| 1. |
- Brandberg, August, 1990-, et al.
(författare)
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Characterization and impact of fiber size variability on the mechanical properties of fiber networks with an application to paper materials
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Cellulose fibers exhibit a wide range of shapes and sizes. This variation influences the mechanical performance of paper and paperboard by affecting the stress distribution inside the network and the degree of fiber-to-fiber bonding which is possible at a given density. However, the methods used to characterize the distribution of fiber sizes in the pulp neglect that the characteristic features of a fiber are generally not independent. Here, we resolve this shortcoming by fitting the fiber population to a multivariate distribution without enforcing normality or independence between the properties. The high-dimensional multivariate function is recast as a set of univariate distribution functions and a series of bivariate distributions connected by a canonical vine. Using a micro-mechanical model of a paper sheet the influence of this improved characterization is investigated. Reasonable margins and a description of the dependency is shown to be superior to assuming independence even for perfectly preserved marginal distributions. This result demonstrates that micro-mechanical models of paper and paperboard cannot by assumption neglect the influence of the interdependence between the characteristic features of fibers.
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| 2. |
- Brandberg, August, 1990-, et al.
(författare)
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Characterization and impact of fiber size variability on the mechanical properties of fiber networks with an application to paper materials
- 2022
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 239-240
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Tidskriftsartikel (refereegranskat)abstract
- Cellulose fibers come in a wide range of shapes and sizes. The heterogeneity of the fiber length, width, wall thickness, curl and external fibrillation is detrimental to the mechanical performance of products such as paper and paperboard. Although micro-mechanical models of these materials sometimes incorporate features of this heterogeneity, so far there is no standardized method of fully incorporating this. We examine a large number of industrial mechanical fiber pulps to determine what information such a standardized method would have to have. We find that the method must allow for both non-Gaussian distributions and dependence between the variables. We present a method of characterizing mechanical pulp under these conditions that views the individual fiber as outcome of a sampling process from a multivariate distribution function. The method is generally applicable to any dataset, even a non-Gaussian one with dependencies. Using a micro-mechanical model of a paper sheet the proposed method is compared with previously presented methods to study whether incorporating both a varying fiber size and dependencies is necessary to match the response of a sheet modeled with measured characterization data. The results demonstrate that micro-mechanical models of paper and paperboard should not neglect the influence of the dependence between the characteristic shape features of the fibers if the model is meant to match physical experiments. © 2022 The Authors
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| 3. |
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| 4. |
- Brandberg, August, 1990-, et al.
(författare)
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Compression failure in dense non-woven fiber networks
- 2020
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Ingår i: Cellulose. - : Springer Science and Business Media LLC. - 0969-0239 .- 1572-882X. ; 27:10, s. 6065-6082
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Tidskriftsartikel (refereegranskat)abstract
- Investigating the compression properties of randomly ordered fiber networks experimentally is difficult which has resulted in ongoing disputes as to the mechanisms controlling the compression strength in such materials. In this work, we investigated compression properties of randomly oriented fiber networks with a special emphasis on cellulose products such as paperboard. We numerically reconstructed the conditions of the short span compression test widely used to quantify the compression strength of paperboard. We found that the phenomenological failure mode of such networks is elasto-plastic buckling. The x-shaped failure mode observed in physical experiments appears when test specimen restraints are included in the model. The most significant improvements to sheet strength can be obtained by improving the elastic properties while the strain to failure is increased most by an improvement of the plastic yield and hardening properties of individual fibers. Bond breaks were confirmed to have a smaller influence on the overall response. Fiber level microscopic buckling was investigated in depth, providing quantitative estimates of the fraction of mass likely to buckle at the microscopic level. The analysis indicated that only a low to moderate number of load carrying fibers can be expected to buckle. The inherent strength reserve in non-ordered fiber networks was investigated by introducing hinge mechanisms throughout the network, and the effect was shown to be small for a small to moderate number of hinges.
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| 5. |
- Brandberg, August, 1990-
(författare)
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Insights in paper and paperboard performance by fiber network micromechanics
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Fiber networks are ubiquitous due to their low cost and high ratio of mechanical performance to weight. Fiber networks made of cellulose fibers from trees are used as information carriers (paper) and as packaging (board). Often the ideal product is both mechanically sturdy and possible to print on. This thesis investigates the underlying reasons for the mechanical performance of paper and board through the discretization and direct simulation of every fiber in the network.In Paper A the effect of fiber-fiber bond geometry on sheet stiffness is investigated. Many packaging products seek to maximize the bending stiffness by employing stiff outer layers and a bulkier layer in the middle. In bulky sheets, the fibers are frequently uncollapsed resulting in a more compliant bonded segment. Because all the loads in the network are transferred via the bonds, such compliance can cause unexpectedly large decreases in mechanical performance. Although many models have been presented which aim to predict the tensile stiffness of a sheet, these predictions tend to overestimate the resulting stiffness. One reason is that the bonds are generally considered rigid. By finite element simulations, we demonstrated the effect of the lumina configuration on the stiffness of the bonded segment on the scale of single fiber-to-fiber bonds, and that the average state of the fiber lumen has a marked effect on the macroscopic response of fiber networks when the network is bulky, has few bonds, or has a low grammage.Compression strength is central in many industrial applications. In paper B we recreated the short span compression test in a simulation setting. The networks considered are fully three-dimensional and have a grammage of 80 to 400 gsm, which is the industrially relevant range. By modeling compression strength at the level of individual fibers and bonds, we showed that fiber level buckling or bifurcation phenomena are unlikely to appear at the loads at which the macroscopic sheet fails.In paper C, we developed a micromechanical model to study the creation of curl in paper sheets subjected to a moisture gradient through the sheet. A moisture gradient is always created during the printing process, which may lead to out-of-plane dimensional instability. We showed that the swelling anisotropy of individual fibers bonded at non-parallel angles causes an additional contribution to the curl observed on the sheet level.
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| 6. |
- Brandberg, August, 1990-
(författare)
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Micro-mechanical characterization and modeling of paper and paperboard
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Fiber networks made of cellulose fibers from trees are used as information carriers (paper) and as packaging (paperboard). This thesis investigates the mechanical performance of paper and paperboard via micro-mechanical modeling and presents new methods for the mechanical characterization of the micro scale, necessary in such models. In Paper A the effect of the fiber-fiber bond geometry on the sheet stiffness is investigated. In thick, low density sheets, the fiber lumen remains open resulting in a more compliant bonded segment. By finite element simulations, we demonstrate the effect of the lumen configuration on the stiffness of the bonded segment. Most important for the stiffness of the segment is the average state of the fiber lumen which has a marked effect on the macroscopic response of fiber networks when the network is sparse. Compression strength is central in many industrial applications. In Paper B we recreated the short span compression test in a simulation setting. The networks considered are three-dimensional and have a grammage of 80--400 gm^-2. By modeling compression strength at the level of individual fibers and bonds, we show that widespread fiber level buckling is unlikely to appear at the loads at which the macroscopic sheet fails. In Paper C we develop a micro-mechanical model to study the creation of curl in paper sheets subjected to a moisture gradient through the thickness of a sheet. A moisture gradient is created during the printing process if the ink is water based, which may lead to out-of-plane deformations (curl). The effect of transverse fiber shrinkage is captured using a multiscale model where the fiber-fiber bond is modeled with volume elements. We show how the swelling anisotropy of individual fibers contributes to the curl of the sheet in such settings. In Paper D we present how to uniquely and compactly describe the distribution of fiber shapes (length, width, wall thickness, curl) used in network simulations. Using a canonical vine structure, fiber shapes measured using an optical image analyzer are used to construct a multivariate distribution function. New fiber geometries can then be generated by sampling from this distribution. Having access to such a complete description with both the distribution of fiber properties and the dependence between properties is shown to be superior to previously presented methods using micro-mechanical simulations of thermo-mechanical (TMP) long fiber sheets. In Paper E we compare sheet testing, micro-mechanical tensile testing, and nanoindentation as methods to extract the elastic material properties of individual pulp fibers. Nanoindentations are performed parallel to and orthogonal to the axis of the fiber after it has gone through all steps of papermaking, and indentation moduli are extracted. By relating the indentation modulus to the components of the anisotropic stiffness tensor, the longitudinal and transverse elastic modulus can be determined via an iterative error minimization scheme. We show that nanoindentation is an alternative to traditional methods with the advantage of yielding the transverse modulus and enabling measurement of the fiber properties after papermaking.
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| 7. |
- Brandberg, August, 1990-, et al.
(författare)
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The effect of geometry changes on the mechanical stiffness of fibre-fibre bonds
- 2017
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Ingår i: Transactions of the 16th Fundamental Research Symposium Held in Oxford: September 2017. - Manchester : Pulp & Paper Fundamental Research Society. - 0992616336 - 9780992616335 ; , s. 683-719
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Konferensbidrag (refereegranskat)abstract
- In this work, we discuss the effect of geometry on the compliance of the fibre bond regions against normal and tangent loads. Since the fibre bonds play a key role in defining the paper strength, the compliance of the bond regions can affect the amount of elastic energy stored in the bonds and thus change not only the strength but also the stiffness of paper products under certain conditions. Using finite element simulation tools, we overcome the major difficulty of performing controlled mechanical testing of the isolated bond region and reveal the key geometrical factors affecting the compliance of the bond region. Specifically, we show that the compliance of the fiber-fiber bond is strongly governed by its geometric configuration after pressing. Among the strongest factors is the collapse of the lumen and the crossing angle. Using the range of obtained stiffness values, we demonstrated the effect the bond stiffness has on the stiffness of the network using fiber-level simulation tools. We show how the dependence of tangent bond stiffness on fiber-to-fiber angle further softens the more compliance cross-machine direction.
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| 8. |
- Brandberg, August, 1990-, et al.
(författare)
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The Role of the Fiber and the Bond in the Hygroexpansion and Curl of Thin Freely Dried Paper Sheets
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the network, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles.
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| 9. |
- Ceccato, Chiara, Professor, et al.
(författare)
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Micro-mechanical modeling of the paper compaction process
- 2021
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Ingår i: Acta Mechanica. - : Springer Nature. - 0001-5970 .- 1619-6937. ; 232:9, s. 3701-3722
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Tidskriftsartikel (refereegranskat)abstract
- Double-roll compaction is a process to create extensible paper and paperboard suitable for replacing plastic in 3D forming applications. Understanding the macro- and micro-mechanisms governing the compaction process allows increasing the stretch potential while maintaining sufficient strength and bending stiffness. In this work, we approach the compaction process of paperboard with micro-mechanical methods featuring the unprecedented level of details otherwise inaccessible with currently available experimental tools. The loading scheme is based on experiments and continuum level simulations. The different levels of compaction and their continuous impact on the fibers’ geometry, void closures, and irreversible deformation of the fibers are thoroughly characterized. We find that the structural changes are concentrated in the fibers oriented within 30 degrees of the direction of compaction. The deformation accumulates primarily in the wall of the fibers in the form of irreversible strains. The spring-back effect beyond the compaction is negligible. For the first time, the role of normal and frictional fiber-to-fiber interactions in the compaction process is investigated and quantified. The frictional interaction between the fibers has a surprisingly low impact on the outcome of the compaction process, and the normal interaction between the fibers has a dominant response. The consequence of this finding is potentially limited impact of the surface modifications targeting the friction.
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| 10. |
- Czibula, Caterina, et al.
(författare)
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The transverse and longitudinal elastic constants of pulp fibers in paper sheets
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Cellulose fibers are a major industrial input, but due to their irregular shape and anisotropic material response, accurate material characterization is difficult. Single fiber tensile testing is the most popular way to estimate the material properties of individual fibers. However, such tests only determine the longitudinal modulus of the fiber. Here, we compare sheet testing, micromechanical testing, and nanoindentation as methods to extract the elastic material properties of the individual fibers. We show that nanoindentation can be used to determine both the longitudinal and the transverse elastic modulus using only two indentations, additionally enabling the measurement of fiber properties in-situ inside a sheet of paper where the complete process history is captured. For the longitudinal modulus, the accuracy is comparable for larger indents, but with an increase of scatter of unknown origin as the probe size is decreased using an atomic force microscopy tip.
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