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Continuum modelling of the mechanical response of paper-based materials

Borgqvist, Eric LU (2016)
Abstract (Swedish)
Popular Abstract in Swedish

För att tillverka en pappersbaserad förpackning är det viktigt att materialet är tillräckligt hållfast. Förpackningsmaterial består ofta av kartong, aluminium och polymerfilmer där kartong utgör den största delen av förpackningen och bidrar mest till styvheten. Det säljs årligen mer än hundra miljarder förpackningar i världen och om kostnaden samt materi- alåtgång för att tillverka en kartong kan reduceras, så kan stora besparingar göras både ekonomiskt och miljömässigt. När förpackningsmaterialet spricker under konverteringen till en förpackning är anledningen till detta inte alltid helt klart. Mycket material och tid kan gå till spillo under felsökningen och det är inte alltid säkert att man... (More)
Popular Abstract in Swedish

För att tillverka en pappersbaserad förpackning är det viktigt att materialet är tillräckligt hållfast. Förpackningsmaterial består ofta av kartong, aluminium och polymerfilmer där kartong utgör den största delen av förpackningen och bidrar mest till styvheten. Det säljs årligen mer än hundra miljarder förpackningar i världen och om kostnaden samt materi- alåtgång för att tillverka en kartong kan reduceras, så kan stora besparingar göras både ekonomiskt och miljömässigt. När förpackningsmaterialet spricker under konverteringen till en förpackning är anledningen till detta inte alltid helt klart. Mycket material och tid kan gå till spillo under felsökningen och det är inte alltid säkert att man finner orsaken till bristerna. Ett verktyg för att analysera hur förpackningsmaterialet belastas kan därmed vara till stor hjälp för att få en ökad förståelse av konverteringsprocessen. Ett sådant verktyg för kartongmaterialet har utvecklats i den här avhandlingen.



En materialmodell som kan beskriva relationen mellan krafter och deformationer som kartongen utsätts för har utvecklats. Kartongen består primärt av cellulosafiber som är ett par millimeter långa med en bredd och tjocklek på cirka 10-50 mikrometer. Karton- gen som har betraktats i detta arbete har en tjocklek på 400 mikrometer. På grund av tillverkningsprocessen så är de flesta av fibrerna riktade åt samma håll, och fibrerna ligger väsentligen ovanpå varandra. Den riktning som fibrerna ligger staplade ovanpå varandra definieras som ut-ur-planet riktningen. Kartongens hållfasthetsegenskaper är som starkast i den riktning som fibrerna ligger i, dvs i-planet och mycket svagare ut-ur-planet. Det kan skilja en faktor hundra i styvhet mellan i-planet och ut-ur-planet. Detta är en av anledningarna som gör modellering av kartongen utmanande.



Fokus i detta arbete har varit inriktat på att simulera bignings och vikningsprocessen med hjälp av den utvecklade modellen. De mycket stora lokala deformationer som sker under dessa processer har studeras med hjälp av modellen. Viker man en obigad kartong uppkommer rynkor vilket gör det mycket svårt att vika kartongen rakt. Dessa rynkor formas på ett instabilt sätt och röntgenbilder visar att fibrerna har omorienterats inuti rynkorna. Det är därför viktigt att man först bigar kartongen så att man kan få väl definierade viklinjer. I bigprocessen pressas ett hanverktyg på kartongen så att kartongen förs in i ett honverktyg. Kartongen skjuvas och skadas genom tjockleken och en viklinje uppkommer, vilket gör att kartongen låter sig formas till en förpackning.



Denna avhandling består av fem artiklar, A-E. I artikel A etableras det termodynamiska ramverk som är basen för modellen och en i-planet modell etableras. I artikel B utökas kontinuum-modellen så att ut-ur-planet egenskaperna kan modelleras. Vikning av en obi- gad kartong samt i-planet kompression studeras i artikel C. För att simulera vikning av bigad kartong behövs skade-variabler införas och två olika skademodeller samt två integra- tionsmetoder studeras i artikel D. I artikel E införs skadevariabler i kartongmodellen och vikning av bigad kartong studeras och simuleras. (Less)
Abstract
Continuum based elasto-plastic-damage models for paperboard have been established in this work. The thesis begins with an introductory section that describes the mechanical properties of paperboard and some of the converting processes during forming of a package. A short review of modeling concepts that have been applied to paperboard is presented and then some key aspects and assumptions developed in this work are summarized. The main part of the thesis consists of the five papers, A, B, C, D and E. In addition to these works, a possible concept to reduce a pathological mesh-dependency is reviewed.



The thermodynamical framework is established in Paper A and a model for the in-plane response is developed. The anisotropy... (More)
Continuum based elasto-plastic-damage models for paperboard have been established in this work. The thesis begins with an introductory section that describes the mechanical properties of paperboard and some of the converting processes during forming of a package. A short review of modeling concepts that have been applied to paperboard is presented and then some key aspects and assumptions developed in this work are summarized. The main part of the thesis consists of the five papers, A, B, C, D and E. In addition to these works, a possible concept to reduce a pathological mesh-dependency is reviewed.



The thermodynamical framework is established in Paper A and a model for the in-plane response is developed. The anisotropy is handled by introducing a set of director vectors that change direction along with the continuum. A distortion hardening yield surface coupled to several scalar internal variables is introduced. The effects of pre-straining a sample in one direction and then subsequently load the sample in the perpendicular direction is studied. The model is compared to measurements obtained with Digital Image Correlation.



In Paper B, the model is further developed to model out-of-plane deformations. A normal vector is introduced to model the out-of-plane direction. Key ingredients in the model includes the specific format for the elastic part of the free energy and an expression for the plastic spin. The spin is used to control the direction of the plastic flow. Simulations are performed on the line crease setup and compared to experimental measurements. Furthermore, the industrial rotation crease setup is studied in detail using the developed model.



The Short-span Compression Test (SCT) and the line folding operation are investigated in Paper C and the deformation patterns extracted from x-ray images are studied. The model parameters are calibrated to uniaxial tests and the SCT, and then the folding of uncreased paperboard is simulated. The simulated global force-displacement/rotation curves matches the measurements and the simulated deformation patterns are similar to that observed experimentally.



A numerical scheme is presented in Paper D, where the governing equations of the elasto-plastic boundary value problem are interpreted as a Differential-Algebraic Equation (DAE) system. In particular, two material models, which includes damage variables, are investigated using the Diagonally Implicit Runge-Kutta (DIRK) scheme. The error obtained using the DIRK-method is compared to the standard implicit Euler method.



In Paper E, the continuum model that has been developed in paper A-C is further enhanced to include the effect of damage. Two damage variables are introduced in the elastic part of the free energy which is associated with out-of-plane deformations. The softening in the out-of-plane normal and shear deformations can then be recovered. The folding of creased paperboard is simulated and compared to measurements. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Perego, Umberto, Politecnico di Milano, Department of Civil and Environmental Engineering, Italy
organization
publishing date
type
Thesis
publication status
published
subject
keywords
paperboard, constitutive modeling, anistropy, finte deformations, plasticity, damage, continuum mechanics
pages
188 pages
defense location
Lecture hall M:E, M-building,Ole Römers väg 1, Lund University Faculty of Engineering, LTH.
defense date
2016-03-18 10:00
ISBN
978-91-7623-665-9
978-91-7623-666-6
language
English
LU publication?
yes
id
f8bbc8c6-d3b3-406c-88d2-0b15bde42f1f (old id 8726286)
date added to LUP
2016-02-23 14:19:05
date last changed
2016-09-19 08:45:19
@phdthesis{f8bbc8c6-d3b3-406c-88d2-0b15bde42f1f,
  abstract     = {Continuum based elasto-plastic-damage models for paperboard have been established in this work. The thesis begins with an introductory section that describes the mechanical properties of paperboard and some of the converting processes during forming of a package. A short review of modeling concepts that have been applied to paperboard is presented and then some key aspects and assumptions developed in this work are summarized. The main part of the thesis consists of the five papers, A, B, C, D and E. In addition to these works, a possible concept to reduce a pathological mesh-dependency is reviewed. <br/><br>
<br/><br>
The thermodynamical framework is established in Paper A and a model for the in-plane response is developed. The anisotropy is handled by introducing a set of director vectors that change direction along with the continuum. A distortion hardening yield surface coupled to several scalar internal variables is introduced. The effects of pre-straining a sample in one direction and then subsequently load the sample in the perpendicular direction is studied. The model is compared to measurements obtained with Digital Image Correlation. <br/><br>
<br/><br>
In Paper B, the model is further developed to model out-of-plane deformations. A normal vector is introduced to model the out-of-plane direction. Key ingredients in the model includes the specific format for the elastic part of the free energy and an expression for the plastic spin. The spin is used to control the direction of the plastic flow. Simulations are performed on the line crease setup and compared to experimental measurements. Furthermore, the industrial rotation crease setup is studied in detail using the developed model. <br/><br>
<br/><br>
The Short-span Compression Test (SCT) and the line folding operation are investigated in Paper C and the deformation patterns extracted from x-ray images are studied. The model parameters are calibrated to uniaxial tests and the SCT, and then the folding of uncreased paperboard is simulated. The simulated global force-displacement/rotation curves matches the measurements and the simulated deformation patterns are similar to that observed experimentally.<br/><br>
<br/><br>
A numerical scheme is presented in Paper D, where the governing equations of the elasto-plastic boundary value problem are interpreted as a Differential-Algebraic Equation (DAE) system. In particular, two material models, which includes damage variables, are investigated using the Diagonally Implicit Runge-Kutta (DIRK) scheme. The error obtained using the DIRK-method is compared to the standard implicit Euler method.<br/><br>
<br/><br>
In Paper E, the continuum model that has been developed in paper A-C is further enhanced to include the effect of damage. Two damage variables are introduced in the elastic part of the free energy which is associated with out-of-plane deformations. The softening in the out-of-plane normal and shear deformations can then be recovered. The folding of creased paperboard is simulated and compared to measurements.},
  author       = {Borgqvist, Eric},
  isbn         = {978-91-7623-665-9},
  keyword      = {paperboard,constitutive modeling,anistropy,finte deformations,plasticity,damage,continuum mechanics},
  language     = {eng},
  pages        = {188},
  school       = {Lund University},
  title        = {Continuum modelling of the mechanical response of paper-based materials},
  year         = {2016},
}