inﬂuence of inhomogeneities on the tensile and compressive mechanical properties...

Influence of inhomogeneities on thetensile and compressive mechanicalproperties of paperboard

Anton Hagman

Doctoral thesis no. 96, 2016

KTH School of Engineering Sciences

Department of Solid Mechanics

Royal Institute of Technology

SE-100 44 Stockholm, Sweden

TRITA HFL-0596ISSN 1104-6813ISRN KTH/HFL/R-16/10-SEISBN 978-91-7595-990-0

Stockholm, Sweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan i

Stockholm framlägges till offentlig granskning för avläggande av teknologie

doktorsexamen torsdagen den 26:e maj 2016 kl. 10:00 i Kollegiesalen,

Kungliga Tekniska högskolan, Stockholm. Fakultetsopponent är Docent Nils

Hallbäck, Karlstads universitet.

Beauty in things exists in the mind which contemplates them.

- David Hume

Abstract

The in-plane properties of paperboard have always been of interestto paper scientists. The reason for this is that they play a significantrole for the usability of the paperboard in converting and end-use.Tensile properties are crucial when the board is fed through printingand converting machines at high speeds. While compressive proper-ties are essential in the later use, e.g. in packages. Inhomogeneitiesaffect both the compressive and tensile properties. For the tensileproperties, it is the inherent heterogeneity of the paperboard thatmight cause problems for the board-maker, especially in the designof more advanced paperboard packages. Varying material properties,through the thickness of the paperboard, are on the other hand fre-quently used by the board-makers, when they wish to achieve highbending stiffness with low fiber usage. It is of interest to know howthis practice affects the local compressive properties. Papers A andB aims to adress this, while Papers C, D and E focus on in-planeheterogeneities and their effect on the paperboard’s behavior.

The first paper, Paper A, investigates the mechanism that causesfailure in the short span compression test (SCT). Three differentmultiply paperboards, chosen to have distinctly different through-thickness profiles were examined. The boards were characterized andthe data was used to simulate SCT. The simulation was conductedwith a finite element model consisting of layers of continuum elementswith cohesive interfaces in-between. From the model it was concludedthat the main mechanism for failure in SCT is delamination due toshear damage.

The second paper, Paper B, was a continuation of Paper A.The effect of the through-thickness profiles on the local compressionstrength was examined for five paperboards. It was concluded thatthe local compression is governed by in-plane stiffness and throughthickness delamination. The delamination damage was in turn de-pendent on the local transverse shear strength and in-plane stiffnessgradients. Furthermore, it was concluded that the pre-delaminationmechanisms were essentially elastic.

In the third paper, Paper C, the tensile test is investigated with

i

focus on sample size and strain distributions. Multiply paperboardswere examined with varying sample sizes using digital image correla-tion (DIC). Different strain behavior was found for different samplesizes, which was dependent on the length to width ratio of the sampleand was caused by activation of local zones with high strainability inthe sample. These zones were of constant size and therefore occupieddifferent amounts of the total sample area.

The fourth paper, Paper D, focuses on the local strain zones seenin Paper C and how they were affected by creping. The thermal re-sponse in paper was studied by thermography. It was observed thatan inhomogeneous deformation pattern arose in the paper samplesduring tensile testing. In the plastic regime a pattern of streaks withincreased temperature could be observed. It was concluded that theheat patterns observed by thermography coincided with the defor-mation patterns observed by DIC. Due to the fibrous network struc-ture, paper has an inhomogeneous microstructure, called formation.It could be shown that the formation was the cause of the inhomo-geneous deformation in paper. Finite element simulations were usedto show how papers with different amount of homogeneity would de-form. Creped papers, where the strain at break has been increased,were analyzed. For these papers it was seen that an overlaid perma-nent damage was created during the creping process. During tensiletesting this was recovered as the paper network structure was strained.

In the fifth and final paper, Paper E, the virtual field method(VFM) was applied on DIC-data from Paper C. This was doneto demonstrate the ability of different VFM-formulations for char-acterization of paperboard stiffness heterogeneity. The specimen wasdivided into three subregions based on the axial strain magnitude.VFM-analysis showed that the subregions had stiffnesses and Pois-son’s ratio’s that varied in a monotonically decreasing fashion, withthe stiffness differences between subregions increasing with appliedtensile stress. The results suggested that high stiffness regions pro-vide only marginal improvement of the mechanical behavior.

Keywords

Paperboard, Inhomogeneities, In-plane properties, Tension, Compres-sion, Shear properties, Delamination

ii

Sammanfattning

Egenskaperna hos ett kartongark kan grovt delas upp i två kategori-er: i-planet egenskaper och ut-ur-planet egenskaper. I-planet egenska-perna har länge varit ett område som pappersmekanister och andrapappersforskare visat intresse för. Anledningen till detta är att deär avgörande för hur väl det går att konvertera kartongen till färdi-ga förpackningar, samt hur väl de förpackningarna klarar sin upp-gift. Dragegenskaperna prövas när kartongen dras genom tryck- ochkonverteringsmaskiner i hög hastighet. Tryckegenskaperna spelar storroll för hur väl en förpackning klarar att staplas och hålla sitt inne-håll intakt. Inhomogeniteter påverkar både drag och tryckegenskaper.Papprets naturliga variation påverkar dragegenskaperna hos kartong-en och kan orsaka problem för kartongmakarna. Särskilt när utveck-lingen går mot mer avancerade kartong utseenden. Å andra sidanså använder sig kartongmakare flitigt av egenskapsvariationer genomtjockleken på kartongen, när dom vill åstadkomma böjstyva kartong-er utan att slösa med fibrer. I detta fall är det intressant att vetahur de lokala kompressionsegenskaperna påverkas av kartongens ut-ur-planet profil. Det första två uppsatserna i denna avhandling, A

och B, handlar om just detta. Uppsatserna C, D och E avhandlarhur i-planet variationer påverkar kartongens egenskaper.

I Artikel A undersöks vilka skademekanismer som aktiveras un-der ett kortspannskompressionstest (SCT). Tre flerskiktskartonger un-dersöktes. De hade valts så att de hade distinkt olika skjuvstyrkepro-filer. Kartongerna karakteriserades och datan användes som materi-aldata i en finit element modell av SCT-testet. Modellen bestod avskikt, betraktade som kontinuum, mellan vilka det fanns kohesivaytor. Huvudmekanismen i SCT var att kartongen delaminerade pågrund av skjuvskador.

Den andra uppsatsen, Artikel B, var en fortsättning på den förs-ta. Denna gång undersöktes fem flerskiktskartonger framtagna så attde hade olika skjuvstyrka beroende på positionen i tjockleksled. Detkonstaterades att kompressionsegenskaperna lokalt styrs av skjuv-styrkeprofilen och styvhetsgradienter. Vidare konstaterades det attmekanismerna innan kartongen delaminerar är, i huvudsak, elastiska.

Den tredje artikeln, Artikel C, fokuserade på hur dragprov på

iii

kartong påverkas av provstorleken och töjningsvariationen. Tre olikaflerskiktskartonger användes som provmaterial och provbitar med oli-ka storlek analyserades. Förutom dragprov så användes digital imagecorrelation (DIC) för analysen. Det visade sig att den globala töjbar-heten varierade med storleken på provet beroende på kvoten mellanlängd och bredd. DIC visade att detta i sin tur berodde på att zo-ner med hög töjbarhet aktiverades i provet. Dessa zoner hade sammastorlek oberoende av provstorlek och påverkade därför den totala töj-barheten olika mycket.

Artikel D undersöker töjningszonerna som sågs i Artikel C samthur de påverkas av kreppning. Vidare undersöktes pappersprovernamed hjälp av termografi. Termografin visade att varma zoner upp-stod i proven när det töjdes. Zonerna blev synliga när provet töjdesplastiskt. Termografi kördes parallellt med DIC på några prover. Detvisade sig att de varma zonerna överenstämde med zoner med hög lo-kal töjning. Vidare kunde det visas att dessa zoner övenstämde medpapperets mikrostruktur, formationen. En finit element analys av hurpapper med olika formation töjs gjordes. Delar av provningen gjordespå kreppade papper som har högre töjbarhet. Det visades sig att nå-gon form av skada hade överlagrats på papprets mikrostruktur underkreppningen, och att den deformationen återtogs när pappret töjdes.

I den sista artikeln, Artikel E, behandlas hur VFM (Virtual Fi-eld Method) kan användas på DIC-data från kartong. DIC-datan somanvändes hämtades från Artikel C. Detta gjordes för att visa påhur olika VFM-formuleringar kan användas för att karakterisera styv-hetsvariationen hos kartong. Provet delades upp i tre subregioner ba-serat på den axiella töjningsgraden. VFM-analysen visade att dessasubregioners styvhet och tvärkontraktionstal sjönk monotont, menatt skillnaden mellan regionerna ökade med ökande spänning. Ävenom endast ett prov undersöktes, så indikerade resultaten att områ-den med hög styvhet endast förbättrar de mekaniska egenskapernamarginellt. Analysen visade också att även om subregionerna inte ärsammanhängande, så har dom liknande mekaniska egenskaper.

iv

Preface

The work presented in this thesis was carried out at the Departmentof Solid Mechanics, KTH Royal Institute of Technology, Stockholm,Sweden between August 2010 and May 2016. The financial supportprovided by BiMaC Innovation is gratefully acknowledged. Workingat the Department of Solid Mechanics has not only given me access toexcellent minds and experimental equipment, but also given me theopportunity to grow in other tasks such as teaching and supervising. Iam grateful for being part of BiMaC Innovation since it both connectsme to a vast body of knowledge and experience, as well as providesme with a natural connection to the industry.

I would like to express my sincere gratitude to my supervisor Do-cent Mikael Nygårds for introducing me to paper mechanics and givingme the opportunity to increase my understanding of this interestingfield. With your guidance and support I have not only learnt a lotabout experimental work on, and modeling of, paperboard, but alsogained an insight into the thoughts of the paper industry.

Furthermore I would like to thank all my friends and colleaguesat the department of Solid Mechanics, for providing an excellent andstimulating work environment. No question is too big, small or ob-scure to be discussed at the coffee table. Special thanks to the col-leagues in the laboratory and the workshop.

Finally I would like to thank my family and friends for all theirsupport. Especially Ulrika for always encouraging and supporting me.

Stockholm, May 2016Anton Hagman

v

List of appended papers

Paper A:

Investigation of shear induced failure during SCT loading of paperboards

Anton Hagman, Hui Huang and Mikael NygårdsNordic Pulp & Paper Research Journal Vol. 28(3), 2013, pp. 415-429

Paper B:

Short compression testing of multi-ply paperboard, influence from shear

strength

Anton Hagman and Mikael NygårdsNordic Pulp & Paper Research Journal Vol. 31(1), 2016, pp. 123-134

Paper C:

Investigation of sample-size effects on in-plane tensile testing of paper-

board

Anton Hagman and Mikael NygårdsNordic Pulp & Paper Research Journal Vol. 27(2), 2012, pp. 295-304

Paper D:

Thermographical analysis of paper during tensile testing and comparison

to digital image correlation

Anton Hagman and Mikael NygårdsReport 595, 2016, Department of solid mechanics, KTH Engineering Sci-

ences, Royal institute of Technology, Stockholm, Sweden. Submitted for

publication.

Paper E:

Stiffness heterogeneity of multiply paperboard examined with VFM

Anton Hagman, J. M. Considine and Mikael NygårdsSEM XIII International Congress and Exposition on Experimental and Ap-

plied Mechanics June 6-9, 2016

vii

In addition to the appended papers, the work has resulted in the followingpublications and presentations1:

Size dependent tensile testingAnton HagmanBiMaC Innovation Centre day 2011, Stockholm, Sweden (OP)

Investigation of sample-size effects on in-plane tensile testing of paperboardAnton Hagman and Mikael NygårdsInternational Paper Physics Conference 2012, Stockholm, Sweden (OP)

Effect of sample-size and geometry on inplane tensile testing of paperboardAnton HagmanFPIRC & PaPSaT Summer Conference 2012, Knivsta, Sweden (PO)

Quasi static analysis of creasing and folding for three paperboardsHuang H., Hagman A., Nygårds M.Mechanics of Materials 02/2014; 69(1):11-34 (JP)

Effect of inhomogenities on the performance of paperboardAnton HagmanCellulose Materials Doctoral Students Summer Conference 2014, Ebernburg

Castle, Germany (OP)

Correlating SCT and shear strength profiles by process and numerical studiesAnton Hagman, Henrik Nord and Mikael NygårdsProgress in Paper Physics Seminars 2014, September 8th-11th, Raleigh,

North Carolina, USA (OP)

Correlating SCT and shear strength profiles by process and numerical studiesAnton Hagman and Mikael NygårdsSvenska mekanikdagar 2015, Linköping, Sweden (OP)

Thermal imaging on tensile tests of deformable papersAnton Hagman, Andreas Gabrielsson, Elisabet Horvath and Mikael NygårdsTokyo Paper 2015, International Paper Physics Conference, 2015 Oct. 29th-

Nov. 1st, Tokyo, Japan (OP)

1OP = Oral Presentation, PP = Proceeding paper, JP = Journal Paper,

PO=Poster.

viii

The contribution of the author to the appended paper was as follows:

Paper A:

Principal author, performed all simulations and experiments except char-acterization of material properties, which was mainly done by Hui Huang.Interpretation of results together with Mikael Nygårds.

Paper B:

Principal author, performed all simulations and experiments.

Paper C:

Principal author, performed all experimental work and analysis. Interpreta-tion of results and outlining of experiments together with Mikael Nygårds.

Paper D:

Principal author, performed all simulations and experiments. The materialswhere provided by Innventia, where they had been characterised accordingto standard procedures.

Paper E:

The paper is a continuation of Paper C initiated by John Considine, whoconducted the VFM studies and did most of the writing. My part is mainlythe DIC measurements.

ix

Contents

Abstract i

Sammanfattning iii

Preface v

List of appended papers vii

About paper 1

How paper is produced . . . . . . . . . . . . . . . . . . . . . . . . . 2Why variations matter . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Previous knowledge 7

Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Compression and out-of-plane properties . . . . . . . . . . . . . . . . 9Tension and in-plane properties . . . . . . . . . . . . . . . . . . . . . 10

Experimental equipment 13

Environmental conditions . . . . . . . . . . . . . . . . . . . . . . . . 13Standard equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Special equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Simulations 19

Contributions in this thesis 21

Short span compression . . . . . . . . . . . . . . . . . . . . . . . . . 21In-plane heterogeneities . . . . . . . . . . . . . . . . . . . . . . . . . 22

Future 27

Summary of appended papers 29

xi

Bibliography 33

Paper A

Paper B

Paper C

Paper D

Paper E

xii

ABOUT PAPER |1

About paper

Paper has been known to, and used by, mankind for at least 2000 years [1].The process of making paper and the use of paper have evolved over time.Through history paper has mainly been used for writing, although severalother uses have emerged over the years. By the end of the 20th century pa-per was used as writing, building, cleaning and packaging material amongothers. As the world enters the 21st century the usefulness of paper as amean to store and convey information diminishes with the rise of the digitalage. Instead its properties as storage for much more physical things, likegoods and liquids, are becoming increasingly important. In this usage pa-per has great advantages as it is cheap, light and renewable. Paper can beused as a packaging material in two principal ways; either as wrapping orconverted into a box or some other type of container. Paper used in pack-aging usually comes in one of two forms; carton board or corrugated board.Corrugated board is made by combining thin flat paper called liner withone or several layers of fluted board in-between. Paperboard is typicallya thick paper with high grammage (>200 g/m2), while carton board is aboard where several layers of different type has been combined into a board,usually with thin dense outer plies and a thick bulky middle ply. Both themultiply paperboard and the corrugated board are designed to achieve thesame goal, high bending stiffness with a small amount of fibers. While thefirst folding of paper into a box is lost in ancient history, corrugated boardhas been around since the end of the 19th century, and advanced multi-ply board is considerably younger than that. Both corrugated board andmultiply paperboard are results of developments within the paper industry.Today paper packaging is ever-present, from luxury packages for perfumesor smart phones, through everyday liquid packaging such as milk cartons,to corrugated boxes containing unassembled furniture, half a ton of pota-toes or bananas that have travelled across the world. All these differentpackages are faced with the challenge of being resistant to varying climate,stacking loads and rough handling while keeping the stored goods protected,and maintaining the outside neat. For everyday packages in general, and

2| ABOUT PAPER

luxury packages in particular, further challenges await. In the competitionwith other packaging materials it is not sufficient for paper to be cheap andrenewable. To gain market shares the visual perception is extremely impor-tant. While a paper-based package is well suited to be colored and printed,it is still confined to fairly simple geometrical shapes, usually with sharpcorners. Some innovative designs can be achieved by folding the packagein intricate ways or by embossing the package with patterns, but comparedto the almost unlimited shapes available in for example plastic packaging,the results are still lacking. The ways presently used to get more advancedpaper packages include; pulp molding, which is used for egg cartons, butresults in rough surfaces, and, die-formed goods such as disposable platesand deep-drawn Easter eggs which have a multitude of wrinkles. Both ofthese products have found their place in niche markets, but neither methodis up to the standards needed to be competitive in a broader sense. To un-derstand why paper, at present, is unsuitable for advanced packaging, andhow to change that, it is important to understand how it is produced, andhow this in turn affects its properties.

How paper is produced

Paper is produced by large machines from pulp. Pulp comes in many va-rieties depending on the raw material; hard wood (shorter fibers), soft-wood (longer fibers), or recycled fibers, as well as the process used toextract it; mechanical-, thermo-mechanical, chemical or chemithermome-canical (CTMP) pulping. The chemical pulping process in turn can beperformed using different chemicals, resulting in different types of pulps.The two most common chemical pulps are kraft (sulfate) and sulfite pulp.Typically mechanical pulp is more fragmented which leads to a more uni-form paper structure with better printing properties, while chemical pulphas a lower fragmentation and is stronger. The mechanical pulp has a bet-ter yield then the chemical pulp [2]. This provides the papermaker withthe possibility to vary the properties of the paper or paperboard that isproduced. The pulp is sprayed onto a wire from the so called headbox.The wire moves at high speed, 10-20 m/s (30-70 km/h), through a seriesof cylinders which press much of the water out of the pulp, before it movesinto a heated drying section. In the drying section, the paper is passedthrough a series of heated cylinders which turn most of the remaining waterinto steam. After the drying section the paper is typically calendared, i.e.pressed between hard cylinders to obtain smoother and more glossy sur-faces, and reeled before further processing. Sizing agents that are used tomodify the appearance and properties of the paper can be added either inthe wet end of the machine or in the last steps of drying. The paper can be

ABOUT PAPER |3

Slice

Breast Roller

Dolly Roller

Couch Roller

Felt Felt Dryer

Pickup Roller

Top FeltHeated Dryer Felt Dryer

Bottom Felt Felt Dryer

Wet End Wet Press Section Dryer Section

Wire mesh Suction boxes

Calender Section

Figure 1: A diagram over a fourdrinier paper machine. The machine in thediagram would produce single ply papers. By Egmason (Own work)[CC BY 3.0], via Wikimedia Commons

coated, to modify the surface appearance and improve printability, usuallythis is done before calendaring. Figure 1 shows a sketch of a fourdrinierpaper machine for paper or a single ply paperboard.

Paperboard can be made in several ways, either by simply making verythick paper, or by joining several individually formed plies before the dryingsection of the paper machine. The process by which paper, and in theextension paperboard, is made has some consequences for its mechanicalbehavior.

Firstly, since the fibers are applied onto a moving wire, they will alignwith the direction of movement, causing paper to be anisotropic. Thisanisotropy can be controlled by varying the speed of the wire and the pres-sure in the head-box, but, for obvious reasons, papermakers want to producepaper at the highest possible speed. The anisotropy can be further influ-enced by how the paper is restrained during drying, cf. [3, 4], but in theend the elastic modulus in the machine direction, MD, is typically 3-5 timeshigher than that in the cross machine direction, CD, and up to a 100 timeshigher than that in the out of plane direction, ZD. The principal directionscan be seen in Figure 2a. Other properties such as strength, yield stressand strain at break also vary depending on the load direction, cf. [5].

Secondly, as the diluted pulp is sprayed onto the wire it does not landuniformly, creating heterogeneities in the paper. The amount of hetero-geneity is usually kept to a minimum, thus acquiring good formation, usingdifferent chemicals in the pulp and by diluting the pulp to a lower consis-tency. Once again a trade-off between speed and quality is unavoidable. Formultiply paperboards a third mechanism affects the behavior of the board.Since different layers are used in different parts of the board, the papermaker

4| ABOUT PAPER

(a) (b)

Figure 2: The anisotropy of paper, with directions indicated (a). And an exam-ple of a multiply paperboard, with a bleached and coated top layer(b). The formation can be seen in the bottom ply thanks to thebacklighting.

can chose the properties of each layer, to control how the board as a wholebehaves, cf. Figure 2b. A typical example of paperboard design is using abulkier middle layer together with denser stronger outer layers to create aboard that has a high bending stiffness. Modern paperboards typically hasbetween three and five plies. Apart from the different properties in eachply the manufacturer can control the behavior of the board by modifyingthe interfaces between them, e.g. by adding starch. An example of how thethrough thickness shear profile can be modified will be discussed in moredetail below. The effect for three boards, with different amounts of starch inthe furnish of the middle plies, can be found in Figure 3. Another exampleof possible modifications is to apply a layer of bleached pulp on one or bothsides of the board to improve the appearance and printability. In this way,the manufactures are able to save both money and the environment by onlyusing fibers, chemicals and other additives were they are needed.

Another important aspect of the paper making is that it is an industrialprocess that deals with immense volumes, both in the printing and in thepackaging industries. The way these volumes, billions of packages and end-less miles of printed paper, are handled is in streamlined processes that relyon the fact that paper is delivered from the manufacturers on rolls. Thismakes the anisotropic properties of paper important. In most printing pa-

ABOUT PAPER |5

per applications the prime need for strength is in the machine direction, asit needs to be able to withstand being pulled through the printing machine.Paperboard that is used in packaging has further challenges to beat, notonly does it need to withstand the handling forces that act on the packages.It also needs to be able to be converted into that package without losingstrength or appearance. The desire to make new advanced packages, com-parable to those made of plastics today, will place even higher demands onthe properties of the paperboard, even some that are not considered today,e.g. extensibility [6].

Why variations matter

The variations in paperboard are, as mentioned, either purposely produced,or unavoidable due to the production methods. In both cases it is somethingthat papermakers and converters have to be very aware of. For the in-planeheterogeneities the goal has been, and still is, to obtain a good formation,i.e. to make the sheets as uniform as possible. This has been a successfulmethod, and it turns out that the variations, when small, even-out on alarger scale and results in a predictable overall behavior. However, whenthe converting of paper and paperboard is pushed further, the local proper-ties become more important, either because the converting procedures onlyaffect small local areas of the board, or because the global strain gets solarge that the response of local areas becomes significant.

The questions that arise due to the out of plane variation are different.In this case the variation is known, or at least planned, and the overallresults are clear. Instead, it is the side effects and combinations of propertiesthat are beneficial in different applications that are of main interest. As anexample the structure, based on the I-beam-principle, that is achived by abulky middle-ply and dense outer plies, can be mentioned. This structuregives an increased bending stiffness of the board, but how does it affect thecompression strength and other properties? Is it beneficial to the convertingoperations? To answer such questions a more fundamental understandingof the underlying mechanisms are needed. Such understanding includes howthe different plies interact with each other, when and where delaminationoccurs and how this affects for example the converting operations. Beforethese and other questions can be answered the current knowledge needs tobe assessed.

6| ABOUT PAPER

PREVIOUS KNOWLEDGE |7

Previous knowledge

Within the paper industry a strong research tradition exists. Although pa-per mechanics always has been present, the research has to a large extentbeen focused on paper chemistry, and production methods. As the indus-try moves into the 21st century, an increased interest for paper mechanicsarises. This is partly due to the transitions that the business is facing, withincreased efficiency demands, and partly because of the new tools that areavailable to analyze the mechanical behavior of paper. Much of what isknown is compiled from research on paper qualities that differ a lot fromthe highly engineered boards that are produced today. Furthermore, muchknowledge is based on empirical relations that do not adress much of theunderlying deformation and damage mechanisms. Especially the multiplypaperboards of today differ significantly from single ply paperboards asthey are highly engineered with different properties in different plies, allwith special requirements. This raises the question whether old relationsstill are valid, and which properties it is that affect the outcome of differenttests. Particularly, since the same classifications and tests are still used toevaluate modern paperboards, as where used on more basic paperboards.Nevertheless, it is hard to make progress without knowing the past, whichis why a short resumé of the background is appropriate.

Modeling

Apart from what is acquired from experiments, much can be learned aboutpaper mechanics from computer simulations. Such simulations can be sortedinto two categories; one where the whole, or parts, of e.g. a package is sim-ulated, the other is simulations which aims at capturing the behavior ofthe paperboard itself, sometimes emulating a specific test method. Whensimulating the performance of a paperboard, there are some different ap-proaches that can and has been considered. One option is to simulate thepaperboard as a two or three dimensional structure, another is to simulatedit as the fiber network it is. Borodulina et al. [7] used the network approach

8| PREVIOUS KNOWLEDGE

in 2011 when they revisited the stress strain curve of paper, that was orig-inally discussed by Seth and Page [8] in 1981. For such network modelsmuch data are needed about the fibers and their fiber-fiber joints as well astheir structure in the network. The nature of the fiber-fiber joints in partic-ular has been discussed for a long time, as an example Page, Tydeman andHunt [9] could be mentioned, but it is still a hot topic. Recently the studiesby Magnusson et al. [10] as well as Marais et al. [11] shed some new lighton the issue. They did experimental work using modern methods as well assimulations to describe the nature of fiber-fiber joints, e.g. to identify theirstrength distributions.

Another way to model paperboard is as a continuum, in this way theneed to know the properties of individual fibers and joints can be avoided.Instead some type of damage criteria is needed. The two common ways todo this is either to include interfaces or to implement continuum damage.Models using continuum damage is usually used for single ply boards. Isaks-son et al. [12] and more recently Borgquist [13] used this kind of method.For multiply paperboards cohesive interfaces are common, such an approachhas been used by e.g. Xia et al. 2002 [14], Beex and Peerlings 2009 [15],Huang and Nygårds 2011 [16] and Hallbäck et al. [17]

The continuum approach is used throughout this thesis. However,this requires good material data as a starting point. Some of the behav-iors of paper have been known for a long time, e.g. Baum, Brennan andHabeger [18] discuss the orthotropic elastic constants in paper and Pageand El-Hosseiny [19] discuss the stress-strain curve of paper based on thefiber properties. As simulations are becoming standard procedures, theways to acquire good material data is of growing interest. Material charac-terization has been done out of interest to expand the knowledge of paperbehavior in general, as well as with the explicit goal of providing inputdata for simulations. Examples of the more general case are the studies onthe out-of-plane properties of paperboard, conducted by Stenberg [5, 20],together with Östlund and Fellers [21, 22], in the early 2000s. Another gen-eral study, that focused on the in-plane orthotropic elastic constants waswritten by Yokoyama and Nakai [23].

Some studies, more focused on providing fast and reliable ways to getinput-data for simulations, were performed by Nygårds [24] and Nygårdset al. in 2009 [25]. The latter study discussed the double notched sheartest, DNS see Figure 3a, which made measuring the through thickness shearprofiles practical in paperboard. Such profiles can be seen in Figure 3b.DNS was first introduced by Nygårds et al. [26] in 2007. In Figure 4 apaperboard that has been subjected to a short compression test is shownwith the measured profile indicated. Another aspect of the mechanicalproperties of paper that is important to be able to simulate accurately


(a)

0 100 200 3000.8

1

1.2

1.4

1.6

1.8

2

Distance from top of paperboard /µm

She

ar s

tren

gth

/MP

a

CDE

(b)

Figure 3: A sketch of the DNS test where a paperboard with two diagonalcuts is pulled in a tensile tester (a). Using this method the shearstrength of the surface between the cuts can be measured. Thepaperboard is laminated on both sides to facilitate handling of thesamples. Examples of the through thickness shear profiles from threeboards, where the shear strength has been altered by adding starchin the furnish of the different layers (b).

is how the material reacts to temperature and moisture. That paper isinfluenced by temperature and moisture has been known for a long time,e.g. by the work of Salmén and Back [27, 28], but it was not until recentlysimulations, by Linvill and Östlund [29], were used to show how moisturein combination with temperature affect the mechanical response of paper.

Compression and out-of-plane properties

The local compression strength is important for the ability of a box towithstand loads. This has been known for a long time. McKee et al. [30]presented a formula to calculate the compression strength of boxes in 1963.This formula, which was intended for corrugated boxes, is based on thebending stiffness and edgewise compression strength of the board. Gran-gård [31] evaluated and further developed the formula for use on cartonboards. This in turn raised the question on how to assess the edgewisecompression strength. Calvin and Fellers [32] investigated how to measurethe compression strength in 1975, where they compared short span andlong span compression of paper. In 1992, Westerlind and Carlsson [33] re-visited the relationship between long span and short span compression forcorrugated board. They found that it was possible to predict the long span


compression from short span tests, using Weibull statistics. For a compre-hensive review of compression test methods, the reader is recommended thechapter written by Fellers and Donner in the handbook of physical testing ofpaper from 2002 [34]. After 2002 there have been new efforts to constructmathematical models for both the short span compressive strength, e.g.Shallhorn, Ju and Gurnagul [35], as well as the box compression resistance,e.g. Ristinmaa, Ottosen and Korin [36]. Experimental work has also beenperformed, such as the comparisons of the compression behavior of differentboard qualities that were performed by Mäkelä in 2010 [37]. During thistime, the research community has also been interested in short span tensiletesting, which has much in common with the short span compression test.Such considerations are addressed regarding the test conditions during zero-span testing by Batchelor et al 2006 [38]. It is in this setting that Paper A,in this thesis, was performed with the goal to examine the deformation anddamage mechanisms when performing short span compression tests (SCT)on multiply paperboards. Special consideration was given to the delamina-tion behavior, since it has been shown to be very influential for converting.This was discussed by Carlsson, de Ruvo and Fellers already in 1983 [39],but also more recently by Beex and Peerlings [15] as well as Nygårds, Justand Tryding [40]. A recent and thorough analysis of the problem, usingFEM, was performed by Huang and Nygårds in four recent articles [16, 41–43]. It was shown that the through thickness shear strength profiles, such asshown in figure 3b, are important for creasing. This raised the question ofhow these profiles, which can be altered by using different furnishes, affectslocal compression, something that was addressed in Paper A. After Paper

A, further studies have been performed, both in an industrial setting, suchas the master thesis by Hansson [44], as well as in a more academic settingsuch as the work on SCT presented by Borgquist [13, Paper C], and thefollow up study presented in Paper B in this thesis.

Tension and in-plane properties

Niskanen [45] wrote a very thorough literature survey on the strength andfracture of paper for the tenth fundamental research symposium coveringthe research history up to that point. Although much of it focuses on thin-ner qualities, a couple of highlights are worth mentioning. Norman [46]shows how the tensile strength of paper is affected by increasing inhomo-geneity in 1965. Htun and de Ruvo [47] correlate the elastic propertiesand the compressive and tensile strengths to the drying stress. Ritala andHuiku [48] discuss how percolation influences the formation, and did somenetwork simulations of heterogeneous networks. Outside of Niskanens re-view of the field, a small study by Malmberg [49] in 1964 can be given as an


Figure 4: A paperboard subjected to short span compression, post collapse. Thethrough thickness shear profile has been indicated on the paperboard,note how its weak points correspond to the delamination in the board.

example of early interest in the size dependency of testing. Since 1994 muchhas happened within the field. In 1996, Tryding [50] mentions size depen-dent results when testing paperboard. The same year Korteoja et al. [51]examined the local strain fields in paper using silicone treated paper. Thatwork was followed by an investigation of the strength distribution in pa-per [52] as well as a study on the progressive damage in paper [53]. In 2003Ostoja-Starzewski and Castro [54] cross-correlated the formation and strainfield using finite element simulations. Wahlström et al. [55] suggested thatthe tensile properties of a multilayer paperboard could be predicted, fromthe properties of its layers using a rule of mixture, with an accuracy suf-ficient for engineering purposes. There are different methods to assess theinhomogeneities in paper, one of them is the method using silicone treatedpapers, as mentioned above. Two other methods are digital image correla-tion and thermography. Digital image correlation has been used on paperfor quite some time. Lyne and Bjelkhagen [56] used an inferometric methodalready in 1981. Ten years later Choi, Thorpe and Hanna [57] used it tostudy strains in wood and paper. Lif et al. [58] studied the hygroexpan-sion of paper in 1995. In 1998 Wiens, Göttsching and Dalpke [59] tried toquantify the local deformations in paper and in 2005 Considine et al. [60]used it to study the local deformation field. Thermography on paper hasan even longer history, Dumbleton et al. [61] looked at temperature profilesduring straining already in 1973. The same year Ebeling [62] used it toassess energy consumption during straining. Yamauchi used it to study thedeforming process of paper in 1993 [63] and 1994 [64]. Tanaka expanded onYamauchis work in 1997 [65], studying fracture, in 2000 studying fractureand deformation [66], and 2003 [67] when thermal maps was compared to


silicone impregnated samples. More recently, 2012, Hyll et al. [68] studiedelastic and plastic energy during deformation and rupture of paper. It iswithin this context that Paper C and Paper D together with Paper E,find their places.

EXPERIMENTAL EQUIPMENT |13

Experimental equipment

Before the main conclusions in this thesis is given, the methods used shouldbe explained. In this section a more in-depth description of the differentexperimental setups that have been used is given. Some of the equipmentsare standardized paper testing equipment and some of a more specializedcharacter. Some equipment, like the TH1 Alwetron, standard tensile testerfrom Lorentzon & Wettre was used in all of the appended papers, otherequipment, like the short span compression tester, in a few papers, whilesome equipment, e.g. the L&W creasability tester, is only described forcomparative reasons.

Environmental conditions

When performing tests on paper and paperboard it is important to keeptrack of the surrounding climate. The reason for this is that paper is sen-sitive to both moisture and temperature causing the same paperboard tohave different properties depending on the environment. This is of specialconcern during longterm testing, but also an important factor in quickerexperiments to ensure the repeatability and comparability of the experi-mental results. Furthermore, it is not only the present conditions that areof importance but also the history. Although the history might be mainlyimportant outside of the laboratory, where for example mechano-sorptivecreep is a big problem for the resistance of packages (see e.g. Coffin [69] orMattsson and Uesaka [70]), it still plays a role for experiments on shortertime scales [27–29]. This is mainly due to the fact that the response of paperto moisture and temperature is not immediate. If nothing else is mentionedall papers and paperboards were conditioned in a standardized climate, i.e.23 ◦C and 50 % relative humidity, where the tests also were performed.

14| EXPERIMENTAL EQUIPMENT

Standard equipment

The equipments presented below is used for standardized paper and paper-board testing, and are usually single purpose, off-the-shelf devices.

Tensile testing

The standardized tensile testing was performed according to ASTM-828,which dictates a 15 mm wide specimen, and a length between the clamps of100 mm. The test should be performed with a strain rate of 100 %/min andin the above mentioned controlled climate. The standardized tests were per-formed on a TH1 Alwetron provided by Lorentzon & Wettre (Stockholm,Sweden). Where the test is performed with the sample laying on a flatsurface while clamped by cylindrical clamps. The results of the test are re-ported as a force displacement curve from where the machine automaticallycalculates properties such as tensile index, specific strength, and strain atbreak among others. The data was usually recalculated to stress and strain,which traditionally has been avoided within paper mechanics due to theuncertainties when measuring paper thickness.

Thickness measurements

The thickness of the different paper and boards in this study was eithermeasured using a micrometer screw gauge, an indicator or using the STFI-method [71], which dictates that the thickness is measured along a line. Thelast option was the most reliable since it gives a thickness profile that thenis averaged.

Short-span compression test (SCT)

The short-span compression test (SCT) is a test that is most commonlyused in industrial quality control. An apparatus to measure the SCT valueis provided by Lorentzon & Wettre. In the test, a 15 mm wide specimenis placed between two clamps, see Figure 5a. During testing the initialdistance between the clamps (L = 0.7 mm) is reduced, and the maximumforce is recorded. The SCT value is defined as the maximum force dividedwith the specimen width w = 15 mm. In Figure 5b a post collapse pictureof a tested paperboard is shown.

Z-strength test

To measure Z strength, i.e. the out of plane tensile strength of the board, acircular piece of paperboard is cut out and glued onto two metal cylinders of


(a) (b)

Figure 5: A sketch of the SCT fixture with dimensions (a). A post collapsepicture of a paperboard undergoing SCT (b). The arrows indicatethe clamping (1) and the compression (2).

the same diameter. The test piece and cylinders are then placed in a tensiletesting machine and pulled apart, while the force displacement curve isrecorded.

Creasing and folding

Neither creasing nor folding was studied in any of the appended articles.However, a short description of both, and how they are measured, is stillof interest since both creasing and folding relates closely to the convertingoperations. A creased and folded board is shown in Figure 6. Creasing,sometimes referred to as scoring, is the process in which the paper is pressedby a rounded male die into a female die. This is done to produce a linealong which the paper can be folded without wrinkling or fracture. Thecrease can be varied depending on the width of the female die as well as theshape and the width of the male die. Further, the creasing depth can bevaried. Creasing is judged by the force needed to make the crease, how thepaperboard delaminates as well as the visual appearance of the crease. Formore information about creasing and the mechanisms at work the readeris referred to the aforementioned works by Huang et al. [43] as well asBeex et al. [15]. How well the paperboard folds is important in converting.The standardized way to measure this, for example to compare an uncreasedboard with a creased one, is to use a L&W Creasability tester equipment(Lorentzon & Wettre Stockholm, Sweden). In this machine the bendingmoment is recorded against the fold angle. For further details about foldingand how it is affected by creasing see for example Huang et al. [43].


Figure 6: Example of a creased and folded paperboard.

Figure 7: A sketch showing DIC and thermography used together. The stereocameras used for the DIC was placed on one side, while the IR-camerawas placed on the other. Note the screening material on the IR-camera side.

Special equipment

In this section general laboratory equipment, as well as some special equip-ment is presented. The two camera equipments (DIC and IR) was usedtogether with the tensile testers. Figure 7, shows how the three equipmentswere used together.

Creping and drying

A lab scale creping device can be used to increase the strain at break ofpapers. It consists of a nip with a lower steel cylinder (diameter 200 mm),and an upper rubber coated steel cylinder (steel diameter 200 mm andrubber thickness 10 mm). During creping the rolls are run with a speeddifference, where the lower steel roll has the highest speed. The papersdesignated for creping were taken from the FEX machine, where they had


been produced, after the press sections, when they had a dryness level ofabout 40 %. Thereafter, they were sealed in plastic bags and stored in arefrigerator until creping could be performed, several days later. Duringthe storing the moisture could be maintained in the sheets. The wet sheetswere run through the creping nip. Thereafter, they were dried on a photomount dryer at 70 ◦C, this drying technique should be considered not toapply any constraints, and hence be equal to free drying. As a comparisonthe sheets were also dried in the one cylinder dryer at FEX, which, to agood approximation, was considered to be restrained drying.

Double notched shear test (DNS)

The double notched shear test was developed, by Nygårds et al. [25], toenable the characterization of the transverse shear strength through thethickness of a paperboard. Test pieces are prepared by grinding two par-allell slots in a paperboard. The slots should be on opposing sides of thepaperboard at an offset of 5 mm from each other. Both slots should bemonotonically deepening, tracking each other. After the slots have beenground, the board is laminated on both sides leaving a small gap over theslots, cf. Figure 3a. This is done to make the board easier to handle andto prevent tensile breakage. The board is then cut into 15 mm stripes witha notch on each side, hence the double notch. The stripes are tested in astandard tensile tester, but due to the lamination the board breaks due toin-plane shearing between the notches. When all stripes have been tested aprofile of the shear strength at different depths is acquired.

The long span compression tester

In SCT very short specimens are tested and only the maximum force isrecorded. In addition, a fairly high pressure is applied to hold the speci-men. To enable characterization of in-plane compression, and to capturethe stress-strain curve, a long compression test (LCT) apparatus that haslateral supports that constrains the buckling of the paperboard was devel-oped by Cavlin and Fellers [32]. In the test a 25 mm wide paper test piecewith a clamping length of 54.6 mm is used. This LCT apparatus availableat Innventia, is a further development of the creep apparatus used by Paneket al. [72]; the main difference is a stepper motor which allows for gradualdeformation. The force is measured with a 50 lb. (222 N) load cell, andthe displacement is measured with LVDT gauges that are connected to twoneedles. The needles have an initial separation of 43 mm, and are positionedat two of the lateral supports that constrain the buckling of the paperboard.The prescribed deformation rate is 0.91 mm/s.


Non standard tensile testing

In many of the appended articles tensile testing of samples with other dimen-sions than those prescribed in the standard test was needed. This, togetherwith the need to be able to mount cameras to capture the tests, broughton the need to perform the test in other machines than the aforementionedTH1 Alwetron. Mainly three different tensile testers were used for this: ei-ther one of two servo hydraulic machines or a smaller servo electric machine.The servohydroulic machines were provided by MTS and Instron and theservo-electric machine was provided by Instron. The machines were fittedwith load cells in the range of 500 to 2000 N. All test were run in displace-ment control, with a strain rate of 100 %/min if nothing else is indicated.The clamps used varied between the different machines, but great care wastaken so that the samples were firmly clamped without being damaged.

Digital image correlation

Digital image correlation (DIC), is a contact free way of measuring the strainfield on a sample. In its simplest form the method consists of a camera thattakes pictures of a random pattern on the sample as it is manipulated. InFigure 9 the pattern used is visible. The pictures are then analyzed usingsoftware that tracks how the pattern moves and from this movement the lo-cal strains are calculated. In this thesis the DIC was performed with a com-mercial system Aramis R© provided by GOM mbH, Braunschweig Germany.This system is a stereo system, using two cameras that makes it possible totrack the out-of-plane deformation as well as the in-plane strains.

Thermography

With a thermal camera it is possible to measure the heat that is emit-ted from a sample. Since it only measures the infrared radiation, it can-not register heat that is convected or conducted away. In this thesis acamera from FLIR R© systems, SC 6000, was used. The camera workedin the mid-wavelength infrared range, recording wavelengths between 3-5µm. Typically a frame rate of 32 Hz was used. Thermography has beenused together with DIC in other research areas than paper mechanics, e.g.Cholewa et al. [73] who developed a new technique to calibrate the equip-ments and then investigated how composites behaved during one-sided heat-ing and compression.

SIMULATIONS |19

Simulations

There are, as aforementioned, a great number of ways to simulate paper-board. The approach that was chosen in this work was to use already im-plemented material models in a commercial finite element software, insteadof using experimental material models or develop new ones. The reasonbehind this decision was twofold. While there are several suggested mate-rial models in the literature, e.g [14, 74–78], most of them are somewhatcomplicated to implement. Which in turn makes them unpractical froman industrial perspective, where commercial pre-implemented models arepreferable. The other reason is that the samples used in the experimentsin this thesis have simple geometries and loads. In simulations that involvesomewhat more advanced geometries, like the SCT simulations, focus has toa large extent been on delamination. This has made the three dimensionalyield behavior, which is what most newly developed models are concernedwith, less influential. Instead the focus has been both on the informationabout underlaying mechanisms that can be gained using simpler modelscombined with well designed experimental work. As well as investigatingthe predictive powers of the built in models, which in turn can help theindustry in their decision making about whether it needs to invest time andmoney into non-standard models.

The commercial software that was primarily used throughout this workwas ABAQUS 6.12 (Dassault Systèmes Simulia Corp.). The element typeused varied between the different analyses. All models were implicitlysolved and the preferred material behavior was elastic-plastic using Hill’sanisotropic yield surface and linear strain hardening. In the SCT modelsthis was complemented with cohesive interfaces that used a traction separa-tion law with an initial elastic response and an exponential damage behaviorto simulate delamination.

20| SIMULATIONS

CONTRIBUTIONS IN THIS THESIS |21

Contributions in this thesis

The purpose of the papers in this thesis is to answer questions about howvariation within a paperboard affects the mechanical properties. There aretwo main reasons why this is important. The first reason is that it is impor-tant to know what is actually tested, when a test is performed. The otherreason is that these properties become very important when paperboard isused in more advanced converting and end-use. The main conclusions whichcan be drawn from the presented papers are outlined below.

Short span compression

In Paper A and B a finite element model for predicting the SCT strengthfor multiply paperboards was developed. The model consisted of continuumplies with cohesive interfaces in-between, cf. Figure 8. The basic materialproperties used in the model was acquired by doing standard tensile test-ing on the individual plies of a paperboard. The plies were separated bygrinding. These properties were then modified in accordance with the outof plane transverse shear strength profile, cf. Figure 3, acquired using thedouble notched shear test. The shear strengths of the interfaces was alsobased on the DNS measurements. The model was able to predict the SCTstrength based on the measured properties, which makes it a useful toolwhen predicting the behavior of new paperboard designs. The simulationsindicate that SCT is a pre-dominantly elastic phenomenon that is governedby stiffness and delamination. The delamination is in turn dependent onthe local shear strength and the stiffness gradient. To successfully predictthe outcome of an SCT test, the ply-wise stiffness together with the shearstrength profile are needed. The model and experiments indicate that it ispossible to alter the SCT values of a multi-ply paperboard without modify-ing the tensile properties by altering the shear strength profile. The shearstrength should preferably be increased in a uniform way across the paper-board. The point where the paperboard will delaminate is primarily decidedby high values of the stiffness gradient and secondarily by weak spots in the

22| CONTRIBUTIONS IN THIS THESIS

Figure 8: The cutout of the model used in Paper A and B. The model con-sisted of continuum plies with interfaces between.

local transverse shear strength.

In-plane heterogeneities

In Paper C the influence of sample size on strainability was investigated.This was primarily done by doing tensile tests on samples of different ge-ometry and size. It was concluded that the strainability was dependent onthe length to width ratio of the sample. To further examine the reasonsbehind this digital image correlation was used on samples with differentsizes. An example of such a test can be seen in Figure 9. From the DIC itwas concluded that the local strain in the sample varied in different zonesof the paperboard. These strain zones first appeared when the sample be-gan to show a plastic response. Something that was further supported bya rudimentary analysis of the strain variations along a line in the sample,as seen in Figure 10. The size of the strain zones were independent of thesample size, which explained how the strainability was affected by samplesize. Finally it was noted that denser boards showed higher strainability,and this was attributed to higher maximum local strains. The DIC datawas revisited in Paper E, where the virtual field method was used to ana-lyze the data. Apart from evaluating how the method could be applied topaperboard the results suggested that high stiffness regions only providedmarginal improvement of the mechanical behavior of the paperboard.

In Paper D the strain zones seen in Paper C was revisited. This timetwo types of single ply papers were examined. The papers chosen were pro-duced to have different anisotropy, due to different head box pressures, butmade of the same pulp. Furthermore some samples was creped to acquirehigher strain at break. The papers were examined using thermography,where the streaks with increased temperature was observed. These streaks


Figure 9: Force/strain graph of a sample pulled in CD. The DIC pictures abovethe graph shows the strain in the CD. The DIC pictures below thegraph shows the strain in the MD. A picture of the ruptured sampleis inserted to the right. On the ruptured sample the printed randompattern is clearly visible.


0 10 20 30 40 50 60 700

1

2

Position along the line

Str

ain/

mea

n st

rain

(who

le li

ne)

−1 0 1 2 3 40

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Mean strain (%)

σ (M

PA

)

0 10 20 30 40 50 6040

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passed time/break time (%)Mat

ch p

eeks

and

val

leys

(%)

0 10 20 30 40 50 60 700

2

4

6

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Str

ain

Figure 10: The four graphs show; Top: Strain profiles along a line in the strain-ing direction on a DIC sample, at different times during straining.Top line is just prior to break, and the red line represents the samplewhen it still is in the linear region. Middle (top): Strain profilesnormalized with mean strain for the whole line. Middle (bottom):Stress strain curve with sample times marked. Bottom: Position ofpeaks and valleys at different times compared to top line.


(a) (b) (c)

Figure 11: The formation of unstrained sample (a). DIC picture of the samesample, prior to break (b). Thermograph of the same sample priorto break (c). Note that the DIC picture is mirrored to match thetwo others, since it was captured form the backside of the paper.

were correlated to the local strain by running thermography and DIC onthe same sample. It was shown that the strain zones correlated to the for-mation of the paper. An example of a thermograph, side by side with aDIC picture at the same global strain, and the unstrained formation canbe seen in Figure 11. Low grammage zones were strained more than denserzones. Using thermography it was also possible to predict where rupturewould occur, but not how the failure propagated. Further it was shown thatit was possible to predict the straining behavior using FEM based on theformation. Increased homogenization should increase the strain at break,as it is the most locally strained part of the paper that initiates rupture,leaving other sections only partially strained compared to their maximumpotential. However it was not an increased homogenization that was thecause for the increased strain at break seen in creped papers. Instead thesuggested mechanism was that the compression of the fiber network causedby the creping was recovered during straining.

FUTURE |27

Future

This thesis has increased the understanding of how variations affect theproperties of paperboard both in compression and tension. It also lays theground work for new research projects and questions. Three examples ofsuch questions are outlined below:

One interesting part is how the in-plane heterogeneity acts during threedimensional forming of geometrically advanced structures. If it is the localor global properties that are limiting, e.g. what kind of variations shouldbe allowed. Further, the out-of-plane profile is also of interest for this kindof forming since the board might need to delaminate during the process.

Another interesting area is how short span compression connects tolong span compression. They have been shown to correlate via weakest linktheory using Weibull statistics, but the correlation is only good for somepaper qualities. During long span testing the collapse is often due to localcollapse or buckling. Perhaps the insights from the studies presented in thiswork could be used to design models of the long span test.

Finally it would be very interesting to see how the out-of-plane varia-tions interact with the in-plane variations. Since all plies are formed sep-arately their individual weaknesses could influence each other, but this inturn should be dependent on how well connected the different layers are. Itcould be imagined that a weaker middle ply effectively buffer the strongerouter plies from each other.

The three mentioned questions are interconnected with each other, butcould also be approached individually. In the end all of them are interestingresearch subjects, that should be ready for exploration.

28| FUTURE

SUMMARY OF APPENDED PAPERS |29

Summary of appended papers

Paper A: Investigation of shear induced failure during SCT loading of paper-boards

In-plane compression has been analyzed experimentally and numericallyusing three machine made multiply paperboards. The paperboards haddifferent shear strength profiles. Both short span compression (SCT) andlong span compression (LCT) were performed. A finite element model of theSCT setup was developed, and the experimental results in MD and CD couldbe well predicted by the model. Using the model we could identify that theSCT failure was initiated by shearing of the interfaces in combination withthe onset of plasticity in the loading direction. The model was used to makea parameter study. It showed that increased SCT values can be achievedby increasing the stiffness of the board or increase the failure displacement.The increase of stiffness was associated with ply properties, while the failuredisplacement was associated with interface properties.

Paper B: Short compression testing of multi-ply paperboard, influence fromshear strength

The influence of the through-thickness shear strength profiles on the shortspan compression test was examined. This was done both with experimentsand finite element simulations on five industrial produced paperboards. Itwas concluded that the short span compression test is governed by in-planestiffness and through thickness delamination. The delamination damagewas in turn dependent on the local transverse shear strength and in-planestiffness gradients. Furthermore, it was concluded that the pre-delaminationmechanisms were elastic. Finally it was possible to alter the results fromthe test by altering the shear strength of the paperboard; this should bedone uniformly over the entire middle ply of the board when an increasedSCT value was what was sought after.

30| SUMMARY OF APPENDED PAPERS

Paper C: Investigation of sample-size effects on in-plane tensile testing of pa-perboard

The impact of sample size on in-plane strain behavior in paperboard wasinvestigated, with the aim to explore the differences between local and globalproperties in paperboard, and try to pinpoint the mechanisms behind suchdifferences. The local properties are of interest in converting as well as forfuture 3D forming of paperboard. It is important to identify differences inbehavior between local and global properties since most paperboards areevaluated against the latter. The methods used for evaluation were tensiletests in controlled environment and speckle photography. The results showthat there is a difference in strain behavior that is dependent of the lengthto width ratio of the sample, that this behavior cannot be predicted bystandard tensile tests and that it depends on the board composition. Thespeckle analysis revealed that the behavior is a result of the activation ofstrain zones in the sample. These zones are relatively constant in size andtherefore contribute differently to total strain in samples of different size.

Paper D: Thermographical analysis of paper during tensile testing and compar-ison to digital image correlation

The thermal response in paper has been studied using thermography. It wasobserved that an inhomogeneous deformation pattern arose in the papersamples during tensile testing. In the plastic regime a pattern of warmerstreaks could be observed in the samples. On the same samples digital imagecorrelation (DIC) was used to study local strain fields. It was concluded thatthe heat patterns observed by thermography coincided with the deformationpatterns observed by DIC. Due to the fibrous network structure paper hasan inhomogeneous microstructure, called formation. It could be shown thatthe formation was the cause of the inhomogeneous deformations in paper.Finite element simulations were used to show how papers with differentamount of homogeneity would deform. Creped papers, where the strainat break has been increased, were analyzed. For these papers it was seenthat an overlaid permanent damage was created during the creping process.During tensile testing this was recovered as the paper network structure wasstrained.

SUMMARY OF APPENDED PAPERS |31

Paper E: Stiffness heterogeneity of multiply paperboard examined with VFM

Mechanical heterogeneity of a multiply paperboard was characterized inuniaxial tension using DIC and VFM. The specimen was divided into threesubregions based on axial strain magnitude. VFM analysis showed that thesubregions had stiffnesses and Poisson’s ratio’s that varied in a monoton-ically decreasing fashion, but with the stiffness differences between subre-gions increasing with applied tensile stress. An Equilibrium Gap analysisshowed improved local equilibrium when comparing a homogeneous analysiswith the subregion analysis. Although only a single specimen was examined,results suggest that high stiffness regions provide only marginal improve-ment of mechanical behavior. The analysis also showed that even thoughthe subregions themselves were non-contiguous, their mechanical behaviorwas similar.

32| SUMMARY OF APPENDED PAPERS

BIBLIOGRAPHY |33

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