The out-of-plane properties of paperboard are important in several converting applications such as printing, sealing, creasing, and calendering. A juxtaposed tensile and compression curve in the z direction (ZD) will, however, appear to have a kink or discontinuity at 0 stress. The purpose of the present work is to capture the continuous transition between tension and compression and to increase the understanding of the complex ZD properties of paperboard by cyclic testing. In this attempt to unify the ZD tensile and compressive behavior of paperboard, samples were laminated to the testing platens using heat seal laminate film. The method for adhering the samples was compared to samples that were laminated and glued to the testing platens. The edge effects of the cutting method were evaluated in compression testing with samples not attached to the testing platens. The flat slope seen in the initial part of the pure compression curve disappeared when the samples were laminated to the testing platens. The flat slope was instead replaced by a continuous response in the transition across 0 N. The stiffness in the transition region resembled the response in tensile testing. When the testing is cycled, the material exhibits a history dependence. Starting the cycle in either compression or tensile will show an effect on the stiffness at the transition, as well as the compressive stiffness. However, the ultimate tensile strength is unaffected.

Paperboard is a common material for packages and other carriers of information. During rotary printing processes, the paperboard is subjected to rapid deformations in the out-of-plane direction as it passes through the nip between the rolls of the printer. Being viscoelastic in nature, the mechanical response of the material to high deformation rates differs from what is measured with conventional testing conducted at slower deformation rates. In this work, a device called the rapid ZD-tester is used to show the response of paperboards subjected to a rapid pressure pulse and compare this to measurements made at lower strain rates in a common universal testing machine. All the tested paperboards show complete recovery within 5 s when being rapidly compressed, while the slower compression to the same pressure leaves a deformation that remains after 5 s. The stiffness response differs between the paperboards, but does not consistently increase or decrease between slow or rapid compressions. The difference in response between slow and rapid compression appears larger for the low-density paperboard in the study.

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

The thermal response in paper has been studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Because of its fibrous network structure, paper has an inhomogeneous micro-structure, which is called formation. It could be shown that the formation was the cause of the inhomogeneous deformations in paper. Finite element simulations was used to show how papers with different degrees of heterogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid compaction of the paper was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.

The in-plane properties of paperboard have always been of interest to paper scientists. Tensile properties are crucial when the board is fed through converting machines at high speeds. Compressive properties are essential in the later use. Inhomogeneities affect both the compressive and tensile properties. For the tensile properties, it is the inherent heterogeneity of the paperboard that might cause problems for the board-maker. Varying material properties, through the thickness of the paperboard, are on the other hand used to achieve high bending stiffness with low fiber usage. It is of interest to know how this practice affects the local compressive properties. Papers A and B aims to address this, while C, D and E focus on in-plane heterogeneities. Paper A investigates the mechanism that causes failure in the short span compression test (SCT). It was concluded that the main mechanism for failure in SCT is delamination due to shear damage. In paper B the effect of the through-thickness profiles on the local compression strength was examined. It was concluded that the local compression is governed by in-plane stiffness and through thickness delamination. The latter was in turn dependent on the local shear strength and in-plane stiffness gradients. In paper C the tensile test is investigated with focus on sample size and strain distributions. The strain behavior was dependent on the length to width ratio of the sample and was caused by activation of local zones with high strainability. Paper D focuses on the strain zones seen in C. The thermal response in paper was studied. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. It was concluded that the heat patterns observed coincided with the deformation patterns. It could be shown that the formation was the cause of the inhomogeneous deformation. In final paper, E, the virtual field method was applied on data from C.

Egenskaperna hos ett kartongark kan grovt delas upp i två kategorier: i-planet egenskaper och ut-ur-planet egenskaper. I-planet egenskaperna har länge varit ett område som pappersmekanister och andra pappersforskare visat intresse för. Anledningen till detta är att de är avgörande för hur väl det går att konvertera kartongen till färdiga förpackningar, samt hur väl de förpackningarna klarar sin uppgift. Dragegenskaperna prövas när kartongen dras genom tryck- och konverteringsmaskiner i hög hastighet. Tryckegenskaperna spelar stor roll för hur väl en förpackning klarar att staplas och hålla sitt innehåll intakt. Inhomogeniteter påverkar både drag och tryckegenskaper. Papprets naturliga variation påverkar dragegenskaperna hos kartongen och kan orsaka problem för kartongmakarna. Särskilt när utvecklingen går mot mer avancerade kartong utseenden. Å andra sidan så använder sig kartongmakare flitigt av egenskapsvariationer genom tjockleken på kartongen, när dom vill åstadkomma böjstyva kartonger utan att slösa med fibrer. I detta fall är det intressant att veta hur 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 avhandlar hur i-planet variationer påverkar kartongens egenskaper.

I Artikel A undersöks vilka skademekanismer som aktiveras under ett kortspannskompressionstest (SCT). Tre flerskiktskartonger undersöktes. De hade valts så att de hade distinkt olika skjuvstyrkeprofiler. Kartongerna karakteriserades och datan användes som materialdata i en finit element modell av SCT-testet. Modellen bestod av skikt, betraktade som kontinuum, mellan vilka det fanns kohesiva ytor. Huvudmekanismen i SCT var att kartongen delaminerade på grund av skjuvskador.

Den andra uppsatsen, Artikel B, var en fortsättning på den första. Denna gång undersöktes fem flerskiktskartonger framtagna så att de hade olika skjuvstyrka beroende på positionen i tjockleksled. Det konstaterades att kompressionsegenskaperna lokalt styrs av skjuvstyrkeprofilen och styvhetsgradienter. Vidare konstaterades det att mekanismerna innan kartongen delaminerar är, i huvudsak, elastiska.

Den tredje artikeln, Artikel C, fokuserade på hur dragprov på kartong påverkas av provstorleken och töjningsvariationen. Tre olika flerskiktskartonger användes som provmaterial och provbitar med olika storlek analyserades. Förutom dragprov så användes digital image correlation (DIC) för analysen. Det visade sig att den globala töjbarheten varierade med storleken på provet beroende på kvoten mellan längd och bredd. DIC visade att detta i sin tur berodde på att zoner med hög töjbarhet aktiverades i provet. Dessa zoner hade samma storlek oberoende av provstorlek och påverkade därför den totala töjbarheten olika mycket.

Artikel D undersöker töjningszonerna som sågs i Artikel C samt hur de påverkas av kreppning. Vidare undersöktes pappersproverna med hjälp av termografi. Termografin visade att varma zoner uppstod i proven när det töjdes. Zonerna blev synliga när provet töjdes plastiskt. Termografi kördes parallellt med DIC på några prover. Det visade sig att de varma zonerna överenstämde med zoner med hög lokal töjning. Vidare kunde det visas att dessa zoner övenstämde med papperets mikrostruktur, formationen. En finit element analys av hur papper med olika formation töjs gjordes. Delar av provningen gjordes på kreppade papper som har högre töjbarhet. Det visades sig att någon form av skada hade överlagrats på papprets mikrostruktur under kreppningen, och att den deformationen återtogs när pappret töjdes.

I den sista artikeln, Artikel E, behandlas hur VFM (Virtual Field Method) kan användas på DIC-data från kartong. DIC-datan som användes hämtades från Artikel C. Detta gjordes för att visa på hur olika VFM-formuleringar kan användas för att karakterisera styvhetsvariationen hos kartong. Provet delades upp i tre subregioner baserat på den axiella töjningsgraden. VFM-analysen visade att dessa subregioners styvhet och tvärkontraktionstal sjönk monotont, men att skillnaden mellan regionerna ökade med ökande spänning. även om endast ett prov undersöktes, så indikerade resultaten att områden med hög styvhet endast förbättrar de mekaniska egenskaperna marginellt. Analysen visade också att även om subregionerna inte är sammanhängande, så har dom liknande mekaniska egenskaper.

The influence of the through-thickness shear strength profiles on the short span compression test was examined. This was done both with experiments and finite element simulations on five industrial produced paperboards. It was concluded that the short span compression test is governed by in-plane stiffness and through thickness delamination The delamination damage was in turn dependent on the local transverse shear strength and in-plane stiffness gradients. Furthermore, it was concluded that the pre-delamination mechanisms were elastic. Finally it was possible to alter the results from the test by altering the shear strength of the paperboard; this should be done uniformly over the entire middle ply of the board if an increased SCT value was what was sought after.

The thermal response in paper has been studied using thermography. It was observed that an inhomogenous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Due to the fibrous network structure paper has an inhomogenous microstructure, called formation. It could be shown that the formation was the cause of the inhomogenous deformations in paper. Finite element simulations were used to show how papers with different amount of homogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid permanent damage was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.

The creasing and folding behavior of three paperboards have been studied both experimentally and numerically. Creasing and folding studies were performed on strips in both the machine direction and the cross machine direction. A finite element model that mimicked the experimental creasing and folding setup was developed, and the creasing and folding behavior could be well predicted for all three paperboards. An experimental characterization scheme consisting of three experiments was proposed, and was shown to be sufficient to predict the creasing and folding behavior. For the whole paperboard the shear strength profiles in the through thickness direction was determined with the notched shear test. Each ply was laid free by grinding, and density measurements and in-plane tension tests were performed on the bottom, middle and top plies of each paperboard. Instead of assuming uniform properties in each ply, the shear strength profiles were used to map the measured properties in the through thickness direction. Numerical simulations were performed when the ply and interface properties of the paperboards were altered to follow different shear strength profiles. This was done in order to mimic different production strategies. It was shown that the interface strengths mainly influenced the folding behavior. Whereas altered the ply properties affected the creasing force needed.