Numerical and Experimental Investigation of Paperboard Creasing and Folding

Transcription

1 Numerical and Experimental Investigation of Paperboard Creasing and Folding Hui Huang Licentiate Thesis No. 111, 2011 KTH School of Engineering Science Department of Solid Mechanics BiMaC Innovation Royal Institute of Technology SE Stockholm Sweden

2 TRITA HFL-0503 ISSN ISRN KTH/HFL/R-11/05-SE

3 Abstract This licentiate thesis aims to increase the understanding of deformation and damage mechanisms of paperboard during converting, especially creasing and folding will be analyzed. A simple two dimensional creasing simulation was performed. In this model, paperboard was modeled as a combination of an anisotropic elastic-plastic continuum model with isotropic hardening and a softening cohesive interface model. The paperboard was composed of four plies with uniform material parameters. Creasing simulations were done on both machine direction (MD) and cross machine direction (CD) samples to two crease depths 0.0 mm and 0.2 mm, respectively. The simulation results showed good agreement with experimental results. The out-of-plane shear properties are dominating factors for creasing and folding. Therefore, a test method to determine shear properties was proposed. This part of the work is based on the most recently proposed test method, the laminated double notch shear test. To improve the technique, double notches with declined slopes, called tilted double notch shear test, were used instead of uniform depth double notches. The influence of shear zone length was also investigated. The results reveal the short shear zone lengths gave higher shear strength and more pronounced shear strength profile. The results from the first two analyses were utilized to study folding of paperboard. The simulation model was the same as in the creasing simulations. However, to improve the model and better account the actual micro structure of paperboard a new material mapping method was proposed. The continuum properties of the plies were assumed to vary in the thickness direction. The shear strengths of the interfaces were determined by using the tilted double notch shear test using a short shear zone length, L = 5 mm. The agreement between simulation results and experiment results was good, and most of the folding properties were captured.

4

5 Preface At February 2008, I was given the opportunity to do my master thesis work at Innventia under supervision of Mikael Nygårds. That was the time I walked into the Paper Packaging Research field, which was a whole new world for me. After finishing the master thesis work, I found myself in love with this research topic, and I chose to continue working in this area. Then my PhD study life was preluded. So far, these two and half years of working in this field has been full of joy and inspiration. There are many people who contributed to this great experience. To express my deeply appreciation, first of all, I want to thank my supervisor Assistant Professor Mikael Nygårds who introduced me to this interesting research area, and gives me invaluable help, advice and support. Working with him in these three years has been a fantastic experience for me. I also want to thank Professor Sören Östlund for his support and advise. At the first year of my PhD studies, Professor Sören Östlund was my first supervisor. Although afterwards my supervision was passed to Assistant Professor Mikael Nygårds, the help and support from Professor Sören Östlund never stopped. I feel grateful for his precious advice and encouragement. My gratitude also goes to M.Sc Martin Öberg, Kurt Lindquist, Yngve Lindvall and other colleagues at the laboratory and workshop. I appreciate your patience and help during my experimental period. For my friends and all the other colleagues at department, I am also thankful to all of you. You are the persons that make me happy every day; you are the persons I know who I can go to when I have problems; and you are the persons that always be there for me anytime. Besides, the financial support from BiMaC Innovation and all the colleagues in BiMaC Innovation are gratefully acknowledged. Last, but by no means least, I want to thank my family, especially my lovely parents: my father Jian-hua and my mother Ya-jun. Without your endless support and love, I would not be such a happy person. All what I ve done and been today are because of your love. You are my dearest treasure and my harbor where I can rest when I feel tired. I deeply appreciate it. Stockholm, March 2011

6

7 List of appended papers Paper A: A simplified material model for finite element analysis of paperboard creasing H. Huang and M. Nygårds Nordic Pulp & Paper Research Journal 25(4): , Paper B: The dependency of shear zone length on the shear strength profiles in paperboard H. Huang and M. Nygårds Report 501, Department of Solid Mechanics, KTH Engineering Sciences, Royal Institute of Technology, Stockholm, Sweden Paper C: Numerical and experimental investigation of paperboard folding H. Huang and M. Nygårds Report 502, Department of Solid Mechanics, KTH Engineering Sciences, Royal Institute of Technology, Stockholm, Sweden

8 Contribution to the papers The author s contributions to the appended papers are as follows: Paper A Principal author. Performed all simulation work. Active part in outlining experiments and interpreting the results. Performed the experiments together with Mikael Nygårds. Paper B Principal author, large active part in outlining experiments and interpreting the results. Performed the experimental work with the help from Mikael Nygårds. Paper C Principal author. Performed all simulation work. Active part in outlining experiments and interpreting the results. Performed the experiments together with Mikael Nygårds.

9 Contents Introduction 11 Paperboard Creasing and Folding 15 Experimental Techniques for Characterization of Paperboard Out-of-Plane Shear Properties 21 Summary of Appended Papers 25 Bibliography 27 9

10 Numerical and Experimental Investigation of Paperboard Creasing and Folding 10

11 Introduction Paper and paperboard are two common material used in almost all industries. They are highly recyclable and environment friendly materials, which results in a rapid utilization growth of these materials. In 2007, the Paper&Paperboard market size had a value of billion USD and a volume of million metric tons. About 50 % of all produced paper is used for packaging, followed by printing and writing. However, the understanding of the mechanical properties of this popular and essential material is still limited, especially the mechanism of paperboard converting. Thus, this thesis work aims to contribute to the effort of understanding paperboard creasing and folding mechanisms by using both experimental and finite element methods. Paperboard is a thick, single or multiply paper based material. The paperboard discussed in this work is a multi-ply commercial paperboard which is composed of several layers of pulp fibers bonded by starch or adhesive material. An example of a SEM picture illustrating the paperboard structure is shown in Figure 1. From Figure 1, the laminate structure of paperboard can be identified, where the middle plies are normally made bulkier. This results in an I-beam structure where high bending stiffness is achieved with as few fibers as possible. Bending stiffness is one of the most important mechanical properties for paperboard packaging. For multi-ply paperboard, bending stiffness is mainly attributed to the outer plies, which have higher density. The middle layer of paperboard contributes less to the total bending stiffness, which is partly due to its own low bending stiffness and partly through its function of separating the surface plies. Therefore, a combination of low density in the middle ply and high density in the surface plies optimizes or maximizes the bending stiffness. In a common manufacturing process of multi-ply paperboard each ply is formed separately, and placed on 11

12 Numerical and Experimental Investigation of Paperboard Creasing and Folding Figure 1: SEM picture of the paperboard thickness profile. top of each other in wet conditions to form the paperboard. Hence, fibers can be oriented in the out-of-plane direction within the plies, while there are no fibers crossing the interfaces. The interfaces can therefore often be considered weaker than the plies. In the manufacturing process, it is however possible to strengthen different interfaces with chemicals, and therefore interfaces can also be made strong. However, due to the multiply structure, interfacial delamination is often a common and important failure mechanism when paperboard fails either due to out-of-plane loading or during creasing. Since each ply of paperboard is composed of pulp fibers, which have a preferred fiber orientation, paperboard can be approximated as an orthotropic material with three principle directions: machine direction (MD), cross-machine direction (CD) and through-thickness direction (ZD). Most fibers in common paperboards are oriented in the machine direction, which thereby is the stiffest direction. The through-thickness direction is the weakest direction among three directions. Due to the difference in fiber orientation in MD, CD, and ZD, the material properties are also different in the different directions as shown in Figure 2, which 12

13 Figure 2: Stress-strain curves from uniaxial tensile tests in MD, CD, 45 degree direction, ZD and out-of-plane shear tests in MD and CD for a multiply paperboard, (Nygårds, 2005). shows the experimental results from uniaxial tensile tests in MD, CD, 45 degree direction between CD and MD, and ZD are shown together with out-of-plane shear tests. Based on Figure 2, ZD stiffness and strength can be about a factor of 100 weaker than in MD. Moreover, the strength and stiffness in the CD is about a factor two weaker than in the MD. 13

14 Numerical and Experimental Investigation of Paperboard Creasing and Folding 14

15 Paperboard Creasing and Folding Creasing and folding are critical process steps in the box forming process. The creasing process starts by placing the paperboard sheet on a female die, and then a male ruler is punched into the female die so that paperboard will be scored at the correct position, which it will thereafter be folded along. Figure 3 shows micrographs of the creasing process. During creasing, fiber-fiber bonds between plies are broken, some fibers are damaged and plastic deformation occurs in the paperboard plies. High shear and compressive stresses arise in the paperboard during the creasing operation. The shear induced delamination in the paperboard reduces the bending stiffness during the subsequent folding process. Due to the local damage in the creased area, the paperboard will ideally behave as a hinge, which improves the folding performance. Hence, one method to judge the quality of the creasing is to see whether the following folding process can be precisely preceeded. To target the creasing quality, there are many factors which can influence the creasing quality, such as paperboard moisture content, width of female ruler, penetration depth, etc. However, the most important factor is the paperboard thickness. Thicker boards need a wider ruler and groove. Therefore they are less sensitive to inaccurate register between the rule and the groove. The paperboard discussed in this work has a thickness of 0.4 mm, and the width of female die is 2.1 mm, the depth 3.0 mm, and the male ruler width is 0.7 mm. After creasing, the paperboard will be folded to form a package. It is desirable to fold 90 degree corners with no cracks on the outside. If an uncreased paperboard is folded, it may result in cracking of the outer-layer. Figure 4 illustrates a good folding sequence, and also identifies deformation and damage mechanisms during folding. From Figure 4, it can be clearly seen that delamination cracks between the plies open up. Tensile stress appears on 15

16 Numerical and Experimental Investigation of Paperboard Creasing and Folding Figure 3: SEM picture of paperboard creasing process, from Dunn (2000) 16

17 out-side of the fold, while the inner ply is compressed in order to activate the bulging of the bottom ply. Moreover, according to Franklin (1970), the ability of paperboard to delaminate sufficiently is an important property for folding. Delamination is a mode of fracture where a paper or paperboard sheet fractures, with the fracture surface parallel to the plane of the sheet. This type of failure is in the case of folding a positive mechanism. Since it can release the stresses on the outside of the fold, which will reduce the risk of cracking at the outside of the fold, the folding operation of paperboard relies heavily on the ability of the board to internally delaminate in order to enable the relief of the compressive stresses generated at the inside of the fold. The delamination stresses are generally 50 to 100 times lower than stresses necessary to create fracture surface normal to the plane of the sheet. Finite element simulations of creasing and folding with multipurpose material models were performed by Xia (2002). A modeling concept consisting of continuum and interface models to represent the paperboard was used. With this concept it became possible to perform simulations where both continuum deformation as well as delamination between plies were presented. Figure 5 shows the model structure concept. The continuum model is expressed in a large deformation framework that accounts for small deformation with large rotations. The interface model was expressed in terms of interface tractions and displacements. Based on this implementation of the two models, it could be concluded that convergence issues is a large problem that needs special attention. The two models were later implemented by Nygårds et al. (2005), and comparisons with experimental creasing and folding data was done, They show that the modeling concept could predict deformation and damage in paperboard during crease loading quite well, but not unloading. However, the drawback with the model of Xia (2002) is that the continuum model only considered the elastic property in the out-of-plane direction. Therefore, an elastic-plastic continuum model was implemented by Nygårds et al. (2009). Then the unloading profile could be better captured. Nevertheless, this model required too many material constants which are difficult to determine accurately. Therefore, in this work, a new simplified model will be suggested in Paper A and further improvments are presented in Paper C. 17

18 Numerical and Experimental Investigation of Paperboard Creasing and Folding Figure 4: Photos of a folding sequence, initial delamination sites are identified by the arrows, from Dunn (2000). 18

19 Figure 5: Schematic of paperboard numerical model concept. 19

20 Numerical and Experimental Investigation of Paperboard Creasing and Folding 20

21 Experimental Techniques for Characterization of Paperboard Out-of-Plane Shear Properties The out-of-plane shear strength is one of the most important material properties for quality control related to creasing and folding. Since a well defined shear strength profile can induce more delamination for creasing and improve subsequent folding. However, development of testing techniques to measure shear strength for paperboard is a topic that still needs improvements. The most common shear test method is the rigid support shear method (Byrd et al. (1975); Waterhouse (1991); Stenberg et al.(2001)), which is schematically shown in Figure 6. In this type of method, the paper samples need to be glued onto a rigid substrate which leads to glue-penetration-problem when testing thin papers. Normally only paper materials with basis weights above approximately 60 g/m 2 (Girlanda and Fellers, 2007) can be tested in the out-of-plane direction. Another limitation of this method is that only the weakest interlaminar shear strength can be captured. Besides, this method is also time consuming, since it needs long time to prepare the test sample. Recently Nygårds et al. (2007) proposed the double notch shear test method (DNS). The advantage of this method is that it does not rely on gluing. It uses tensile loading to induce shear failure because of two fabricated notches, one on each side of paperboard. The interlaminar shear strength at different thickness positions can also be obtained by this method. 21

22 Numerical and Experimental Investigation of Paperboard Creasing and Folding Figure 6: Schematic of rigid support shear methods, sample is glued between two rigid supports. However, tensile failure can be induced by the notches when the shear zone is too large and the remaining ligaments are too thin. To avoid this drawback, the laminated notch shear test (NST) was proposed in Nygårds et al.(2009). The notched test piece is laminated by plastic foil so that tensile failure is avoided. Figure 7 illustrates the process of NST. In Paper B laminated double notch shear test will be further investigated, especially with respect to the influence of distance between the notches. 22

23 Figure 7: Manufacturing and testing procedure for the laminated notched shear test. (a) Paperboard with thickness h is the starting point, (b) two grooves are ground, (c) the paperboard is laminated with plastics, (d) the sample is tested in a tensile testing machine, (e) failure occurs between the two grooves, from Nygårds et al. (2009) 23

24 Numerical and Experimental Investigation of Paperboard Creasing and Folding 24

25 Summary of Appended Papers Paper A: A simplified material model for finite element analysis of paperboard creasing. This paper propose a simplified material model to simulate paperboard creasing. Paperboard was modeled as a two dimensional multilayered structure with a softening interface model connecting the paperboard plies. The paperboard plies were modeled using an anisotropic elastic model with a Hill yield surface and isotropic hardening. The model has less material constants than the models previously presented in the literature, and the material constants can more easily be determined from uniaxial experiments. The model was tested by performing simulations of creasing of paperboard with a two dimensional finite element model, which mimicked a laboratory creasing device. Creasing experiments and simulations at two different creasing depths were performed, and the reaction force and the displacement of the male ruler were analysed. Simulations and experiments were performed both in the paperboard machine direction and the cross machine direction. The force-displacement curves from the simulations and the experiments were compared, with good agreement. Paper B: The dependency of shear zone length on the shear strength profiles in paperboard. Paper B presents a further investigation and improvement of the laminated double notch shear test method proposed by Nygårds et al.(2009). In this work, tilted notches were proposed so that the testing procedure can be simplified and accelerated. Besides, the influence of the shear zone length was also investigated. According to the results, both 25

26 Numerical and Experimental Investigation of Paperboard Creasing and Folding the measured shear strength values and the through-thickness shear strength profiles varied significantly with different shear zone lengths. The longer shear zone gave lower shear strength values and more steady profiles, while the shorter shear zones gave higher strength values and more pronounced shear strength profiles that better followed the paperboard ply structure. Paper C: Numerical and experimental investigation of paperboard folding. Paper C used experimental results from Paper B to enhance the numerical model from Paper A for numerical investigation of paperboard folding. In this work, the paperboard material model was defined by the same combination of an anisotropic elastic-plastic continuum model with isotropic hardening and a softening interface model, which was used in Paper A. A material mapping method was proposed to define the material parameters of the continuum models, according to the experimental observations of the paperboard property variations in the thickness direction. Based on the discovery of various out-of-plane shear strength in Paper B, the tilted laminated double notch shear test technique was used to measure the shear strengths for the paperboard interfaces. The new material model and data were validated by simulations of the creasing process. Thereafter, folding investigations were done. The simulation results and experimental results showed good agreement. 26

27 Bibliography A. Franklin: Print quality and runnability of coated paper., Print Technology, 14:21-24, J.F. Waterhouse: The failure envelope of paper when subjected to combined out-of-plane stress., The International Paper Physics Conference, Hawaii, USA, , O. Girlanda and C. Fellers: Evaluation of the tensile stress-strain properties in the thickness direction of paper materials., Nord. Pulp Paper Res. J. 22(1):49-56, H. M. Dunn: Micromechanics of paperboard deformation., Master thesis, Massachusetts institute of technology, Cambridge, Mass., USA., M. Nygårds: 3DM - Three dimensional finite element modelling of paperboard., Technical Report 339, Innventia (formely STFI-Packforsk), M. Nygårds, C. Fellers and S. Östlund: Measuring the stress-strain properties of paperboard., J. Pulp Paper Sci. 33(2):1-5, M. Nygårds, C. Fellers and S. Östlund: Development of the notched shear test., Adv. In Pulp and Paper Res. Oxford , M. Nygårds, M. Just and J. Tryding: Experimental and numerical studies of creasing of paperboard., Int. J. Solids Struct. 46: , N. Stenberg, C. Fellers, and S. Östlund: Measuring the stress-strain properties of paperboard in the thickness direction., J. Pulp Paper Sci. 27(6): , L.V. Byrd, V.C. Setterholm, and J. F. Wichmann: Method for measuring the interlaminar shear properties of paper., Tappi J. 58(10): Q.S. Xia: Mechanics of inelastic deformation and delamination in paperboard., PhD thesis, Massachusetts institute of technology, Cambridge, Mass., USA,

28 Numerical and Experimental Investigation of Paperboard Creasing and Folding 28