Numerical and Experimental Study of Embossing of Paperboard

Transcription

1 Numerical and Experimental Study of Embossing of Paperboard A material characterization of one specific paperboard quality Numerisk och Experimentell Studie av Prägling på Kartong En material karakterisering av en specifik kartong kvalité Lisa Runesson Faculty of Health, Science and Technology Degree Project for Master of Science in Engineering, Mechanical Engineering 30 ECTS Credits Supervisor: Nils Hallbäck Examiner: Jens Bergström

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3 ACKNOWLEDGEMENTS The master thesis presented in this report has been carried out in partial fulfilment of the degree Master of Science in Mechanical Engineering at Karlstad University, Sweden. The work was performed at Stora Enso Research Centre in Karlstad, Sweden during the spring of I would like to dedicate a special thanks to my supervisor Ann-Kristin Wallentinsson at Stora Enso Research Centre. Wallentinsson trusted me during the entire work and gave me the opportunity of taking high responsibility in order to reach the goals. I would also like to thank my colleagues, at Stora Enso Research Centre, Niklas Elvin, Göran Niklasson, Daniel Ekbåge and Claes Åkerblom. Without their guidance and support during this thesis this would not have been possible. I would also like to thank my supervisor Nils Hallbäck, Associate professor, at Karlstad University for a great work of support and feedback during the process in this work. Lisa Runesson Karlstad, June 2016 ii

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5 ABSTRACT This master thesis has its main focus within embossing operations and how different factors influence the result. The work was performed at Stora Enso Research Centre in Karlstad, Sweden. Embossing is relatively complex operation to analyze since the paperboard can be exposed of both bending, shear and compression at the same time. The techniques used today for evaluating embossing on paperboard consist of experimental setups. These experimental techniques needed to be complemented in order to simplify the approach for embossing evaluations. The aim of this thesis was to develop a simulation material model, created with Finite Element Method by using Abaqus (2014), which capture the experimental behavior of embossed paperboard. The goals were to understand which material properties that are of high importance in embossing operations, and how sensitive the simulation material model is at small geometry changes of the embossing tool. A three dimensional finite element material model has been created in Abaqus (2014). The analysis was performed as dynamic quasistatic where an implicit solver was used. The simulation material model consisted of a continuum model, which describes the behavior of the plies, and an interface model implemented as cohesive elements, which describes the inelastic delamination between the plies. The continuum model was defined as an anisotropic linear elastic-plastic material model with isotropic linear hardening together with Hill s yield criterion. The interface model was defined with an anisotropic elastic-plastic traction-separation law and an exponential damage evolution model. The purpose of the experimental tests was to capture the behavior of embossed paperboard and the goal was then to recreate the behavior in the simulation model. The results in this thesis focus on the relationship between the applied force and the displacement. An experimental and numerical study of out-of-plane compression has also been conducted, where the aim was to determine the out-of-plane elastic modulus, E ZD. According to embossing results, the embossing results showed an exponential hardening behavior while the numerical results, unfortunately, showed a declining hardening behavior. Despite this, some understanding regarding which parameters that are of utmost importance have been achieved. The material parameters which had the highest influence on embossed paperboards seem to be the out-of-plane shear properties. This thesis also shows that the material model is sensitive of small changes of the tool geometry. The proportion of shear, bending and compression are strongly dependent on if the tool has sharp edges or if the edges are more rounded. iv

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7 SAMMANFATTNING Detta examensarbete har sitt huvudfokus inom präglings operationer och hur olika faktorer påverkar resultatet. Arbetet har utförts på Stora Enso Research Center in Karlstad, Sverige. Prägling är relativt komplext att analysera då materialet utsätts för både böjning, skjuvning och kompression samtidigt vid belastning. De tekniker som används idag för att utvärdera hur prägling påverkar olika kartong kvaliteér består av experimentella uppställningar. Dessa tekniker behövs kompletteras för att förenkla tillvägagångssättet kring hur prägling utvärderas. Syftet med denna avhandling var att utveckla en simulerad materialmodell, skapad med Finita Element Metoden i Abaqus (2014), som fångar det experimentella beteendet av präglad kartong. Målet med denna avhandling var att förstå vilka materialparametrar som har en viktig roll inom prälings operationer samt att analysera hur känslig materialmodellen är vid små geometri ändringar av präglingsverktyget. En tredimensionell finita element materialmodel har modellerats i Abaqus (2014). Analysen genomfördes som Dynamisk/Implicit kvasi-statisk. Den simulerade materialmodellen bestod av en kontinuummodell, som beskriver beteendet av respektive skikt, och en delamineringmodell implementerad som kohesiva element, som beskriver de oelastiska delamineringarna mellan skikten. Kontinuum-modellen var definerad som ett anisotropt linjärt elastisk-plastisk material med isotrop linjärt hårdnande tillsammans med Hills flytspänningskriterium. Delamineringsmodellen var definerad med en anisotrop elastisk-plastisk drag-separationslag och en exponentiell evolution modell, som tar hänsyn till kartongens mjuknande beteende. Syftet med de experimentella testarna var att fånga beteendet av den präglade kartongen och målet var sedan att återskapa detta beteende i simuleringsmodellen. Resultaten från denna avhandling har sitt fokus kring relationen mellan pålagd kraft och förskjutning. En experimentell och numeriskt studie av kompression i tjockleksriktningen har också genomförts där syftet var att bestäma elasticitetsmodulen, E ZD. Vid jämförelse mellan de experimentella och numeriska resultaten från prägling, visar de experimentella mätningarna ett exponentiellt hårdnande beteende medans den numeriska simuleringen visar en nedåtgående hårdnande beteende. Trots detta har en viss förståelde gällande vilka materialparametrar som har en viktig roll inom prägling uppnåtts. De materialparametrar som verkar ha stor betydelse inom prägling är skjuvegenskaperna i tjockleksriktningen. Denna avhandling visar också att simuleringsmodellen är känslig för små geometri ändringar av präglingsverktyget. Andelen skjuvning, böjning och kompression är starkt beroende av om verktyget har skarpa kanter eller om kanterna är med rundade. vi

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9 Table of Contents 1 INTRODUCTION BACKGROUND PROBLEM FORMULATION OVERVIEW DESCRIPTION OF PAPERBOARD MATERIAL REVIEW OF PREVIOUS WORK METHOD MATERIAL MODEL CONTINUUM MODEL INTERFACE MODEL EXPERIMANTAL METHODS AND ASSUMPTIONS FOR CHARACTERIZATION OF PAPERBOARD PROPERTIES OUT-OF-PLANE COMPRESSION TEST EMBOSSING - EXPERIMENTAL SETUPS IMPLEMENTATION OF THE FEM MODEL IN ABAQUS RESULTS OUT-OF-PLANE COMPRESSION RESULTS EMBOSSING RESULTS DISCUSSION CONCLUSION REFERENCES APPENDIX A APPENDIX B APPENDIX C viii

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11 1 INTRODUCTION 1.1 BACKGROUND Stora Enso [1] is a world leading company in the forest industry where sustainability is of a high priority. Their focus is to develop renewable solutions in areas such as fiberbased packaging, products of biomaterial, wood products and paper. Their vision is to replace non-renewable material by innovating and developing new products. In the packaging industry, Stora Enso has developed different types of embossing tools to decorate their paperboard packages. The purpose of embossing is to create more elegant packages and thereby add value for the customers. The embossing tools are divided into two categories based on their movement pattern. The categories are rotational and stationary. Embossing, in this case, is a three dimensional pattern created into a paperboard material, illustrated in Figure 1. The principle of embossing is that a paperboard material is placed between a male die and a female die, where the forming board is in the thickness direction. Embossing is a complex operation since the paperboard can be exposed of both bending, shear and compression at the same time. Figure 1. Illustration of an embossing pattern created on a paperboard. 1.2 PROBLEM FORMULATION The techniques used today for evaluating embossing on paperboard consist of experimental setups. The evaluations involve for example investigation about whether a specific paperboard quality has the capacity to withstand a certain embossing geometry and height, without any cracks initiation. These experimental techniques need to be complemented in order to simplify the approach for embossing evaluations. In order to effective their research a simulation model is requested. Through a simulation model the thickness of the paperboard and its properties can easily be adjusted, which is very advantageous. The simulations contribute to an early awareness about how different material properties responds in different types of embossing operations, and also if the required embossing height is possible. Since different paperboard qualities can be 1

12 analyzed in an early state, the manufacturing cost will be reduced and results in an advantageous effect for both the company and the environment. The aim of this thesis was to develop a simulation model, created with Finite Element Method by using Abaqus (2014), which capture the experimental behavior of embossed paperboard. The goals were to understand which material properties that are of high importance in embossing operations, and how sensitive the material model is at small geometry changes of the embossing tool. In this thesis one specific paperboard quality was analyzed. The embossing tool was configured as simple as possible with a stationary movement pattern. The embossing geometry was circular with a diameter of 6 mm where the edges, for both the male die and the female die, were rounded with a radius of 0.5 mm, illustrated in Figure 2. Figure 2. Illustration of the embossing tool cross section geometry. 1.3 OVERVIEW DESCRIPTION OF PAPERBOARD MATERIAL Paperboard is a widely used packaging material and its use increasing every year due its low manufacturing cost and its ability to be 100% recyclable. Paperboard material consists of a network of bonded fibers and due to the fiber structure the material has a high degree of anisotropy. The high anisotropy originates from the manufacturing process where the distribution of the fiber orientations is created. Three directions are defined where the in-plane direction represent the machine direction, MD, and the cross direction, CD, while the out-of-plane direction represents of the thickness direction, ZD. The different directions are shown in Figure 3. Most of the paper fibers are lying in the in-plane direction and are predominantly oriented in MD, while there are practically no fibers aligned in the out-of-plane direction. Due to the network structure paperboard material exhibits an exponential behavior when it is compressed. 2

13 Figure 3. The principal directions of paperboard material (Andersson [2]). According to Huang et. al. [3], Stenberg et. al. [4] and Xia [5], the stiffness is highest in MD and can be 1-5 times higher than the stiffness in CD and 100 times higher than the stiffness in ZD. Paper material exhibits several features which make the material quite complex. Paperboard is a complex material due to its high anisotropy, its non-linear inelastic material response and its delamination between the plies when the paperboard deforms. The high anisotropy can cause numerical problems when creating a simulation model. According to Huang et. al. [3], Stenberg et. al. [4] and Xia [5], the material can be treated as an orthotropic with principal material directions in MD, CD and ZD. Paperboard is normally defined as a thicker paper material where the paperboard is built up in ZD consisting of several layers. In this thesis the paperboard was designed as a multi-ply material with a sandwich structure, illustrated in Figure 4. The different plies are bonded chemically together, hence almost no fibers are crossing the plies. Figure 4. Illustration of the multi-ply material with its sandwich structure and its respective plies (Andersson [2]). 3

14 The multi-ply material consisted of two outer plies and one middle plie, where the outer plies had a higher density compared to the middle plie. The outer plies were developed with a higher tensile stiffness, while the middle ply was made weaker which resulted in enhanced formability of the paperboard. The construction was used to obtain light weight with a high stiffness as possible. 1.4 REVIEW OF PREVIOUS WORK Embossing operations are a relatively new technique to design different types of paperboard packages. It is therefore a gap of information about how paperboard behaves during different types of embossing operations. In order to understand the main mechanisms and behaviors in paperboard material a literature study of creasing has been done. Creasing operations was assumed to be sufficiently similar to embossing operation. The literature study, in this thesis, was therefore based on previous work of creasing operations. One consistent factor found from the literature study was that the paperboard model consists of two constitutive models, one continuum model and one interface model. The continuum model describes the behavior of the plies and the interface model, consisting of cohesive elements, describes the inelastic delamination between the plies. The combination of those two constitutive models seems to be a good foundation for the paperboard model. This assumption was based on its good ability to capture accurately behavior during complex loadings, such as creasing and folding. Xia [5] proposed a three dimensional material model for large deformations. The model was developed to be elastic-plastic in the in-plane direction while the out-of-plane direction only consisted of elastic components. The model contained a non-quadratic multi-surface yield function, anisotropic hardening, different behavior in compression and tension and a nonlinear elastic description through the thickness. However, the assumption about only elastic components in the out-of-plane direction was derived from the theory that the model is used together with an interface model, which account for damage in the out-of-plane direction. Nygårds et al. [6] implemented the model proposed by Xia [5] to study the out-of-plane behavior. It was found that the elastic outof-plane model did not capture the experimental creasing behavior during unloading. Andersson [2] developed a material model for small deformations with elastic-plastic behavior by improving the model presented by Xia [5]. The model was improved by adding plastic behavior in the out-of-plane direction. Andersson [2] utilized the work by Stenberg [7] when modeling the behavior of the normal components in the thickness direction. Stenberg [7] accounted for nonlinear elasticity. The shear behavior in the outof-plane model was proposed to be linear elastic with isotropic hardening, where the yield criterion was modelled with a parabolic yield surface and an associative flow rule. Improvements were shown in the creasing simulations, especially as regards the unloading part. It should however be noted that no experimental measurements of the out-of-plane shear properties were done and the parameters were freely chosen. 4

15 However, Andersson [2] reached the same conclusion as Nygårds et al [6]. It is important to account for plasticity in all components due to high compressive strains developing during creasing. Nygårds et al. [8] presented a work where the aim was to implement an experimental and numerical study of creasing by utilizing certain parts of the model proposed by Xia [5]. The properties in the in-plane continuum model were described by an elastic-plastic model. The elasticity was assumed to linear, while the plastic behavior was modelled as suggested by Xia [5]. The model was assumed to be elastic in tension while it was assumed to be elastic-plastic in compression. This assumptions was based on that paperboard consist of a network structure which exhibit an exponential behavior when it is compressed. Instead the interface model was modeled to capture the inelastic behavior in out-of-plane tension. The simulation results showed good agreement with the experimental results. Nygårds et al. [8] observed that the properties from the out-ofplane shear, out-of-plane compression and the friction between the male ruler and the paperboard have a high influence of the results and are therefore of high importance. Huang et. al [9] proposed a simplified two dimensional material model where the aim was to improve the concept of a two dimensional models for creasing. The continuum model was described by an elastic-plastic material model where orthotropic linear elasticity and Hill s yield criterion with isotropic linear hardening was used. The cohesive elements in the interface model were described with an orthotropic elasticplastic cohesive law and an exponential damage evolution model. The numerical and experimental results where compared and showed that the creasing behavior were predicted quite good. Huang et al. [3] observed that for good predictability of the process the continuum plastic properties are important. The aim with the work was to characterize the most important properties needed for creasing, and subsequently draw assumptions for the remaining properties. The shear strength profile was believed to be important due to the mechanism activated during the creasing operation. The shear strength profiles was used to estimate the continuum properties in the through thickness direction. According to Nygårds and Huang [9] the continuum model can be well described as orthotropic linear elastic-plastic with isotropic linear hardening together with Hill s yield criterion. The model was also implemented in the work by Huang et al. [3]. The cohesive elements in the interface model were described by an orthotropic elastic cohesive damage law along with an exponential damage evolution. The proposed two dimensional model better predicted the unloading part compared to the work suggested by Huang et. al [9]. Huang et al. [3] analyzed the influence of the interface strength and the continuum properties on creasing. It was shown that different interface strengths generally have a small influence on the creasing results while the continuum properties have a larger impact on the force-displacement curve during the creasing operation. 5

16 2 METHOD This master thesis has its main focus within embossing operations and how different factors influence the result. An experimental and numerical study of compression in ZD has also been conducted, based on Nygårds et al. [8] and Huang et al. [10]. The study of compression includes experimental tests and measurements where the aim was to determine the out-of-plane elastic modulus, E ZD. The numerical study includes simulations both with and without interfaces in the material model. The study of embossing contains a comparison between experimental and numerical results. The purpose of the experimental tests was to capture the behavior of embossed paperboard and the goal was then to recreate the behavior in the simulation model. The simulation model for embossing operations was analyzed in more detailed. The material parameters which were changed in the respective analysis were changed in all plies at the same time, while the remaining parameters were kept constant. The parameters that were varied and the parameters which were kept constant are described in section 3, Results. The in-plane material properties which have been analyzed were the elastic moduli, E, in MD and CD. The analyzed out-of-plane material properties were the shear moduli, G, in MD-ZD and CD-ZD, the yield stress, σ, in ZD and the yield shear stresses, τ, in MD- ZD and CD-ZD. The influence of the initial stiffness, K, in all directions of the interface model was analyzed. How the interface model influence the continuum model was analyzed in two ways. Firstly, the simulation model was modeled without interfaces and secondly, the number of interfaces was increased. Different friction coefficients, µ, between the contact surfaces; paperboard to male die and paperboard to female die was also included in the analysis. As a final part of the analysis the embossing tool rounding edges were changes from 0.5 mm to 0.25 mm. Due to delimitation of time the majority of the steps were analyzed only for the loading part of embossing. The results in this thesis focus on the relationship between the applied force and the displacement. 6

17 2.1 MATERIAL MODEL The simulation material model used to represent the paperboard was constructed in a similar way as the models presented in the literature study, i.e. the model consisted of two constitutive models, a continuum model and an interface model CONTINUUM MODEL The continuum model in this thesis was based on previous work of Huang et. al. [3] and [9]. The continuum model was described as an anisotropic linear elastic-plastic material model with isotropic linear hardening together with Hill s yield criterion, available in Abaqus [11]. The elastic model was defined by the elastic moduli,,,, the shear moduli,,,, and the Poisson s ratios,,,. Hill s yield criterion is an anisotropic yield model which makes it possible to add different yield stresses and yield shear stresses in different directions. The yield criterion evaluates when plasticity occurs in the material model, i.e. once the yield criterion is fulfilled the material start to deform plastically. The criterion was formulated with the initial yield stresses,,,, and the initial yield shear stresses,,,. MD was taken as the reference direction for each ply INTERFACE MODEL The interface model was represented by cohesive elements, available in Abaqus [11]. The cohesive elements accounts for delamination between the plies and also within the plies which can occur when the model is exposed to loading. They were described with an anisotropic elastic-plastic traction-separation law and an exponential damage evolution model, available in Abaqus [11]. The model requires 8 different parameters. Three initial stiffness parameters three failure stresses and two parameters which describe the exponential damage evolution model, the effective separation at complete failure, and the dimensionless parameter α. The cohesive elements are elastic until they reach their failure stresses and then they starts to soften according to the exponential damage evolution law. The exponential damage evolution law was used to account for the softening behavior in the paperboard. 7

18 Figure 5. Illustration of the cohesive element and its principal directions (Andersson [2]). The index parameter n refers to the behavior in ZD and the index parameters s and t refer to the shear behavior in MD and CD respectively, as illustrated in Figure 5. The interface model had the same description in all interfaces, i.e. the 8 different parameters were set to be the equal. Figure 6. Illustration of paperboard and its associated parts (Andersson [2]). Beex et. al. [12] and [13] discovered that the simulation model for creasing is relatively insensitive to small changes of the total number of interface layers. Based on previous work, Huang et. al [3] and [8], it seems as if a number of three interfaces is an optimum choice. Therefore the material model in this embossing analysis was modeled with three interfaces. Two interfaces were placed between respective the continuum plies and one interface was placed in the center of the middle ply, as illustrated in Figure EXPERIMANTAL METHODS AND ASSUMPTIONS FOR CHARACTERIZATION OF PAPERBOARD PROPERTIES The material properties needed for the simulation material model have been characterized. Some of the parameters have directly been measured from standard test, while others have been estimated. All the experimental tests were performed at a temperature of 23 C and a humidity of 50%, and followed the standard atmosphere, ISO 8

19 187:1990. Before all tests the paperboard was prepared where the top, middle and bottom plies were separated from each other in a machine called Fortuna. This preparation was performed by Stora Enso Research Centre. The structural properties, thickness and density, obtained by Stora Enso Research Centre are tabulated in Table 1. The paperboard was composed of six layers which are shown in Figure 7. Table 1. The thickness and density of each ply and the whole paperboard Thickness [µm] Density [kg/m 3 ] Whole paperboard Top ply Middle ply Bottom ply Figure 7. The specific paperboard and its consisting layers. A description of the different layers starting from the bottom; the bottom layers represent the first outer ply consisting of light coating together with chemical pulp, the center layer represent the middle ply consisting of chemical thermo mechanical pulp, CTMP and the top layers represent the second outer ply consisting of triple coating and chemical pulp. When the material model is numerically implemented in Abaqus (2014), the high anisotropy can cause numerical problems, as mentioned in section 1.3. According to Huang et. al. [3], Stenberg et. al. [4] and Xia [5], the material can be treated as an orthotropic material. The out-of-plane Poisson s ratios were assumed to be zero in all plies, i.e. (2.1) The continuum model consists of two parts, an in-plane model and an out-of-plane model. These two models cover different behavior of the paperboard. The in-plane model accounts for the behavior in MD and CD and the shear between these two directions, while the behavior in ZD and the shear between ZD and the two in-plane direction are accounted for in the out-of-plane model. Hooke s generalized law has been used together with the assumption in equation 2.1 which results in that the in-plane and the out-of-plane properties are independent. The two models can then be separated and 9

20 solved independently, which is preferred from a numerical point of view. The in-plane and the out-of-plane models are formulated in equation 2.2 and 2.3 respectively. (2.2) (2.3) To measure the in-plane elastic moduli and the in-plane yield stresses a tensile test in and the direction for each ply has been done. The tests were performed by Stora Enso Research Centre in Karlstad, Sweden and followed the tensile test standard, ISO :1994. The stress-strain curves were obtained from the test and the parameters, mentioned above, were measured. The initial yield stresses were taken as the stresses where the plastic strain was 0.1%. Additionally, the initial in-plane yield shear stress was replaced by according to Huang [14]. It is difficult to accurately determine the in-plane shear modulus from an inplane shear test of a paperboard material. The shear modulus and the Poisson ratios and were therefore estimated by utilizing some assumptions. By using Hooke s law combined with the symmetry of the stiffness tensor, equation 2.5, and the empirical relation, equation 2.6, presented by Baum et al. [15] the shear modulus has been determined, equation 2.4. (2.4) (2.5) From equation 2.5 and 2.6 it was possible to determine the Poisson s ratios, and, according to (2.6) (2.7) 10

21 (2.8) The hardening modulus, H, was determined from the MD tensile test as mentioned earlier. Where the hardening modulus, H, for each ply were taken as the linear slope between the yield point and the failure point, equation 2.9. (2.9) where is the yield stress, is the failure stress and is the effective plastic strain at failure. Hill s yield criterion was utilized in order to account for the anisotropic plasticity. Hill s yield criterion is a simple extension of von Mises yield criterion. Hill s yield criterion can be expressed in terms of rectangular Cartesian stress components, as (2.10) where F, G and H are constants and defined as Each represents the initial yield stresses. The six yield stresses are implemented in Abaqus (2014) through the anisotropic yield ratios,. The six yield ratios are defined as where is the specified reference yield stress, i.e. in this case. (2.11) Further assumption was made regarding the initial yield stress. According to Huang, H. [3] and Huang et. al. [14] the initial yield stress, is challenging to determine, due to that delamination can occur before the material is exposed to plastic deformation. Small values of the yield ratios can cause numerical problems in terms of convergence problems. This derives from the high degree of anisotropy in the paper material. Therefore the initial yield stress was increased and assumed to the same 11

22 value measured for. According to Huang et al. [3] this approximation ensures that the yield criterion is real. In this work, the out-of-plane shear moduli and and the initial out-ofplane yield shear stresses and were based on previously reported values by Huang, H. [9] and [16]. The determination of the out-of-plane elastic modulus has been a part of this thesis and is described in more detail in section The three stiffness parameters were calculated based on the assumption suggested by Hagman et. al [17]. The assumption is based on that the material model captures the elastic behavior through the continuum model. The elastic stiffness in the interface model was therefore set to be stiffer than the elastic stiffness in the middle ply, according to: and where t was set to 1mm. The three failure stresses and the two parameters which describe the exponential damage evolution, the effective separation at complete failure and the dimensionless parameter were based on previously reported values by Huang, H. [9] OUT-OF-PLANE COMPRESSION TEST Compression tests of paperboard were carried out in a universal testing machine manufactured by Zwick Roell, Figure 8. The machine was coupled together with the software testxpert II, which is a control program for the testing machine. Compression test has earlier not been performed in the machine, which was a high risk factor in this thesis. Evaluation of the method have been made and are presented in section 5, Discussion. Figure 8. The universal testing machine coupled together with the software, testxpert II. 12

23 Figure 9. The fixed closed module. Figure 10. The compression tool, male die and flat bottom part. The testing device consisted of a closed module with an associated compression tool, which was placed into a vertical channel in the module. The module was fixed while different tools could be used to test different geometries. The closed module and the compression tool are shown in Figure 9 and 10. The tool used consisted of a male die and a flat bottom part. The geometry of the male die was circular with 6 mm in diameter where the edge was rounded with a radius of 0.05 mm, as illustrated in Figure 11. The tool was designed in such a way that the torque was eliminated during the testing. This was achieved by a free bullet placed on top of the male die, i.e. between the machine and the male die, see Figure 12 and 13. Figure 11. Compression tool geometry and its dimensions. 13

24 Figure 12. The distance between the machine and the male die. The free bullet is placed beside the male die. Figure 13. The distance between the machine and the male die. The free bullet is placed on top of the male die. Before the tests started a compliance curve was created. The curve was created by performing a test without specimen in the module. This curve was used for all further tests in order to compensate for the elastic deformation that occur in the testing machine, the module and the tool at use. Figure 14. A specimen of the paperboard placed into the narrow opening gap of the closed module. At compression tests, a strip specimen of the paperboard was placed into the narrow opening gap of the closed module and placed between the male die and the flat bottom part, as illustrated in Figure 14. The tests were performed for the whole paperboard and for each individual ply; top, middle and bottom. The compression tests were performed in force control mode and force versus displacement traces were recorded. Compression was analyzed at three different loads, 100N, 120N and 160N. Several tests were done with the same load, but on different sample areas, in order to account for uneven distribution of fibers and to check for the replicability of the method. If the fiber distribution has a higher density in the area of compression a higher force will be needed to reach the same displacement, compared to if the fiber distribution was of a 14

25 low density. At determination of the elastic modulus the initial area of the forcedisplacement curves were analyzed, in order to decide a suitable range. The elastic modulus was determined for each individual plies and also for the whole paperboard. The elastic modulus,, and the related stress,, and strain,, were calculated according to (2.12) (2.13) (2.14) where F is the applied load, A is the contact area between the male die and the paperboard, is the total thickness change and is the original thickness of the paperboard. Furthermore, the total elastic modulus,, was summed according to equation 2.15, where the plies were coupled in series. Thus, a comparison between the measured value from the whole paperboard and the summed value of each individual ply has been done. This analysis was done for two reasons. Firstly, due to that the machine which separates the plies from each other can cause damage to the plies, and hence decrease the value of the out-of-plane elastic modulus. Secondly, the plies behave differently depending on whether they are individual or together. (2.15) where is the total thickness of the whole paperboard,, and are the thickness of the top-, middle- and bottom ply, respectively and, and are the out-of-plane elastic moduli of the top-, middle- and bottom ply, respectively. It was shown that the measured elastic modulus of each individual ply generated a too weak simulation model. The interfaces in the simulation model affect the model by cause weakening and hence decrease the elastic modulus of the whole material model. The elastic modulus for each individual ply; top-, middle- and bottom ply, in the simulation model, were therefore increased with a factor of 14, 5 and 20 respectively, in order to capture the experimental behavior. At this stage, all material parameters needed for the simulation material model were characterized. 15

26 2.3 EMBOSSING - EXPERIMENTAL SETUPS Experimental setups of the embossing operations were performed by the same method as the one mentioned for the compression tests, i.e. in a universal testing machine together with the data software, testxpert II. The operation consisted of the same closed module, shown in Figure 9. Embossing operations has earlier not been performed in the machine, which was a high risk factor in this thesis. As mentioned in section 1.2, the embossing tool consisted of a male die and a female die where the geometry was circular with a diameter of 6 mm. The edges, for both the male die and the female die, were rounded with a radius of 0.5 mm. The tool geometry is illustrated in Figure 15 and 16. Figure 17 shows the inside of the closed module, where the female die was placed in the vertical channel. The closed module with the associated embossing tool was developed in order to be used in this thesis. Figure 15. Embossing tool geometry and its dimensions. Figure 16. Embossing tool, male and female die. Figure 17. Showing the inside of closed module. 16

27 Torque-free operations were achieved in the same way as mentioned for the compression tests. The compliance curve derived for the compression tests was utilized in the embossing operations as well. In the embossing operations, a strip specimen of paperboard was placed into the opening of the module and placed between the male die and the female die, as shown in Figure 14. The tests were performed for the whole paperboard. They were done in force control mode and force versus displacement traces were recorded. The embossing was analyzed at a load which corresponds to a displacement of 0.5 mm. Several tests were done with the same load but on different sample areas in order to account for uneven distribution of fibers and to check the replicability of the method. The embossing height was investigated in a macroscope instrument, model VR-3200, manufactured by Keyence. The path along the paperboard in MD was plotted as height versus distance along the paperboard. The same path was recreated in the simulation model. 2.4 IMPLEMENTATION OF THE FEM MODEL IN ABAQUS A three dimensional simulation model was created in Abaqus (2014) where the aim was to recreate the experimental behavior of both compression and embossing. The created simulation material model was used in both operations. The other parts; male die, female die and the flat bottom plate, used in the two operations, are shown in Figure The construction of the two operations was built-up equal. The only difference was that the flat bottom plate, Figure 20, was used in compression while in embossing the female die was used, Figure 19. Figure 18. The male die used in both compression and embossing. R = 0.05 mm in compression; R = 0.5 mm and R = 0.25 mm in embossing. Figure 19. The female die used in embossing. R = 0.5 mm and R = 0.25 mm. 17

28 Figure 20. The flat bottom plate used in compression. Since the two operations were virtually identical, this section mainly contains a description of the embossing simulations. The tools were modeled as discrete rigid bodies with the same dimensions as the ones used experimentally. The finite element simulations were performed as quasi-static analysis by using Abaqus/Dynamic Implicit (2014). An implicit solver uses an implicit integration scheme to solve finite element equations. The implicit integration implies that each increment is iterated until physical equilibrium has been reached. The paperboard was modeled as single solid deformable. The dimensions were 10 mm in MD and CD and mm in ZD. The part was partitioned by creating datumplanes, two datum-planes for each interface, and further divided in six sections by using a built-in partition tool, available in Abaqus [11]. The six sections represent the top-, middle- and bottom plies and the three interfaces, shown in Figure 21. The thickness of each interface was mm and their positions are tabulated in Table 2. The top-, middle and bottom plies were assigned with different properties. The interface model was implemented as cohesive element where the properties for each interface were approximated to be equal. Due to the choice of dynamic simulation the density of the interfaces needed to be defined. The density of each interface was set to equal to the density of the ply the interface was placed in, i.e. the density from either the top-, middle or bottom ply. Figure 21. Showing how the simulation material model was partitioned. 18

29 Table 2. The interface position (measured in direction from the top surface) Partition position 1 [mm] Partition position 2 [mm] Interface Interface Interface Figure 22. The meshed paperboard. The material model was assigned with an element shape of wedge-sweep elements. The total number of elements for the paperboard was 64890, shown in Figure 22. The continuum plies were modelled with 6-noded linear triangular prism elements (C3D6). The interfaces were modelled with element type, COH3D6, which is a linear 6-noded three-dimensional cohesive element. The cohesive elements needed to be assigned with stack orientation in order to define the contact between the continuum elements and the cohesive elements. Due to the anisotropy a coordinate system was defined. A global coordinate system with axis 1, 2 and 3 was used, where the 1, 2 and 3 axis corresponds to MD, ZD and CD respectively. In Figure the assembly of the three parts is shown. The three parts were constrained by defining surface-to-surface contact between the male die and the paperboard and between the female die and the paperboard, using contact interaction in Abaqus [11]. The contact between the paperboard and both the male die and the female die was defined in the tangential and normal direction. Hard contact was defined in normal direction which implies that no overclosure of the two surfaces is allowed. In the tangential direction friction was applied by using the penalty method. The friction coefficient between male die and the paperboard was set to 0.1 while the friction between the female die and the paperboard was set to

30 Figure 23. Assembly of the three part; male die, paperboard and female die. Figure 24. Assembly of the three part; male die, paperboard and female die. Figure 25. A cut view in MD of the assembly. Since the male die and the female die were modeled as discrete rigid bodies the boundary conditions were defined in the reference points, which were placed in the center of the respective parts. The movement of the male die was fixed in the vertical direction and the motion was specified to a certain displacement, i.e. the simulations were deformation-controlled. The female die was fixed in all directions. Both parts are shown in Figure 26 and 27 where the arrows show the reference positions. In order to save computer time the paperboard was modeled as small as possible. The outer ends were therefore constrained in both MD and CD, where the paper was seen as restrained in a larger sheet, as shown in Figure 28. The boundary conditions are tabulated in Table 3. 20

31 Figure 26. Showing where the reference point was placed on the male die. Figure 27. Showing where the reference point was placed on the female die. Figure 28. Showing the ends of the paperboard which was constrained in both MD and CD. Table 3. The boundary conditions of both the embossing and the compression tests Part at reference point at outer edges Male die u MD = u CD = 0, u ZD 0 Female die / flat plate u MD = u CD = u ZD = 0 Paperboard u MD = u CD = u ZD = 0 The outputs were obtained from the history field output, where the reaction force and the displacement of the male die in the moving direction was selected. 21

32 reaction force, F [N] reaction force, F [N] 3 RESULTS 3.1 OUT-OF-PLANE COMPRESSION RESULTS The experimental compression tests were performed for the whole paperboard and for each individual plies; top, middle and bottom. Observe that the thickness of the paperboard is included in the value of the displacement. The tests were performed at three different loads of the as shown in Figure As mentioned in section 1.3, the outer plies had a higher density compared to the middle plie. The results in the Figures shows that the outer plies are stiffer compared to the middle ply. This observation was established since the middle ply reached a much higher deformation compared to the outer plies ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 29. Experimental out-of-plane compression tests at 100 N. Bottom ply (dotted line), top ply (long-dashed line), whole paperboard (dashed-dotted line) and middle ply (short-dashed line) ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 30. Experimental out-of-plane compression tests at 120 N. Bottom ply (dotted line), top ply (long-dashed line), whole paperboard (dashed-dotted line) and middle ply (short-dashed line). 22

33 reaction force, F [N] reaction force, F [N] reaction force, F [N] ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 31. Experimental out-of-plane compression tests at 160 N. Bottom ply (dotted line), top ply (long-dashed line), whole paperboard (dashed-dotted line) and middle ply (short-dashed line) ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 32. Experimental out-of-plane compression tests at 100 N, 120 N and 160 N for each ply. Bottom ply (dotted line), top ply (long-dashed line) and middle ply (short-dashed line) ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 33. Experimental out-of-plane compression tests at 100 N, 120 N and 160 N for the whole paperboard. 23

34 In Figure 32 and 33 are the results presented in Figure separated, where the individual plies are shown in Figure 32 and the whole paperboard is shown in Figure 33. This was done in order to analyze the initial area on the force-displacements curves. The range of forces used for the determination of the out-of-plane elastic modulus was between 3.5 N and 14.0 N. The calibration and the adjusted of the out-of-plane elastic modulus are presented in Table 5. The summed value of each individual ply was determined to be 3.5 MPa, while the measured value of the whole paperboard was 17 MPa. From this calculation it was concluded that the machine which separates the plies causes damage to the plies which leads to reduced stiffness. But how much damage the machine has caused cannot be defined since the plies behave differently depending on whether they are individual or together. The determined values of each individual ply generated a too weak simulation model, since it only reached an elastic modulus of 4 MPa. The values in the simulation model were adjusted to new values in order to capture the measured value of the whole paperboard. The adjusted values generated a simulation model with an elastic modulus of 19 MPa, which was assumed to be sufficiently equal to the measured value of the whole paperboard. A comparison between these two cases, i.e. the simulation model with the original values and the simulation model with the adjusted values, is presented in appendix A. Table 5. The calibration and the corrugation of the out-of-plane elastic modulus Original value of [MPa] Adjusted value of [MPa] Whole paperboard Top ply Middle ply Bottom ply Summed value Simulation model Summed according to equation 2.15 The results from the simulated compression test, with the material properties presented in appendix B, together with the experimental compression tests are shown in Figure 34. The displacement in the simulation was set to be 0.05 mm. The numerical result showed good agreement regarding the loading part, but not as regards the unloading part. Numerical compression tests where the simulation model was modeled both and without interfaces are shown in Figure 35. The result shows that the interfaces have relatively high influence on the compression test. The interfaces results in easier formability of the paperboard, since a lower force is needed to reach the same displacement. 24

35 reaction force, F [N] reaction force, F [N] ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure 34. Comparison between experimental and numerical results of out-of-plane compression tests. Simulated compression (solid line) and experimental compression (dashed-dotted lines) ,01 0,02 0,03 0,04 0,05 0,06 displacement, u [mm] Figure 35. Numerical results of out-of-plane compression tests with and without interfaces. With interfaces (solid line) and without interfaces (dotted line). 25

36 reaction force, F [N] 3.2 EMBOSSING RESULTS Both the numerical and the experimental embossing operations were performed only on the whole paperboard. Observe that the thickness of the paperboard is included in the value of the displacement. The experimental operations were performed at a force which corresponds to a displacement close to 0.5 mm, while the displacement in the simulation model was set to 0.5 mm. The result from the numerical operation, where the simulation material model was modeled with the material properties presented in appendix B, is shown in Figure ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 36. Numerical embossing result, including both loading and unloading. The influence of the in-plane material properties and was analyzed and the result is shown in Figure 37. Both were changed while the remaining properties were fixed. The values, which the elastic moduli were changes to, are tabulated in Table 4. The result shows that the elastic moduli in MD and CD have a small influence on the results. The analysis of the out-of-plane properties is presented in Figure 38. The stress was changed while the remaining properties were fixed. It should be noted that when changing the stress, the stress must also be changed equally as mush to prevent convergence problems in the simulation model. The convergence problems occur due to the material anisotropy which becomes too large if the values are unequal. The shear moduli and were changed while the remaining properties were fixed, and also the shear stresses and were changes while the remaining properties were fixed. The results, in Figure 37 and 38, shows that the properties which have the highest influence on the simulation model are the out-ofplane shear stresses and. Therefore, these parameters were analyzed in more detail and the results are presented in Figure 39, where the stresses were increased with a factor of 2, 4 and 5.5 respectively. Table 4. The selected values when the in-plane material properties were analyzed Top ply Middle ply Bottom ply [MPa] [MPa]

37 reaction force, F [N] reaction force, F [N] reaction force, F [N] ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 37. Numerical embossing results where the in-plane material properties were analyzed. Original model (solid line) and increased E MD and E CD (dotted line) ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 38. Numerical embossing results where the out-of-plane material properties were analyzed. Original model (solid line), decreased (x0.4) σ ZD (dotted line), increased (x1.5) G MD-ZD and G MD-ZD (short-dashed line) and increased (x2.0) τ MD-ZD and τ CD-ZD (long-dashed line) ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 39. Numerical embossing results where the stresses τ MD-ZD and τ CD-ZD were analyzed. Original model (solid line), increased (x2.0) τ MD-ZD and τ CD-ZD (long-dashed line), increased (x4.0) τ MD-ZD and τ CD-ZD (dotted line) and increased (x5.5) τ MD-ZD and τ CD-ZD (short-dashed line). Figure 40 shows the analysis of how the interface model affects the embossing operations. The initial stiffness parameters were changes in all plies while the remaining properties were fixed but the result was almost unaffected. The number of interfaces, on the other hand, seems to have a higher influence on embossing operations, 27

38 reaction force, F [N] reaction force, F [N] but the difference was still marginally small. The number of interfaces was increased from three to five. The dashed-dotted line represents the simulation without interfaces, where the numerical results did not have the ability to reach a displacement of 0.5 mm. This shows that, in a numerical point of view, it is beneficial to modulate the simulation model with interfaces since the model can be formed easier ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 40. Numerical embossing results where the interface model was analyzed. Original model (solid line), increased K (dotted line), increased number of interfaces (dashed line) and without interfaces (dasheddotted line). The results from where the friction between the contact areas were analyzed are shown in Figure 41. It is shown that the friction coefficient, µ, has a relatively low influence on the embossing operation ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 41. Numerical embossing results where the friction between the contact surfaces was analyzed. µ=0 (dotted line), µ= 0.1(short-dashed line) and µ=0.28 (long-dashed line). 28

39 reaction force, F [N] reaction force, F [N] The numerical and the experimental results from embossing are shown in Figure 42. Initially the numerical result shows good agreement to the experiments, but at a force of 10 N the curves unfortunately begin to deviate ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 42. Numerical and experimental embossing results. Simulated embossing operation (solid line) and experimental embossing operation (dotted line). As a final part of this thesis two different embossing tools were analyzed where their rounding edges were changed. The results are shown in Figures The numerical results in Figure 43 show a relatively large difference regarding the loading part while the unloading part is partially similar. The experimental results in Figure 44 show that the behavior at loading and at unloading was similar, but that the force needed to reach the specified displacement was dissimilar. This shows that small changes of the embossing tool have a high influence on the results. When the rounding radius was sharper, i.e mm, a higher force was required in order to reach the same displacement, compared to the tool with a rounding radius of 0.5 mm ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 43. Numerical embossing results where the rounding edges were changed. R=0.5 mm (solid line) and R=0.25 mm (dashed line). 29

40 reaction force, F [N] ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure 44. Experimental embossing results where the rounding edges were changed. R=0.5 mm (solid line) and R=0.25 mm (dashed line). The embossing height of the two embossed paperboards was investigated in a macroscope instrument and the results are shown in Figure 46 and 48. The corresponding curve obtained from the simulation model is shown in Figure 45 and 47. Two notes should be done regarding the results. Firstly, the numerical results include both the loading and the unloading part of embossed paperboard, while the results from the macroscope only contain the unloading part. This is because the used universal testing machine not has the ability to capture this type of curve. Secondly, the axis that corresponds to the distance along the paperboard does not have the same scale size and hence the results can see slightly misleading. In Figure the embossed simulation model is shown at both loading and unloading. The results show that at a rounding radius of 0.5 mm the paperboard was exposed to a lot of bending, while at a rounding radius of 0.25 mm shear was more dominant. 30

41 Displacment, u [mm] Displacement, u [mm] Displacement, u [mm] Displacement, u [mm] 0,6 0,5 0,4 0,3 0,2 0,1 0 Distance along the paperboard in MD Figure 45. Numerical results of the embossing height. R = 0.5 mm. At loading (dashed line) and at unloading (solid line). 0,6 0,5 0,4 0,3 0,2 0,1 0 Distance along the paperbord in MD Figure 46. Macroscope result of the embossing height at unloading. R = 0.5 mm. 0,6 0,5 0,4 0,3 0,2 0,1 0 Distance along the paperboard in MD Figure 47. Numerical results of the embossing height. R = 0.25 mm. At loading (dashed line) and at unloading (solid line). 0,6 0,5 0,4 0,3 0,2 0,1 0 Distance along the paperboard in MD Figure 48. Macroscope result of the embossing height at unloading. R = 0.25 mm. 31

42 Figure 49. Embossing displacement, in MD, at loading. R = 0.5 mm. Figure 50. Embossing displacement, in MD, at unloading. R = 0.5 mm. Figure 51. Embossing displacement, in MD, at loading. R = 0.25 mm. Figure 52. Embossing displacement, in MD, at unloading. R = 0.25 mm. 32

43 4 DISCUSSION According to the embossing results, the experimental measurements captured an exponential hardening behavior while, unfortunately, the numerical simulations showed a declining hardening behavior. As mentioned in section 1.4 embossing is a relatively new technique to design different types of paperboard packages. Since there was a gap of information about how paperboard behaves during embossing, the literature study was based on previous work of creasing operations. The assumption that creasing operations are sufficiently similar to embossing appears to be a good assumption, when analyzing an overview of the mechanisms involved in embossing. In order to reach a higher understanding of embossing operations the analysis needs to be further developed. When analyzing the experimental compression tests, Figures 29-31, a few observations were made. As expected the curves show an exponential hardening behavior in compression, and the top and bottom plies were significantly stronger than the middle ply. When comparing the curves it can be seen that when the applied load was increased the difference between the middle ply and the whole paperboard was decreased. The middle ply is the ply which has the highest degree of compressibility, which is consistent with how the paperboard is manufactured. According to the compression results, the numerical simulation showed good agreement to the experimental loading part, but not as regards the unloading part, see Figure 34. The simulation material model generated a curve which was tangent to the experimental loading part but unfortunately, only an elastic behavior was captured. Since only elastic deformation was obtained, the curve which represents the unloading part returned to the origin. The difference between the experimental and the numerical tests was that the experimental specimens included a time-dependent behavior, which the simulation model did not. An observation of the experimental compressed specimen after a relatively long time showed that the remaining deformation was close to zero. In order to capture the exponential hardening behavior in the numerical tests a time-dependent simulation model is required. The interface model resulted in an increased formability of the paperboard, see Figure 35. The theory behind this is that delamination between the layers occurs when high shear stresses are achieved in the continuum model and hence the paperboard can be formed easier. Something which is very remarkable is that if a specimen is exposed to pure compression, the result should not be affected by the interface model. In this case, the compression results have been affected which indicates that pure compression has not been achieved. Presumably, the sharp rounding radius of 0.05 mm on the male die has contributed to a certain degree of shear in the material. The used compression tool 33

44 was of a small dimension which probably also has contributed to high edge defects in the material, which is not preferable. In contrast to compression, the embossing results from the simulation model with and without interfaces were basically equal, as shown in Figure 40. This is probably because the embossed material has been exposed to more bending than shear, due to that the used embossing tool was constructed with a larger rounding radius, i.e. 0.5 mm instead of 0.05 mm. What proportion of shear and bending the material has been exposed to seem to strongly depend on the rounding radius of the embossing tool, which can be seen in Figure When the rounding radius was 0.5 mm bending was more dominant while when the rounding radius was 0.25 mm shear was more dominant. Based on these observations, it is recommended that the different loading cases, bending, shear and compression should be analyzed in greater detailed, in order to achieve a higher understanding of how the simulation model behaves in different types of embossing operations. Figure shows the remaining embossing height after loading. The numerical result obtained a value of 0.45 mm while the experimental measurements showed a value around 0.3 mm. The values are slightly different but the actual difference is hard to define. The experimental embossed specimen has probably returned more than the simulation model since the deformation is time-dependent. In order to investigate this in more detail macroscopic measurements should be performed over a longer time. The material parameters which seem to have an important role in embossing operations are the out-of-plane shear parameters, which also were shown for the creasing operation, based on Nygårds et. al. [8]. One factor which separates embossing operations from creasing operations is how the paperboard is loaded. Only one direction at the time is loaded at creasing, i.e. MD or CD, while in embossing both directions is involved at the same time. The out-of-plane shear properties in previous work are modified in order to be used in creasing operations. The out-of-plane shear components have not been obtained by measurement, instead different values has been tested in the simulation model until the results corresponds to the experimental behavior. Since this work partially was based on these modified parameters, it is possible to conclude that they need to be modified to values which correspond to the embossing behavior. The other material parameters which were analyzed in this thesis gave no remarkable difference. If this is due to that shear stresses affects the results in such a high degree that they take over, or if they actually do not have an influence on the results is difficult to draw conclusions about. A simplified simulation material model was created in order to strengthen the statements about the out-of-plane shear properties. As mentioned in section 2.2 Hill s yield criterion is developed to account for anisotropic plasticity. The simplified model was modeled with isotropic plasticity by implementing von Mises yield criterion, i.e. only the hardening modulus, H, was defined. The result from this simulation is presented in Figure C1 in appendix C, and shows an exponential 34

45 hardening behavior. This reinforces the theories regarding that the declining hardening behavior probably was due to incorrect shear stresses. The other parameters needed in Hill s yield criterion was not based on previous work. The experimental method used in out-of-plane compression and embossing has never been used before, which was a significant risk when accurate results are of interest. It is therefore difficult to draw conclusions regarding the obtained data, if they are of high accuracy or not. One conclusion which can be drawn is that the method captured a hardening behavior at loading which was expected, but if the obtained displacement is correct is more unsecure. Several tests were performed with the same load but on different sample areas. It was shown that when the tests were force-controlled the method generated results of high replicability, while when the tests were deformationcontrolled the results were unsecure. This was the reason why the experimental tests were performed force-controlled instead of deformation-controlled, as the simulations. Usually, compression tests are performed with specimens who are smaller than the tool. This is used in order to ensure that edge defects are eliminated and that pure compression has been achieved. In this thesis the tool was much smaller than the specimen. Therefore, it is recommended to further develop the method where the tool is larger than the specimen. It would also be beneficial if the method was developed in such a way that deformation controlled tests with high replicability are possible. 35

46 5 CONCLUSION The embossing results showed an exponential hardening behavior while the numerical results, unfortunately, showed a declining hardening behavior. Despite this, some understanding regarding which parameters that are of utmost importance have been achieved. The assumption that creasing operation is sufficiently similar to embossing operation appears to be a good assumption, when analyzing an overview of the mechanisms involved in embossing. This thesis shows that the material parameters which have the highest influence on embossing of paperboard are the out-of-plane shear properties. Conclusions regarding these parameters can also be drawn. They need to be modified to values which correspond to the embossing behavior, instead of creasing behavior. This thesis also shows that the material model is sensitive of small changes of the tool geometry. The proportion of shear, bending and compression are strongly dependent on if the tool has sharp edges or if the edges are more rounded. In order to achieve a higher understanding of how paperboard behaves during embossing operations, the different loading cases; bending, shear and compression are required to be analyzed in greater detail. 36

47 6 REFERENCES [1] Stora Enso, Available: [2] Andersson, T. A small deformation model for the elasto-plastic behavior of paper and paperboard. Master of Science Thesis, Div. of Solid Mechanics Lund University. (2006). [3] Huang, H., Hagman, A. and Nygårds, M. Quasi static analysis of creasing and folding for three paperboards, Int. J. Mechanical of Materials. 69 (2014) [4] Stenberg, N. and Fellers, C. The out-of-plane Poisson s ratios of paper and paperboard, Nord. Pulp Paper Res. J. 17 (2002) 387. [5] Xia, Q. S. Mechanics of inelastic deformation and delamination in paperboard, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, USA. (2002). [6] Nygårds, M., Hallbäck, N., Just, M. and Tryding, J. A finite element model for simulation of creasing and folding of paperboard, ABAQUS User s conference 2005, Stockholm, (2005). [7] Stenberg, N. A model for the through-thickness elastic-plastic behavior of paper, Int. J. Solids Struct. 40 (2003) [8] Nygårds, M., Just, M. and Tryding, J. Experimental and numerical studies of creasing of paperboard, Int. J. Solids Struct. 46 (2009) [9] Huang, H. and Nygårds, M. A simplified material model for finite element analysis of paperboard creasing, Nord. Pulp Paper Res. J. 25 (2010) [10] Huang, H. and Nygårds, M. The dependency of shear zone length on the shear strength profiles in paperboard. Experimental Mechanics 52 (2012) [11] Abaqus. ABAQUS User s Manual. ABAQUS Inc, Providence, PI, USA, edition (2014). [12] Beex, L.A.A. and Peerlings, R.H.J. An experimental and computational study of laminated paperboard creasing and folding, Int. J. Solids Struct. 46 (2009) [13] Beex, L.A.A. and Peerlings, R.H.J. On the influence of delamination on laminated paperboard creasing and folding. Phil. Trans. R. Soc. A., 370 (2012) [14] Huang, H. Numerical and experimental investigation of paperboard converting processes. Department of solid mechanics, KTH Engineering Sciences, Royal institute of Technology, Stockholm, Sweden. 82 (2013). [15] Baum, G., Brennan, D. and Habeger, C. Orthotropic elastic constants of paper, Tappi J. 64 (1981)

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49 reaction force, F [N] 7 APPENDIX A ,02 0,04 0,06 0,08 0,1 displacement, u [mm] Figure A1. Showing the two models which were compared when the out-of-plane elastic moduli of each ply were determined. Simulation model with its original values (dotted line), simulation model with its adjusted values (dashed line) and experimental measurement (solid line). 39

50 8 APPENDIX B Table B1. Material parameters in the continuum model Top ply Middle ply Bottom ply Elastic parameters E MD [MPa] E CD [MPa] E ZD [MPa] G MD-CD [MPa] G MD-ZD [MPa] G CD-ZD [MPa] ν MD-CD ν MD-ZD ν CD-ZD Hardening and initial yielding H [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] Table B2. Material parameters in the interface model [MPa/mm] [MPa/mm] [MPa/mm] [mm] [MPa] [MPa] [MPa] α

51 reaction force, F [N] 9 APPENDIX C ,1 0,2 0,3 0,4 0,5 0,6 displacement, u [mm] Figure C1. Showing an exponential hardening behavior when isotropic plasticity was applied and a declining hardening behavior when anisotropic plasticity was applied. Experimental embossing (solid line), simulation with von Mises yield criterion (dashed line) and simulation with Hill s yield criterion (dashed-dotted line). Figure C2. The meshed paperboard used when von Mises yield criterion was applied. 41