carbides, Materials & Design 45(2013) 271-278.
https://doi.org/10.1016/j.matdes.2012.08.075

[9] *Hardmetals - Determination of transverse rupture strength*, ISO 3327:2009 (2009)
# Potential of near-surface temperature regulation in hybrid additive manufactured forging dies

PEDDINGHAUS Julius¹,ª*, SIEGMUND Martin¹,ᵇ, SIRING Janina¹,ᶜ,
WESTER Hendrik¹,ᵈ, GIEDENBACHER Jochen²,ᵉ, HUSKIC Aziz²,ᵉ,
BEHRENS Bernd-Arno¹,⁹ and BRUNOTTE Kai¹,ʰ

¹Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

²Forschung & Entwicklung (Research & Development), University of Applied Sciences Upper Austria, Stelzhamerstr. 23, 4600 Wels, Austria

ªpeddinghaus@ifum.uni-hannover.de, ᵇsiegmund@ifum.uni-hannover.de,

ᶜsiring@ifum.uni-hannover.de, ᵈwester@ifum.uni-hannover.de,

ᵉjochen.giedenbacher@fh-wels.at, ᶜaziz.huskic@fh-wels.at,

⁹behrens@ifum.uni-hannover.de, ᵇbrunotte@ifum.uni-hannover.de

**Keywords:** Additive Manufacturing, Forging, Wear Protection

**Abstract.** Recent advances in the field of additive manufacturing (AM) have enabled the utilisation of Laser Powder Bed Fusion (L-PBF) for tool steels under high load conditions. Design elements, such as internal cooling channels, which are not achievable through subtractive manufacturing can therefore be used to functionalise and optimise hot forging tools. Thermal control is crucial for hot forging dies as the performance and endurance of the tools is highly dependent on the input and dissipation of heat in the surface zone during forging. A modified forging tool with conformal internal cooling channels generated through a hybrid L-PBF manufacturing process was developed in prior work [1]. The objective in the presented research is the experimental evaluation of the effect of conformal temperature control in the novel tool concept on the temperature dependent tool deterioration mechanisms in forging conditions. The actively controlled water temperature was varied between room temperature for maximum cooling and 180 °C, representing an exemplary base temperature in steady state serial forging. After 1,000 cycles, the tool wear conditions are analysed optically and through destructive microstructure analysis to characterise the effect of the temperature management on the deterioration mechanisms. The results show a significant impact of subsurface temperature control on the wear mechanisms of forging dies. Abrasive wear can be limited to a minimum through internal cooling with major reduction in thermal loads. Increased base temperatures reduce run-in time but increase abrasion.

**Introduction**

Wear significantly limits the economic efficiency of hot metal forging processes, as tool life is significantly shorter than in other manufacturing methods due to extensive tool loads. Thermal, mechanical, tribological and chemical loads are superimposed periodically for each forging cycle and lead to the gradual deterioration of the tool surface. The most significant influence is the high heat input from the billet, that reaches up to 1250 °C for hot forging of steel. The high temperature and the periodical temperature change from heat input from the billet and the subsequent output through the spray application of cooling lubricant primarily leads to thermally induced stress in the tool surface [2]. The water-component of the lubricant evaporates, cooling the surface and leaving behind a film of solid lubricant, e.g. graphite. This method of cooling and lubrication is commonly used to positively influence the tribo-system and the thermal conditions in the forging tool [3]. The secondary effect of the thermal loads in forging can be even more significant. The

<figure><img src="image_842.png" /></figure>
# Potential of near-surface temperature regulation in hybrid additive manufactured forging dies

PEDDINGHAUS Julius¹,ª*, SIEGMUND Martin¹,ᵇ, SIRING Janina¹,ᶜ,
WESTER Hendrik¹,ᵈ, GIEDENBACHER Jochen²,ᵉ, HUSKIC Aziz²,ᵉ,
BEHRENS Bernd-Arno¹,⁹ and BRUNOTTE Kai¹,ʰ

¹Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

²Forschung & Entwicklung (Research & Development), University of Applied Sciences Upper Austria, Stelzhamerstr. 23, 4600 Wels, Austria

ªpeddinghaus@ifum.uni-hannover.de, ᵇsiegmund@ifum.uni-hannover.de,
ᶜsiring@ifum.uni-hannover.de, ᵈwester@ifum.uni-hannover.de,
ᵉjochen.giedenbacher@fh-wels.at, ᶜaziz.huskic@fh-wels.at,
⁹behrens@ifum.uni-hannover.de, ᵇbrunotte@ifum.uni-hannover.de

**Keywords:** Additive Manufacturing, Forging, Wear Protection

**Abstract.** Recent advances in the field of additive manufacturing (AM) have enabled the utilisation of Laser Powder Bed Fusion (L-PBF) for tool steels under high load conditions. Design elements, such as internal cooling channels, which are not achievable through subtractive manufacturing can therefore be used to functionalise and optimise hot forging tools. Thermal control is crucial for hot forging dies as the performance and endurance of the tools is highly dependent on the input and dissipation of heat in the surface zone during forging. A modified forging tool with conformal internal cooling channels generated through a hybrid L-PBF manufacturing process was developed in prior work [1]. The objective in the presented research is the experimental evaluation of the effect of conformal temperature control in the novel tool concept on the temperature dependent tool deterioration mechanisms in forging conditions. The actively controlled water temperature was varied between room temperature for maximum cooling and 180 °C, representing an exemplary base temperature in steady state serial forging. After 1,000 cycles, the tool wear conditions are analysed optically and through destructive microstructure analysis to characterise the effect of the temperature management on the deterioration mechanisms. The results show a significant impact of subsurface temperature control on the wear mechanisms of forging dies. Abrasive wear can be limited to a minimum through internal cooling with major reduction in thermal loads. Increased base temperatures reduce run-in time but increase abrasion.

**Introduction**

Wear significantly limits the economic efficiency of hot metal forging processes, as tool life is significantly shorter than in other manufacturing methods due to extensive tool loads. Thermal, mechanical, tribological and chemical loads are superimposed periodically for each forging cycle and lead to the gradual deterioration of the tool surface. The most significant influence is the high heat input from the billet, that reaches up to 1250 °C for hot forging of steel. The high temperature and the periodical temperature change from heat input from the billet and the subsequent output through the spray application of cooling lubricant primarily leads to thermally induced stress in the tool surface [2]. The water-component of the lubricant evaporates, cooling the surface and leaving behind a film of solid lubricant, e.g. graphite. This method of cooling and lubrication is commonly used to positively influence the tribo-system and the thermal conditions in the forging tool [3]. The secondary effect of the thermal loads in forging can be even more significant. The

<figure><img src="image_850.png" /></figure>
surface-near zone is heated up drastically, resulting in the weakening of the tool material. A reduction in hardness lowers the capacity for wear resistance of the tool steel significantly. Further, in some areas with very high heat input, temperatures can reach such levels, that the flow stress of the tool steel is reduced, plasticising the surface near zones and leading to local deformation. The role of high surface temperatures for the wear and tool life in hot forging of steel is commonly acknowledged [4]. The superposition of the thermal loads with the other loads therefore leads to a critical collective, resulting in extensive surface deteriorating effects. Thermal management of the active tool surfaces can therefore be seen as a promising approach to compensate these effects. Spray cooling, which represents the status quo in terms of surface cooling, is however limited due to the process sequence as it can only be applied in between forging operations [3].

A promising alternative is inner cooling of the tools through cooling channels. Prior work has evaluated the potential for this method for the thermal regulation of forging tools and limit the effect of running-in processes and process interruptions [5]. While this approach was applied to control the base temperature, further work was carried out to manufacture tools with cooling channels in closer proximity to the active tool surfaces to counteract the wear mechanisms. It can be expected, that wear can be significantly reduced, if the weakening effect of the temperature on the tool surface is reduced. The main challenge lies in the fabrication of such inner cavities, which is very limited for conventional machining techniques. Therefore, the approach of sintering the tools with an insert of low melting material, copper in this case, to achieve an inner cavity was applied. The results however showed, that the applied sintering method negatively effects the material microstructure and homogeneity [6].

Recent advances in the field of additive manufacturing (AM) have opened new possibilities to generate more complex tool structures with inner cavities which can be utilised as cooling channels. Especially the method of Laser Powder Bed Fusion (L-PBF) represents a promising fabrication method to generate filigree inner cavities which can enable near-surface conformal cooling of tools [7]. This method has been applied for tools in different manufacturing processes with high thermal sensitivity.

The most common applications so far are primary shaping processes for metal and thermoplastic materials. Thermoplastics have very narrow process temperature windows and the filling of the moulds or dies highly depends on the temperature-dependant flow behaviour of the material. Temperature control through fluid media in conformal channels allows for a significantly higher homogeneity even in complex moulds and can therefore increase component quality and achievable geometrical complexity [8]. Thermal homogeneity also plays a crucial role in die casting of metals, especially for pressure die casting with filigree structures. The heat input into the tools through the casting process is conventionally removed through subsequent spray cooling, similar to the forging process. Cooling through conformal channel networks can increase the cooling rate and uniformity. The main benefits for this application lie in the reduction of cycle time, improved surface quality of the cast parts and the reduced shrinkage porosity [9]. This concept has also been applied in hot metal forming processes. Cooling through the tool is essential for press hardening of sheet metal components. The cooling efficiency is the most significant factor to achieve short cycle times and high economic efficiency in this process. Conformal channels, fabricated through the L-PBF process can reduce the cycle time by up to 55% due to their higher cooling effect [10]. Another forming process with high sensitivity in terms of the thermal properties is extrusion. This continuous forming process is characterised by high temperatures and high mechanical loads in the tools and is primarily applied for the production of aluminium profiles. The quality and productivity can be significantly improved through superior thermal control and temperature homogeneity [11].

These applications of L-PBF-fabricated conformal cooling channels have demonstrated the high potential for this method to increase productivity and quality in manufacturing through
surface-near zone is heated up drastically, resulting in the weakening of the tool material. A reduction in hardness lowers the capacity for wear resistance of the tool steel significantly. Further, in some areas with very high heat input, temperatures can reach such levels, that the flow stress of the tool steel is reduced, plasticising the surface near zones and leading to local deformation. The role of high surface temperatures for the wear and tool life in hot forging of steel is commonly acknowledged [4]. The superposition of the thermal loads with the other loads therefore leads to a critical collective, resulting in extensive surface deteriorating effects. Thermal management of the active tool surfaces can therefore be seen as a promising approach to compensate these effects. Spray cooling, which represents the status quo in terms of surface cooling, is however limited due to the process sequence as it can only be applied in between forging operations [3].

A promising alternative is inner cooling of the tools through cooling channels. Prior work has evaluated the potential for this method for the thermal regulation of forging tools and limit the effect of running-in processes and process interruptions [5]. While this approach was applied to control the base temperature, further work was carried out to manufacture tools with cooling channels in closer proximity to the active tool surfaces to counteract the wear mechanisms. It can be expected, that wear can be significantly reduced, if the weakening effect of the temperature on the tool surface is reduced. The main challenge lies in the fabrication of such inner cavities, which is very limited for conventional machining techniques. Therefore, the approach of sintering the tools with an insert of low melting material, copper in this case, to achieve an inner cavity was applied. The results however showed, that the applied sintering method negatively effects the material microstructure and homogeneity [6].

Recent advances in the field of additive manufacturing (AM) have opened new possibilities to generate more complex tool structures with inner cavities which can be utilised as cooling channels. Especially the method of Laser Powder Bed Fusion (L-PBF) represents a promising fabrication method to generate filigree inner cavities which can enable near-surface conformal cooling of tools [7]. This method has been applied for tools in different manufacturing processes with high thermal sensitivity.

The most common applications so far are primary shaping processes for metal and thermoplastic materials. Thermoplastics have very narrow process temperature windows and the filling of the moulds or dies highly depends on the temperature-dependant flow behaviour of the material. Temperature control through fluid media in conformal channels allows for a significantly higher homogeneity even in complex moulds and can therefore increase component quality and achievable geometrical complexity [8]. Thermal homogeneity also plays a crucial role in die casting of metals, especially for pressure die casting with filigree structures. The heat input into the tools through the casting process is conventionally removed through subsequent spray cooling, similar to the forging process. Cooling through conformal channel networks can increase the cooling rate and uniformity. The main benefits for this application lie in the reduction of cycle time, improved surface quality of the cast parts and the reduced shrinkage porosity [9]. This concept has also been applied in hot metal forming processes. Cooling through the tool is essential for press hardening of sheet metal components. The cooling efficiency is the most significant factor to achieve short cycle times and high economic efficiency in this process. Conformal channels, fabricated through the L-PBF process can reduce the cycle time by up to 55% due to their higher cooling effect [10]. Another forming process with high sensitivity in terms of the thermal properties is extrusion. This continuous forming process is characterised by high temperatures and high mechanical loads in the tools and is primarily applied for the production of aluminium profiles. The quality and productivity can be significantly improved through superior thermal control and temperature homogeneity [11].

These applications of L-PBF-fabricated conformal cooling channels have demonstrated the high potential for this method to increase productivity and quality in manufacturing through
thermal management. It can be assumed, that this method can also be beneficial to enhance tool life in hot forging of steel [1]. The described applications however have in common, that the loads are significantly lower, than in hot forging. The primary shaping processes of die casting and thermoplastic processing both show significantly lower mechanical loads due to the fluid or semifluid state of the material. The temperatures are also significantly lower. Aluminium extrusion is applied at lower temperatures as well, but shows high mechanical loads. These loads are not as dynamic as in forging, as it is a continuous process [11]. The loads in press hardening are also significantly lower than in bulk metal forming [12]. L-PBF-fabricated steel can show porosity and lower ductility compared to conventionally processed material, which can be critical for dynamically loaded forging tools [13]. The question therefore arises, whether the achievable material properties in L-PBF-fabrication are sufficient to transfer the concept of L-PBF-fabricated conformal cooling channels to hot forging of steel. This largely depends on the tool steel and the quality resulting from the L-PBF process.

The challenge for L-PBF processing lies in the introduced thermal stress which can lead to cracking. Recent advances in L-PBF technology have enabled the processing of such steel grades. The key is the thermal control of the powder bed. Preheating of the powder bed substrate enables the processibility of hot work tool steels, such as AISI H10 (1.2365) [14], which is the subject of the presented study. The transfer of conformal thermal control channels to the field of hot forging of steel can therefore be deemed as possible.

Prior work by the authors was carried out in the development of a tool steel L-PBF process for H10 and the design of an internally cooled forging die. Process parameters were established for this steel and a cooling channel concept was numerically designed to balance the benefits of high cooling efficiency close to the surface with the stability of the tool. To reduce the manufacturing costs, a hybrid tool concept was applied, limiting the costly L-PBF-manufacturing to thermally highly loaded sections where the capabilities of AM are absolutely necessary [1]. A similar approach to address the economic downsides of additive manufacturing was also applied for extrusion dies [11] and for plastic injection moulding [8].

Based on the prior work, the presented research aims at identifying the potential of L-PBF-fabricated conformal cooling channels by qualifying the L-PBF process route for hot forging tools and comparatively evaluating the effect of active temperature regulation on tool degradation.

## Materials and Methods

The test setup chosen to evaluate the application potential of conformal cooling channels in hot forging dies is based on prior work by the authors [1] and is displayed in Fig. 1. The active dies, shown in Fig. 1(a) consist of two components of AISI H10 tool steel (1.2365). Two different cooling channel cross section geometries were compared in terms of their influence on the cooling effect. A circular cross section with a diameter of 2 mm located at a distance of 3.25 mm from the mandrel radius was chosen for maximum cooling effect. In comparison, an elliptic cross section with a diameter varying between 1.5 mm and 2 mm located at 5 mm from the mandrel radius was chosen for a reduced cooling effect to evaluate the significance of the channel design on tool deterioration.

After the mandrel cap is applied onto the tool base through L-PBF, the tool base was stress-relief annealed and both components were quenched and tempered to a hardness of 48 according to HRC. Before testing, the mandrel was surface finished in a machining process. Detailed information on the L-PBF process route is given in [1]. For the fabrication process, a laser power of 225 W, a scanning speed of 700 mm/s, a volumetric energy density of 102 J/mm³ and a substrate temperature of 250 °C was applied. The tools were then assembled in the forging press in the setup, shown in Fig. 1(b). The hybrid tool is the upper tool and is supplied with water as coolant through the drilled channels in the tool base, displayed in Fig. 1(d). To evaluate the cooling effect a type
thermal management. It can be assumed, that this method can also be beneficial to enhance tool life in hot forging of steel [1]. The described applications however have in common, that the loads are significantly lower, than in hot forging. The primary shaping processes of die casting and thermoplastic processing both show significantly lower mechanical loads due to the fluid or semifluid state of the material. The temperatures are also significantly lower. Aluminium extrusion is applied at lower temperatures as well, but shows high mechanical loads. These loads are not as dynamic as in forging, as it is a continuous process [11]. The loads in press hardening are also significantly lower than in bulk metal forming [12]. L-PBF-fabricated steel can show porosity and lower ductility compared to conventionally processed material, which can be critical for dynamically loaded forging tools [13]. The question therefore arises, whether the achievable material properties in L-PBF-fabrication are sufficient to transfer the concept of L-PBF-fabricated conformal cooling channels to hot forging of steel. This largely depends on the tool steel and the quality resulting from the L-PBF process.

The challenge for L-PBF processing lies in the introduced thermal stress which can lead to cracking. Recent advances in L-PBF technology have enabled the processing of such steel grades. The key is the thermal control of the powder bed. Preheating of the powder bed substrate enables the processibility of hot work tool steels, such as AISI H10 (1.2365) [14], which is the subject of the presented study. The transfer of conformal thermal control channels to the field of hot forging of steel can therefore be deemed as possible.

Prior work by the authors was carried out in the development of a tool steel L-PBF process for H10 and the design of an internally cooled forging die. Process parameters were established for this steel and a cooling channel concept was numerically designed to balance the benefits of high cooling efficiency close to the surface with the stability of the tool. To reduce the manufacturing costs, a hybrid tool concept was applied, limiting the costly L-PBF-manufacturing to thermally highly loaded sections where the capabilities of AM are absolutely necessary [1]. A similar approach to address the economic downsides of additive manufacturing was also applied for extrusion dies [11] and for plastic injection moulding [8].

Based on the prior work, the presented research aims at identifying the potential of L-PBF-fabricated conformal cooling channels by qualifying the L-PBF process route for hot forging tools and comparatively evaluating the effect of active temperature regulation on tool degradation.

## Materials and Methods

The test setup chosen to evaluate the application potential of conformal cooling channels in hot forging dies is based on prior work by the authors [1] and is displayed in Fig. 1. The active dies, shown in Fig. 1(a) consist of two components of AISI H10 tool steel (1.2365). Two different cooling channel cross section geometries were compared in terms of their influence on the cooling effect. A circular cross section with a diameter of 2 mm located at a distance of 3.25 mm from the mandrel radius was chosen for maximum cooling effect. In comparison, an elliptic cross section with a diameter varying between 1.5 mm and 2 mm located at 5 mm from the mandrel radius was chosen for a reduced cooling effect to evaluate the significance of the channel design on tool deterioration.

After the mandrel cap is applied onto the tool base through L-PBF, the tool base was stress-relief annealed and both components were quenched and tempered to a hardness of 48 according to HRC. Before testing, the mandrel was surface finished in a machining process. Detailed information on the L-PBF process route is given in [1]. For the fabrication process, a laser power of 225 W, a scanning speed of 700 mm/s, a volumetric energy density of 102 J/mm³ and a substrate temperature of 250 °C was applied. The tools were then assembled in the forging press in the setup, shown in Fig. 1(b). The hybrid tool is the upper tool and is supplied with water as coolant through the drilled channels in the tool base, displayed in Fig. 1(d). To evaluate the cooling effect a type
K thermocouple was inserted in the centric bore 3 mm from the tool surface, as shown in Fig. 1(c) and the temperature was recorded throughout each test series.

<figure><img src="image_843.png" /><figcaption>Figure 1: Forging test setup: (a) Hybrid tool concept, (b) Installation in forging press, (c) Temperature measurement location, (d) Water flow through hybrid tool</figcaption></figure>

The tests were carried out on a fully automated eccentric forging press (SP 30d by Eumuco) with an overall force capacity of 3.15 MN. The billets of AISI 4140 (1.7225) are heated to a forming temperature range of 1200-1250 °C in an inductive push-through heating system. After heating, the billet is picked up by a handling robot and placed in the press and forged. After forging, the workpiece is ejected and a separate robot with a spray arm applies graphite-based lubricant to the tools, before the next billet is supplied. The lubricant Graphitex 289 by the supplier Tribo-Chemie GmbH was diluted to a concentration of 10% with water according to supplier specification. The setup reaches a cycle time of 6 s. A tool base heating system with regulated heating cartridges is used to maintain a tool base temperature of 180 °C before and throughout the test series.

The temperature control of the coolant was realised with a temperature control unit Thermo-5 by HB-Therm, designed for plastic injection moulding. The closed loop water system as well as all water lines are designed for high pressure to ensure the fluid state even at temperatures exceeding 100 °C. Two different parameter sets were chosen for testing. Based on [5], a water temperature (T<sub>w</sub>) of 180 °C was applied to maintain a constant tool base temperature, resulting in a system pressure of 10.5 bar. This temperature represents the stationary process state and can prevent any running-in times and a constant temperature of the tool surface despite process interruptions. A cooling effect can still be expected, as the surface temperature far surpasses this level during forging. The other temperature chosen was 20 °C as it represents the maximum cooling effect to room temperature that is possible for this system, resulting in 2 bar system pressure. The two cooling parameter variants and the two different channel cross sections result in a total of 4 tested tools. In addition, two reference tools, also manufactured with cooling channels through the described L-PBF methods, were tested. One was tested with the base temperature control system set to 180 °C but without fluid circulation, and the other reference tool was tested without any thermal management strategy apart from spray lubrication. Each tool was tested for a total of 1,000 forging cycles to ensure comparability among them.

In order to correlate the effect of the different thermal management strategies with the resulting tool degradation mechanisms, the surface of each tested tool was characterised after testing. The analysis was carried out in two stages. The first step was non-destructive analysis consisting of photographic imaging with focus stacking and 3D scanning with the 3D-Profilometer VR-3200 by Keyence. 3D scans were carried out for each tool before and after the forging tests and compared
K thermocouple was inserted in the centric bore 3 mm from the tool surface, as shown in Fig. 1(c) and the temperature was recorded throughout each test series.

<figure><img src="image_851.png" /><figcaption>Figure 1: Forging test setup: (a) Hybrid tool concept, (b) Installation in forging press, (c) Temperature measurement location, (d) Water flow through hybrid tool</figcaption></figure>

The tests were carried out on a fully automated eccentric forging press (SP 30d by Eumuco) with an overall force capacity of 3.15 MN. The billets of AISI 4140 (1.7225) are heated to a forming temperature range of 1200-1250 °C in an inductive push-through heating system. After heating, the billet is picked up by a handling robot and placed in the press and forged. After forging, the workpiece is ejected and a separate robot with a spray arm applies graphite-based lubricant to the tools, before the next billet is supplied. The lubricant Graphitex 289 by the supplier Tribo-Chemie GmbH was diluted to a concentration of 10% with water according to supplier specification. The setup reaches a cycle time of 6 s. A tool base heating system with regulated heating cartridges is used to maintain a tool base temperature of 180 °C before and throughout the test series.

The temperature control of the coolant was realised with a temperature control unit Thermo-5 by HB-Therm, designed for plastic injection moulding. The closed loop water system as well as all water lines are designed for high pressure to ensure the fluid state even at temperatures exceeding 100 °C. Two different parameter sets were chosen for testing. Based on [5], a water temperature (T<sub>w</sub>) of 180 °C was applied to maintain a constant tool base temperature, resulting in a system pressure of 10.5 bar. This temperature represents the stationary process state and can prevent any running-in times and a constant temperature of the tool surface despite process interruptions. A cooling effect can still be expected, as the surface temperature far surpasses this level during forging. The other temperature chosen was 20 °C as it represents the maximum cooling effect to room temperature that is possible for this system, resulting in 2 bar system pressure. The two cooling parameter variants and the two different channel cross sections result in a total of 4 tested tools. In addition, two reference tools, also manufactured with cooling channels through the described L-PBF methods, were tested. One was tested with the base temperature control system set to 180 °C but without fluid circulation, and the other reference tool was tested without any thermal management strategy apart from spray lubrication. Each tool was tested for a total of 1,000 forging cycles to ensure comparability among them.

In order to correlate the effect of the different thermal management strategies with the resulting tool degradation mechanisms, the surface of each tested tool was characterised after testing. The analysis was carried out in two stages. The first step was non-destructive analysis consisting of photographic imaging with focus stacking and 3D scanning with the 3D-Profilometer VR-3200 by Keyence. 3D scans were carried out for each tool before and after the forging tests and compared
to determine the tool material removed through abrasive wear. The results are crucial to evaluate the overall performance of the tested tools in terms of wear and surface effects. Afterwards, the tools were prepared to metallographic specimens, grinded, polished and etched with a 10% HNO3 solution. Light microscopic images and microhardness profiles were taken to obtain insights on the acting deterioration mechanisms in the surface zones.

## Results and Discussion

An exemplary cross section of a tool is displayed in Fig. 2. These images are representative for all tested tools, as no significant differences were detected in the cooling channel and in the joining zone. All tools show a seamless connection to the conventionally manufactured base as seen on the right detail image. The fibre orientation can be seen in the conventionally manufactured wrought material, but not in the L-PBF manufactured mandrel cap. A difference in hardness between the conventionally manufactured base and the cap could not be detected for any of the tested tools. These analyses were carried out after forging. No damage to the overall tool structure was detected for all analysed tools and parameter sets. Therefore, the strength of the L-PBF-manufactured forging tools can be considered as sufficient and the L-PBF method as technologically viable in this scale. Further testing is necessary to evaluate whether long term effects over more than 1,000 forging cycles show any different tendency. Furthermore, the scalability in terms of size of the L-PBF manufactured specimens must be further evaluated as well. Preliminary work by the authors on this topic has shown, that specific heat treatment strategies may be necessary when applying this hybrid tool manufacturing method for larger dimensions.

<figure><img src="image_844.png" /><figcaption>Figure 2: Tool cross section: left: Inner channel surface, right: Joint zone between bulk and L-PBF section</figcaption></figure>

The inner surface of the channels, displayed in the left image, show a rough structure due to L-PBF manufacturing with un-melted powder particles. Rough surface requires subsequent machining on outer active die surfaces but are unchanged in the inner cavities due to inaccessibility. They can be assumed as highly beneficial for heat transfer from the tool to the cooling medium due to the increased specific surface and the resulting turbulent flow. Turbulent flow can however limit throughput and therefore heat removal. This has to be taken into consideration for the temperature profiles

The tool temperature development, displayed in Fig. 3 for the initial process begin for all tests, shows a major difference between the processes with and without thermal management through water cooling. The temperature curves are much more consistent for the water-controlled test series. Both reference tools show major decreases due to forging process interruptions, while the temperature stays constant, for the water-controlled tests even during interruptions, as the temperature control system stays active. This result shows the great potential of actively controlled dies to reduce running-in periods at the begin of production or after interruptions to a minimum.
to determine the tool material removed through abrasive wear. The results are crucial to evaluate the overall performance of the tested tools in terms of wear and surface effects. Afterwards, the tools were prepared to metallographic specimens, grinded, polished and etched with a 10% HNO3 solution. Light microscopic images and microhardness profiles were taken to obtain insights on the acting deterioration mechanisms in the surface zones.

## Results and Discussion

An exemplary cross section of a tool is displayed in Fig. 2. These images are representative for all tested tools, as no significant differences were detected in the cooling channel and in the joining zone. All tools show a seamless connection to the conventionally manufactured base as seen on the right detail image. The fibre orientation can be seen in the conventionally manufactured wrought material, but not in the L-PBF manufactured mandrel cap. A difference in hardness between the conventionally manufactured base and the cap could not be detected for any of the tested tools. These analyses were carried out after forging. No damage to the overall tool structure was detected for all analysed tools and parameter sets. Therefore, the strength of the L-PBF-manufactured forging tools can be considered as sufficient and the L-PBF method as technologically viable in this scale. Further testing is necessary to evaluate whether long term effects over more than 1,000 forging cycles show any different tendency. Furthermore, the scalability in terms of size of the L-PBF manufactured specimens must be further evaluated as well. Preliminary work by the authors on this topic has shown, that specific heat treatment strategies may be necessary when applying this hybrid tool manufacturing method for larger dimensions.

<figure><img src="image_852.png" /><figcaption>Figure 2: Tool cross section: left: Inner channel surface, right: Joint zone between bulk and L-PBF section</figcaption></figure>

The inner surface of the channels, displayed in the left image, show a rough structure due to L-PBF manufacturing with un-melted powder particles. Rough surface requires subsequent machining on outer active die surfaces but are unchanged in the inner cavities due to inaccessibility. They can be assumed as highly beneficial for heat transfer from the tool to the cooling medium due to the increased specific surface and the resulting turbulent flow. Turbulent flow can however limit throughput and therefore heat removal. This has to be taken into consideration for the temperature profiles

The tool temperature development, displayed in Fig. 3 for the initial process begin for all tests, shows a major difference between the processes with and without thermal management through water cooling. The temperature curves are much more consistent for the water-controlled test series. Both reference tools show major decreases due to forging process interruptions, while the temperature stays constant, for the water-controlled tests even during interruptions, as the temperature control system stays active. This result shows the great potential of actively controlled dies to reduce running-in periods at the begin of production or after interruptions to a minimum.
The benefit, specifically for this method with conformal surface-near cooling channels, is the point of regulation in close proximity to the surface, minimising latency of the applied regulation.

<figure><img src="image_845.png" /><figcaption>Figure 3: Tool temperature development over the initial 1,000 s of serial forging for each tested tool</figcaption></figure>

For the tools cooled down to 20 °C, a slightly lower temperature is achieved with the circular channel, as it is closer to the surface and has a slightly larger diameter. The difference can however be seen as minor, when comparing it with the other recorded temperatures. The temperature oscillation at 180 °C water temperature is slightly higher for the circular channel compared to the elliptical channels. The smaller amplitude can be explained with the larger distance from the surface with more mass of the tool steel acting as attenuation. The major difference and the high potential of the cooling method can be derived from the comparison between the temperature profiles in reference tools and the cooled tools. Without control, a constant temperature of approx. 170 °C is reached, while the tool with base temperature control of 180 °C reaches a level exceeding 250 °C. The temperature for the 20 °C cooled tools does not exceed 50 °C, which can have a significant impact on the surface zone mechanisms.

The non-destructive tests show no significant differences in wear behaviour between the two applied channel cross section geometries oval and circular. The assumption, that these differences are minor compared to the differences between the temperature control parameters can be confirmed. The results displayed in Fig. 4 are shown exemplarily for the cooling channels with an oval cross section. The displayed reference is without tool base heating as both reference tools showed no significant differences in their behaviour, despite the difference in temperature peaks.

The reference without thermal control (right in Fig. 4) shows cracking and significant negative deviations resulting from abrasive wear in the mandrel radius. The material loss due to abrasion for the tool with a water temperature of 180 °C (centre of Fig. 4) however is significantly higher. This can be explained with the counteraction of the channel temperature control with the applied cooling lubricant. For the reference tool, the surface temperature is reduced and no further heat input occurs on the tool surface before the next forging cycle. The tool regulated at 180 °C on the other hand is heated back up directly through the water channel beneath the surface, resulting in a surface temperature, higher than for the reference. The extensive wear for the tool with a water
The benefit, specifically for this method with conformal surface-near cooling channels, is the point of regulation in close proximity to the surface, minimising latency of the applied regulation.

<figure><img src="image_853.png" /><figcaption>Figure 3: Tool temperature development over the initial 1,000 s of serial forging for each tested tool</figcaption></figure>

For the tools cooled down to 20 °C, a slightly lower temperature is achieved with the circular channel, as it is closer to the surface and has a slightly larger diameter. The difference can however be seen as minor, when comparing it with the other recorded temperatures. The temperature oscillation at 180 °C water temperature is slightly higher for the circular channel compared to the elliptical channels. The smaller amplitude can be explained with the larger distance from the surface with more mass of the tool steel acting as attenuation. The major difference and the high potential of the cooling method can be derived from the comparison between the temperature profiles in reference tools and the cooled tools. Without control, a constant temperature of approx. 170 °C is reached, while the tool with base temperature control of 180 °C reaches a level exceeding 250 °C. The temperature for the 20 °C cooled tools does not exceed 50 °C, which can have a significant impact on the surface zone mechanisms.

The non-destructive tests show no significant differences in wear behaviour between the two applied channel cross section geometries oval and circular. The assumption, that these differences are minor compared to the differences between the temperature control parameters can be confirmed. The results displayed in Fig. 4 are shown exemplarily for the cooling channels with an oval cross section. The displayed reference is without tool base heating as both reference tools showed no significant differences in their behaviour, despite the difference in temperature peaks.

The reference without thermal control (right in Fig. 4) shows cracking and significant negative deviations resulting from abrasive wear in the mandrel radius. The material loss due to abrasion for the tool with a water temperature of 180 °C (centre of Fig. 4) however is significantly higher. This can be explained with the counteraction of the channel temperature control with the applied cooling lubricant. For the reference tool, the surface temperature is reduced and no further heat input occurs on the tool surface before the next forging cycle. The tool regulated at 180 °C on the other hand is heated back up directly through the water channel beneath the surface, resulting in a surface temperature, higher than for the reference. The extensive wear for the tool with a water
temperature of 180 °C shows, that this concept of regulating the tool base temperature close to the tool surface is not suitable for application in hot forging of steel.

<figure><img src="image_846.png" /><figcaption>Figure 4: Photographic images (top) and geometrical deviation (bottom) before and after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

The tool cooled to 20 °C (left in Fig. 4) shows no negative geometric deviation at all. It can be assumed, that no significant abrasive wear has taken place. This result indicated, that conformal cooling can prohibit wear in hot forging dies. The cooling effect possibly reduces the surface temperature far enough to prevent the weakening effect of the subsurface zone in contact with the billet, which is further assessed in the following results of the destructive analysis. The tool does however show positive geometric deviation at the mandrel radius correlating with a rough surface in this area. This effect can be explained with adhesion of the billet material. When taking the results of the recorded temperatures into account, it can be assumed that the surface temperature was below 100 °C at the time of cooling lubricant application. If this is the case, the fluid component of the lubricant cannot evaporate and no solid lubricant film is formed on the active die surface. This limits the performance of the lubricant, which is designed to act as a separating layer to prevent direct contact between tool and billet. The lubricant is therefore ineffective due to the effectivity of the conformal cooling strategy. To further utilise the identified major potential of tool life enhancement through conformal cooling, a novel lubrication strategy, that does not rely on the evaporation of water, must be applied to improve the tribo-system. Possible solutions could be oil-based lubricants or lubricants with a carrier medium with lower evaporation point such as alcohol. Alternatively, further testing at intermediate water temperatures slightly above 100 °C could be taken into consideration, but must be carefully chosen, as the results for 180 °C show that a negative effect on wear is possible.

The destructive tests confirm the results seen in non-destructive tests. Both the tool without temperature regulation and the tool with a water temperature of 180 °C show significant thermally influenced zones at the die radius in the micrographs in Fig. 5. The thickness of the bright zone is greater for the tool heated to 180 °C, which is consistent with the stronger wear, seen in the non-destructive results. Both tools with higher thermal impact show significant cracks that are strongly distorted due to local plastic deformation of the surface zone. The strongest deformation occurs in
temperature of 180 °C shows, that this concept of regulating the tool base temperature close to the tool surface is not suitable for application in hot forging of steel.

<figure><img src="image_854.png" /><figcaption>Figure 4: Photographic images (top) and geometrical deviation (bottom) before and after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

The tool cooled to 20 °C (left in Fig. 4) shows no negative geometric deviation at all. It can be assumed, that no significant abrasive wear has taken place. This result indicated, that conformal cooling can prohibit wear in hot forging dies. The cooling effect possibly reduces the surface temperature far enough to prevent the weakening effect of the subsurface zone in contact with the billet, which is further assessed in the following results of the destructive analysis. The tool does however show positive geometric deviation at the mandrel radius correlating with a rough surface in this area. This effect can be explained with adhesion of the billet material. When taking the results of the recorded temperatures into account, it can be assumed that the surface temperature was below 100 °C at the time of cooling lubricant application. If this is the case, the fluid component of the lubricant cannot evaporate and no solid lubricant film is formed on the active die surface. This limits the performance of the lubricant, which is designed to act as a separating layer to prevent direct contact between tool and billet. The lubricant is therefore ineffective due to the effectivity of the conformal cooling strategy. To further utilise the identified major potential of tool life enhancement through conformal cooling, a novel lubrication strategy, that does not rely on the evaporation of water, must be applied to improve the tribo-system. Possible solutions could be oil-based lubricants or lubricants with a carrier medium with lower evaporation point such as alcohol. Alternatively, further testing at intermediate water temperatures slightly above 100 °C could be taken into consideration, but must be carefully chosen, as the results for 180 °C show that a negative effect on wear is possible.

The destructive tests confirm the results seen in non-destructive tests. Both the tool without temperature regulation and the tool with a water temperature of 180 °C show significant thermally influenced zones at the die radius in the micrographs in Fig. 5. The thickness of the bright zone is greater for the tool heated to 180 °C, which is consistent with the stronger wear, seen in the non-destructive results. Both tools with higher thermal impact show significant cracks that are strongly distorted due to local plastic deformation of the surface zone. The strongest deformation occurs in
the bright zone indicating that this zone inhibits the strongest weakening effect of the high contact temperatures. The tool cooled to 20 °C does however also show a thermally affected zone, without bright sections, disproving the assumption, that thermal effects are entirely inhibited. The quantity and depth of cracks is also significantly decreased for the strongly cooled tool. This can be led back to the ineffective cooling lubricant, as the thermal shock is reduced due to the lack of evaporative cooling on the die surface. The strong cooling does not just limit abrasive wear and local plastic deformation of the surface zone, it can also reduce thermal cracking in the surface.

<figure><img src="image_847.png" /><figcaption>Figure 5: Micrographs of mandrel radius after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

In order to contextualise and validate the findings from the micrographs, microhardness-depth-profiles perpendicular to the surface at the mandrel radius were taken for all tested tools. Two representative exemplary tools are shown in Fig. 6. The bright zone in the tool with a water temperature of 180 ° shows an increase in hardness exceeding the core hardness of the tool indicating a self-hardening effect occurring due to high temperatures in the subsurface zone exceeding the austenising temperature of the tool steel. The other side of the specimen however shows a hardness profile similar to the tool cooled to 20 °C. The results of the non-destructive analysis must be taken into account as well, as a significant portion of the surface has been removed due to abrasive wear over the entire circumference. The missing bright zone has presumably been removed shortly before the end of the test series due to extensive plastic deformation and abrasive wear. The surface zone of the tool with a water temperature of 20 °C is significantly softened as well, to a slightly shallower depth. These results confirm, the findings from the micrographs, that the thermal softening of the tool edge has not been inhibited entirely through the strong cooling effect. The softening however does not seem to be significant for wear in this forging process. Plastic deformation and overheating beyond an annealing level seem to be the tool life defining effects. It can therefore be summarized that conformal cooling of hot forging dies can be a highly effective measure to inhibit deteriorating mechanisms of the tool surface and extend tool life substantially.
the bright zone indicating that this zone inhibits the strongest weakening effect of the high contact temperatures. The tool cooled to 20 °C does however also show a thermally affected zone, without bright sections, disproving the assumption, that thermal effects are entirely inhibited. The quantity and depth of cracks is also significantly decreased for the strongly cooled tool. This can be led back to the ineffective cooling lubricant, as the thermal shock is reduced due to the lack of evaporative cooling on the die surface. The strong cooling does not just limit abrasive wear and local plastic deformation of the surface zone, it can also reduce thermal cracking in the surface.

<figure><img src="image_855.png" /><figcaption>Figure 5: Micrographs of mandrel radius after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

In order to contextualise and validate the findings from the micrographs, microhardness-depth-profiles perpendicular to the surface at the mandrel radius were taken for all tested tools. Two representative exemplary tools are shown in Fig. 6. The bright zone in the tool with a water temperature of 180 ° shows an increase in hardness exceeding the core hardness of the tool indicating a self-hardening effect occurring due to high temperatures in the subsurface zone exceeding the austenising temperature of the tool steel. The other side of the specimen however shows a hardness profile similar to the tool cooled to 20 °C. The results of the non-destructive analysis must be taken into account as well, as a significant portion of the surface has been removed due to abrasive wear over the entire circumference. The missing bright zone has presumably been removed shortly before the end of the test series due to extensive plastic deformation and abrasive wear. The surface zone of the tool with a water temperature of 20 °C is significantly softened as well, to a slightly shallower depth. These results confirm, the findings from the micrographs, that the thermal softening of the tool edge has not been inhibited entirely through the strong cooling effect. The softening however does not seem to be significant for wear in this forging process. Plastic deformation and overheating beyond an annealing level seem to be the tool life defining effects. It can therefore be summarized that conformal cooling of hot forging dies can be a highly effective measure to inhibit deteriorating mechanisms of the tool surface and extend tool life substantially.
<figure><img src="image_848.png" /><figcaption>Figure 6: Hardness-depth profiles of mandrel radius after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

## Summary

The concept of additively manufactured tools with conformal cooling channels for hot forging of steel was evaluated in terms of its application potential. The following findings can be summarized:

* The hybrid L-PBF manufacturing route was qualified for hot forging applications.

* Temperature regulation in conformal channels at tool base temperature levels of 180 °C is unfavourable, as abrasive wear is increased, but running-in times can be minimised.

* Thermal softening of the subsurface zone is of secondary importance for wear in hot forging operations compared to the plasticisation of the subsurface zone due to overheating.

* Conformal cooling of hot forging dies can significantly inhibit tool degradation mechanisms and extend tool life.

* Novel lubrication approaches are required to fully utilise the application potential of conformal cooling in hot forging processes as water-based solid lubricants are ineffective due to the lack of evaporation below 100 °C surface temperature.

The presented findings establish the basis for a wide spectrum of further research in the field of active tool cooling in hot forging of steel. Topics, are modification of the tribo-system through adapted lubrication, surface coating and diffusion treatments to further enhance tool life and the potential of utilizing other, non-hot-work tool steels through the lower surface temperatures.

## Acknowledgements

The results presented in this paper were obtained within the research project "AVIF A318". The authors thank the Research Association of the Working Group of the Iron- and Metal-processing Industry e.V. (AVIF) for their financial support of this project.

## References

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

[2] Z. Gronostajski, M. Kaszuba, M. Hawryluk, M. Zwierzchowski. A review of the degradation mechanisms of the hot forging tools. Archiv.Civ.Mech.Eng 14, (2014) 528-539. https://doi.org/10.1016/j.acme.2014.07.002

[3] M. Hawryluk, Z. Gronostajski, J. Ziemba, Ł. Dworzak, P. Jabłoński, M. Rychlik. Analysis of the influence of lubrication conditions on tool wear used in hot die forging processes. eksploatacja
<figure><img src="image_856.png" /><figcaption>Figure 6: Hardness-depth profiles of mandrel radius after 1,000 forging cycles for elliptical cooling channels</figcaption></figure>

## Summary

The concept of additively manufactured tools with conformal cooling channels for hot forging of steel was evaluated in terms of its application potential. The following findings can be summarized:

* The hybrid L-PBF manufacturing route was qualified for hot forging applications.

* Temperature regulation in conformal channels at tool base temperature levels of 180 °C is unfavourable, as abrasive wear is increased, but running-in times can be minimised.

* Thermal softening of the subsurface zone is of secondary importance for wear in hot forging operations compared to the plasticisation of the subsurface zone due to overheating.

* Conformal cooling of hot forging dies can significantly inhibit tool degradation mechanisms and extend tool life.

* Novel lubrication approaches are required to fully utilise the application potential of conformal cooling in hot forging processes as water-based solid lubricants are ineffective due to the lack of evaporation below 100 °C surface temperature.

The presented findings establish the basis for a wide spectrum of further research in the field of active tool cooling in hot forging of steel. Topics, are modification of the tribo-system through adapted lubrication, surface coating and diffusion treatments to further enhance tool life and the potential of utilizing other, non-hot-work tool steels through the lower surface temperatures.

## Acknowledgements

The results presented in this paper were obtained within the research project "AVIF A318". The authors thank the Research Association of the Working Group of the Iron- and Metal-processing Industry e.V. (AVIF) for their financial support of this project.

## References

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

[2] Z. Gronostajski, M. Kaszuba, M. Hawryluk, M. Zwierzchowski. A review of the degradation mechanisms of the hot forging tools. Archiv.Civ.Mech.Eng 14, (2014) 528-539. https://doi.org/10.1016/j.acme.2014.07.002

[3] M. Hawryluk, Z. Gronostajski, J. Ziemba, Ł. Dworzak, P. Jabłoński, M. Rychlik. Analysis of the influence of lubrication conditions on tool wear used in hot die forging processes. eksploatacja
i niezawodnosc – Maintenance and reliability 20 (2) (2018) 169–176.
http://dx.doi.org/10.17531/ein.2018.2.01

[4] E. Summerville, K. Venkatesan, C. Subramanian. Wear processes in hot forging press tools. Materials & Design 16 (5) (1995) 289-294. https://doi.org/10.1016/0261-3069(96)00010-6

[5] B. Müssig. Temperierung von Schmiedewerkzeugen zur Erhöhung der Bauteilgenauigkeit. Dissertation, Hannover, Germany (2002). https://doi.org/10.15488/9621

[6] B.-A. Behrens, M. Bonhage, I. Y. Malik, C. Bonk. Tempering control of forging processes by integration of cavities, in: B. Denkena, T. Mörke (Eds.), Cyber-Physical and Gentelligent Systems in Manufacturing and Life Cycle, Academic Press, Cambridge (USA), pp. 378-398. https://doi.org/10.1016/C2016-0-00374-1

[7] F. Klocke, K. Arntz, M. Teli, K. Winands, M. Wegener, S. Oliari, State-of-the-art Laser Additive Manufacturing for Hot-work Tool Steels, Procedia CIRP 63 (2017) 58-63, https://doi.org/10.1016/j.procir.2017.03.073

[8] F. Marin, A.F. de Souza, C.H. Ahrens, L.N.L. de Lacalle. A new hybrid process combining machining and selective laser melting to manufacture an advanced concept of conformal cooling channels for plastic injection molds. Int J Adv Manuf Technol 113 (2021) 1561–1576. https://doi.org/10.1007/s00170-021-06720-4

[9] A. Armillotta, R. Baraggi, S. Fasoli. SLM tooling for die casting with conformal cooling channels. The International Journal of Advanced Manufacturing Technology, 71 (2014) 573-583. https://doi.org/10.1007/s00170-013-5523-7

[10] R. Muvunzi, D. M. Dimitrov, S. Matope, T. Harms. A case study on the design of a hot stamping tool with conformal cooling channels. The International Journal of Advanced Manufacturing Technology, 114 (2021) 1833-1846. https://doi.org/10.1007/s00170-021-06973-z

[11] R. Hölker, A.E. Tekkaya, A.E. Advancements in the manufacturing of dies for hot aluminum extrusion with conformal cooling channels. Int J Adv Manuf Technol 83 (2016) 1209–1220. https://doi.org/10.1007/s00170-015-7647-4

[12] S. Madhankumar, K.H. Narayanan, V. Harini, K.V. Gokulraj, S. Selvakumar, R. Dharshini, K. Dharshini, T.R. Harikrishnan. Study and selection of hot forging die materials and hardness. Materials Today: Proceedings, 45 (2021) 6563-6566. https://doi.org/10.1016/j.matpr.2020.11.472

[13] F. Deirmina, N. Peghini, B. AlMangour, D. Grzesiak, M. Pellizzari. Heat treatment and properties of a hot work tool steel fabricated by additive manufacturing. Materials Science and Engineering: A, 753 (2019) 109-121. https://doi.org/10.1016/j.msea.2019.03.027

[14] N. Wild, J. Giedenbacher, A. Huskic, J. Zenisek, J. Wolfartsberger. Selective Laser Melting of AISI H10 (32CrMoV12-28) with substrate preheating for crack prevention. Procedia Computer Science, 200 (2022) 1274-1281. https://doi.org/10.1016/j.procs.2022.01.328
i niezawodnosc – Maintenance and reliability 20 (2) (2018) 169–176.
http://dx.doi.org/10.17531/ein.2018.2.01

[4] E. Summerville, K. Venkatesan, C. Subramanian. Wear processes in hot forging press tools. Materials & Design 16 (5) (1995) 289-294. https://doi.org/10.1016/0261-3069(96)00010-6

[5] B. Müssig. Temperierung von Schmiedewerkzeugen zur Erhöhung der Bauteilgenauigkeit. Dissertation, Hannover, Germany (2002). https://doi.org/10.15488/9621

[6] B.-A. Behrens, M. Bonhage, I. Y. Malik, C. Bonk. Tempering control of forging processes by integration of cavities, in: B. Denkena, T. Mörke (Eds.), Cyber-Physical and Gentelligent Systems in Manufacturing and Life Cycle, Academic Press, Cambridge (USA), pp. 378-398. https://doi.org/10.1016/C2016-0-00374-1

[7] F. Klocke, K. Arntz, M. Teli, K. Winands, M. Wegener, S. Oliari, State-of-the-art Laser Additive Manufacturing for Hot-work Tool Steels, Procedia CIRP 63 (2017) 58-63, https://doi.org/10.1016/j.procir.2017.03.073

[8] F. Marin, A.F. de Souza, C.H. Ahrens, L.N.L. de Lacalle. A new hybrid process combining machining and selective laser melting to manufacture an advanced concept of conformal cooling channels for plastic injection molds. Int J Adv Manuf Technol 113 (2021) 1561–1576. https://doi.org/10.1007/s00170-021-06720-4

[9] A. Armillotta, R. Baraggi, S. Fasoli. SLM tooling for die casting with conformal cooling channels. The International Journal of Advanced Manufacturing Technology, 71 (2014) 573-583. https://doi.org/10.1007/s00170-013-5523-7

[10] R. Muvunzi, D. M. Dimitrov, S. Matope, T. Harms. A case study on the design of a hot stamping tool with conformal cooling channels. The International Journal of Advanced Manufacturing Technology, 114 (2021) 1833-1846. https://doi.org/10.1007/s00170-021-06973-z

[11] R. Hölker, A.E. Tekkaya, A.E. Advancements in the manufacturing of dies for hot aluminum extrusion with conformal cooling channels. Int J Adv Manuf Technol 83 (2016) 1209–1220. https://doi.org/10.1007/s00170-015-7647-4

[12] S. Madhankumar, K.H. Narayanan, V. Harini, K.V. Gokulraj, S. Selvakumar, R. Dharshini, K. Dharshini, T.R. Harikrishnan. Study and selection of hot forging die materials and hardness. Materials Today: Proceedings, 45 (2021) 6563-6566. https://doi.org/10.1016/j.matpr.2020.11.472

[13] F. Deirmina, N. Peghini, B. AlMangour, D. Grzesiak, M. Pellizzari. Heat treatment and properties of a hot work tool steel fabricated by additive manufacturing. Materials Science and Engineering: A, 753 (2019) 109-121. https://doi.org/10.1016/j.msea.2019.03.027

[14] N. Wild, J. Giedenbacher, A. Huskic, J. Zenisek, J. Wolfartsberger. Selective Laser Melting of AISI H10 (32CrMoV12-28) with substrate preheating for crack prevention. Procedia Computer Science, 200 (2022) 1274-1281. https://doi.org/10.1016/j.procs.2022.01.328
# Influences of die shape and calibration strokes on surface near residual stresses of rotary swaged steel tubes

LANGSTÄDTLER Lasse<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,*, CHARNI Dhia<fnref n="4" />,ᵇ, SCHENCK Christian<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,ᶜ, EPP Jeremy<fnref n="3" />,<fnref n="4" />,ᵈ and KUHFUSS Bernd<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,ᵉ

**Keywords:** Forming, Rotary Swaging, Residual Stresses, Steel Tubes

**Abstract.** Forming processes offer a great potential to make production more sustainable by including both the shaping of the geometry and the improvement of the material properties. Through a better understanding of the decisive influencing factors on the resulting material properties of the part, this potential can be particularly exploited and leads to the chance of shortening process chains by e.g. saving heat treatment steps. The part properties during rotary swaging can be improved by strain-induced residual stresses. Thereby, compressive residual stresses can increase the resistance to fatigue fracture, to crack propagation and to corrosion. However, rotary swaging of tubes can lead to undesirable residual tensile stresses at the surface with high fluctuations. Therefore, a better understanding of the rotary swaging process and the actual material flow is necessary. The aim is to realize compressive residual stresses with low fluctuations. Thereby, it is of interest to be able to set residual stresses independently of the desired workpiece geometry. In this paper, rotary swaging of E355 steel tubes (Ø20 mm x 3 mm) was carried out with two different process adaptions. These two adaptions are the number of calibration strokes and the die geometry. They show different influences on surface near residual stresses.

**Introduction**

Rotary swaging is an incremental cold forming process that is used industrially to reduce and profile the cross-section of parts that are subject to high mechanical loads, such as axle shafts and steering spindles [1]. Furthermore, it has gained importance as a manufacturing process for aerospace industries [2]. In particular, the advantage of producing complex geometries within tight tolerances enables a cost-efficient production of lightweight components. The rotary swaging machine consists of a swaging head, a lubricant supply, a clamping device and a feeding system, Fig. 1a.

In the process, the forming dies - as part of the pressure column together with the cylinder roller, base jaw and spacer within the outer ring - rotate around the workpiece and simultaneously strike with a stroke frequency of approximately 35 Hz towards the centerline of the swaging head. During this, the workpiece is axially fed into the swaging head and retracted after the forming process, Fig. 1b. Here, the die amplitude results from rolling of the cylinder roller over the cam.

<figure><img src="image_849.png" /></figure>

<footnote n="1">¹University of Bremen, Bibliothekstraße 1, 28359 Bremen, Germany</footnote>

<footnote n="2">²bime - Bremen Institute for Mechanical Engineering, Badgasteiner Straße 1, 28359 Bremen, Germany</footnote>

<footnote n="3">³MAPEX - Center for Materials and Processes, 28334 Bremen, Germany</footnote>

<footnote n="4">⁴Leibniz Institute for Materials Engineering (IWT), Badgasteiner Str. 3, 28359 Bremen, Germany</footnote>

<footnote>ªlangstaedtler@bime.de, ᵇcharni@iwt-bremen.de, ᶜschenck@bime.de, ᵈdepp@iwt-bremen.de, ᵉkuhfuss@bime.de</footnote>
# Influences of die shape and calibration strokes on surface near residual stresses of rotary swaged steel tubes

LANGSTÄDTLER Lasse<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,a*, CHARNI Dhia<fnref n="4" />,b, SCHENCK Christian<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,c, EPP Jeremy<fnref n="3" />,<fnref n="4" />,d and KUHFUSS Bernd<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,e

**Keywords:** Forming, Rotary Swaging, Residual Stresses, Steel Tubes

**Abstract.** Forming processes offer a great potential to make production more sustainable by including both the shaping of the geometry and the improvement of the material properties. Through a better understanding of the decisive influencing factors on the resulting material properties of the part, this potential can be particularly exploited and leads to the chance of shortening process chains by e.g. saving heat treatment steps. The part properties during rotary swaging can be improved by strain-induced residual stresses. Thereby, compressive residual stresses can increase the resistance to fatigue fracture, to crack propagation and to corrosion. However, rotary swaging of tubes can lead to undesirable residual tensile stresses at the surface with high fluctuations. Therefore, a better understanding of the rotary swaging process and the actual material flow is necessary. The aim is to realize compressive residual stresses with low fluctuations. Thereby, it is of interest to be able to set residual stresses independently of the desired workpiece geometry. In this paper, rotary swaging of E355 steel tubes (Ø20 mm x 3 mm) was carried out with two different process adaptions. These two adaptions are the number of calibration strokes and the die geometry. They show different influences on surface near residual stresses.

**Introduction**

Rotary swaging is an incremental cold forming process that is used industrially to reduce and profile the cross-section of parts that are subject to high mechanical loads, such as axle shafts and steering spindles [1]. Furthermore, it has gained importance as a manufacturing process for aerospace industries [2]. In particular, the advantage of producing complex geometries within tight tolerances enables a cost-efficient production of lightweight components. The rotary swaging machine consists of a swaging head, a lubricant supply, a clamping device and a feeding system, Fig. 1a.

In the process, the forming dies - as part of the pressure column together with the cylinder roller, base jaw and spacer within the outer ring - rotate around the workpiece and simultaneously strike with a stroke frequency of approximately 35 Hz towards the centerline of the swaging head. During this, the workpiece is axially fed into the swaging head and retracted after the forming process, Fig. 1b. Here, the die amplitude results from rolling of the cylinder roller over the cam.

<figure><img src="image_857.png" /></figure>

<footnote n="1">¹University of Bremen, Bibliothekstraße 1, 28359 Bremen, Germany</footnote>

<footnote n="2">²bime - Bremen Institute for Mechanical Engineering, Badgasteiner Straße 1, 28359 Bremen, Germany</footnote>

<footnote n="3">³MAPEX - Center for Materials and Processes, 28334 Bremen, Germany</footnote>

<footnote n="4">⁴Leibniz Institute for Materials Engineering (IWT), Badgasteiner Str. 3, 28359 Bremen, Germany</footnote>

<footnote>ªlangstaedtler@bime.de, ᵇcharni@iwt-bremen.de, ᶜschenck@bime.de, ᵈdepp@iwt-bremen.de, ᵉkuhfuss@bime.de</footnote>
<figure><img src="image_850.png" /></figure>

<figure><img src="image_851.png" /><figcaption>Figure 1: Rotary swaging machine: (a) picture of the rotary swaging machine, (b) schematic drawing of the machine parts, pressure column (top right) and forming die (bottom right)</figcaption></figure>

Due to the incremental character of the process, the desired workpiece properties and geometry arise through the interaction of die shape and circumferential and lateral feed. As an example, the influence of die shape was numerically investigated in [3, 4] showing the effect of changes of die geometry in the reduction zone.

In detail, rotary swaging induces a locally distributed material flow which is related to the described geometric change that as well causes a change of material properties by e.g. work hardening [5] and residual stresses [6]. These changes build up gradually with each forming stroke. In previous studies, the final residual stress fields on the surface of steel tubes and bars were investigated and found to be sensitive to different process parameters like spacer height [7] or forming sequence [8] in the sense of homogenizing and reducing fluctuations. Rotary swaging of different workpiece materials was investigated and showed tensile as well as compressive stresses at the surface [9, 10]. Investigations of the influence of the die shape showed that swaging with round and flat dies leads to different residual stresses and can produce different geometrical features [7].

However, the aim is to find process-integrated solutions to adjust residual stresses and to generate the workpiece geometry independently. Furthermore, it is preferable that no additional process steps are required to generate the desired workpiece properties. Therefore, two different strategies were followed, a variation of the calibration strokes during retraction and an adjustment of the die geometry.

## Materials and Methods

Experimental Setup. In this study, infeed rotary swaging of annealed (700°C, 2h) EN 1.0580 (SAE-AISI 1026) steel tubes (Ø20 mm x 3 mm) from $d_0$ = 20 mm to a final outer diameter of $d_1$ = 15 mm was investigated. The experiments were conducted on a swaging machine Felss HU 32V. The workpieces were hydraulically clamped and axially fed by a linear direct drive into the swaging head. In all tests, the infeed speed was set to 1000 mm/min using a spacer height of 5.08 mm. Rotary swaging dies with the similar base geometry in the reduction zone with $\alpha$ = 10°, in the calibration zone with $l_c$ = 20 mm and transition radius $r_t$ = 20 mm were used, Fig. 2.
<figure><img src="image_858.png" /></figure>

<figure><img src="image_859.png" /><figcaption>Figure 1: Rotary swaging machine: (a) picture of the rotary swaging machine, (b) schematic drawing of the machine parts, pressure column (top right) and forming die (bottom right)</figcaption></figure>

Due to the incremental character of the process, the desired workpiece properties and geometry arise through the interaction of die shape and circumferential and lateral feed. As an example, the influence of die shape was numerically investigated in [3, 4] showing the effect of changes of die geometry in the reduction zone.

In detail, rotary swaging induces a locally distributed material flow which is related to the described geometric change that as well causes a change of material properties by e.g. work hardening [5] and residual stresses [6]. These changes build up gradually with each forming stroke. In previous studies, the final residual stress fields on the surface of steel tubes and bars were investigated and found to be sensitive to different process parameters like spacer height [7] or forming sequence [8] in the sense of homogenizing and reducing fluctuations. Rotary swaging of different workpiece materials was investigated and showed tensile as well as compressive stresses at the surface [9, 10]. Investigations of the influence of the die shape showed that swaging with round and flat dies leads to different residual stresses and can produce different geometrical features [7].

However, the aim is to find process-integrated solutions to adjust residual stresses and to generate the workpiece geometry independently. Furthermore, it is preferable that no additional process steps are required to generate the desired workpiece properties. Therefore, two different strategies were followed, a variation of the calibration strokes during retraction and an adjustment of the die geometry.

## Materials and Methods

Experimental Setup. In this study, infeed rotary swaging of annealed (700°C, 2h) EN 1.0580 (SAE-AISI 1026) steel tubes (Ø20 mm x 3 mm) from $d_0$ = 20 mm to a final outer diameter of $d_1$ = 15 mm was investigated. The experiments were conducted on a swaging machine Felss HU 32V. The workpieces were hydraulically clamped and axially fed by a linear direct drive into the swaging head. In all tests, the infeed speed was set to 1000 mm/min using a spacer height of 5.08 mm. Rotary swaging dies with the similar base geometry in the reduction zone with $\alpha$ = 10°, in the calibration zone with $l_c$ = 20 mm and transition radius $r_t$ = 20 mm were used, Fig. 2.
<figure><img src="image_852.png" /><figcaption>Figure 2: Sketch of dies at bottom dead center (two out of four forming dies are shown)</figcaption></figure>

In the exit zone, the workpiece was gradually unloaded. The dies featured a round shape perpendicular to the infeed direction, whereas the die radius $r$ varied for the dies V1-V3 as given by Fig. 3. Furthermore, due to manufacturing issues the height $H$ slightly varied for the different die variants. The rotary swaging dies V1 were made of ®ASP2013 high-speed steel and tungsten carbide (WC) coated. The rotary swaging dies V2 were made of cold working steel (AISI D2) and provided with a diamond like coating (DLC). The rotary swaging dies V3 were made of cold working steel (AISI D2) and not coated. According to the swaged workpiece diameter $d_1$, which was given by the set of dies, and the die radius $r$, the forge value $S$ was calculated with Eq. 1 [1].

$$S = \frac{d_1}{2r} \qquad (1)$$

<figure><img src="image_853.png" /><figcaption>Figure 3: Rotary swaging die variants and properties: (a) radius $r$ and height $H$ (measured values), (b) forge value $S$ and materials</figcaption></figure>

The influence of additional calibration strokes on residual stresses fluctuations was investigated using a reduced retraction speed with dies V2. Starting with no retraction hence no additional calibration strokes by stopping the swaging machine, the retraction speed – constant within each test – was varied and reduced from $v_R$ = -2000 mm/min to $v_R$ = -100 mm/min. As a consequence, the number of calibration strokes on the surface increased. Previous investigations showed that
<figure><img src="image_860.png" /><figcaption>Figure 2: Sketch of dies at bottom dead center (two out of four forming dies are shown)</figcaption></figure>

In the exit zone, the workpiece was gradually unloaded. The dies featured a round shape perpendicular to the infeed direction, whereas the die radius r varied for the dies V1-V3 as given by Fig. 3. Furthermore, due to manufacturing issues the height H slightly varied for the different die variants. The rotary swaging dies V1 were made of ®ASP2013 high-speed steel and tungsten carbide (WC) coated. The rotary swaging dies V2 were made of cold working steel (AISI D2) and provided with a diamond like coating (DLC). The rotary swaging dies V3 were made of cold working steel (AISI D2) and not coated. According to the swaged workpiece diameter d₁, which was given by the set of dies, and the die radius r, the forge value S was calculated with Eq. 1 [1].

$$S = \frac{d_1}{2r} \qquad (1)$$

<figure><img src="image_861.png" /><figcaption>Figure 3: Rotary swaging die variants and properties: (a) radius r and height H (measured values), (b) forge value S and materials</figcaption></figure>

The influence of additional calibration strokes on residual stresses fluctuations was investigated using a reduced retraction speed with dies V2. Starting with no retraction hence no additional calibration strokes by stopping the swaging machine, the retraction speed – constant within each test – was varied and reduced from vR = -2000 mm/min to vR = -100 mm/min. As a consequence, the number of calibration strokes on the surface increased. Previous investigations showed that
fluctuations manly appeared at the surface. Hence, in these tests residual stresses were only measured at and near the surface.

The influence of the die radius r on the residual stresses at the surface and below the surface was investigated using different swaging dies V1, V2 and V3. These tests were performed with a retraction speed of - 500 mm/min which was chosen as a compromise between process time and calibration properties. According to manufacturing issues, a difference in the height H of 0.05 mm was measured. Furthermore, due to die material and coating, the friction conditions varied between the used dies whereas the influence on the residual stresses was assumed to be low.

Measurement setup. The diameter d₁ was measured in 60° steps circumferential around the workpiece at two different length positions. Mean values and standard deviations were calculated. The roundness of the workpiece was measured with a Taylor Hobson TalyRond 252 at a distance of 30 mm and 170 mm from the reduction zone as roundness deviation RONt.

X-ray diffraction (XRD) was used for residual stress analysis. Due to its low penetration depth in steel of a few micrometers, this method was applied for surface residual stress measurement as well as by local material removal (etching) to assess depth profiles. For this, the residual stress measurement was performed with a commercial 8-axis diffractometer Type ETA 3003 from GE inspection technologies, equipped with a position sensitive detector. A beam of 1 mm diameter of Vanadium filtered Cr-Kα radiation was used. All residual stresses were determined using the sin²ψ-method with the {211} diffraction peak of α-iron along 13 χ-angles between -45° and +45° and X-ray elastic constant ½ S2 = 5.81 10⁻⁵ MPa⁻¹ [11]. Axial residual stresses were determined. They correlated with tangential residual stresses as showed in previous studies [12]. The residual stresses were measured starting at a distance of 50 mm to the reduction zone.

## Results

Geometries measurement. The variation of the retraction speed had no measurable influence on the elongation of the workpiece, i.e. the global axial material flow which manly takes place during infeeding. The diameter was constant with 15.088 mm ± 0.01 mm and the roundness was constant with 12.18 µm ± 0.56 µm for all retraction speeds.

The variation of the die shape had no significant influence on the elongation of the workpiece (±0.01 mm). The diameter of the workpieces slightly varied with die shape due to the difference in height H and the forge value S. Due to the difference in the radial and tangential material flow in each forming increment, as well the roundness changed with the die shape, Fig. 4.

<figure><img src="image_854.png" /><figcaption>Figure 4: Geometry values of rotary swaged workpieces with different die variants: (a) diameter d₁, (b) roundness deviation RONt</figcaption></figure>

Residual stresses measurement. An exemplary comparison for retraction speeds vR = -2000 mm/min and vR = -100 mm/min is given in Fig. 5. The residual stresses showed a clear sensitivity on the retraction speed.
fluctuations manly appeared at the surface. Hence, in these tests residual stresses were only measured at and near the surface.

The influence of the die radius r on the residual stresses at the surface and below the surface was investigated using different swaging dies V1, V2 and V3. These tests were performed with a retraction speed of - 500 mm/min which was chosen as a compromise between process time and calibration properties. According to manufacturing issues, a difference in the height H of 0.05 mm was measured. Furthermore, due to die material and coating, the friction conditions varied between the used dies whereas the influence on the residual stresses was assumed to be low.

Measurement setup. The diameter d₁ was measured in 60° steps circumferential around the workpiece at two different length positions. Mean values and standard deviations were calculated. The roundness of the workpiece was measured with a Taylor Hobson TalyRond 252 at a distance of 30 mm and 170 mm from the reduction zone as roundness deviation RONt.

X-ray diffraction (XRD) was used for residual stress analysis. Due to its low penetration depth in steel of a few micrometers, this method was applied for surface residual stress measurement as well as by local material removal (etching) to assess depth profiles. For this, the residual stress measurement was performed with a commercial 8-axis diffractometer Type ETA 3003 from GE inspection technologies, equipped with a position sensitive detector. A beam of 1 mm diameter of Vanadium filtered Cr-Kα radiation was used. All residual stresses were determined using the sin²ψ-method with the {211} diffraction peak of α-iron along 13 χ-angles between -45° and +45° and X-ray elastic constant ½ S2 = 5.81 10⁻⁵ MPa⁻¹ [11]. Axial residual stresses were determined. They correlated with tangential residual stresses as showed in previous studies [12]. The residual stresses were measured starting at a distance of 50 mm to the reduction zone.

## Results

Geometries measurement. The variation of the retraction speed had no measurable influence on the elongation of the workpiece, i.e. the global axial material flow which manly takes place during infeeding. The diameter was constant with 15.088 mm ± 0.01 mm and the roundness was constant with 12.18 µm ± 0.56 µm for all retraction speeds.

The variation of the die shape had no significant influence on the elongation of the workpiece (±0.01 mm). The diameter of the workpieces slightly varied with die shape due to the difference in height H and the forge value S. Due to the difference in the radial and tangential material flow in each forming increment, as well the roundness changed with the die shape, Fig. 4.

<figure><img src="image_862.png" /><figcaption>Figure 4: Geometry values of rotary swaged workpieces with different die variants: (a) diameter d₁, (b) roundness deviation RONt</figcaption></figure>

Residual stresses measurement. An exemplary comparison for retraction speeds vR = -2000 mm/min and vR = -100 mm/min is given in Fig. 5. The residual stresses showed a clear sensitivity on the retraction speed.
<figure><img src="image_855.png" /><figcaption>Figure 5: Exemplary axial residual stresses $\sigma_z$ along the axial position z for retraction speed -2000 mm/min and -100 mm/min</figcaption></figure>

Mean values and standard deviation values of these profiles were plotted in Fig. 6 as a function of the total number of calibration strokes per workpiece according to the retraction speed. It can be observed that by an increased number of strokes the mean value slightly decreased by 15% from around -350 MPa to -300 MPa. However, the deviation respectively the residual stresses fluctuations were reduced by 300% from about ±100 MPa to about ±25 MPa.

<figure><img src="image_856.png" /><figcaption>Figure 6: Mean value and deviation of axial residual stresses $\sigma_z$ depending on the number of calibration strokes during retraction, cp. [12]</figcaption></figure>

After rotary swaging with different die shapes (V1-V3), the workpieces showed different residual stresses on the surface and below the surface, Fig. 7. Using dies V1 and V2, the workpieces showed compressive residual stresses of around -400 MPa on the surface and as well in the compressive range up to 100 µm below the surface. Using rotary swaging dies V3 resulted in residual stresses close to zero at the surface. Below the surface the residual stresses on the workpieces which were rotary swaged with the dies V1 and V2 changed to low tensile range in the depth below 100 µm. However, for die V3 the residual stresses stayed close to zero slightly shifting into the compressive range.
<figure><img src="image_863.png" /><figcaption>Figure 5: Exemplary axial residual stresses $\sigma_z$ along the axial position z for retraction speed -2000 mm/min and -100 mm/min</figcaption></figure>

Mean values and standard deviation values of these profiles were plotted in Fig. 6 as a function of the total number of calibration strokes per workpiece according to the retraction speed. It can be observed that by an increased number of strokes the mean value slightly decreased by 15% from around -350 MPa to -300 MPa. However, the deviation respectively the residual stresses fluctuations were reduced by 300% from about ±100 MPa to about ±25 MPa.

<figure><img src="image_864.png" /><figcaption>Figure 6: Mean value and deviation of axial residual stresses $\sigma_z$ depending on the number of calibration strokes during retraction, cp. [12]</figcaption></figure>

After rotary swaging with different die shapes (V1-V3), the workpieces showed different residual stresses on the surface and below the surface, Fig. 7. Using dies V1 and V2, the workpieces showed compressive residual stresses of around -400 MPa on the surface and as well in the compressive range up to 100 µm below the surface. Using rotary swaging dies V3 resulted in residual stresses close to zero at the surface. Below the surface the residual stresses on the workpieces which were rotary swaged with the dies V1 and V2 changed to low tensile range in the depth below 100 µm. However, for die V3 the residual stresses stayed close to zero slightly shifting into the compressive range.
<figure><img src="image_857.png" /><figcaption>Figure 7: Axial residual stresses $\sigma_z$ depth profile for different die variants V1-V3, cp. [12]</figcaption></figure>

## Discussion

The depth profile of residual stresses can be significantly changed by the die geometry. The forging value S was the most influencing parameter in this study. With a value S < 1, the radius of the die (perpendicular to the infeed direction) is larger than the resulting outer radius of the part. Only tiny residual stresses were built at and near the surface. In contrast, with a forge value of S ≈ 1 beneficial compressive residual stresses were produced at the surface that decreased in the depth and changed to tensile stresses below a depth of 80 µm. Other parameters like height of the die H and coating dependent friction conditions showed minor influence. Additionally, theses residual stresses at the surface could be homogenized by increasing the number of calibration strokes during retraction of the workpiece with reduced velocity.

## Conclusion and Summary

The results introduce two different approaches of adjusting residual stresses in rotary swaging of EN 1.0580 (SAE-AISI 1026) steel tubes. The following observations can be summarized:

* Process-integrated solution was found for residual stresses calibration by reduced retraction speed.

* Calibration strokes contributed to more homogeneously distributed compressive residual stresses at the surface with less fluctuations.

* Forging value S had a significant influence on the residual stresses at the surface and in the depth of the workpiece.

* Residual stresses close to zero as well as in the high compressive range were generatable by rotary swaging with different die shapes without additional annealing steps.

The results enable both the manufacturing process and the resulting components becoming more sustainable. Thereby, the approaches influence the residual stresses in a process-integrated manner with constant workpiece geometry.

## Future Work

The method of changing the number of calibration strokes by a changed retraction speed was based on the idea of a uniform distribution of calibration strokes on the surface. Here, it is needed to find a constant process kinematic to evenly distribute the strokes on the surface. As the rotation of the workpiece was not measured or controlled, it was only assumed to be nearly constant during the retraction for an homogenic distribution of strokes. As a consequence, a measurement device was
<figure><img src="image_865.png" /><figcaption>Figure 7: Axial residual stresses $\sigma_z$ depth profile for different die variants V1-V3, cp. [12]</figcaption></figure>

## Discussion

The depth profile of residual stresses can be significantly changed by the die geometry. The forging value S was the most influencing parameter in this study. With a value S < 1, the radius of the die (perpendicular to the infeed direction) is larger than the resulting outer radius of the part. Only tiny residual stresses were built at and near the surface. In contrast, with a forge value of S ≈ 1 beneficial compressive residual stresses were produced at the surface that decreased in the depth and changed to tensile stresses below a depth of 80 µm. Other parameters like height of the die H and coating dependent friction conditions showed minor influence. Additionally, these residual stresses at the surface could be homogenized by increasing the number of calibration strokes during retraction of the workpiece with reduced velocity.

## Conclusion and Summary

The results introduce two different approaches of adjusting residual stresses in rotary swaging of EN 1.0580 (SAE-AISI 1026) steel tubes. The following observations can be summarized:

* Process-integrated solution was found for residual stresses calibration by reduced retraction speed.

* Calibration strokes contributed to more homogeneously distributed compressive residual stresses at the surface with less fluctuations.

* Forging value S had a significant influence on the residual stresses at the surface and in the depth of the workpiece.

* Residual stresses close to zero as well as in the high compressive range were generatable by rotary swaging with different die shapes without additional annealing steps.

The results enable both the manufacturing process and the resulting components becoming more sustainable. Thereby, the approaches influence the residual stresses in a process-integrated manner with constant workpiece geometry.

## Future Work

The method of changing the number of calibration strokes by a changed retraction speed was based on the idea of a uniform distribution of calibration strokes on the surface. Here, it is needed to find a constant process kinematic to evenly distribute the strokes on the surface. As the rotation of the workpiece was not measured or controlled, it was only assumed to be nearly constant during the retraction for an homogenic distribution of strokes. As a consequence, a measurement device was
applied to the machine to measure the rotation angle in future work. A reduced retraction speed increased the process time. As a result, for a future use of the approach a compromise between the fluctuation remaining and the process time has to be considered in the subsequent process design.

## Acknowledgements

This research is funded by the Deutsche Forschungsgemeinschaft (German Research Foundation)-374789876 within the sub-project (EP 128/5-2 and KU 1389/16-2) "Control of component properties in rotary swaging process" of the priority program SPP 2013 "The utilization of residual stresses induced by metal forming."

## References

[1] P. Grupp, C. Kienhöfer, Rotary Swaging Technology, Felss GmbH, Germany, (2003).

[2] S.-J. Lim, H.-J. Choi, C.-H. Lee, Forming characteristics of tubular product through the rotary swaging process. Journal of Materials Processing Technology 209 (1), (2009) 283-288.
https://doi.org/10.1016/j.jmatprotec.2007.08.086

[3] A. Ameli, M.R. Movahhedy: A parametric study on residual stresses and forging load in cold radial forging process. Int. J. of Advanced Manufacturing Technology 33, (2007) 7-17.
https://doi.org/10.1007/s00170-006-0453-2

[4] G. Singh, R. Raj, V. Narayanan K I, U.K. Arora, R. Jayaganthan, The effect of die design on residual stresses of Zr-4 alloy processed by swaging, Procedia Struc. Integrity 46, (2023) 149-154.
https://doi.org/10.1016/j.prostr.2023.06.025

[5] ASM Committee on Rotary Swaging, Rotary Swaging of Bars and Tubes, in: Metals Handbook Vol. 14 Forming and Forging, 9th ed, Ohio, Am. Society for Metals, (1988) 268-309.

[6] D. Charni, S. Ishkina, J. Epp, M. Herrmann, C. Schenck, H.W. Zoch, B. Kuhfuss, Residual stress generation in rotary swaging, Proceedings of the 5th International Conference on New Forming Technology, Bremen, Germany, (2018).
https://doi.org/10.1051/matecconf/201819004001

[7] S. Ortmann-Ishkina, D. Charni, M. Herrmann, Y. Liu, J. Epp, C. Schenck, B. Kuhfuss: Development of residual stresses by infeed rotary swaging of steel tubes, Archive of Applied Mechanics, (2021). https://doi.org/10.1007/s00419-021-01905-5

[8] L. Langstädtler, K. Moazzez, D. Charni, C. Schenck, J. Epp, B. Kuhfuss, Residual stresses generation in multi-stage rotary swaging of steel tubes, Lecture Notes in Mechanical Engineering, Springer, (2024).

[9] H. Hoche, F. Jaeger, A. Franceschi, M. Oechsner and P. Groche, Formation of Residual Stresses in Austenitic Stainless Steels by Infeed and Recess Rotary Swaging. in: Daehn, G. et al. (eds) Forming the Future, The Minerals, Metals & Materials Series, Springer (2021).
https://doi.org/10.31224/osf.io/6uks7

[10] I.C. Noyan, J.B. Cohen, Residual Stress Measurements by Diffraction and Interpretation, Springer, New York, (1987). https://doi.org/10.1007/978-1-4613-9570-6

[11] L. Kunčická, A. Macháčková, N. P. Lavery, R. Kocich, J. C.T. Cullen, L. M. Hlaváč, Effect of thermomechanical processing via rotary swaging on properties and residual stress within tungsten heavy alloy, Int. J. of Refractory Metals & Hard Materials 87, (2020).
https://doi.org/10.1016/j.ijrmhm.2019.105120

[12] Research report of the priority program SPP2013, Utz Verlag – in print, Germany, (2024).
applied to the machine to measure the rotation angle in future work. A reduced retraction speed increased the process time. As a result, for a future use of the approach a compromise between the fluctuation remaining and the process time has to be considered in the subsequent process design.

## Acknowledgements

This research is funded by the Deutsche Forschungsgemeinschaft (German Research Foundation)-374789876 within the sub-project (EP 128/5-2 and KU 1389/16-2) "Control of component properties in rotary swaging process" of the priority program SPP 2013 "The utilization of residual stresses induced by metal forming."

## References

[1] P. Grupp, C. Kienhöfer, Rotary Swaging Technology, Felss GmbH, Germany, (2003).

[2] S.-J. Lim, H.-J. Choi, C.-H. Lee, Forming characteristics of tubular product through the rotary swaging process. Journal of Materials Processing Technology 209 (1), (2009) 283-288.
https://doi.org/10.1016/j.jmatprotec.2007.08.086

[3] A. Ameli, M.R. Movahhedy: A parametric study on residual stresses and forging load in cold radial forging process. Int. J. of Advanced Manufacturing Technology 33, (2007) 7-17.
https://doi.org/10.1007/s00170-006-0453-2

[4] G. Singh, R. Raj, V. Narayanan K I, U.K. Arora, R. Jayaganthan, The effect of die design on residual stresses of Zr-4 alloy processed by swaging, Procedia Struc. Integrity 46, (2023) 149-154.
https://doi.org/10.1016/j.prostr.2023.06.025

[5] ASM Committee on Rotary Swaging, Rotary Swaging of Bars and Tubes, in: Metals Handbook Vol. 14 Forming and Forging, 9th ed, Ohio, Am. Society for Metals, (1988) 268-309.

[6] D. Charni, S. Ishkina, J. Epp, M. Herrmann, C. Schenck, H.W. Zoch, B. Kuhfuss, Residual stress generation in rotary swaging, Proceedings of the 5th International Conference on New Forming Technology, Bremen, Germany, (2018).
https://doi.org/10.1051/matecconf/201819004001

[7] S. Ortmann-Ishkina, D. Charni, M. Herrmann, Y. Liu, J. Epp, C. Schenck, B. Kuhfuss: Development of residual stresses by infeed rotary swaging of steel tubes, Archive of Applied Mechanics, (2021). https://doi.org/10.1007/s00419-021-01905-5

[8] L. Langstädtler, K. Moazzez, D. Charni, C. Schenck, J. Epp, B. Kuhfuss, Residual stresses generation in multi-stage rotary swaging of steel tubes, Lecture Notes in Mechanical Engineering, Springer, (2024).

[9] H. Hoche, F. Jaeger, A. Franceschi, M. Oechsner and P. Groche, Formation of Residual Stresses in Austenitic Stainless Steels by Infeed and Recess Rotary Swaging. in: Daehn, G. et al. (eds) Forming the Future, The Minerals, Metals & Materials Series, Springer (2021).
https://doi.org/10.31224/osf.io/6uks7

[10] I.C. Noyan, J.B. Cohen, Residual Stress Measurements by Diffraction and Interpretation, Springer, New York, (1987). https://doi.org/10.1007/978-1-4613-9570-6

[11] L. Kunčická, A. Macháčková, N. P. Lavery, R. Kocich, J. C.T. Cullen, L. M. Hlaváč, Effect of thermomechanical processing via rotary swaging on properties and residual stress within tungsten heavy alloy, Int. J. of Refractory Metals & Hard Materials 87, (2020).
https://doi.org/10.1016/j.ijrmhm.2019.105120

[12] Research report of the priority program SPP2013, Utz Verlag – in print, Germany, (2024).
# Rolling process variation estimation using a Monte-Carlo method

WEINER Max¹,ª*, RENZING Christoph¹,ᵇ, SCHMIDTCHEN Matthias¹,ᶜ, PRAHL Ulrich¹,ᵈ

¹Institute of Metal Forming, TU Bergakademie Freiberg, Germany

ªmax.weiner@imf.tu-freiberg.de, ᵇchristoph.renzing@imf.tu-freiberg.de,

ᶜmatthias.schmidtchen@imf.tu-freiberg.de, ᵈulrich.prahl@imf.tu-freiberg.de

**Keywords:** Rolling, Simulation, Monte Carlo, Precision, Tolerance, PyRoll

**Abstract.** No technical process is totally certain, but subjected to uncertainties. They may originate in the process itself or in the input materials and determine the precision of the product. Two questions are here especially of interest: 1) How do variations in the input workpiece evolve within the process? 2) Which process steps are crucial to influence this behavior? Answers to these questions can be obtained by analyzing production data or by numerical methods. The usage of Monte-Carlo-methods for estimation of variations and tolerances is a well proven approach in some fields, but was first applied by the authors to rolling processes. The inputs are all varied at once by drawing random samples from given distributions, so cross-dependencies are included in the analysis. The method has the favor of general applicability, i.e. the simulation procedure can be regarded as black box. So the method is generally agnostic to the used simulation core, but needs a large number of simulation evaluations, so fast simulation models are favorable.

## Introduction

The term Monte Carlo Method (MCM) generally refers to a class of methods, which are characterized by the use of random numbers. These methods are rather diverse and serve different purposes. Here, the term shall be used for the concept of drawing random numbers as input for a function and analysing the results of several evaluations of this function, with different random inputs, with statistical methods. A detailed overview on this type of Monte Carlo methods is given by [1]. The nature of the function can be complex, even of a black-box type, where nothing about the internals of the function is known but the input and output interfaces. In this case, Monte Carlo methods can provide valuable information about the behavior of the function while altering inputs.

Here, the function equals the simulation procedure, so it is generally known, but complex. For example, it is generally not possible, to compute derivatives of the outputs in dependence on the inputs in an analytical way. Even numerical derivation is hard, due to the multi-dimensional nature of most natural or technical systems.

The use of Monte Carlo methods for the analysis of variations in technical processes was reported before in the field of assembly of complex structures, like in mechanical engineering and building construction (f.e. [2]–[7]). The authors have previously used a similar approach to model powder morphology influences in sintering processes [8], [9]. In [10] the authors showed the difference between variations originating in the input workpiece and within the process. Were the first tend to vanish along the process, the latter tend to accumulate. Here, the efficiency of input variation elimination shall be regarded more detailed to help identifying crucial points to act on in the process regarding variational behavior.

Rolling simulation is currently dominated by the use of finite element (FE) based models. These are offering high accuracy and high resolution results at the expense of high computational resource usage. So these methods are inconvenient for the current need, as a Monte Carlo based analysis of a rolling process needs hundreds to thousands of simulation runs, depending on the count and variance of inputs, as well as the sensitivity of the process. Therefore, one-dimensional

<figure><img src="image_858.png" /></figure>
# Rolling process variation estimation using a Monte-Carlo method

WEINER Max¹,ª*, RENZING Christoph¹,ᵇ, SCHMIDTCHEN Matthias¹,ᶜ, PRAHL Ulrich¹,ᵈ

¹Institute of Metal Forming, TU Bergakademie Freiberg, Germany

ªmax.weiner@imf.tu-freiberg.de, ᵇchristoph.renzing@imf.tu-freiberg.de,

ᶜmatthias.schmidtchen@imf.tu-freiberg.de, ᵈulrich.prahl@imf.tu-freiberg.de

**Keywords:** Rolling, Simulation, Monte Carlo, Precision, Tolerance, PyRoll

**Abstract.** No technical process is totally certain, but subjected to uncertainties. They may originate in the process itself or in the input materials and determine the precision of the product. Two questions are here especially of interest: 1) How do variations in the input workpiece evolve within the process? 2) Which process steps are crucial to influence this behavior? Answers to these questions can be obtained by analyzing production data or by numerical methods. The usage of Monte-Carlo-methods for estimation of variations and tolerances is a well proven approach in some fields, but was first applied by the authors to rolling processes. The inputs are all varied at once by drawing random samples from given distributions, so cross-dependencies are included in the analysis. The method has the favor of general applicability, i.e. the simulation procedure can be regarded as black box. So the method is generally agnostic to the used simulation core, but needs a large number of simulation evaluations, so fast simulation models are favorable.

## Introduction

The term Monte Carlo Method (MCM) generally refers to a class of methods, which are characterized by the use of random numbers. These methods are rather diverse and serve different purposes. Here, the term shall be used for the concept of drawing random numbers as input for a function and analysing the results of several evaluations of this function, with different random inputs, with statistical methods. A detailed overview on this type of Monte Carlo methods is given by [1]. The nature of the function can be complex, even of a black-box type, where nothing about the internals of the function is known but the input and output interfaces. In this case, Monte Carlo methods can provide valuable information about the behavior of the function while altering inputs.

Here, the function equals the simulation procedure, so it is generally known, but complex. For example, it is generally not possible, to compute derivatives of the outputs in dependence on the inputs in an analytical way. Even numerical derivation is hard, due to the multi-dimensional nature of most natural or technical systems.

The use of Monte Carlo methods for the analysis of variations in technical processes was reported before in the field of assembly of complex structures, like in mechanical engineering and building construction (f.e. [2]–[7]). The authors have previously used a similar approach to model powder morphology influences in sintering processes [8], [9]. In [10] the authors showed the difference between variations originating in the input workpiece and within the process. Were the first tend to vanish along the process, the latter tend to accumulate. Here, the efficiency of input variation elimination shall be regarded more detailed to help identifying crucial points to act on in the process regarding variational behavior.

Rolling simulation is currently dominated by the use of finite element (FE) based models. These are offering high accuracy and high resolution results at the expense of high computational resource usage. So these methods are inconvenient for the current need, as a Monte Carlo based analysis of a rolling process needs hundreds to thousands of simulation runs, depending on the count and variance of inputs, as well as the sensitivity of the process. Therefore, one-dimensional

<figure><img src="image_866.png" /></figure>
approaches shall be used here. These offer less accuracy and limited resolution, but are computable within fractions of seconds on typical personal computer systems. The current work uses the open-source rolling simulation framework PyRolL [11] as simulation core, which is developed by the authors. PyRolL is a fast, open and flexible software package mainly aimed at groove rolling in reduction passes. The models used for the different parts of the problem can be exchanged and extended with low effort to the users needs.

## Methods

The Institute of Metal Forming operates a semi-continuous pilot rolling plant, which is the object of the current investigation. It consists of a two-high reversing roughing stand and four continuous finishing stands. The pass schedule of the current work consists of 10 oval-round reversing passes followed by 4 oval-round continuous finishing passes. A 50 mm round workpiece made of a mild structural steel is rolled down to 8 mm diameter. The detailed properties of the schedule are of minor importance for the statements of this work and are therefore left out here.

<figure><img src="image_859.png" /><figcaption>Figure 1: Chart of the Concept of Variation Estimation Using Monte Carlo Techniques</figcaption></figure>

### Monte Carlo Approach.
The basic idea of the approach shown here is to simulate the rolling process several times with different input values, which are drawn by a random number generator according to predefined statistical distributions. Afterwards, the distribution of the results can be analyzed by classic methods of descriptive statistics to obtain information about the process’ variational behavior. The principle is shown in Fig. 1. This approach provides information about the overall variational behavior of the process. If a single source of variation is introduced in the input, the reaction of the process on this variable can be analyzed. If needed, several input variables can be varied at once to regard their combined influence. The tracing back of result variations to the input can be done using classic correlation methods of descriptive statistics, however, with the same typical caveats. The main benefit of the approach is, that no information about the internals of the simulation procedure is needed for variational analysis, especially there is no need for derivatives of result values in dependence on the input. The simulation procedure can generally be treated as black box with defined input and output interfaces.

### Core Simulation Procedure.
In the current work, the open-source rolling simulation framework PyRolL [11] was used to simulate the rolling process. PyRolL provides a large library of model approaches to the partial problems of a rolling process. Here, models combining empirical approaches with simplified analytical solutions were used, because of their low computational
approaches shall be used here. These offer less accuracy and limited resolution, but are computable within fractions of seconds on typical personal computer systems. The current work uses the open-source rolling simulation framework PyRolL [11] as simulation core, which is developed by the authors. PyRolL is a fast, open and flexible software package mainly aimed at groove rolling in reduction passes. The models used for the different parts of the problem can be exchanged and extended with low effort to the users needs.

## Methods

The Institute of Metal Forming operates a semi-continuous pilot rolling plant, which is the object of the current investigation. It consists of a two-high reversing roughing stand and four continuous finishing stands. The pass schedule of the current work consists of 10 oval-round reversing passes followed by 4 oval-round continuous finishing passes. A 50 mm round workpiece made of a mild structural steel is rolled down to 8 mm diameter. The detailed properties of the schedule are of minor importance for the statements of this work and are therefore left out here.

<figure><img src="image_867.png" /><figcaption>Figure 1: Chart of the Concept of Variation Estimation Using Monte Carlo Techniques</figcaption></figure>

### Monte Carlo Approach.
The basic idea of the approach shown here is to simulate the rolling process several times with different input values, which are drawn by a random number generator according to predefined statistical distributions. Afterwards, the distribution of the results can be analyzed by classic methods of descriptive statistics to obtain information about the process’ variational behavior. The principle is shown in Fig. 1. This approach provides information about the overall variational behavior of the process. If a single source of variation is introduced in the input, the reaction of the process on this variable can be analyzed. If needed, several input variables can be varied at once to regard their combined influence. The tracing back of result variations to the input can be done using classic correlation methods of descriptive statistics, however, with the same typical caveats. The main benefit of the approach is, that no information about the internals of the simulation procedure is needed for variational analysis, especially there is no need for derivatives of result values in dependence on the input. The simulation procedure can generally be treated as black box with defined input and output interfaces.

### Core Simulation Procedure.
In the current work, the open-source rolling simulation framework PyRolL [11] was used to simulate the rolling process. PyRolL provides a large library of model approaches to the partial problems of a rolling process. Here, models combining empirical approaches with simplified analytical solutions were used, because of their low computational
effort. The simulation was done with the basic configuration of PyRolL, which includes the empirical roll force and torque model of Hensel and Spittel [12], an integral thermal model approach according to Hensel and Poluchin [13], contact area estimation according to Zouhar [14] and roll flattening according to Hitchcock [15]. Spreading was simulated using the equivalent flat pass method according to Lendl [16]–[18] in conjunction with the spreading equation of Wusatowski [19]. These models are well known and proven approximate approaches to the simulation of elongation passes. Details of software construction and model equations are provided in the documentation of PyRolL [20].

## Results and Discussion

A commonly found statement from practical experience is, that the variation in the input workpiece is equalized after 3 to 4 passes. To prove this statement, several amounts of input workpiece variation in diameter and temperature were used to simulate the variational behavior with the Monte Carlo approach. The distributions of input diameter and temperature were assumed as normal with standard deviations chosen to be 1 %, 2 %, 5 %, and 10 % of the mean input value.

<figure><img src="image_860.png" /><figcaption>Figure 2: Evolution of Filling Ratio Deviation with Different Initial Standard Deviations of Diameter</figcaption></figure>

The variation of input diameter was investigated by regard on the filling ratio (the ratio of current profile width to usable width of the groove) in each pass as shown in Fig. 2. One will notice, that the standard deviation of the filling ratio decreases rapidly in the first passes and is almost equalized after the third pass, no matter which initial deviation was used. So for the matters of shape the initial hypothesis can be confirmed. Regarding the workpiece temperature the case is different. Fig. 3 shows the standard deviations of workpiece temperatures after each pass. The deviation of workpiece temperature also decreases with each pass, but remains higher at higher initial deviations. Note, that deviations in workpiece temperature highly influence the evolution of the microstructure and therefore the product material properties. It can be stated, that shape deviations in input are of minor importance, because they are efficiently equalized in the rolling process. However, deviations in temperature tend to be still remarkable in the output workpiece.
effort. The simulation was done with the basic configuration of PyRolL, which includes the empirical roll force and torque model of Hensel and Spittel [12], an integral thermal model approach according to Hensel and Poluchin [13], contact area estimation according to Zouhar [14] and roll flattening according to Hitchcock [15]. Spreading was simulated using the equivalent flat pass method according to Lendl [16]–[18] in conjunction with the spreading equation of Wusatowski [19]. These models are well known and proven approximate approaches to the simulation of elongation passes. Details of software construction and model equations are provided in the documentation of PyRolL [20].

## Results and Discussion

A commonly found statement from practical experience is, that the variation in the input workpiece is equalized after 3 to 4 passes. To prove this statement, several amounts of input workpiece variation in diameter and temperature were used to simulate the variational behavior with the Monte Carlo approach. The distributions of input diameter and temperature were assumed as normal with standard deviations chosen to be 1 %, 2 %, 5 %, and 10 % of the mean input value.

<figure><img src="image_868.png" /><figcaption>Figure 2: Evolution of Filling Ratio Deviation with Different Initial Standard Deviations of Diameter</figcaption></figure>

The variation of input diameter was investigated by regard on the filling ratio (the ratio of current profile width to usable width of the groove) in each pass as shown in Fig. 2. One will notice, that the standard deviation of the filling ratio decreases rapidly in the first passes and is almost equalized after the third pass, no matter which initial deviation was used. So for the matters of shape the initial hypothesis can be confirmed. Regarding the workpiece temperature the case is different. Fig. 3 shows the standard deviations of workpiece temperatures after each pass. The deviation of workpiece temperature also decreases with each pass, but remains higher at higher initial deviations. Note, that deviations in workpiece temperature highly influence the evolution of the microstructure and therefore the product material properties. It can be stated, that shape deviations in input are of minor importance, because they are efficiently equalized in the rolling process. However, deviations in temperature tend to be still remarkable in the output workpiece.
<figure><img src="image_861.png" /><figcaption>Figure 3: Evolution of Workpiece Temperature Deviation with Different Initial Standard Deviations of Temperature</figcaption></figure>

<figure><img src="image_862.png" /><figcaption>Figure 4: Correlation Between Temperature Change and Variation Elimination</figcaption></figure>

Also, it can be observed in Fig. 3, that the distinct roll passes and inter-pass ranges differ in their influence on the elimination of temperature deviation. Fig. 4 shows the dependence of the relative change in temperature standard deviation, which is the absolute change in standard variation normed on the current standard deviation, in dependence on the absolute change in temperature within a pass or transport (inter-pass range). Approximately, linear correlations can be observed if roll passes and transport are regarded separately. The linear regression of the transports goes approximately through the origin, which seems natural, since no change in temperature will effect no change in temperature deviation as well. The case is different for the roll passes, were are zero temperature change does nevertheless effect a decrease of deviation. This is explained by counteracting temperature influences in roll passes. Zero temperature change in transports means that no heat flows occur. However, in roll passes, zero temperature change means that heat generation by deformation is in equilibrium with heat loss by roll contact.
<figure><img src="image_869.png" /><figcaption>Figure 3: Evolution of Workpiece Temperature Deviation with Different Initial Standard Deviations of Temperature</figcaption></figure>

<figure><img src="image_870.png" /><figcaption>Figure 4: Correlation Between Temperature Change and Variation Elimination</figcaption></figure>

Also, it can be observed in Fig. 3, that the distinct roll passes and inter-pass ranges differ in their influence on the elimination of temperature deviation. Fig. 4 shows the dependence of the relative change in temperature standard deviation, which is the absolute change in standard variation normed on the current standard deviation, in dependence on the absolute change in temperature within a pass or transport (inter-pass range). Approximately, linear correlations can be observed if roll passes and transport are regarded separately. The linear regression of the transports goes approximately through the origin, which seems natural, since no change in temperature will effect no change in temperature deviation as well. The case is different for the roll passes, were are zero temperature change does nevertheless effect a decrease of deviation. This is explained by counteracting temperature influences in roll passes. Zero temperature change in transports means that no heat flows occur. However, in roll passes, zero temperature change means that heat generation by deformation is in equilibrium with heat loss by roll contact.
## Summary and Conclusion

A Monte Carlo method was applied to investigate the variational behavior of a rolling process regarding shape and temperature evolution. Variations were found to tend to vanish along the process line. Shape deviations were found to vanish rapidly within a few roll passes. Temperature deviations were found to decrease, but remain remarkable until the last pass. A linear correlation between the decrease in standard deviation and the temperature change within a roll pass or inter-pass range was identified. From previous investigations [10] it is known, that variations arising in the process tend to accumulate in contrast to the input variations investigated here.

These observations lead to the following conclusions regarding the variational behavior of rolling processes:

* Shape deviations of the input workpiece are of minor importance.

* Uniform heating preliminary to the rolling process is of high importance for uniformity of output workpiece properties.

* Large changes applied in processing steps on a certain property help to achieve low deviations in this property.

* Introduction of additional variations in the process has to be avoided.

These conclusions are in accordance to practical knowledge.

## References

[1] C. Lemieux, *Monte Carlo and Quasi-Monte Carlo Sampling*. Springer New York, 2009.
https://doi.org/10.1007/978-0-387-78165-5.

[2] C.-Y. Lin, W.-H. Huang, M.-C. Jeng, and J.-L. Doong, "Study of an assembly tolerance allocation model based on Monte Carlo simulation," *Journal of Materials Processing Technology*, vol. 70, no. 1, pp. 9-16, Oct. 1997. https://doi.org/10.1016/S0924-0136(97)00034-4.

[3] Z. Shen, G. Ameta, J. J. Shah, and J. K. Davidson, "A Comparative Study Of Tolerance Analysis Methods," *Journal of Computing and Information Science in Engineering*, vol. 5, no. 3, pp. 247-256, May 2005. https://doi.org/10.1115/1.1979509.

[4] J.-Y. Dantan and A.-J. Qureshi, "Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation," *Computer-Aided Design*, vol. 41, no. 1, pp. 1-12, Jan. 2009. https://doi.org/10.1016/j.cad.2008.11.003.

[5] A.-J. Qureshi, J.-Y. Dantan, V. Sabri, P. Beaucaire, and N. Gayton, "A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation," *Computer-Aided Design*, vol. 44, no. 2, pp. 132-142, Feb. 2012.
https://doi.org/10.1016/j.cad.2011.10.004.

[6] H. Yan, X. Wu, and J. Yang, "Application of Monte Carlo Method in Tolerance Analysis," *Procedia CIRP*, vol. 27, pp. 281-285, Jan. 2015. https://doi.org/10.1016/j.procir.2015.04.079.

[7] C. Rausch, M. Nahangi, C. Haas, and W. Liang, "Monte Carlo simulation for tolerance analysis in prefabrication and offsite construction," *Automation in Construction*, vol. 103, pp. 300-314, Jul. 2019. https://doi.org/10.1016/j.autcon.2019.03.026.

[8] M. Weiner, M. Schmidtchen, and U. Prahl, "A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part I: Model Development and Case Studies," *Adv Eng Mater*, Feb. 2022. https://doi.org/10.1002/adem.202101513.

[9] M. Weiner, T. Zienert, M. Schmidtchen, J. Hubálková, C. G. Aneziris, and U. Prahl, "A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part II: Statistical Powder Modelling," *Adv Eng Mater*, Jun. 2022. https://doi.org/10.1002/adem.202200443.
## Summary and Conclusion

A Monte Carlo method was applied to investigate the variational behavior of a rolling process regarding shape and temperature evolution. Variations were found to tend to vanish along the process line. Shape deviations were found to vanish rapidly within a few roll passes. Temperature deviations were found to decrease, but remain remarkable until the last pass. A linear correlation between the decrease in standard deviation and the temperature change within a roll pass or inter-pass range was identified. From previous investigations [10] it is known, that variations arising in the process tend to accumulate in contrast to the input variations investigated here.

These observations lead to the following conclusions regarding the variational behavior of rolling processes:

* Shape deviations of the input workpiece are of minor importance.

* Uniform heating preliminary to the rolling process is of high importance for uniformity of output workpiece properties.

* Large changes applied in processing steps on a certain property help to achieve low deviations in this property.

* Introduction of additional variations in the process has to be avoided.

These conclusions are in accordance to practical knowledge.

## References

[1] C. Lemieux, *Monte Carlo and Quasi-Monte Carlo Sampling*. Springer New York, 2009.
https://doi.org/10.1007/978-0-387-78165-5.

[2] C.-Y. Lin, W.-H. Huang, M.-C. Jeng, and J.-L. Doong, "Study of an assembly tolerance allocation model based on Monte Carlo simulation," *Journal of Materials Processing Technology*, vol. 70, no. 1, pp. 9-16, Oct. 1997. https://doi.org/10.1016/S0924-0136(97)00034-4.

[3] Z. Shen, G. Ameta, J. J. Shah, and J. K. Davidson, "A Comparative Study Of Tolerance Analysis Methods," *Journal of Computing and Information Science in Engineering*, vol. 5, no. 3, pp. 247-256, May 2005. https://doi.org/10.1115/1.1979509.

[4] J.-Y. Dantan and A.-J. Qureshi, "Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation," *Computer-Aided Design*, vol. 41, no. 1, pp. 1-12, Jan. 2009. https://doi.org/10.1016/j.cad.2008.11.003.

[5] A.-J. Qureshi, J.-Y. Dantan, V. Sabri, P. Beaucaire, and N. Gayton, "A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation," *Computer-Aided Design*, vol. 44, no. 2, pp. 132-142, Feb. 2012.
https://doi.org/10.1016/j.cad.2011.10.004.

[6] H. Yan, X. Wu, and J. Yang, "Application of Monte Carlo Method in Tolerance Analysis," *Procedia CIRP*, vol. 27, pp. 281-285, Jan. 2015. https://doi.org/10.1016/j.procir.2015.04.079.

[7] C. Rausch, M. Nahangi, C. Haas, and W. Liang, "Monte Carlo simulation for tolerance analysis in prefabrication and offsite construction," *Automation in Construction*, vol. 103, pp. 300-314, Jul. 2019. https://doi.org/10.1016/j.autcon.2019.03.026.

[8] M. Weiner, M. Schmidtchen, and U. Prahl, "A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part I: Model Development and Case Studies," *Adv Eng Mater*, Feb. 2022. https://doi.org/10.1002/adem.202101513.

[9] M. Weiner, T. Zienert, M. Schmidtchen, J. Hubálková, C. G. Aneziris, and U. Prahl, "A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part II: Statistical Powder Modelling," *Adv Eng Mater*, Jun. 2022. https://doi.org/10.1002/adem.202200443.
[10] M. Weiner, "Estimation of rolling process variation by usage of a Monte-Carlo method," presented at the ESAFORM 2023, May 2023, pp. 1575-1582. https://doi.org/10.21741/9781644902479-170.

[11] M. Weiner, Renzing, C., M. Stirl, and M. Schmidtchen, "PyRolL - An Extensible OpenSource Framework for Rolling Simulation" *Journal of Open Source Software*, Jan. 2024. https://doi.org/10.21105/joss.06200

[12] A. Hensel and T. Spittel, *Kraft- und Arbeitsbedarf bildsamer Formgebungsverfahren*. Leipzig: VEB Deutscher Verlag für Grundstoffindustrie, 1978.

[13] A. Hensel, P. Poluchin, and W. Poluchin, *Technologie der Metallformung*, 1st ed., vol. 1. Leipzig: Deutscher Verlag für Grundstoffindustrie, 1990.

[14] G. Zouhar, *Umformungskräfte beim Walzen in Streckkaliberreihen*, vol. 1. Berlin: Akademie Verlag Berlin, 1960.

[15] J. H. Hitchcock and W. Trinks, "Roll neck bearings," ASME, New York, Report of Special Research Committee on Roll Neck Bearings, 1935.

[16] A. E. Lendl, "Rolled Bars - Part I - Calculation of Spread between non parallel roll surfaces," *Iron and Steel*, vol. 21, no. 14, pp. 397-402, 1948.

[17] A. E. Lendl, "Rolled Bars - Part II - Application of Spread Calculation to Pass Design," *Iron and Steel*, vol. 21, no. 14, pp. 601-604, 1948.

[18] A. E. Lendl, "Rolled Bars - Part III - Application of Spread Calculation to Diamond Passes," *Iron and Steel*, vol. 22, no. 12, pp. 499-501, 1949.

[19] Z. Wusatowski, *Fundamentals of Rolling*, vol. 1. London: Pergamon Press, 1969. https://doi.org/10.1016/B978-0-08-012276-2.50006-2

[20] PyRolL v2.1.3 Documentation. https://pyroll.readthedocs.io.
[10] M. Weiner, "Estimation of rolling process variation by usage of a Monte-Carlo method," presented at the ESAFORM 2023, May 2023, pp. 1575-1582. https://doi.org/10.21741/9781644902479-170.

[11] M. Weiner, Renzing, C., M. Stirl, and M. Schmidtchen, "PyRolL - An Extensible OpenSource Framework for Rolling Simulation" *Journal of Open Source Software*, Jan. 2024. https://doi.org/10.21105/joss.06200

[12] A. Hensel and T. Spittel, *Kraft- und Arbeitsbedarf bildsamer Formgebungsverfahren*. Leipzig: VEB Deutscher Verlag für Grundstoffindustrie, 1978.

[13] A. Hensel, P. Poluchin, and W. Poluchin, *Technologie der Metallformung*, 1st ed., vol. 1. Leipzig: Deutscher Verlag für Grundstoffindustrie, 1990.

[14] G. Zouhar, *Umformungskräfte beim Walzen in Streckkaliberreihen*, vol. 1. Berlin: Akademie Verlag Berlin, 1960.

[15] J. H. Hitchcock and W. Trinks, "Roll neck bearings," ASME, New York, Report of Special Research Committee on Roll Neck Bearings, 1935.

[16] A. E. Lendl, "Rolled Bars - Part I - Calculation of Spread between non parallel roll surfaces," *Iron and Steel*, vol. 21, no. 14, pp. 397-402, 1948.

[17] A. E. Lendl, "Rolled Bars - Part II - Application of Spread Calculation to Pass Design," *Iron and Steel*, vol. 21, no. 14, pp. 601-604, 1948.

[18] A. E. Lendl, "Rolled Bars - Part III - Application of Spread Calculation to Diamond Passes," *Iron and Steel*, vol. 22, no. 12, pp. 499-501, 1949.

[19] Z. Wusatowski, *Fundamentals of Rolling*, vol. 1. London: Pergamon Press, 1969. https://doi.org/10.1016/B978-0-08-012276-2.50006-2

[20] PyRolL v2.1.3 Documentation. https://pyroll.readthedocs.io.
# Impact of hot rolling on the r-values of 6000 series aluminium alloys

SARBAN Ali A.¹,ᵃ

¹ Aluminium Duffel BV, A. Stocletlaan 87, 2570 Duffel, Belgium

ᵃali.sarban@aluminiumduffel.com

**Keywords:** Aluminium, 6000 Series, Hot Rolling, R-Values, Rolling Speed, Rolling Temperature

**Abstract.** Crystallographic texture of sheet metal influences formability significantly. Lankford coefficient or the so-called r-value, a texture related property, is a property often specified as a customer requirement and therefore a property that requires close monitoring and control during the production process. Through systematic experiments, it is demonstrated how hot rolling, especially hot tandem rolling influences r-values of wrought aluminium alloys. A tandem rolling model has been developed that enables control of final r-value for a given 6016 alloy with a given downstream process. The model clearly shows how entry temperature and exit speed of tandem mill can be used to control the final product's r-value. The model that provides a metallurgical explanation for the effect, can be used to steer the tandem mill in such a manner that a minimum r-value is guaranteed and at the same time, variations of r-value along the length of the strip are minimized or suppressed. The model also provides a better alternative to the existing and conventional tandem mill steering methodology based on constant exit temperature. The proposed methodology is based on keeping a (nearly) constant Zener-Hollomon parameter along the length of the strip during tandem rolling.

**Introduction**

Continuously increasing demands on reducing CO₂ emission has significantly increased the use of
Aluminum alloys in car body applications. 6000 series aluminum alloys have received special
attention due to excellent combination of mechanical and corrosion properties. Trends towards
lower thickness combined with higher shape complexity of body panels are additionally leading
to higher demands on formability of the sheet metal. Therefore, mechanical properties describing
the formability such as Lankford coefficient or so-called r-value, strain hardening exponent,
elongation, forming limit curves etc. are receiving more and more attention in sheet metal
manufacturing as well as body panel production. The mechanical properties constitute also the
basis for the numerical simulation of press parts.

To what extent numerical simulations can predict the actual behavior of the material during
forming based on the formability indicators such as r-value is not the subject matter of the current
paper, but they are considered important and therefore meeting the requirements of the automotive
manufacturers by the sheet metal manufacturer is essential.

**Background**

Though there are no strong and conclusive evidences that suggest higher r-values lead to better
formability, requirements of the current standards still must be met. Increasing r-values of 6016
alloys produced at Aluminium Duffel has been the motivation for a project aiming at
understanding the effect of manufacturing process parameters on this indicator. As the hot rolling
process of aluminium alloys is known to significantly affect the crystallographic texture [1], this
study has been focused on investigating the effect of hot tandem rolling on the r-values of a
specific 6016 alloy.

<figure><img src="image_863.png" /></figure>
# Impact of hot rolling on the r-values of 6000 series aluminium alloys

SARBAN Ali A.¹,ᵃ

¹ Aluminium Duffel BV, A. Stocletlaan 87, 2570 Duffel, Belgium

ᵃali.sarban@aluminiumduffel.com

**Keywords:** Aluminium, 6000 Series, Hot Rolling, R-Values, Rolling Speed, Rolling Temperature

**Abstract.** Crystallographic texture of sheet metal influences formability significantly. Lankford coefficient or the so-called r-value, a texture related property, is a property often specified as a customer requirement and therefore a property that requires close monitoring and control during the production process. Through systematic experiments, it is demonstrated how hot rolling, especially hot tandem rolling influences r-values of wrought aluminium alloys. A tandem rolling model has been developed that enables control of final r-value for a given 6016 alloy with a given downstream process. The model clearly shows how entry temperature and exit speed of tandem mill can be used to control the final product's r-value. The model that provides a metallurgical explanation for the effect, can be used to steer the tandem mill in such a manner that a minimum r-value is guaranteed and at the same time, variations of r-value along the length of the strip are minimized or suppressed. The model also provides a better alternative to the existing and conventional tandem mill steering methodology based on constant exit temperature. The proposed methodology is based on keeping a (nearly) constant Zener-Hollomon parameter along the length of the strip during tandem rolling.

**Introduction**

Continuously increasing demands on reducing CO₂ emission has significantly increased the use of
Aluminum alloys in car body applications. 6000 series aluminum alloys have received special
attention due to excellent combination of mechanical and corrosion properties. Trends towards
lower thickness combined with higher shape complexity of body panels are additionally leading
to higher demands on formability of the sheet metal. Therefore, mechanical properties describing
the formability such as Lankford coefficient or so-called r-value, strain hardening exponent,
elongation, forming limit curves etc. are receiving more and more attention in sheet metal
manufacturing as well as body panel production. The mechanical properties constitute also the
basis for the numerical simulation of press parts.

To what extent numerical simulations can predict the actual behavior of the material during
forming based on the formability indicators such as r-value is not the subject matter of the current
paper, but they are considered important and therefore meeting the requirements of the automotive
manufacturers by the sheet metal manufacturer is essential.

**Background**

Though there are no strong and conclusive evidences that suggest higher r-values lead to better
formability, requirements of the current standards still must be met. Increasing r-values of 6016
alloys produced at Aluminium Duffel has been the motivation for a project aiming at
understanding the effect of manufacturing process parameters on this indicator. As the hot rolling
process of aluminium alloys is known to significantly affect the crystallographic texture [1], this
study has been focused on investigating the effect of hot tandem rolling on the r-values of a
specific 6016 alloy.

<figure><img src="image_871.png" /></figure>
## Manufacturing Process

Manufacturing process starts with casting of ingots either by Direct chill Casting (DC) or Electro-Magnetic Casting (EMC). In the current study, only DC was considered. After a homogenization and pre-heating, the ingot is hot rolled in a single stand reversing break-down mill to an intermediate gauge of about 20-40 mm and subsequently further hot rolled in a 3-stand tandem mill to the final hot rolled gauge of about 5-10 mm. The hot rolled material is coiled at an exit temperature of about 250-350 °C that is left for cooling in the air. After reaching the ambient temperature, the material is cold rolled to final gauge of about 1.0 to 1.50 mm. An intermediate annealing step may exist at an intermediate gauge between the hot rolled gauge and finish gauge. The final product is finally solution heat treated.

<figure><img src="image_864.png" /><figcaption>Figure 1. Schematic of manufacturing process</figcaption></figure>

Final product is subjected to tensile testing according to ISO 6892-1 after allowing a certain number of days for natural aging. R-values are measured in rolling, transverse and 45° to rolling direction at a tensile strain of 8-12%. R-values hereafter in this report refer to those in the transverse direction.

## Experiments and Modeling

The tandem mill was chosen for the study due to its simpler nature to model compared with a break-down mill. Also, relatively thin gauges in the tandem mill justify the assumption that temperature and strain rate across the thickness in the roll bite are uniform and therefore an average strain rate can be considered over the cross section. Average strain rate in the tandem mill was calculated from equation (1) which was derived by dividing the effective homogenous strain in plane strain by the duration of contact.

$$ \dot{\epsilon} = \frac{100 V \ln(t_{in}/t_{exit})}{3\sqrt{3D(t_{in}-t_{exit})/2}} \quad (1) $$

Where V is the linear speed at the exit of the last stand in m/min, D is the roll diameter in mm, t_in is the entry gauge to the tandem mill and t_exit is the exit gauge from the mill (both in mm). This is clearly a rough approximation as all stands are represented as one, but enough to take the most important parameters into account for the purpose of our investigation.

Temperature was measured continuously at the entry and exit of the mill that would allow calculation of instantaneous Zener-Hollomon parameter.

As temperature and strain rate play the most important role in recrystallization and texture development [2-5], several rolling experiments were conducted with the aim to cover a wide range of temperatures and strain rates with practical significance. The materials were processed to the end from which samples were taken for testing and analyses as the aim of the study was r-values of the finished product. Having an exact knowledge of hot rolling process parameters (entry and exit tandem temperatures and tandem speed) for the collected samples is essential for the modeling and analyzes purpose, therefore, location of samples on the end product were traced back to the tandem gauge to identify the entry and exit temperatures for the samples. Under standard rolling conditions where an exit temperature is targeted, speed varies a lot which makes the identification
## Manufacturing Process

Manufacturing process starts with casting of ingots either by Direct chill Casting (DC) or Electro-Magnetic Casting (EMC). In the current study, only DC was considered. After a homogenization and pre-heating, the ingot is hot rolled in a single stand reversing break-down mill to an intermediate gauge of about 20-40 mm and subsequently further hot rolled in a 3-stand tandem mill to the final hot rolled gauge of about 5-10 mm. The hot rolled material is coiled at an exit temperature of about 250-350 °C that is left for cooling in the air. After reaching the ambient temperature, the material is cold rolled to final gauge of about 1.0 to 1.50 mm. An intermediate annealing step may exist at an intermediate gauge between the hot rolled gauge and finish gauge. The final product is finally solution heat treated.

<figure><img src="image_872.png" /><figcaption>Figure 1. Schematic of manufacturing process</figcaption></figure>

Final product is subjected to tensile testing according to ISO 6892-1 after allowing a certain number of days for natural aging. R-values are measured in rolling, transverse and 45° to rolling direction at a tensile strain of 8-12%. R-values hereafter in this report refer to those in the transverse direction.

## Experiments and Modeling

The tandem mill was chosen for the study due to its simpler nature to model compared with a break-down mill. Also, relatively thin gauges in the tandem mill justify the assumption that temperature and strain rate across the thickness in the roll bite are uniform and therefore an average strain rate can be considered over the cross section. Average strain rate in the tandem mill was calculated from equation (1) which was derived by dividing the effective homogenous strain in plane strain by the duration of contact.

$$ \dot{\epsilon} = \frac{100 V \ln(t_{in}/t_{exit})}{3\sqrt{3D(t_{in}-t_{exit})/2}}. \qquad (1) $$

Where V is the linear speed at the exit of the last stand in m/min, D is the roll diameter in mm, t_in is the entry gauge to the tandem mill and t_exit is the exit gauge from the mill (both in mm). This is clearly a rough approximation as all stands are represented as one, but enough to take the most important parameters into account for the purpose of our investigation.

Temperature was measured continuously at the entry and exit of the mill that would allow calculation of instantaneous Zener-Hollomon parameter.

As temperature and strain rate play the most important role in recrystallization and texture development [2-5], several rolling experiments were conducted with the aim to cover a wide range of temperatures and strain rates with practical significance. The materials were processed to the end from which samples were taken for testing and analyses as the aim of the study was r-values of the finished product. Having an exact knowledge of hot rolling process parameters (entry and exit tandem temperatures and tandem speed) for the collected samples is essential for the modeling and analyzes purpose, therefore, location of samples on the end product were traced back to the tandem gauge to identify the entry and exit temperatures for the samples. Under standard rolling conditions where an exit temperature is targeted, speed varies a lot which makes the identification
of relevant speed for the taken sample difficult. For this reason, tandem mill was operated at a constant speed for these experiments. Entry and exit temperatures to the tandem mill and exit speeds were recorded for further analyses and modeling. These experiments are graphically represented below.

<figure><img src="image_865.png" /><figcaption>Figure 2. Graphical representation of first experiments at constant speed</figcaption></figure>

Texture in aluminum alloys for the most part is developed during hot rolling and r-value of the final product is strongly dependent on the texture [6, 7]. Even though intensity of various texture components may change downstream in the process, fingerprint of hot rolled texture will still be dominant. Our strategy in this work was to relate the r-values of the final product to the hot rolling conditions in the tandem mill affecting recrystallization.

Various investigations in the past [2, 5, 8] have successfully modelled the recrystallization behavior of aluminum alloys after hot rolling. Time for 50% recrystallization is often modelled by equations of type

$$f = Z_{def}^{b} \cdot Z_{rex}. \qquad (2)$$

Where $Z_{def}$ is the well-known Zener-Hollomon parameter defined as

$$Z_{def} = \dot{\epsilon} \exp \left( \frac{Q_{def}}{R T_{in}} \right).$$

which may be considered as a measure of stored energy in the material during hot deformation and in which, $Q_{def}$ is the activation energy for deformation and R is the universal gas constant.

$Z_{rex}$ describes the kinetics of recrystallization after hot deformation and is defined by

$$Z_{rex} = \exp \left( \frac{Q_{rex}}{R T_{exit}} \right).$$

where $Q_{rex}$ is the activation energy for recrystallization.

In the above expressions, $T_{in}$ and $T_{exit}$ are deformation temperature and holding temperature in K which correspond to entry temperature to tandem and coil temperature after tandem respectively.

For all experiments, f-values were calculated and r-values of those experiments were plotted against ln(f), good correlation was found as shown in Figure 3 below. Model constants ($Q_{def}$, $Q_{rex}$ and b) where taken from literature as the main interest lied in the trends rather than in absolute values.
of relevant speed for the taken sample difficult. For this reason, tandem mill was operated at a constant speed for these experiments. Entry and exit temperatures to the tandem mill and exit speeds were recorded for further analyses and modeling. These experiments are graphically represented below.

<figure><img src="image_873.png" /><figcaption>Figure 2. Graphical representation of first experiments at constant speed</figcaption></figure>

Texture in aluminum alloys for the most part is developed during hot rolling and r-value of the final product is strongly dependent on the texture [6, 7]. Even though intensity of various texture components may change downstream in the process, fingerprint of hot rolled texture will still be dominant. Our strategy in this work was to relate the r-values of the final product to the hot rolling conditions in the tandem mill affecting recrystallization.

Various investigations in the past [2, 5, 8] have successfully modelled the recrystallization behavior of aluminum alloys after hot rolling. Time for 50% recrystallization is often modelled by equations of type

$$f = Z_{def}^{b} \cdot Z_{rex}. \qquad (2)$$

Where $Z_{def}$ is the well-known Zener-Hollomon parameter defined as

$$Z_{def} = \dot{\epsilon} \exp \left( \frac{Q_{def}}{R T_{in}} \right).$$

which may be considered as a measure of stored energy in the material during hot deformation and in which, $Q_{def}$ is the activation energy for deformation and R is the universal gas constant.

$Z_{rex}$ describes the kinetics of recrystallization after hot deformation and is defined by

$$Z_{rex} = \exp \left( \frac{Q_{rex}}{R T_{exit}} \right).$$

where $Q_{rex}$ is the activation energy for recrystallization.

In the above expressions, $T_{in}$ and $T_{exit}$ are deformation temperature and holding temperature in K which correspond to entry temperature to tandem and coil temperature after tandem respectively.

For all experiments, f-values were calculated and r-values of those experiments were plotted against ln(f), good correlation was found as shown in Figure 3 below. Model constants ($Q_{def}$, $Q_{rex}$ and b) where taken from literature as the main interest lied in the trends rather than in absolute values.
<figure><img src="image_866.png" /><figcaption>Figure 3. r-values correlate strongly with ln(f) in separate groups of holding temperature Texit.</figcaption></figure>

Since exit temperature from the mill was not a target, variations of it were inevitable and these variations seemed to negatively affect the fit between the measured r-values and values predicted by the model (Figure 3). To confirm this, a new set of experiments were designed and performed targeting specific exit temperatures following the scheme of Figure 4.

<figure><img src="image_867.png" /><figcaption>Figure 4. Scheme of second set of experiments targeting exit temperature</figcaption></figure>

Results of these experiments are presented in Figure 5 below.

<figure><img src="image_868.png" /><figcaption>Figure 5. Reducing the variations in exit temperature improves the correlation between r-values and function f.</figcaption></figure>

Thus, by suppressing variations in the exit temperature, the fit between r-values and ln(f) improved.

Even though equation (2) seems to be able to predict the r-value reasonably, but relative role of entry and exit temperatures on it is still not clear.

From the plots of Figure 1, values of ln(f) at a given r-value, say 0.6, can be extracted for every Texit. We call the values of function f at this given r-value, f₀, which is clearly a different value for every Texit. By doing so, following table is obtained.
<figure><img src="image_874.png" /><figcaption>Figure 3. r-values correlate strongly with ln(f) in separate groups of holding temperature Texit.</figcaption></figure>

Since exit temperature from the mill was not a target, variations of it were inevitable and these variations seemed to negatively affect the fit between the measured r-values and values predicted by the model (Figure 3). To confirm this, a new set of experiments were designed and performed targeting specific exit temperatures following the scheme of Figure 4.

<figure><img src="image_875.png" /><figcaption>Figure 4. Scheme of second set of experiments targeting exit temperature</figcaption></figure>

Results of these experiments are presented in Figure 5 below.

<figure><img src="image_876.png" /><figcaption>Figure 5. Reducing the variations in exit temperature improves the correlation between r-values and function f.</figcaption></figure>

Thus, by suppressing variations in the exit temperature, the fit between r-values and ln(f) improved.

Even though equation (2) seems to be able to predict the r-value reasonably, but relative role of entry and exit temperatures on it is still not clear.

From the plots of Figure 1, values of ln(f) at a given r-value, say 0.6, can be extracted for every Texit. We call the values of function f at this given r-value, f₀, which is clearly a different value for every Texit. By doing so, following table is obtained.
<table><caption>Table 1. Values of function ln(f) at r = 0.6 for different values of T<sub>exit</sub>.</caption><tr><td>T<sub>exit</sub></td><td>263</td><td>281</td><td>284</td><td>294</td><td>322</td></tr><tr><td>ln(f<sub>0</sub>)</td><td>22.3</td><td>20.8</td><td>20.6</td><td>19.9</td><td>17.9</td></tr></table>

ln (f) can be written as:

$$ \ln(f) = b \ln(Z_{def}) + \ln(Z_{rex}) = b \ln(\dot{\epsilon}) + \frac{b Q_{def}}{R \cdot T_{in}} + \frac{Q_{rex}}{R \cdot T_{exit}} $$

At a fixed value of r, say 0.6, we rename f to f₀ and introduce a new parameter B:

$$ B = \frac{\ln(f_0)}{b} - \frac{Q_{rex}}{b R(T_{exit})} = \frac{\ln(f_0) - \ln(Z_{rex})}{b} \quad (3) $$

and we arrive at

$$ \dot{\epsilon} = \exp \left\{ B - \frac{Q_{def}}{R \cdot T_{in}} \right\}. \quad (4) $$

It can easily be seen that $B = \ln(Z_{def})$.

Now for each pair of T<sub>exit</sub> and ln (f₀) in Table 1, parameter B can be calculated to obtain Table 2.

<table><caption>Table 2. Values of B calculated from equation (3) using values of Table 1.</caption><tr><td>T<sub>exit</sub></td><td>263</td><td>281</td><td>284</td><td>294</td><td>322</td></tr><tr><td>ln (f<sub>0</sub>)</td><td>22.3</td><td>20.8</td><td>20.6</td><td>19.9</td><td>17.9</td></tr><tr><td>B</td><td>50</td><td>50</td><td>50</td><td>50</td><td>50</td></tr></table>

As seen in Table 2, all combinations of T<sub>exit</sub> and f₀ result in the same value of B indicating that exit temperature has had no effect on the r-value. It follows automatically from equation (4) that a constant Z<sub>def</sub> value is enough to provide a constant r-value. Plot of Figure 5 confirms this statement.

<figure><img src="image_869.png" /><figcaption>Figure 6. Good correlation between Zener-Hollomon parameter and the r-values independent from T<sub>exit</sub>.</figcaption></figure>

Holding temperatures or T<sub>exit</sub> in this study have probably not been sufficiently high to trigger recrystallization and therefore Parameter B appears to be independent from it. To confirm this, a DSC test was done on a quenched hot band material after tandem mill to determine the recrystallization peak temperature. Results of this test is shown in Figure 7.
<table><caption>Table 1. Values of function ln(f) at r = 0.6 for different values of T<sub>exit</sub>.</caption><tr><td>T<sub>exit</sub></td><td>263</td><td>281</td><td>284</td><td>294</td><td>322</td></tr><tr><td>ln(f<sub>0</sub>)</td><td>22.3</td><td>20.8</td><td>20.6</td><td>19.9</td><td>17.9</td></tr></table>

ln (f) can be written as:

$$ \ln(f) = b \ln(Z_{def}) + \ln(Z_{rex}) = b \ln(\dot{\epsilon}) + \frac{b Q_{def}}{R \cdot T_{in}} + \frac{Q_{rex}}{R \cdot T_{exit}} $$

At a fixed value of r, say 0.6, we rename f to f₀ and introduce a new parameter B:

$$ B = \frac{\ln(f_0)}{b} - \frac{Q_{rex}}{b R(T_{exit})} = \frac{\ln(f_0) - \ln(Z_{rex})}{b} \quad (3) $$

and we arrive at

$$ \dot{\epsilon} = \exp \left\{ B - \frac{Q_{def}}{R \cdot T_{in}} \right\}. \quad (4) $$

It can easily be seen that $B = \ln(Z_{def})$.

Now for each pair of T<sub>exit</sub> and ln (f₀) in Table 1, parameter B can be calculated to obtain Table 2.

<table><caption>Table 2. Values of B calculated from equation (3) using values of Table 1.</caption><tr><td>T<sub>exit</sub></td><td>263</td><td>281</td><td>284</td><td>294</td><td>322</td></tr><tr><td>ln (f<sub>0</sub>)</td><td>22.3</td><td>20.8</td><td>20.6</td><td>19.9</td><td>17.9</td></tr><tr><td>B</td><td>50</td><td>50</td><td>50</td><td>50</td><td>50</td></tr></table>

As seen in Table 2, all combinations of T<sub>exit</sub> and f₀ result in the same value of B indicating that exit temperature has had no effect on the r-value. It follows automatically from equation (4) that a constant Z<sub>def</sub> value is enough to provide a constant r-value. Plot of Figure 5 confirms this statement.

<figure><img src="image_877.png" /><figcaption>Figure 6. Good correlation between Zener-Hollomon parameter and the r-values independent from T<sub>exit</sub>.</figcaption></figure>

Holding temperatures or T<sub>exit</sub> in this study have probably not been sufficiently high to trigger recrystallization and therefore Parameter B appears to be independent from it. To confirm this, a DSC test was done on a quenched hot band material after tandem mill to determine the recrystallization peak temperature. Results of this test is shown in Figure 7.
<figure><img src="image_870.png" /><figcaption>Figure 7. Recrystallization peak temperature determined by DSC test on one of the hot rolled materials of the study.</figcaption></figure>

The highest heating rate is most relevant for this study as recrystallization of hot rolled material will start to take place with a minimum delay and loss of driving force.

Recrystallization peak temperatures in Figure 7 are much higher than holding temperatures in this study and therefore we conclude that no recrystallization has taken place immediately after hot rolling. Microstructure of the hot band material after coiling and cooling is shown in Figure 8.

<figure><img src="image_871.png" /><figcaption>Figure 8. Across thickness microstructure of naturally cooled hot band after tandem mill. No recrystallization has taken place</figcaption></figure>

## Practical Application

Based on what discussed, a minimum value of Zener-Hollomon parameter ($Z_{def}$) is required to reach a minimum desired r-value and having a (nearly) constant $Z_{def}$ throughout the coil is necessary to obtain a (nearly) constant r-value throughout the coil. A constant $Z_{def}$ implies a relationship between rolling speed and temperature as demonstrated in Figure 9.

<figure><img src="image_872.png" /><figcaption>Figure 9. Desired relationship between tandem entry temperature and tandem speed to achieve a constant $Z_{def}$. The curve represents a certain minimum r-value (axis scales are arbitrary here)</figcaption></figure>
<figure><img src="image_878.png" /><figcaption>Figure 7. Recrystallization peak temperature determined by DSC test on one of the hot rolled materials of the study.</figcaption></figure>

The highest heating rate is most relevant for this study as recrystallization of hot rolled material will start to take place with a minimum delay and loss of driving force.

Recrystallization peak temperatures in Figure 7 are much higher than holding temperatures in this study and therefore we conclude that no recrystallization has taken place immediately after hot rolling. Microstructure of the hot band material after coiling and cooling is shown in Figure 8.

<figure><img src="image_879.png" /><figcaption>Figure 8. Across thickness microstructure of naturally cooled hot band after tandem mill. No recrystallization has taken place</figcaption></figure>

## Practical Application

Based on what discussed, a minimum value of Zener-Hollomon parameter ($Z_{def}$) is required to reach a minimum desired r-value and having a (nearly) constant $Z_{def}$ throughout the coil is necessary to obtain a (nearly) constant r-value throughout the coil. A constant $Z_{def}$ implies a relationship between rolling speed and temperature as demonstrated in Figure 9.

<figure><img src="image_880.png" /><figcaption>Figure 9. Desired relationship between tandem entry temperature and tandem speed to achieve a constant $Z_{def}$. The curve represents a certain minimum r-value (axis scales are arbitrary here)</figcaption></figure>
Thus, desired relationship between entry temperature and speed is in such way that increasing temperature requires an increase in speed and vice versa. All the speed-Temperature combinations above the curve in Figure 8 will consequently result in higher r-values than that represented by the curve (0.6 here) and combinations below the curve will result in lower r-values (assuming identical processing conditions downstream in the process).

## Conclusions

Despite several operations between hot rolling and final product, there is a clear and visible connection between the tandem rolling process and r-value of final product. Entry temperature to the tandem mill and speed of rolling significantly affect the r-value of the final product. Lower temperatures and higher speeds increase the r-value (Figure 5, Figure 7). Exit temperature from the tandem mill seems not to influence the r-value (for the alloy studied here and within the temperature range of this study). Combined effect of entry temperature and rolling speed described by the Zener-Hollomon parameter can effectively be used to influence the r-value of the final product. This relationship between temperature and speed can be used to steer the rolling mill in such a way that not only a minimum r-value is safeguarded, but also variations of it along the length are minimized.

## Acknowledgements

This work was part of an improvement project in Aluminium Duffel BV and the author is grateful for the support and permission to conduct all the necessary experiments and tests.

## References

[1] Texture control by thermomechanical processing of AA6xxx Al-Mg-Si sheet alloys for automotive applications - a review. O. Engler, J. Hirsch. Materials science and engineering, A336, (2002) pp.249-262. https://doi.org/10.1016/S0921-5093(01)01968-2

[2] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part I. Microstructural evolution. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 611-620. https://doi.org/10.1007/s11663-998-0096-9

[3] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part II. Textural evolution. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 621-633. https://doi.org/10.1007/s11663-998-0097-8

[4] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part III. Overall model development and validation. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 709-719. https://doi.org/10.1007/s11663-998-0106-y

[5] Mathematical model of deformation and microstructural evolution during hot rolling of Aluminum alloy 5083. M.A. Wells et al. Materials science and technology, 19 (2003), pp. 467-476. https://doi.org/10.1179/026708303225010713

[6] Recrystallization textures and plastic anisotropy in Al-Mg-Si sheet alloys. O. Engler, J. Hirsch. Materials Science Forum, 217-222 (1996), pp. 479-486. https://doi.org/10.4028/www.scientific.net/MSF.217-222.479
Thus, desired relationship between entry temperature and speed is in such way that increasing temperature requires an increase in speed and vice versa. All the speed-Temperature combinations above the curve in Figure 8 will consequently result in higher r-values than that represented by the curve (0.6 here) and combinations below the curve will result in lower r-values (assuming identical processing conditions downstream in the process).

## Conclusions

Despite several operations between hot rolling and final product, there is a clear and visible connection between the tandem rolling process and r-value of final product. Entry temperature to the tandem mill and speed of rolling significantly affect the r-value of the final product. Lower temperatures and higher speeds increase the r-value (Figure 5, Figure 7). Exit temperature from the tandem mill seems not to influence the r-value (for the alloy studied here and within the temperature range of this study). Combined effect of entry temperature and rolling speed described by the Zener-Hollomon parameter can effectively be used to influence the r-value of the final product. This relationship between temperature and speed can be used to steer the rolling mill in such a way that not only a minimum r-value is safeguarded, but also variations of it along the length are minimized.

## Acknowledgements

This work was part of an improvement project in Aluminium Duffel BV and the author is grateful for the support and permission to conduct all the necessary experiments and tests.

## References

[1] Texture control by thermomechanical processing of AA6xxx Al-Mg-Si sheet alloys for automotive applications - a review. O. Engler, J. Hirsch. Materials science and engineering, A336, (2002) pp.249-262. https://doi.org/10.1016/S0921-5093(01)01968-2

[2] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part I. Microstructural evolution. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 611-620. https://doi.org/10.1007/s11663-998-0096-9

[3] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part II. Textural evolution. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 621-633. https://doi.org/10.1007/s11663-998-0097-8

[4] Modelling the Microstructural changes during hot tandem rolling of AA5xxx Aluminum alloys: Part III. Overall model development and validation. M.A. Wells et al. Metallurgical and materials transactions, 29B (1998), pp. 709-719. https://doi.org/10.1007/s11663-998-0106-y

[5] Mathematical model of deformation and microstructural evolution during hot rolling of Aluminum alloy 5083. M.A. Wells et al. Materials science and technology, **19** (2003), pp. 467-476. https://doi.org/10.1179/026708303225010713

[6] Recrystallization textures and plastic anisotropy in Al-Mg-Si sheet alloys. O. Engler, J. Hirsch. Materials Science Forum, 217-222 (1996), pp. 479-486. https://doi.org/10.4028/www.scientific.net/MSF.217-222.479
Formability of metallic materials: A MS
in honor of Prof. Banabic, Prof. Barlat
and Prof. Kuwabara

<figure><img src="image_873.png" /></figure>
Formability of metallic materials: A MS
in honor of Prof. Banabic, Prof. Barlat
and Prof. Kuwabara

<figure><img src="image_881.png" /></figure>
# Influence of an optical strain rate controlled tensile testing method on mechanical properties of sheet metals

NAUMANN David¹,ª*, MERKLEIN Marion¹,ᵇ

¹Institute of Manufacturing Technology (LFT), Friedrich-Alexander-Universität Erlangen-
Nürnberg, Egerlandstraße 13, 91058 Erlangen, Germany

ªdavid.naumann@fau.de, ᵇmarion.merklein@fau.de

**Keywords:** Tensile Test, Strain Rate Control, DIC

**Abstract.** Precise material characterization is a key factor not only for representative finite-element-analysis (FEA) in production technology, but also for product development in general. Hereby, the tensile test is of particular importance, as it can be used to determine the most relevant material parameters. These are used to ensure a better process and tool design but therefore material behavior has to be determined to a high level of precision [1]. Especially in the field of metal forming, strain rate sensitive material properties like work hardening, yield point or tensile strength need to be measured at constant strain rate to provide coherent data for material models in numerical forming simulations [2]. Current testing procedures control the strain rate with a feedback control, in which various measuring systems can be used. From this comes the necessity to investigate the influence of a strain rate controlled tensile testing procedure compared to a conventional crosshead-displacement controlled one. Thus, in the scope of this study, an optical strain rate controlled (OSRC) tensile test procedure with a digital image correlation (DIC) system, and a universal testing machine (UTM) was developed. The resulting mechanical properties and the evolution of the strain rate during the test of the steel DP600 (CR330Y590T-DH) and DC05 (CR4) were analyzed at a nominal strain rate of 0.4 %/s. In addition, the results obtained from displacement strain rate controlled (DSRC) tensile tests were compared. The results demonstrate that OSRC testing method enables the measurement of mechanical material properties at a higher level of precision in terms of constant strain rate compared to DSRC procedure.

**Introduction**

One of the greatest challenges facing society in the 21st century is climate change and the scarcity of natural resources. In order to meet these challenges, the European Parliament is placing a stronger focus on material efficiency in the area of production, for example with the Eco-Design Directive [3]. The aim is not only to improve product and process design in terms of greater resource efficiency, but also to enable the development of lightweight structures. In the mobility sector in particular, a reduction in weight leads to a reduction in environmentally harmful carbon dioxide emissions.

The usage of FEA is state of the art in both product and process development in order to make rapid and resource-efficient progress. To do so, precise material data as an input for such simulations is a key factor to get reliable results. Such material data is gained from characterization tests with standardized specimens like the tensile test in accordance with ISO 6892-1. In the field of sheet metal forming, for example, the hardening behavior can be determined in this way up to the uniform elongation. Due to the strain rate sensitivity most metals exhibit, it is crucial to measure material data at a constant strain rate to receive coherent data for material cards in numerical simulations [2]. Strain rate is calculated with the gauge length L₀ and the speed of the moving part v(t) as follows:

<figure><img src="image_874.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.
# Influence of an optical strain rate controlled tensile testing method on mechanical properties of sheet metals

NAUMANN David¹,ª*, MERKLEIN Marion¹,ᵇ

¹Institute of Manufacturing Technology (LFT), Friedrich-Alexander-Universität Erlangen-
Nürnberg, Egerlandstraße 13, 91058 Erlangen, Germany

ªdavid.naumann@fau.de, ᵇmarion.merklein@fau.de

**Keywords:** Tensile Test, Strain Rate Control, DIC

**Abstract.** Precise material characterization is a key factor not only for representative finite-element-analysis (FEA) in production technology, but also for product development in general. Hereby, the tensile test is of particular importance, as it can be used to determine the most relevant material parameters. These are used to ensure a better process and tool design but therefore material behavior has to be determined to a high level of precision [1]. Especially in the field of metal forming, strain rate sensitive material properties like work hardening, yield point or tensile strength need to be measured at constant strain rate to provide coherent data for material models in numerical forming simulations [2]. Current testing procedures control the strain rate with a feedback control, in which various measuring systems can be used. From this comes the necessity to investigate the influence of a strain rate controlled tensile testing procedure compared to a conventional crosshead-displacement controlled one. Thus, in the scope of this study, an optical strain rate controlled (OSRC) tensile test procedure with a digital image correlation (DIC) system, and a universal testing machine (UTM) was developed. The resulting mechanical properties and the evolution of the strain rate during the test of the steel DP600 (CR330Y590T-DH) and DC05 (CR4) were analyzed at a nominal strain rate of 0.4 %/s. In addition, the results obtained from displacement strain rate controlled (DSRC) tensile tests were compared. The results demonstrate that OSRC testing method enables the measurement of mechanical material properties at a higher level of precision in terms of constant strain rate compared to DSRC procedure.

**Introduction**

One of the greatest challenges facing society in the 21st century is climate change and the scarcity of natural resources. In order to meet these challenges, the European Parliament is placing a stronger focus on material efficiency in the area of production, for example with the Eco-Design Directive [3]. The aim is not only to improve product and process design in terms of greater resource efficiency, but also to enable the development of lightweight structures. In the mobility sector in particular, a reduction in weight leads to a reduction in environmentally harmful carbon dioxide emissions.

The usage of FEA is state of the art in both product and process development in order to make rapid and resource-efficient progress. To do so, precise material data as an input for such simulations is a key factor to get reliable results. Such material data is gained from characterization tests with standardized specimens like the tensile test in accordance with ISO 6892-1. In the field of sheet metal forming, for example, the hardening behavior can be determined in this way up to the uniform elongation. Due to the strain rate sensitivity most metals exhibit, it is crucial to measure material data at a constant strain rate to receive coherent data for material cards in numerical simulations [2]. Strain rate is calculated with the gauge length L₀ and the speed of the moving part v(t) as follows:

<figure><img src="image_882.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.
$$ \dot{\epsilon}(t) = \frac{d\epsilon}{dt} = \frac{v(t)}{L_0}. \qquad (1) $$

Peters et al. showed that forming operations like deep drawing show a temporal and spatial distribution of strain rates over the sheet metal, hence strain rate sensitivity should be considered in forming simulations [4]. Closed loop strain rate controlled characterization tests are available with tactile and optical extensometers. These extensometers allow an in-situ strain measurement on the specimen, which is fed back to the testing machine to control the crosshead speed. This achieves a constant strain rate throughout the whole test for the used gauge length. Bartholomew et al. developed already in the early 1950s a machine, to carry out optical controlled constant strain rate tensile tests [5]. To analyze the material behavior under biaxial load, Suttner and Merklein developed an optical strain rate controlled hydraulic bulge test with a 3D-DIC system [6]. Hereby it is not only possible to conduct experiments with a constant strain rate, but also to perform strain rate jumps during bulging. However, the influence of the test procedure on the determination of mechanical parameters from the tensile test with optical controlled strain rate has not yet been comprehensively investigated.

## Objective and Methodology

The objective of this research is the experimental investigation of the influence the OSRC tensile testing procedure has on the determination of mechanical properties of sheet metals in comparison to a DSRC procedure. Therefore, different tensile tests with specimen geometries according with ISO 6892-1 A80 were conducted. To investigate the influence of different material strengths, the tests were carried out with the deep drawing grade steel DC05 and the higher strength dual phase steel DP600. Both steels were tested at a nominal sheet thickness of 1.2 mm.

Fig. 1 shows the applied methodology. To validate the new developed characterization method, at first the process is analyzed with respect to the strain rate evolutions regarding accuracy and repeatability for which the standard deviation and the root mean square error (RMSE) as key figures are used. For the influence on the determination of the mechanical properties, strain rate sensitive properties like yield (YS) and tensile strength (TS), anisotropy (lankford-coefficient), hardening exponent (n) and uniform and fracture elongation values (UE and FS) are evaluated for the rolling direction, diagonal direction and transversal direction and contrasted in conclusion.

<figure><img src="image_875.png" /><figcaption>Fig. 1. Methodology</figcaption></figure>

## Experimental Setup

A UTM (ZwickRoell GmbH & Co. KG Z100) with a maximum force of 100 kN and a maximum crosshead speed of 600 mm/min was used to conduct quasi static flat tensile tests with a nominal strain rate of 0.4 %/s. The strain measurement for the live control and the post processing was done
$$ \dot{\epsilon}(t) = \frac{d\epsilon}{dt} = \frac{v(t)}{L_0}. \qquad (1) $$

Peters et al. showed that forming operations like deep drawing show a temporal and spatial distribution of strain rates over the sheet metal, hence strain rate sensitivity should be considered in forming simulations [4]. Closed loop strain rate controlled characterization tests are available with tactile and optical extensometers. These extensometers allow an in-situ strain measurement on the specimen, which is fed back to the testing machine to control the crosshead speed. This achieves a constant strain rate throughout the whole test for the used gauge length. Bartholomew et al. developed already in the early 1950s a machine, to carry out optical controlled constant strain rate tensile tests [5]. To analyze the material behavior under biaxial load, Suttner and Merklein developed an optical strain rate controlled hydraulic bulge test with a 3D-DIC system [6]. Hereby it is not only possible to conduct experiments with a constant strain rate, but also to perform strain rate jumps during bulging. However, the influence of the test procedure on the determination of mechanical parameters from the tensile test with optical controlled strain rate has not yet been comprehensively investigated.

## Objective and Methodology

The objective of this research is the experimental investigation of the influence the OSRC tensile testing procedure has on the determination of mechanical properties of sheet metals in comparison to a DSRC procedure. Therefore, different tensile tests with specimen geometries according with ISO 6892-1 A80 were conducted. To investigate the influence of different material strengths, the tests were carried out with the deep drawing grade steel DC05 and the higher strength dual phase steel DP600. Both steels were tested at a nominal sheet thickness of 1.2 mm.

Fig. 1 shows the applied methodology. To validate the new developed characterization method, at first the process is analyzed with respect to the strain rate evolutions regarding accuracy and repeatability for which the standard deviation and the root mean square error (RMSE) as key figures are used. For the influence on the determination of the mechanical properties, strain rate sensitive properties like yield (YS) and tensile strength (TS), anisotropy (lankford-coefficient), hardening exponent (n) and uniform and fracture elongation values (UE and FS) are evaluated for the rolling direction, diagonal direction and transversal direction and contrasted in conclusion.

<figure><img src="image_883.png" /><figcaption>Fig. 1. Methodology</figcaption></figure>

## Experimental Setup

A UTM (ZwickRoell GmbH & Co. KG Z100) with a maximum force of 100 kN and a maximum crosshead speed of 600 mm/min was used to conduct quasi static flat tensile tests with a nominal strain rate of 0.4 %/s. The strain measurement for the live control and the post processing was done
with a ARAMIS 12M SRX 3D-DIC system from Carl Zeiss GOM Metrology GmbH. The schematic setup of the optical closed loop control is depicted in Fig. 2. The adaptive feedback control consists of the 3D-DIC system, which provides an analog live signal, with an acquisition rate of 50 Hz in the range between 0 V and 10 V, of the gauge length to the electronic control unit (testControll II) of the UTM. Here, the signal is utilized to adapt the crosshead speed for a constant strain rate over the gauge length. For the evaluation, the software GOM Correlate Pro 2022 was used.

<figure><img src="image_876.png" /><figcaption>Fig. 2. Schematic setup of the applied DIC-OSRC with an UTM</figcaption></figure>

To decrease the user impact and to increase the repeatability of the testing results, an automatic CAD-fitting was applied. Thereby, the centerpoint of the gauge length L₀ can be determined and used for the position of the virtual extensometer, which is needed for the OSRC method and the subsequent evaluation. In Fig. 3 is the fitting process with the different coordinate systems and the resulting coordinate system, used for controlling and evaluation, shown.

<figure><img src="image_877.png" /><figcaption>Fig. 3. Positioning of the coordinate system via CAD-fitting</figcaption></figure>

Based on that, the so received corrected position and centerpoint, the virtual extensometer for controlling the test and the area for strain averaging are automatically aligned. Fig. 4 shows the placement of the area along L₀ and the different extensometers with gauge lengths of 80 mm, 40 mm and 20 mm. With the gauge lengths, the impact of the control mode can be analysed with respect to the diffuse necking of the specimen after reaching the uniform elongation. For all OSRC trials in this scope, the extensometer with a length of 80 mm was used.
with a ARAMIS 12M SRX 3D-DIC system from Carl Zeiss GOM Metrology GmbH. The schematic setup of the optical closed loop control is depicted in Fig. 2. The adaptive feedback control consists of the 3D-DIC system, which provides an analog live signal, with an acquisition rate of 50 Hz in the range between 0 V and 10 V, of the gauge length to the electronic control unit (testControll II) of the UTM. Here, the signal is utilized to adapt the crosshead speed for a constant strain rate over the gauge length. For the evaluation, the software GOM Correlate Pro 2022 was used.

<figure><img src="image_884.png" /><figcaption>Fig. 2. Schematic setup of the applied DIC-OSRC with an UTM</figcaption></figure>

To decrease the user impact and to increase the repeatability of the testing results, an automatic CAD-fitting was applied. Thereby, the centerpoint of the gauge length L₀ can be determined and used for the position of the virtual extensometer, which is needed for the OSRC method and the subsequent evaluation. In Fig. 3 is the fitting process with the different coordinate systems and the resulting coordinate system, used for controlling and evaluation, shown.

<figure><img src="image_885.png" /><figcaption>Fig. 3. Positioning of the coordinate system via CAD-fitting</figcaption></figure>

Based on that, the so received corrected position and centerpoint, the virtual extensometer for controlling the test and the area for strain averaging are automatically aligned. Fig. 4 shows the placement of the area along L₀ and the different extensometers with gauge lengths of 80 mm, 40 mm and 20 mm. With the gauge lengths, the impact of the control mode can be analysed with respect to the diffuse necking of the specimen after reaching the uniform elongation. For all OSRC trials in this scope, the extensometer with a length of 80 mm was used.
<figure><img src="image_878.png" /><figcaption>Fig. 4 Areas on tensile specimen used for controlling and evaluation</figcaption></figure>

## Results

Fig. 5 shows the areal strain rate evolutions for both investigated steels and methods in rolling direction (RD). The strain rate of the conventional approach with the DSRC reaches nearly the nominal value of 0.4 %/s but decreases directly afterwards. After a decrease of the strain rate to 0.31 %/s respectively 0.32 %/s, both strain rates rise to maximum of about 0.62 %/s respectively 0.68 %/s. Banerjee et al. observed a similar strain rate evolution during DSRC tensile testing [7]. The not-constant progression of the strain rate is based on not considered factors like machine stiffness, specimen gripping and the associated influence of the specimen heads. These factors do not affect the OSRC method, due to the 3D-DIC in-situ strain measurement on the specimen surface. Therefore, the progress of the strain rate obtained by OSRC experiments is constant at 0.4%/s over the whole test with minimal fluctuations until the fracture of the specimen.

<figure><img src="image_879.png" /><figcaption>Fig. 5. Strain rate evolutions for DC05 and DP600 with different control modes</figcaption></figure>

Tab. 1 summarises the parameters of the strain rate curves. The averaged values of the strain rates of the DSRC tests are 0.369 %/s for DC05 and 0.428 %/s for DP600. With the OSRC test, the averaged values meet the nominal value of 0.4 %/s with a very high accuracy which is displayed by the low RMSE of 2.4·10⁻⁵ %/s and 5.6·10⁻⁵ %/s with a maximum deviation each of 0.037 %/s respectively 0.084 %/s. The OSRC method provides a significant increase in the precision of constant strain rate testing over the entire trial.
<figure><img src="image_886.png" /><figcaption>Fig. 4 Areas on tensile specimen used for controlling and evaluation</figcaption></figure>

## Results

Fig. 5 shows the areal strain rate evolutions for both investigated steels and methods in rolling direction (RD). The strain rate of the conventional approach with the DSRC reaches nearly the nominal value of 0.4 %/s but decreases directly afterwards. After a decrease of the strain rate to 0.31 %/s respectively 0.32 %/s, both strain rates rise to maximum of about 0.62 %/s respectively 0.68 %/s. Banerjee et al. observed a similar strain rate evolution during DSRC tensile testing [7]. The not-constant progression of the strain rate is based on not considered factors like machine stiffness, specimen gripping and the associated influence of the specimen heads. These factors do not affect the OSRC method, due to the 3D-DIC in-situ strain measurement on the specimen surface. Therefore, the progress of the strain rate obtained by OSRC experiments is constant at 0.4%/s over the whole test with minimal fluctuations until the fracture of the specimen.

<figure><img src="image_887.png" /><figcaption>Fig. 5. Strain rate evolutions for DC05 and DP600 with different control modes</figcaption></figure>

Tab. 1 summarises the parameters of the strain rate curves. The averaged values of the strain rates of the DSRC tests are 0.369 %/s for DC05 and 0.428 %/s for DP600. With the OSRC test, the averaged values meet the nominal value of 0.4 %/s with a very high accuracy which is displayed by the low RMSE of 2.4·10⁻⁵ %/s and 5.6·10⁻⁵ %/s with a maximum deviation each of 0.037 %/s respectively 0.084 %/s. The OSRC method provides a significant increase in the precision of constant strain rate testing over the entire trial.
<table><caption>Tab. 1. Strain rate values for OSRC and DSRC tensile tests</caption><thead><tr><th></th><th>Method</th><th>Nominal strain rate [%/s]</th><th>Measured averaged strain rate [%/s]</th><th>RMSE [%/s]</th><th>Max. Absolute deviation [%/s]</th></tr></thead><tbody><tr><td rowspan="2">DC05 (RD)</td><td>DSRC</td><td>0.4</td><td>0.369 ± 0.004</td><td>0.012</td><td>0.224</td></tr><tr><td>OSRC</td><td>0.4</td><td>0.399 ± 0.006</td><td>2.4·10<sup>-5</sup></td><td>0.037</td></tr><tr><td rowspan="2">DP600 (RD)</td><td>DSRC</td><td>0.4</td><td>0.428 ± 0.004</td><td>0.011</td><td>0.278</td></tr><tr><td>OSRC</td><td>0.4</td><td>0.400 ± 0.007</td><td>5.6·10<sup>-5</sup></td><td>0.084</td></tr></tbody></table>

Fig. 6 shows the strain rate distribution over a tensile specimen during elongation until fracture. To make the distribution visible, three different lengths of extensometers are used like demonstrated in Fig. 4. Due to diffuse necking both steels exhibit, strain localization and thus, strain rate localization occurs. This leads to significant increase of strain rate in the region of necking.

<figure><img src="image_880.png" /><figcaption>Fig. 6. Comparison of different extensometer lengths for OSRC and DSRC</figcaption></figure>

The influence of the OSRC testing on the UTM crosshead speed is shown in Fig. 7. The crosshead speed for the DSRC trial is constant as depicted in equation 1. With a clamping length of 120 mm, which is the parallel span of the specimen and a nominal strain rate of 0.4 %/s, the crosshead speed results in 28.8 mm/min. The influence of the OSRC testing on the crosshead speed is shown in Fig. 7. Vice versa to the strain rate evolution, the crosshead speed of the OSRC trial is in the beginning above the speed of the DSRC trial. The crosshead speed then decreases nearly linear to a value of about 18 mm/min to the specimen fracture.
<table><caption>Tab. 1. Strain rate values for OSRC and DSRC tensile tests</caption><thead><tr><th></th><th>Method</th><th>Nominal strain rate [%/s]</th><th>Measured averaged strain rate [%/s]</th><th>RMSE [%/s]</th><th>Max. Absolute deviation [%/s]</th></tr></thead><tbody><tr><td rowspan="2">DC05 (RD)</td><td>DSRC</td><td>0.4</td><td>0.369 ± 0.004</td><td>0.012</td><td>0.224</td></tr><tr><td>OSRC</td><td>0.4</td><td>0.399 ± 0.006</td><td>2.4·10<sup>-5</sup></td><td>0.037</td></tr><tr><td rowspan="2">DP600 (RD)</td><td>DSRC</td><td>0.4</td><td>0.428 ± 0.004</td><td>0.011</td><td>0.278</td></tr><tr><td>OSRC</td><td>0.4</td><td>0.400 ± 0.007</td><td>5.6·10<sup>-5</sup></td><td>0.084</td></tr></tbody></table>

Fig. 6 shows the strain rate distribution over a tensile specimen during elongation until fracture. To make the distribution visible, three different lengths of extensometers are used like demonstrated in Fig. 4. Due to diffuse necking both steels exhibit, strain localization and thus, strain rate localization occurs. This leads to significant increase of strain rate in the region of necking.

<figure><img src="image_888.png" /><figcaption>Fig. 6. Comparison of different extensometer lengths for OSRC and DSRC</figcaption></figure>

The influence of the OSRC testing on the UTM crosshead speed is shown in Fig. 7. The crosshead speed for the DSRC trial is constant as depicted in equation 1. With a clamping length of 120 mm, which is the parallel span of the specimen and a nominal strain rate of 0.4 %/s, the crosshead speed results in 28.8 mm/min. The influence of the OSRC testing on the crosshead speed is shown in Fig. 7. Vice versa to the strain rate evolution, the crosshead speed of the OSRC trial is in the beginning above the speed of the DSRC trial. The crosshead speed then decreases nearly linear to a value of about 18 mm/min to the specimen fracture.
<figure><img src="image_881.png" /><figcaption>Fig. 7. Crosshead speeds for different testing methods</figcaption></figure>

In the following part, the influence of the testing method on the determination of the mechanical properties is presented. Fig. 8 displays the comparison of different mechanical values for DC05 obtained in DSRC and OSRC experiments. For most parameters, the difference is negligible small or not measurable. Only for the strain hardening exponent n in 45° and 90° to the rolling direction, an impact of the testing method was observed. Here, the measured value for n in diagonal (DD) and transversal direction (TD) is 0.253 respectively 0.257 for DSRC and 0.247 respectively 0.250 for OSRC. The small standard deviations in the determination of the yield and tensile stress for both methods indicates a high repeatability. Only for the ultimate elongation (UE), the experiments with the OSRC trial provides a higher standard deviation for all testing directions compared to DSRC.

<figure><img src="image_882.png" /><figcaption>Fig. 8. Overview of strain rate sensitive material properties of DC05 obtained from DSRC and OSRC tensile tests</figcaption></figure>

The difference in the measurement of the strain hardening exponent which is present for DC05 could not be observed for DP600 as Fig. 9 indicates. Here, for all values, no significant impact of the testing method could be demonstrated. Due to the lower strain rate sensitivity of DP600 in comparison to DC05, no influence can be measured. Additionally, the quasi-static strain rate of
<figure><img src="image_889.png" /><figcaption>Fig. 7. Crosshead speeds for different testing methods</figcaption></figure>

In the following part, the influence of the testing method on the determination of the mechanical properties is presented. Fig. 8 displays the comparison of different mechanical values for DC05 obtained in DSRC and OSRC experiments. For most parameters, the difference is negligible small or not measurable. Only for the strain hardening exponent n in 45° and 90° to the rolling direction, an impact of the testing method was observed. Here, the measured value for n in diagonal (DD) and transversal direction (TD) is 0.253 respectively 0.257 for DSRC and 0.247 respectively 0.250 for OSRC. The small standard deviations in the determination of the yield and tensile stress for both methods indicates a high repeatability. Only for the ultimate elongation (UE), the experiments with the OSRC trial provides a higher standard deviation for all testing directions compared to DSRC.

<figure><img src="image_890.png" /><figcaption>Fig. 8. Overview of strain rate sensitive material properties of DC05 obtained from DSRC and OSRC tensile tests</figcaption></figure>

The difference in the measurement of the strain hardening exponent which is present for DC05 could not be observed for DP600 as Fig. 9 indicates. Here, for all values, no significant impact of the testing method could be demonstrated. Due to the lower strain rate sensitivity of DP600 in comparison to DC05, no influence can be measured. Additionally, the quasi-static strain rate of