Licentiate Thesis in Solid Mechanics

On the relation between paperboard properties and packaging performanceGUSTAV MARIN

Stockholm, Sweden 2021

kth royal institute of technology

On the relation between paperboard properties and packaging performanceGUSTAV MARIN

Licentiate Thesis in Solid MechanicsKTH Royal Institute of TechnologyStockholm, Sweden 2021

Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Licentiate of Engineering on Monday the 18h January 2021, at 1:15 p.m. in seminar room 4303, Teknikringen 8D, KTH Stockholm

© Gustav Marin ISBN 978-91-7873-743-7TRITA-SCI-FOU 2020:048 Printed by: Universitetsservice US-AB, Sweden 2020

Abstract

Paper-based materials, such as paperboard, are commonly used as packaging materials. In addition to the advantage that wood as a raw material is renewable, there are also many other benefits of paperboard. From a mechanical point of view, paperboard has a high bending stiffness compared to its relatively low weight and has a high foldability, which both are properties of significance in the design of packages. However, a distinct drawback with paperboard is its significant sensitivity to moisture. The moisture reduces the mechanical properties of the paperboard and consequently reduces the performance of the package. This thesis is starting with an investigation of the relation between moisture and different mechanical properties on a continuum material level, and then these relations are applied on the packaging design level through experimental testing and simulations.

In Paper A, a material characterization was performed on a series of five paperboards with different grammages from the same producer. Five types of mechanical tests to characterize the paperboards’ material properties were performed:

• In-plane tensile test, • Out-of-plane tensile test, • Short-span Compression Test (SCT), • Bending stiffness test, • Double-notch shear test.

All tests were performed at several levels of relative humidity (RH). Linear relations between the mechanical properties normalized with their respective value at 50 % RH and moisture ratio were found.

Paper B examined whether the linear relationships discovered in Paper A are true also for other paperboard series as well. Therefore, 15 paperboards from four producers were investigated in this study, at the same levels of RH as before. Here, the in-plane stiffnesses and strengths and SCT-values were evaluated as a function of moisture. When also the moisture ratios in the investigated paperboards were normalized, it turned out that all paperboards followed the same linear relationship between normalized mechanical property and normalized moisture ratio. Additionally, a bilinear elastic-plastic in-plane model was developed, that can predict the stress-strain relation of an arbitrary paperboard at an arbitrary moisture level, and without requiring any mechanical testing except at standard condition (50% RH, 23 °C).

In Paper C, this relation was used to estimate input material parameters for simulating a Box Compression Test (BCT) at different moisture levels. The result showed that it was possible to accurately predict the load-compression curve of a BCT when moisture was accounted for.

Sammanfattning

Som förpackningsmaterial betraktat är pappersbaserade material, som exempelvis kartong, väldigt intressanta material. Utöver att råvaran trä är förnyelsebar finns även många andra fördelar med kartong. Ur ett mekaniskt perspektiv är kartong exempelvis väldigt styv i förhållande till sin vikt och har generellt väldigt hög vikbarhet, vilket båda är egenskaper som lämpar sig väl för en förpackning. En klar nackdel med kartong är dess känslighet för fukt. Fukten reducerar kartongens mekaniska egenskaper, vilket följaktligen leder till att förpackningens prestanda försämras. I den här licentiatavhandlingen undersöktes initialt sambanden mellan fukt och mekaniska egenskaper på materialnivå, för att sedan överföra sambanden till förpackningsnivå genom experimentell provning och simuleringar.

I Artikel A utfördes en materialkaraktärisering på en kartongserie innehållande fem kartonger med varierande ytvikter från samma tillverkare. Fem typer av mekaniska prov genomfördes för att karaktärisera kartongernas respektive materialegenskaper:

• Dragprov (i planet), • Dragprov (ut ur planet), • Korta kompressionsprov (SCT), • Böjstyvhetsprov, • Skjuvprofilsprov.

Samtliga prov utfördes vid flera olika nivåer av relativ fuktighet (RH). Linjära relationer mellan mekanisk egenskap normerad med motsvarande värde vid 50 % RH och fukt noterades.

I Artikel B undersöktes huruvida de linjära sambanden som upptäcktes i Artikel A stämmer även för andra kartongserier. 15 kartonger från fyra producenter undersöktes därför i denna studie vid samma fukthalter som tidigare. I den här studien undersöktes endast dragprov i planet, samt SCT. När även fuktkvoterna i de undersökta kartongerna normerades visade det sig att alla kartonger följde samma linjära relation mellan normerad mekanisk egenskap och normerat fuktinnehåll. Utöver detta utvecklades en bilinjär elastisk-plastisk i-planet-modell som kan prediktera en godtycklig kartongs spännings-töjningsförhållande för godtycklig fuktnivå, utan att någon mekanisk provning utöver standardklimat (50 % RH, 23 °C) behöver genomföras.

I Artikel C utnyttjades det linjära sambandet mellan mekanisk egenskap och fuktkvot genom att prediktera de ingående materialegenskaperna som användes vid simuleringar av boxkompressionsprovning vid olika fuktnivåer. Simuleringarna jämfördes med experimentell provning och visade sig kunna prediktera experimentella resultat vid olika fukthalter bra.

Preface

The work presented in this thesis was carried out at Research Institutes of Sweden (RISE), and at the Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden between June 2018 and July 2020. The work would not have been possible without the generous financial support of STFI’s Association of Interested Parties (STFIs Intressentförening).

I would like to express my sincere gratitude to my supervisor Dr. Mikael Nygårds for giving me this opportunity, convincing me to return to the field of paper mechanics and constantly pushing me forward. I really appreciate our discussions and your guidance in this thesis has been tremendously valuable.

Furthermore, I would like to show my appreciation to my supervisor professor Sören Östlund for introducing me to paper mechanics and for providing guidance and feedback throughout this project.

I would like to thank all my colleagues at RISE and Department of Engineering Mechanics at KTH. In particular, Dr. Prashanth Srinivasa, Dr. Anton Hagman and Dr. Carl-Magnus Everitt without whom I would probably still be struggling with the thesis. I really appreciate that I have the opportunity to disturb your work with my questions every day. I furthermore wish to thank Cecilia Rydefalk for sharing the struggles that the position as an industry employed PhD student entails.

Finally, I would like to thank my family and friends for all their support. Especially my wife Matilda, for supporting me through these years of strange working hours. A final thanks to my son Harald, who makes sure that I do not oversleep in the mornings.

Stockholm, December 2020

Gustav Marin

List of appended papers

Paper A: Stiffness and strength properties of five paperboards and their moisture dependency

Gustav Marin, Mikael Nygårds and Sören Östlund

Tappi Journal, Vol. 19 No. 2:71–85, 2020

Paper B: Elastic-plastic model for the mechanical properties of paperboard as a function of moisture

Gustav Marin, Mikael Nygårds and Sören Östlund

Nordic Pulp and Paper Research Journal, May 2020

Paper C: Experimental and FE-simulated box compression tests on paperboard packages at different moisture levels

Gustav Marin, Prashanth Srinivasa, Mikael Nygårds and Sören Östlund

Accepted for publication in Packaging Technology and Science, December 2020

Contribution to the papers

Paper A: Principal author and performed all experimental work and analysis. Marin, Nygårds and Östlund jointly evaluated and interpreted the results.

Paper B: Principal author and performed all experimental work and analysis. Marin, Nygårds and Östlund jointly evaluated and interpreted the results.

Paper C: Principal author and performed all experimental work, simulations and analysis. Srinivasa wrote the initial code that Marin developed for this study. Marin, Nygårds, Srinivasa and Östlund jointly evaluated and interpreted the results.

In addition to the appended papers, the project has resulted in the following presentations:

Stiffness and strength properties of five paperboards and their moisture dependency Gustav Marin, Mikael Nygårds and Sören Östlund Presented at TAPPI PaperCon, Indianapolis, USA, 2019

Box compression strength of packages in different climates Gustav Marin and Mikael Nygårds Presented at IAPRI symposium, Enschede, Netherlands, 2019

Modelling the moisture dependent elastic-plastic properties of paperboard Gustav Marin, Mikael Nygårds and Sören Östlund Presented at Progress in Paper Physics Seminars, Jyväskylä, Finland, 2020

Contents

1 Introduction ............................................................................................................................... 1 1.1 Paper as an engineering material .................................................................................... 1 1.2 Packaging performance ................................................................................................... 3

2 Method ........................................................................................................................................ 4 2.1 Material characterization ................................................................................................. 4

2.1.1 In-plane tensile test ..................................................................................................... 4 2.1.2 Out-of-plane shear test ............................................................................................... 4

2.2 Packaging testing .............................................................................................................. 5 2.3 Finite Element Model ...................................................................................................... 6

3 Results and discussion .............................................................................................................. 7 4 Conclusions .............................................................................................................................. 10 5 Bibliography ............................................................................................................................. 11

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1 Introduction The world is facing innumerable environmentally related challenges, where plastic waste is one of them. Around 25.8 billion tonnes of plastic waste are generated each year only in Europe. Approximately 1.5 – 4 % of the global plastics production end up in the ocean every year. These numbers are relevant for the packaging industry, since 59 % of the plastic waste is due to packaging [1]. Because of this, the European Union is taking actions by banning single-use plastics by 2021 [2]. The required reduction of plastic use in future, environmentally friendly packages is a huge possibility for the paper industry, since paper is relatively cheap, but also a recyclable material. However, it also entails new requirements and challenges, which means that increased knowledge and development of new tools are required.

1.1 Paper as an engineering material

Even if paper is frequently used in almost everyone’s daily life, it is a quite complex material. Two commonly used types of paper-based packaging materials are paperboard and corrugated board. The distinct difference between the two types is that paperboard consists of one or more solid plies, while the typical construction of a corrugated board is two thin outside layers (liner) and a corrugated fluting layer in between. The difference can be seen in Figure 1.

(a) (b) Figure 1. Cross-section view of a multiply paperboard (a) and a corrugated board (b).

Paper-based materials are manufactured in a paper machine with a length of a few hundred meters, which usually consists of three sections: forming, pressing and drying. Initially, a liquid suspension with a solid fibre content of approximately 1 % is uniformly spread out on a moving wire. A consequence of reducing nonuniformities in the mass distribution of the solid content on the wire, is that the fibres rotates parallel to the machine direction due to a necessary speed difference between the furnish jet and the wire. Water is later removed through suction units and pressing cylinders which forms a web with a solid content of approximately 50 %. [3] In this section, the density and thickness of the paper is determined. Finally, the web is dried through a series of hot cylinders. When water disappears from the web, joints are formed between fibres. To prevent fluttering during drying, a tension is applied to the web. This tension prevents the web from shrinking in MD and contributes further to the anisotropy of the paper. Hence, the manufacturing process of the paper results in an anisotropy of the paper described by three principal directions: machine direction (MD), cross-machine direction (CD) and the through-thickness direction (ZD). The in-plane stiffness and strength are larger in MD compared to CD, and for ZD, the tensile strength for paperboard is typically two magnitudes smaller than in MD [4]. A commonly used approximation is that the anisotropy of paperboard is orthotropic, i.e. the stiffness properties are symmetric with respect to the three material directions, respectively.

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For multiply paperboards, the furnish mixture of the different plies can vary, depending on the required properties of the board. One of the main advantages of paperboard as a packaging material is its high bending stiffness in relation to its relatively low weight. When optimizing the board for bending stiffness, it is desirable to achieve high tensile stiffness in the outer plies, and to separate them with one or several low-density plies, analogous to the function of an I-beam structure. Another advantage with paperboard as a packaging material is its foldability. When a paperboard is converted from board to a package, it is common to crease it first to avoid surface cracks and achieve a straight folding line. By creasing the paperboard, transverse shear occurs between the plies which causes delaminations and micro cracks. The damage is thereby concentrated to the inside of the paperboard, a hinge is created and surface cracks can be avoided during the subsequent folding, see Figure 2.

(a) (b)

Figure 2. A paperboard during a creasing procedure (a) and a folded paperboard after creasing (b).

The most distinct drawback with paperboard as a packaging material is its significant sensitivity to moisture. The paper-water interaction could either be through contact between paperboard and liquid, i.e. hydrosorption or by changing the relative humidity (RH): hygrosorption. Regardless how the paperboard is exposed to moisture, the fibres will swell which causes reduced mechanical properties. In the literature, it is established that the in-plane strength and stiffness is reduced by 50 % when the relative humidity is changed from 22 % to 90 %. This holds for both MD and CD [5,6].

There are several ways to express the relation between mechanical properties and moisture. One property frequently used to evaluate the amount of moisture is relative humidity (RH). This gives a measure of the surrounding environment at which the experiments were performed. However, a huge disadvantage is that it does not provide any information regarding the moisture level in the actual paperboard. To account for this, the moisture content (ISO 287:2017)

𝑚𝑐 =𝑚𝑤𝑎𝑡𝑒𝑟

𝑚𝑡𝑜𝑡𝑎𝑙 (1)

is frequently used in the literature: a ratio between the mass of water and the total mass. An alternative way of evaluating the moisture in the material the moisture ratio

𝑚𝑟 = 𝑚𝑡𝑜𝑡𝑎𝑙−𝑚𝑑𝑟𝑦

𝑚𝑑𝑟𝑦. (2)

A clear advantage with moisture ratio is its linear relation to the stiffness and strength indices [7].

Although experimental testing of paperboard at different climates have been thoroughly investigated in the literature, most published data comes from studies performed on laboratory sheets, whose mechanical properties differ from commercially produced paperboards [8]. Therefore, one requirement for this thesis was to use commercial machine-made paperboards.

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1.2 Packaging performance

Designing and performing experimental material testing is one key to understand the complexity of paperboard materials, and why a paperboard for instance fracture during packaging converting. Material characterization can be performed to determine the mechanical properties of the paperboard. Analogously, experimental testing can be performed on packages to evaluate their performance. For instance, the stacking performance is commonly evaluated by performing a Box Compression Test (BCT). From this test, the box compression strength defined by the BCT-value is obtained, i.e. the maximum force a box can carry before failure.

As an example of BCT, the work by McKee [9] establishes a relation between the box compression strength and elastic buckling of panels, described by compression strength and bending stiffness for boxes made of corrugated board. A similar relation to predict the box compression strength for paperboard boxes is described by Grangård [10].

A critical drawback with box compression strength is the limited amount of information available for design: it does not provide any information about deformation shapes, compression stiffness response or failure mechanisms, etc. The BCT strength of a package have been predicted in an alternative approach by Ristinmaa et al. [11] by analyzing the deformation behaviours of panels loaded in compression. The approach predicts the strength by introducing yield curves representing folds created during testing. A panel with a low height/width aspect ratio will have different yield lines compared to a panel with a high aspect ratio. Ristinmaa et al. establishes that the corners of a panel carry a large part of the load during a box compression test and that the yield lines commonly propagate from the corners into the interior of the panel. The corner region fails at peak load due to a plastic collapse mechanism, rather than a due to a stability issue. Consequently, a local failure criterion is activated at peak load.

Commonly, analytical models for prediction of BCT are typically phenomenological and therefore dependent of additional package testing. If something is changed in the package design, additional testing must be performed before these models are applicable. However, testing is quite expensive and time consuming, and when the packaging industry is facing a demanding future, new tools must be utilized. One possible way forward is to use Finite Element Analysis (FEA) in the developing process. By using FEA in the package design process, other variables besides strength can be accounted for. It will be possible to study stress and strain fields that arise during loading, and which can contribute to better understanding of the important mechanisms activated in the loaded package. In addition, it is possible to isolate and modify different design parameters, such as the perimeter of the package, mechanical properties of the packaging material etc. and see how they affect the behaviour of the package. In the end, this may lead to better knowledge and development of improved sustainable packages and paperboard materials.

One of the main difficulties in simulations of paper-based materials is the complexity of the material. The complexity comes from different aspects, where the anisotropy and the thin sheet material are two important factors on a continuum material level. An FE-software requires a material model describing the stress-strain relation in the material. Different approaches are suggested in the literature. The recent trends and challenges are reviewed by Simon [12]. The material can for instance be described either on a fibre network scale [13], or on a paper sheet scale, with three principal material directions (MD, CD and ZD). Several models at different level of complexity have been developed. However, Simon concludes that there is no model (yet) that simultaneously accounts for effects such as anisotropy, nonlinearity, temperature, moisture, time dependency etc.

The purpose of this thesis was not to develop a model that accounts for all these complex effects. On the contrary, the focus was to investigate how FEA can be used in a user-friendly way in order to increase the knowledge of how packaging material fails on a paper sheet

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scale. In addition, the moisture dependence of packages was analysed experimentally and included in the FE-simulations.

2 Method This thesis is categorized into three different main areas:

• Material characterization • Package testing (BCT) • Simulations of BCT

2.1 Material characterization

In order to utilize the advantages of FEA in the packaging design process, some input data are required. A material characterization was performed on different commercial paperboards from different manufacturers to achieve material data. Here, the most frequently used test methods in the thesis are described.

2.1.1 In-plane tensile test From an in-plane tensile test, the material properties tensile strength, tensile stiffness and strain at break were obtained. By following ISO 194-3:2005 with an Alwetron TH1 apparatus (Lorentzen & Wettre, Stockholm, Sweden), a specimen with dimensions length, L = 100 mm, and width, b = 15 mm, was subjected to a displacement-controlled test at a rate of 100 mm/mm. The force was measured with a load cell to obtain a force-elongation curve, from which stress, , and strain, , were evaluated according to

𝜎 = 𝐹𝐴

= 𝐹𝑏𝑡

(3)

and

𝜀 = 𝛿𝐿 , (4)

where t is the thickness of the board and δ is the elongation of the specimen. The elastic modulus was calculated following ISO1924-3:2005. All experiments were performed at moisture levels 20, 50, 70 and 90 % RH at 23°C, and the test pieces were, prior to testing, conditioned for 24 hours to ensure equilibrium.

2.1.2 Out-of-plane shear test To determine the out-of-plane shear stiffness, a rigid block shear test was performed at 50 % RH at 23°C. The experimental setup consisted of two steel plates according to Figure 3, mounted in a uniaxial tensile tester (MTS System Corp.; Eden Praire, MN, US). The blocks were exposed to a tensile force and allowed failure in any layer of the paperboard. The dimensions of the specimen were 21 × 70 mm2. The tests followed an earlier established testing procedure [14].

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Figure 3. Rigid block shear test.

2.2 Packaging testing

Packaging performance was evaluated by stacking performance: the maximum load a package can carry before collapsing. In Paper C, box compression tests (BCT) were performed on a geometry according to Figure 4, where (a) is the drawing of the blank, and (b) is a mounted box.

(a) (b) Figure 4. Drawing of the blank (a) and mounted package (b).

The paperboard packages were compressed between two parallel steel plates in a uniaxial MTS-system. The setup is illustrated in Figure 5. The tests were performed in a controlled climate room at 50, 70 and 90 % RH at 23°C. From the tests, force-compression curves were obtained using an MTS load cell.

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Figure 5. Test equipment for BCT.

2.3 Finite Element Model

The FE-model were created using LS-PrePost and solved implicitly by using the Massively Parallel Processing (MPP) solver. A geometry was created according to Figure 6.

Figure 6. Transparent view of the FE-model.

The paperboard was modelled as a homogeneous material, neglecting the layered structure of the material. Due to this, the model could not simultaneously represent the bending stiffness and the in-plane stiffness accurately. Here, the in-plane stiffness was prioritized in order to reduce the errors at the initial stage of loading. It can therefore be assumed that the bending stiffness of the panels is slightly underestimated in the model. Furthermore, the material was modelled as an elastic orthotropic material with an additional failure criterion, expressed by the strengths in MD and CD, using Mat_054 in LS Dyna. The material model is further described in Paper C. The elements were four-noded, fully integrated, shell elements with four in-plane integration points and four integration points through the shell thickness.

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3 Results and discussion Evaluation of the moisture dependency of the mechanical properties (in-plane stiffness and strength, SCT-values, bending stiffness and out-of-plane shear strength) showed that there was, to a good approximation, a linear relation between the mechanical properties and the moisture ratio for each investigated board, which is partly previously known from the literature [7]. However, when both axes were normalized with the corresponding value at standard climate (50 % RH, 23°C), a linear master-curve regardless of paperboard type and manufacturer was established in Paper B. This is shown for the tensile strength in Figure 7.

Figure 7. Normalized tensile strength as function of normalized moisture ratio for 15 boards in both MD

and CD.

The physical interpretation from the results in Figure 7 is that if the amount of moisture in any paperboard is doubled, the strength would be reduced by approximately 35 %. Thus, it is possible to express any of the investigated mechanical properties as a linear equation:

In an analogous way, this was performed for the stiffness and the SCT-values, which were the mechanical properties investigated in Paper B, and the parameters a and b for the linear relations are summarized in Table 1.

Table 1. Parameters for the linear relation between normalized property and normalized moisture ratio.

Normalized property a b R2 Strength -0.35 1.36 0.96 Stiffness -0.37 1.40 0.96 SCT -0.51 1.51 0.96

Since the relation between stiffness and strength, respectively, and moisture, expressed by Eq. (5) and Table 1, were established as a master curve, it is possible to estimate the stiffness or the strength at any moisture level (in the range of 20 % to 90 % RH), if the moisture ratio is known for the moisture level of interest. Also, the results in Paper A and Paper B indicates that this is valid for other mechanical parameters as well, but the parameters a and b will have different values.

𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦50% RH

= 𝑎𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦𝑚𝑟

𝑚𝑟50% RH+ 𝑏𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦. (5)

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If the relative mechanical properties of the paperboards from Figure 7 are plotted against the non-normalized moisture ratio, see Figure 8, they do not coincide due to different water uptake. It is noted that standard climate corresponds to approximately 4.25-4.75 % moisture ratio for the investigated boards in this study. A difference of 1 percentage points in moisture ratio (x-axis in Figure 8) will approximately cause a 10 % deviation in relative strength. This emphasizes the paperboards’ sensitivity to moisture, and the importance of measuring the correct value of the moisture ratio (or moisture content) when measuring the mechanical properties.

Figure 8. Normalized strength as a function of moisture ratio for four different paperboards.

However, a linear relation between normalized property and normalized moisture, such as in Figure 7, are important experimental results as input values for the simulations. The material model used in Paper C was primarily based on the in-plane stiffness and strength, which made it possible to adjust the input data for different moisture levels without performing any additional testing.

Figure 9 shows the deformation shapes after failure from the physical experiments and the simulations. The deformed shapes were similar to the yield line patterns described by Ristinmaa et al [11].

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(a) (b)

Figure 9. Deformation shapes post-peak for a physical BCT (a) and FEA (b).

The load-compression curves from physical experiments are compared to the results from the FE-simulations at different moisture levels in Figure 10.

Figure 10. Comparison of experiments and simulations for different moisture levels.

The initial part of the curves aside, the numerical predictions of the experimental data are adequate. From the experiments, an initial slack in each curve was noted. This is due to the presence of horizontal creases. Perturbations of the top and bottom flaps were not accounted for in the FEA. From Figure 10, it should be emphasized that the simulations at 70 % and 90 % RH were based on estimated input values calculated from Eq. (5) and test data at 50 % RH.

It was also noted that modelling of the mechanical properties of the creases had a significant impact on the stiffness response of the package. A method for reducing the mechanical properties of the creases was suggested in Paper C, where two relative ratios were used: relative crease strength in folding (RCS) and relative tensile strength (RTS). Further reliability of the model and the crease reduction method were investigated by simulating the same package geometry but using another (thicker) paperboard material, and the results were adequately accurate.

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4 Conclusions In this thesis, and particularly in Paper A, it was concluded that different mechanical properties normalized with the properties at standard climate, decrease linearly when the moisture ratio of the paperboard is increased. Furthermore, when the moisture ratio is normalized with the moisture ratio at standard climate, the results from all investigated paperboards in Paper B, to a good approximation, followed the same linear relation. This made it possible to estimate a mechanical property for any board at different moisture levels by knowing only:

• the mechanical property at standard climate (50 % RH and 23°C), and • the parameters a and b that describes the linear relation.

In Paper C, this relation was used to estimate input material parameters for simulating a Box Compression Test (BCT) at different moisture levels. The result showed that it was possible to accurately predict the load-compression curve of a BCT when moisture was accounted for. Furthermore, it was found that modelling of the mechanical properties of the creases are important for capturing the stiffness response of the package.

Further reliability of the model was investigated by simulating the same package geometry but using another (thicker) paperboard material. The investigation showed satisfying accuracy. A future study is motivated, where the operation window of the creases in relation to moisture ratio needs to be further investigated.

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5 Bibliography [1] European commission (2018), “A European Strategy for Plastics in a Circular Economy”, accessed 20 September 2020, <https://eur-lex.europa.eu/resource.html?uri=cellar:2df5d1d2-fac7-11e7-b8f5-01aa75ed71a1.0001.02/DOC_1&format=PDF>

[2] European parliament (2019), “DIRECTIVE (EU) 2019/904 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 5 June 2019 on the reduction of the impact of certain plastic products on the environment”, accessed 20 September 2020, <https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32019L0904&from=EN>

[3] Niskanen, K., ed. (2012) “Mechanics of paper products”, pp. 22-24. Walter de Gruyter GmbH & CO

[4] Niskanen, K., ed. (2012) “Mechanics of paper products”, p. 17. Walter de Gruyter GmbH & CO

[5] Benson, R.E. (1971) “Effect of relative humidity and temperature on tensile stress-strain properties of kraft linerboards”, Tappi Journal, 54(4), pp. 170-177.

[6] Uesaka, T. (2002) “Dimensional stability and environmental effect on paper properties”, Chapter 3 in Handbook of Physical Testing of Paper, Eds R.E. Mark et al.

[7] Ek, M., ed. (2009) “Pulp and Paper Chemistry and Technology: Volume 4 Paper Products Physics and Technology”, p. 142. Walter de Gruyter GmbH & CO.

[8] Niskanen, K., ed. (2012) “Mechanics of paper products”, p. 5. Walter de Gruyter GmbH & CO

[9] McKee, R.C., Gander J.W. and Wachuta J.R. (1963) “Compression strength formula for corrugated boxes”, Paperboard Packaging 48(8) 149-159.

[10] Grangård, H. (1970). “Compression of board cartons. 1. Correlation between actual tests and empirical equations”. Svensk Papperstidning-Nordisk Cellulosa, 73(15), 462.

[11] Ristinmaa, M., Ottosen N. S., Korin C. (2012) ”Analytical Prediction of Package Collapse Loads - Basic Considerations”, Nordic Pulp and Paper Research Journal 27(4): 806-813.

[12] Simon, J-W. (2020) “A Review of Recent Trends and Challenges in Computational Modeling of Paper and Paperboard at Different Scale”, Archives of Computational Methods in Engineering. DOI: https://doi.org/10.1007/s11831-020-09460-y

[13] Kulachenko A, Uesaka T (2012) “Direct simulations of fiber network deformation and failure”. Mechanics of Materials 51:1–14

[14] Nygårds, M., Fellers, C., Östlund, S. (2007) ”Measuring out-of-plane shear properties of paperboard”, Journal of Pulp and Paper Science 33(2): 105-109.