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Effect of fiber and bond strength variations on the tensile stiffness and strength of fiber networks
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0002-5112-1289
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0003-3611-2250
2016 (English)Report (Refereed)
Abstract [en]

As fiber and bond characterization tools become more sophisticated, the information from the fiber scale becomes richer. This information is used for benchmarking of different types of fibers by the paper and packaging industries. In this work, we have addressed a question about the effect of variability in the fiber and fiber bond properties on the average stiffness and strength of fiber networks. We used a fiber-scale numerical model and reconstruction algorithm to address this question. The approach was verified using the experimental sheets having fiber data acquired by a fiber morphology analyzer and corrected by microtomographic analysis of fibers in these sheets. We concluded, among other things, that it is sufficient to account for the average bond strength value with an acceptable number of samples to describe dry network strength, as long as the bond strength distribution remains symmetric. We also found that using the length-weighted average for fiber shape factor and fiber length data neglects the important contribution from the distribution in these properties on the mechanical properties of the sheets.

Place, publisher, year, edition, pages
2016. , p. 25
Keywords [en]
fibers, bonds, stress-strain curve, paper strength, network simulation
National Category
Paper, Pulp and Fiber Technology
Identifiers
URN: urn:nbn:se:kth:diva-188480OAI: oai:DiVA.org:kth-188480DiVA, id: diva2:935135
Note

QC 20160613

Available from: 2016-06-10 Created: 2016-06-10 Last updated: 2018-02-19Bibliographically approved
In thesis
1. Micromechanics of Fiber Networks
Open this publication in new window or tab >>Micromechanics of Fiber Networks
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The current trends in papermaking involve, but are not limited to, maintaining the dry strength of paper material at a reduced cost. Since any small changes in the process affect several factors at once, it is difficult to relate the exact impact of these changes promptly. Hence, the detailed models of the network level of a dry sheet have to be studied extensively in order to attain the infinitesimal changes in the final product.

In Paper A, we have investigated a relation between micromechanical processes and the stress–strain curve of a dry fiber network during tensile loading. The impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds, is discussed. In Paper B, we studied the impact of the chemical composition of the fiber cell wall, as well as its geometrical properties, on the fiber mechanical properties using the three-dimensional model of a fiber with helical orientation of microfibrils at a range of different microfibril angles (MFA). In order to accurately characterize the fiber and bond properties inside the network, via statistical distributions, microtomography studies on the handsheets have been carried out. This work is divided into two parts: Paper C, which describes the methods of data acquisition and Paper D, where we discuss the extracted data. Here, all measurements were performed at a fiber level, providing data on the fiber width distribution, width-to-height ratio of isotropically oriented fibers and contact density. In the last paper, we utilize data thus obtained in conjunction with fiber morphology data from Papers C and D to update the network generation algorithm in order to produce more realistic fiber networks. We also successfully verified the models with the help of experimental results from dry sheets tested under uniaxial tensile tests. We carry out numerical simulations on these networks to ascertain the influence of fiber and bond parameters on the network strength properties.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. p. 32
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 97
Keywords
Network simulation, Mechanical properties, Fibers, Fiber-to-fiber bonds, Free fiber length, Number of contacts, Contact density, Paper properties, X-ray microtomography
National Category
Paper, Pulp and Fiber Technology
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:kth:diva-188481 (URN)978-91-7595-994-8 (ISBN)
Public defence
2016-09-02, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20160613

Available from: 2016-06-13 Created: 2016-06-10 Last updated: 2016-06-13Bibliographically approved
2. Beam-to-Beam Contact and Its Application to Micromechanical Simulation of Fiber Networks
Open this publication in new window or tab >>Beam-to-Beam Contact and Its Application to Micromechanical Simulation of Fiber Networks
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral thesis covers the topic of modeling the three-dimensional fiber net- works with the finite element method. It contains the part addressing the numerical aspects of the modeling, namely, the contact formulation and application of the developed methods to the fundamental questions such as the effect of randomness in fiber properties and effect of fines and hygroexpansion.

In the approached used in the work,  the fibers were meshed with beam elements  and the bond between fibers is modeled using point-wise beam-to-beam contact. Contact between beam elements is a specific category of contact problems, which  was introduced by Wriggers and Zavarise in 1997 for normal contact [1] and later extended by Zavarise and Wriggers to include tangential and frictional contact [2]. These formulations encompass a large number of derivations and provide the consistent tangent matrix. We showed, however, the resulting numerical implementations based on these consistent formulations are not sufficiently robust in modeling random fiber networks with a large number of contacts.  In the first papers, we proposed a simpler non-consistent formulation, which turned out to be superior in terms of convergence stability with respect to the load step size for a wide range of loading cases. Having these advantages, it remained equally accurate as the original formulation.  The first paper covered the formulation of normal and tangential contact, and the second paper contains two formulations with both the consistent and non-consistent linearizations for in-plane rotational contact of beams.

We use the developed formulations to address fundamental problems within the area of fiber networks, which  cannot  be solved  purely  with  experimental  tools.  In  the third article, we investigated the effect of fiber and bond strength variations on the tensile stiffness and strength of fiber networks and concluded that in cases of skewed distribution, using mean values for fiber and bond properties instead of the distributions is not always adequate to assess the changes these properties have on the average mechanical characteristics of the entire network.

In the fourth paper, the mechanisms behind the improvement of stiffness and strength after PFI refining in the papermaking process is investigated. The PFI refiner is very popular for studying the effect of refining in the lab scale. By using a combination of experimental and numerical tools, we found that density, which is often mentioned as  the main reason behind the improvement of mechanical properties after PFI re- fining, cannot solely explain the degree of the change observed experimentally. We concluded the remaining part of the improvement is caused by the fibrillar fines, in particular, by the fines that cannot be detected with modern automated fiber characterization tools due to the limited resolution of such tools.

Finally, in the fifth paper, we suggested a multi-scale model to study hygroexpan- sion/shrinkage properties of paper. Due to the anisotropy of the fibers, the stress transfer at the bonded sites has a dominant role in the behavior of paper when exposed to moisture change. While we modeled the bonds between fibers using point-wise contact elements, such stress transfer requires a finite contact area. To solve this limitation and yet preserve the advantages for using beams for modeling fiber networks, we developed a concurrent multi-scale approach.  In this approach,  the bond model is resolved for every bond in the network, and the exchange between the network and bond model is maintained through the current configuration of the fibers being passed to the bond scale,  and the inelastic strains being transferred   back to the network scale. We demonstrated the effectiveness of such approach by comparing it with a full-scale continuum model.  Using this approach, we were able  to complete the existing experimental observation with key insights using the ad- vantage of having unlimited access to the details of the network at each stage of the deformation.

Abstract [sv]

Denna doktorsavhandling behandlar modellering av tredimensionella fiber-nätverk med finita element metoden. Dels studeras numeriska aspekter av modelleringen, framförallt formuleringen av kontakten mellan fibrer, och dels tillämpningar av de utvecklade metoderna på fundamentala frågor som effekten av spridning i fiberegenskaper, inverkan av finmaterial och hygroexpansion.

I den metod som används i avhandlingen representeras fibrer av balkelement och fogen mellan fibrer modelleras med hjälp av en punktvis balk-till-balk kontakt. Kontakt mellan balkelement är en särskild typ av kontaktproblem som introducerades av Wriggers och Zavarise 1997 för normal kontakt [1] och sedan utvidgades av Zavarise och Wriggers till att inkludera även tangentiell kontakt samt kontakt med friktionsvillkor [2]. Dessa formuleringar bygger på omfattande  härledningar som resulterar i en konsistent tangentstyvhetsmatris. I avhandlingen visas att den numeriska implementeringen av den konsistenta formuleringen inte är tillräckligt robust för att användas vid  slumpmässigt deponerade fibernätverk som innehåller ett stort antal kontakter. I de två första artiklarna i avhandlingen presenteras en enklare, icke- konsistent, formulering som visar sig ha ett mer stabilt konvergensbeteende för ett stort antal lastfall. Utöver detta är formuleringen lika exakt som den konsistenta formuleringen.  Den första artikeln behandlar formuleringen av normal och tangentiell kontakt och den andra artikeln innehåller två formuleringar med både konsistenta  och icke-konsistenta linjäriserade formuleringar för rotationskontakt mellan balkar i ett plan.

Vi använde de utvecklade formuleringarna för att studera fundamentala problem inom fibernätverk som inte kan lösas med rent experimentella metoder. I den tredje artikeln undersöks effekten av variationer i fiber- och fogstyrka på dragstyvhet och nätverksstyrka och slutsatsen kan dras att för skeva fogstyrkefördelningar leder användandet av medelvärden för fibrers och fogars styrkeegenskaper istället för hela fördelningen inte till en representativ beskrivning av nätverket.

I den fjärde artikeln undersöks mekanismerna bakom förbättringar i styvhet och styrka efter PFI-malning, vilket är en vanlig metod för att studera effekterna av malning på laboratorieskala. Genom användning av en kombination av experimentella och numeriska metoder fanns att en ökning i densitet, som ofta beskrivs som en av de huvudsakliga anledningarna bakom förbättringar av de mekaniska egenskaper efter PFI-malning, inte ensamt kan förklara de förändringar som observeras experimentellt. Slutsatsen är därför att den återstående delen av förbättringen orsakas av finmaterial, särskilt sådant som inte kan upptäckas med hjälp av moderna automatiska fiberkaraktäriseringsverktyg på grund av dessas begränsade upplösning.

Slutligen, i den femte artikeln, presenteras en flerskalig modell för att studera hygro- expansion och krympningsegenskaper hos papper. På grund av fibrernas anisotropi har spänningsöverföringen i fiberfogarna en dominerande inverkan på pappersegenskaper när det utsätts för fuktförändringar. Vi modellerade fogarna mellan fibrer med hjälp av punktkontakter, men i själva verket krävs en finit kontaktarea för att korrekt beskriva spänningsöverföringen mellan fibrerna. För att överkomma denna begränsning och samtidigt bevara fördelarna med att använda balkelement utvecklades en flerskalig modell. I denna modell beskrivs varje kontakt i nätverket explicit. Via den aktuella fiberkonfigurationen överförs information till kontaktmodellen och denna  i sin tur återför de inelastiska töjningarna till nätverkssimuleringen. Effektiviteten i en sådan modell demonstreras genom jämförelser med en fullskalig kontinuummodell. Med hjälp av den flerskaliga modellen kunde befintliga experimentella observationer kompletteras med nya insikter tack vare den obegränsade tillgången till detaljer i nätverket i varje steg av deformationsanalysen.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 19
Series
TRITA-SCI-FOU ; 2018:06
Keywords
fiber network, beam-to-beam contact, rotational contact, non-consistent, simulation, finite element, multiscale, microscale, micromechanics, paper, refining, beating, fine, hygroexpansion, shrinkage, drying
National Category
Applied Mechanics Other Mechanical Engineering Paper, Pulp and Fiber Technology
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:kth:diva-223233 (URN)978-91-7729-684-3 (ISBN)
Public defence
2018-03-09, F3, Lindstedtsvägen 26, KTH, 10:00 (English)
Opponent
Supervisors
Note

QC 20180219

Available from: 2018-02-15 Created: 2018-02-15 Last updated: 2019-01-10Bibliographically approved

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