Abstract
To evaluate the influence of different normal pressures and the fiber orientation on the in-plane compression behavior of paperboard during the deep drawing process, a new method was developed. In addition, the influence of the wrinkle formation on the dynamic coefficient of friction and the bending resistance was examined. To evaluate the eligibility of the in-plane compression testing method, a validation strategy was developed to compare the results from the new alternative tests with the punch force profiles from the deep drawing process within an empirical model.
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A New Method to Evaluate the In-plane Compression Behavior of Paperboard for the Deep Drawing Process
Alexander Lenske,a,* Tobias Müller,b Nicole Ludat,a Marek Hauptmann,a,c and Jens-Peter Majschak a
To evaluate the influence of different normal pressures and the fiber orientation on the in-plane compression behavior of paperboard during the deep drawing process, a new method was developed. In addition, the influence of the wrinkle formation on the dynamic coefficient of friction and the bending resistance was examined. To evaluate the eligibility of the in-plane compression testing method, a validation strategy was developed to compare the results from the new alternative tests with the punch force profiles from the deep drawing process within an empirical model.
DOI: 10.15376/biores.17.2.2403-2427
Keywords: In-plane compression; Friction behavior; Bending resistance; Empirical model; Paperboard; Tribocharging; Deep drawing process; 3D-forming
Contact information: a: Fraunhofer Institute for Processing Technology IVV, Heidelbergerstraße 20, 01189 Dresden, Germany; b: Chair of Processing Machines/Processing Technology, Technische Universität Dresden, Bergstrasse 120, 01069 Dresden Germany; c: Chair of packaging machines and packaging technologies, Steinbeis-Hochschule, Ernst-Augustin-Str. 15, 12489 Berlin, Germany;
* Corresponding author: alexander.lenske@ivv-dresden.fraunhofer.de
GRAPHICAL ABSTRACT
INTRODUCTION
Deep drawing of paperboard with rigid tools and immediate compression is characterized by drawing a paperboard blank with a punch into a forming cavity against the resistance induced through a blankholder (Hauptmann and Majschak 2011). During the forming process a compression force develops in-plane within the paperboard blank due to the excess material from the difference between the outer perimeter of the paperboard blank and the inner perimeter of the forming cavity, resulting in inevitable wrinkles (Hauptmann et al. 2015; Wallmeier et al. 2015; Müller et al. 2017). Mark (2002) presented different methods to characterize the in-plane compression behavior of paperboard within substitute tests, but none of them used a defined normal load orthogonal to the plane of the paperboard blank to simulate the characteristic blankholder force from the deep drawing process.
The purpose of this paper is to present a newly developed method to investigate the in-plane compression behavior of paperboard under a defined normal load orthogonal to the plane of the paperboard blank to meet the requirements of the deep drawing process. The in-plane compression behavior of a commercially available paperboard material was determined based on three different normal loads and the fiber direction of the paperboard sample. To evaluate the eligibility of the newly developed method to investigate the in-plane compression behavior as a substitute test for the deep drawing process, a validation strategy was developed. Within the validation strategy four variations of the deep drawing process were presented to isolate the overlapping process forces of the forming process. In addition to that, the respective punch force profiles of the forming process variations were compared to reconstructed punch force profiles from results of the newly developed in-plane compression method as well as results from friction and bending tests.
EXPERIMENTAL
Materials
In the experiments to be described, the commercially available material called Trayforma Natura (Stora Enso, Imatra, Finland) was used, which consists of three layers of virgin-quality fiber, with a grammage of 350 g/m2, and a thickness of
0.43 mm to 0.45 mm (www.storaenso.com).
Methods
3-D forming equipment and variants of the deep drawing process
All deep drawing tests were conducted with the same tool-setup in a servo-hydraulic press described in Hauptmann and Majschak (2011). The tool-setup consists of a forming cavity, a blankholder, and a punch, as shown in Fig. 1a. The forming cavity, the blankholder, and the punch were made of polished stainless steel (Material No. X5CrNi18-10 or 1.4301 in accordance with the DIN EN 10027-2 (2015) standard). To reduce the friction between the paperboard sample and the tool surfaces, the blankholder and the upper part of the forming cavity were prepared with self-adhesive PTFE-foil (Polytetrafluorethylene glass fabric foil 0.13 AS AD-T, Hightechflon Films and Fabrics, Konstanz, Germany) (Fig. 1a). Preliminary tests showed that the PTFE-foil could not be applied to the area of the infeed radius and the inner contour of the forming cavity with reproducible results. Therefore, it was only applied to the circular ring surface under the blankholder.
Figure 1a shows also the schematic of deep drawing process variant 1. The geometrical data of the tool-setup, as listed in Tab. 1, was taken from Lenske et al. (2017), except for the drawing clearance aGap. By reducing the radius of the drawing punch rP, the distance aGap between cavity and punch increased significantly in relation to the thickness of the paperboard material. Because of that, there was no contact between the paperboard material and the inner contour of the forming cavity, preventing any friction in this area.
Fig. 1. a) Tool-setup schematic for deep drawing process variant 1 with the location of the self-adhesive PTFE-foil; b) Schematic of the effective process force components during deep drawing process variant 1; c) Schematic of the modified paperboard sample used in deep drawing process variant 1, 2 and 3
The blankholder was positioned at a defined distance dBH.1, 30 millimeters above the paperboard sample. Since no blankholder force was applied during deep drawing process variant 1, the friction between the paperboard sample and the tool surfaces could be kept as low as possible, but at the same time the paperboard sample blank was bent around the punch edge. To avoid in-plane compression, the paperboard sample was modified with triangular cutouts (Fig. 1c). Because of that, no excess material was compressed within wrinkles due to the lateral movement of the paperboard material during the deep drawing process variant. The cutouts were evenly distributed around the circumference of the paperboard sample, each with an opening angle Sample of 3 ° starting from a radius rFC. These modified paperboard samples were also used in deep drawing process variant 2 and 3. The only effective process force within deep drawing process variant 1 was the bending force around the punch edge FB.PE.1 (sP) (Fig. 1b), which can be measured completely isolated from all other process forces within the punch force FP.1 during the punch movement sP.
Table 1. Geometrical Data and Parameters of the Deep Drawing Process Variants
Figure 2a shows the schematic of deep drawing process variant 2. In contrast to deep drawing process variant 1, the blankholder was positioned at a defined distance dBH.2, 3 millimeters above the modified paperboard. Since no blankholder force was applied during deep drawing process variant 2, the friction between the modified paperboard sample and the tool surfaces was kept as low as possible, but at the same time the modified paperboard sample blank was bended around the punch edge and the infeed radius. Due to the modified paperboard sample, no in-plane compression occurred. Because of that, the effective process forces within deep drawing process variant 2 were the bending force components around the punch edge FB.PE.2 (sP) and around the infeed radius FB.IR.2 (sP), as well as the spring-back force FB.SB.2 (sP), which could be measured completely isolated from all other process forces within punch force profile FP.2 (sP) (Fig. 2b).
Fig. 2. a) Tool-setup schematic for deep drawing process variant 2 b) Schematic of the effective process force components during deep drawing process variant 2
Figure 3a shows the schematic of deep drawing process variant 3. In contrast to deep drawing process variant 1 and 2, the blankholder applied a constant normal load pN.BH onto the modified paperboard sample. As a result, friction forces were acting between the modified paperboard sample and the blankholder FF.BH.3 (sP), the forming cavity FF.FC.3 (sP), and the infeed radius FF.IR.3 (sP) (Fig. 3a) as an addition to the bending force components FB.PE.3 (sP), FB.IR.3 (sP), and FB.SB.3 (sP) (Fig. 3b). All process forces within deep drawing process variant 3 could be measured within punch force profile FP.3 (sP) (Fig. 3b).
Fig. 3. a) Tool-setup schematic for deep drawing process variant 3 and effective friction force components; b) Schematic of the effective bending force components during deep drawing process variant 3
Figure 4a shows the schematic of deep drawing process variant 4. In contrast to deep drawing process variant 1, 2, and 3, the blankholder applied a constant normal load pN.BH onto a paperboard sample without triangular cutouts (Fig. 4c). As a result, friction forces were active between the paperboard sample and the blankholder FF.BH.4 (sP), the forming cavity FF.FC.4 (sP), and the infeed radius FF.IR.4 (sP) (Fig. 4a) as an addition to the bending force components FB.PE.4 (sP), FB.IR.4 (sP), and FB.SB.4 (sP) and the in-plane compression force FIPC.4 (sP) (Fig. 4b). All process forces within deep drawing process variant 4 could be measured within punch force profile FP.4 (sP) (Fig. 4b).
Fig. 4. a) Tool-setup schematic for deep drawing process variant 4 and effective friction force components; b) Schematic of the effective bending and in-plane compression force components during deep drawing process variant 3
To compare the in-plane compression force FIPC.4 (sP) of deep drawing process variant 4 and the results of the newly developed in-plane compression method, the in-plane compression ratio kDDP.4 for deep drawing process variant 4 was determined. In general, the in-plane compression ratio k is the ratio between the in-plane compression movement and the total length of the paperboard sample. In deep drawing process variant 4 the maximum in-plane compression movement is the difference between the outer perimeter of the paperboard sample blank and the inner perimeter of the forming cavity (Fig. 4c). The total length of the paperboard sample is then the outer perimeter of the paperboard sample blank. To describe the progression of the in-plane compression ratio kDDP.4, the movement of the paperboard sample below the blankholder sPS.BH was used, which ended after 25 millimeters, when the paperboard sample was completely drawn into the forming cavity (Fig. 4a and 4c).
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In-plane compression measurement equipment
The in-plane compression testing method (Fig. 5a), in the following abbreviated with IPCTM, is based on a similar approach to investigate the in-plane compression behavior of paperboard from Lenske et al. (2017a) and mounted on the flexible testing rig described in Lenske et al. (2017b).
Fig. 5. a) Schematic side-view of the in-plane compression testing method (IPCTM) with tool-samples prepared with PTFE-foil; b) Schematic detail-view of tool-sample 2, the paperboard sample, the compression plate and the metal sheet
A rectangular paperboard sample was positioned between two tool-samples. A compression plate served as end-stop for the paperboard sample. The compression plate was attached to a force sensor (KD9363s, ME Messsysteme, Henningsdorf, Germany; measuring range ± 2,5 kN; accuracy class 0.1%) and the surrounding frame structure. On the other side of the paperboard sample, a metal sheet was attached to a force sensor (KD9363s, ME Messsysteme, Henningsdorf, Germany; measuring range ± 12 kN; accuracy class 0.1%) within a metal frame and could be moved due to the pulling system described in Lenske et al. (2017b). The metal sheet must be slightly thinner than the thickness of the paperboard sample to avoid contact between the tool samples and the metal sheet. The thickness of the metal sheet tMS.IPCTM was therefore determined as 0.4 mm (Fig. 5b). During the IPCTM, the upper tool arrangement applied a constant normal pressure pN.IPCTM (sIPCTM) onto the paperboard sample blank due to the force control of the pushing system described in Lenske et al. (2017b). The in-plane compression force FIPC.IPCTM resulted from the movement sIPCTM of the metal sheet into the paperboard sample with a defined relative velocity vIPCTM against the end-stop of the compression plate. The compression plate was positioned two tenths of a millimeter from the two tool-samples away, to record the in-plane compression force FIPC.IPCTM (sIPCTM) without disturbance of any other force component such as friction. As a result of the IPCTM, the paperboard samples showed a significant wrinkle formation (Fig. 10). In order to investigate the influence of this wrinkle formation on the friction and bending behavior, the paperboard samples with wrinkle formation were used within the strip-testing method (STM) (Fig. 6a) and the modified two-point bending test (MTPBT) (Fig. 8a). For this purpose, the width of the paperboard samples wPS.IPCTM was expanded (Tab. 2). The paperboard samples with wrinkle formation for the STM and MTPBT were produced without investigating the in-plane compression force FIPC.IPCTM. The tool-samples were fully covered with self-adhesive PTFE foil (Fig. 5a). The in-plane compression ratio was adapted from deep drawing process variant 4 and transferred to the paperboard sample blank for the IPCTM. The geometrical data and parameters used for the IPCTM are listed in Table 2.
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Table 2. Geometrical Data and Parameters of the IPCTM
Friction measurement equipment
The evaluation of the friction behavior of the paperboard material was carried out with the strip-testing method (STM) (Fig. 6a), according to Lenske et al. (2017b). The tool-samples were fully covered with self-adhesive PTFE foil. The geometry of the tool- and paperboard samples used during the STM are shown in Fig. 6b and listed in Table 3. The orientation of the paperboard sample with wrinkle formation during the STM is shown in Fig. 6c.
Fig. 6. a) Schematic side-view of the Strip-testing method (STM) according to
Lenske et al. (2017b) with tool-samples prepared with PTFE-foil; b) Schematic detail-view of tool-sample 2 and a paperboard sample; c) Schematic detail-view of tool-sample 2 and a paperboard sample with wrinkle formation
Table 3. Geometrical Data and Parameters of the STM
To examine the effect of the transition from the area covered with PTFE-foil into the area consisting of the polished stainless steel within deep drawing process variant 3 and 4 at the infeed radius (Figs. 3a and 4a), the double strip-testing method (DSTM) (Fig. 7a), was used according to Lenske et al. (2018). Within the DSTM, the tool-samples were only covered partially with self –adhesive PTFE-foil, representing the area between the blankholder and the upper part of the forming cavity. The length of the PTFE-foil covered area of the tool sample lTS.PTFE.DSTM is shown in Fig. 7b, as well as all other relevant geometry descriptions of the tool and paperboard samples. The infeed radius of the forming cavity was represented through the part of the tool-sample within the DSTM, which was uncovered with PTFE-foil lTS.SS.DSTM and consisted of polished stainless steel (Material No. X5CrNi18-10 or 1.4301 in accordance with the DIN EN 10027-2 (2015) standard). The paperboard sample started the sliding movement sDSTM from the line, which marked the transition from PTFE-foil to polished stainless steel. The geometrical data and parameters used for the DSTM are listed in Table 4. The normal forces, which were used for the DSTM, were selected according to the normal forces in Lenske et al. (2018).
Fig. 7. a) Schematic side-view of the Double strip-testing method (DSTM) according to
Lenske et al. (2018) with tool-samples partially prepared with PTFE-foil; b) Schematic detail-view of tool-sample 2 and a paperboard sample
Table 4. Geometrical Data and Parameters of the DSTM
Bending measurement equipment
A modified two-point bending test (MTPBT) (Fig. 8a) according to
DIN 53121 (2008) was used to examine the bending resistance of the paperboard material, built on the base of the flexible testing rig from Lenske et al. (2017b). For this purpose, the force sensor from the friction measurement system was removed and the lower tool assembly was connected to the machine frame. The upper tool arrangement, driven by an electromechanical servo-cylinder (Serac KH30, Ortlieb, Kirchheim, Germany; constant force range ± 30 kN) could then pass the lower tool arrangement without hindrance. The movement of the upper tool arrangement bent the paperboard sample around the edge of lower tool sample. The bending force FB.MTPBT (sMTPBT) was measured through a force sensor (KD9363s, ME Messsysteme, Hennigsdorf, Germany; measuring range ± 10 kN; accuracy class 0.1%) between the electromechanical servo-cylinder and the upper tool arrangement and evaluated as bending resistance WB.MTPBT (sMTPBT) in relation to the paperboard sample width wPS.MTPBT in order to compare the results of the MTPBT for paperboard samples without wrinkle formation and paperboard samples with wrinkle formation, which were produced within the IPCTM. Both tool samples were positioned at a defined distance from each other. The distance corresponded to the drawing clearance aGap within the tool-set of the forming process (Fig. 1a and Table 1). Figure 8b shows the paperboard sample without wrinkle formation and Fig. 8c with wrinkle formation and the corresponding bending lines as an example of the positioning within the MTPBT. Within the deep drawing process, the wrinkles always run radially from the center of the base geometry to the edge of the wall section of the drawn part. Because of that, the bending line is always orthogonal to the direction of the wrinkle orientation. For example, a paperboard sample that was modified during the IPCTM with a wrinkle formation in MD was consequently loaded in the MTPBT orthogonally to the wrinkle orientation, which was arranged parallel to CD. The calculation of the bending resistance WB.MTPBT (sMTPBT) of the paperboard sample with wrinkle formation was also based on the original sample length lPS.IPCTM of 42 mm before the in-plane compression.
Fig. 8. a) Modified two-point bending test schematic according to DIN 53121 (2008); Positioning of the paperboard sample and the bending line in relation to the fiber-direction during the MTPBT b) without wrinkle formation and c) with wrinkle formation
Table 5 summarizes geometrical data and parameters for the MTPBT.
Table 5. Geometrical Data and Parameters of the MTPBT
Test procedure
To ensure that there was no contamination of the paperboard samples, clean surgical gloves were worn, and the metal tools for the deep drawing process as well as for the substitute tests were cleaned before each test series with a sterile cotton wipe soaked with acetone. In addition to that, before each test series, fresh PTFE-foil was attached to each of the tool surfaces according to the descriptions above. All the repetitions of a test series with the same parameter setup were performed using fresh paperboard samples for each repetition. Each test series performed with the substitute tests and all deep-drawing process variants were performed with 10 repetitions in a row, except for one test series from the STM. To show the influence of triboelectric charging during the friction test, the test series shown in Fig. 13a was performed with 200 repetitions in a row. The tools used for the substitute tests were composed of polished stainless steel (Material No. X5CrNi18-10 or 1.4301 in accordance with the DIN EN 10027-2 (2015) standard) and were separately grounded on the side of the tool bulk. The deep drawing process variants and the substitute tests were performed under standard climate conditions (23 °C; 50% relative humidity) and with unheated tools at 23 °C.
RESULTS AND DISCUSSION
In-plane Compression
During the IPCTM, the total force FT.IPCTM, the in-plane compression force FIPC.IPCTM, and the friction force FF.IPCTM against the lower tool sample were recorded according to Figure 5a. Figure 9 shows the progression of the three force curves as a mean value from a test series of 10 repetitions in line of the main fiber direction in MD and with a normal pressure pN.IPCTM of 0.3 MPa. The total force FT.IPCTM must be the sum of the in-plane compression force FIPC.IPCTM and two times the friction force FF.IPCTM from the paperboard sample against both tool samples. Trayforma has the same virgin fiber material layers on both sides. Because of that, the friction force FF.IPCTM should be the same against both tool samples. Figure 9 shows, therefore, the difference FDiff.IPCTM between the total force FT.IPCTM and two times the friction force FF.IPCTM. The difference force FDiff.IPCTM and the in-plane compression force FIPC.IPCTM were almost exactly the same in terms of progression and amount, meaning that FIPC.IPCTM was measured without the influence of any friction forces in contrast to the results in Wallmeier et al. (2021).
Fig. 9. Measured and calculated force profiles and tool movement during the IPCTM at a normal pressure pN.IPCTM of 0.3 MPa in MD direction of the paperboard sample
The progression of the in-plane compression force FIPC.IPCTM increased steadily at the beginning of the IPCTM to a global maximum and then decreased to an almost constant plateau. The global maximum probably marks the point at which the in-plane compression had exhausted the compensatory capacity of the fiber structure of the paperboard sample mentioned in Hauptmann et al. (2015). After this point, the paperboard material must move out of the in-plane to evade the increasing compression force. This assumption is reinforced by evaluating the position of the upper tool sample trough the movement signal of the electromechanical servo-cylinder (Serac KH30, Ortlieb, Kirchheim, Germany; constant force range ± 30 kN). The accumulation of paperboard material results in an increasing counterforce against the normal pressure of the upper tool arrangement. In order to maintain the default constant normal pressure due to the force control of Serac KH30, the upper tool must move away from the increasing material accumulation. Because of the tool movement, the paperboard material could more easily evade the in-plane compression from the metal sheet, resulting in a reduced compression force FIPC.IPCTM after the global maximum depicted in Fig. 9. To prove this hypothesis, future research should add a camera setup to the IPCTM to record the progression of the wrinkle formation in relation to the position of the metal sheet, similar to the approach described in Wallmeier et al. (2021).
Figure 10 shows a paperboard sample from the test series depicted in Fig. 9, after the IPCTM from a side view with a distinct wrinkle formation. The left side of the compressed paperboard sample shows damage of the fiber structure because of the contact with the metal sheet. The metal sheet had penetrated the paperboard sample, slicing the fiber structure apart. In relation to the total length lPS.IPCTM of the paperboard sample the penetration depth must be considered negligible. However, in future work, the penetration depth of the metal sheet and the corresponding thickness of the metal sheet should be observed more closely.
Fig. 10. Paperboard sample after the IPCTM from the test series depicted in Fig. 9, with distinctive wrinkle formation
Figure 11a shows the influence of the anisotropy of the paperboard sample on the progression of the in-plane compression force FIPC.IPCTM for the fiber orientation in MD, CD, and 45° from MD pivoted (MD-45-CD) at 0.3 MPa normal pressure.
Fig. 11. Influence of the anisotropy of the paperboard sample at a normal pressure pN.IPCTM of 0.3 MPa during the IPCTM on the a) in-plane compression force FIPC.IPCTM (sIPCMT) and b) global maximum values of the in-plane compression force FIPC.IPCTM (sIPCMT)
The compression force FIPC.IPCTM was highest along the main fiber orientation in MD. Due to the manufacturing process of natural fiber materials, most of the individual fibers were aligned in MD, compared to only a few in CD. Assuming that the individual fibers act as thin cylinders, the mechanical load along their height can theoretically be viewed as an Euler’s buckling case. This means that the individual fiber resisted the external mechanical load until the cylinder structure buckled and finally broke. When the mechanical resistance of the fiber structure was mainly applied by the number of individual fibers that are arranged along the load direction, the resulting compression force must decrease from MD to CD. The evaluation of the global maxima of the in-plane compression force curves FIPC.IPCTM in Fig. 11b shows a linear relationship between the fiber orientations and the corresponding maximum in-plane compression forces.
The influence of normal pressure on the progression of the in-plane compression force is shown in Fig. 12a for two normal pressures at 0.3 and 0.5 MPa in MD. For a better overview, the normal pressure in between, 0.4 MPa, was omitted. Both in-plane compression force curves were almost identical. This result supported the conceptual model, mentioned above, that the mechanical resistance of the fiber structure was mainly applied only by the number of individual fibers that are arranged along the in-plane load direction. A higher normal pressure orthogonal to the in plane of the paperboard sample decreased only the out-of-plane tool movement and therefore the free spaces where the excess material can go to avoid the in-plane compression force, probably resulting in a better distributed wrinkle formation (Hauptmann and Majschak 2011). Figure 12b shows the global maxima of the in-plane compression force curves for three normal pressure levels in MD, CD, and 45° from MD pivoted (MD-45-CD).