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Pulp refining is an essential process step prior to paper production. The contribution of fines production during refining to the resulting paper strength so far has mostly been considered qualitatively. A quantitative and experimental evaluation regarding their effect has not yet been published. Unbleached softwood kraft pulp was refined using a PFI mill and a disc refiner at different refining intensities. Prior to handsheet forming, fines were removed in a lab scale pressure screen from one part of the refined and unrefined samples in order to investigate the difference in tensile strength between sheets with and without fines, which were furthermore produced with and without additional wet pressing. It was found, that fines formed in a disc refiner at 250 kWh/t are responsible for up to 25% of the breaking length increase, while the PFI mill at 10,000 revolutions fines only contribute to a maximum of 12%. In terms of fines efficiency, the disc refiner was able to achieve higher results compared to the PFI mill, which however might be attributed to the higher fibre flexibilization in the PFI mill. Thus fines formed in the refining process are of high importance for strength development especially for the disc refiner.

This study addresses the question of how the difference in mechanical properties of the individual layers in a multi-ply commercial paperboard affects the outcome of the tray-forming operation. Two commercially produced paperboards with nearly identical mechanical properties when conventionally tensile tested were considered. These boards are produced on different machines with the same target grammage and density. Despite the similar mechanical properties, their performance in a given tray-forming operation was drastically different, with one of the boards showing an unacceptable failure rate. To investigate the difference seen during converting operations, a detailed multi-ply finite element model was built to simulate the converting operation. The present model considers a critical area of the paperboard known to exhibit failures. To derive the constitutive relations for each ply in the sub-model, both boards were split to single out individual plies which were then tensile tested. Including the properties of individual plies revealed large differences between the boards when it comes to the distribution of the properties in the thickness direction. In particular, the top plies differed to a large extent. This is attributed to the difference in refining energies for the plies. The results from the three-ply sub-model demonstrated the importance of including the multi-ply structure in the analysis. Weakening of the top ply facing the punch by using lower refining energy considerably increased the risk of failure of the entire board. These results suggest that there is room for optimizing the board performance by adjusting the refining energy at the ply level. Graphical 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.

Nordic pulp & paper research journal 36(3), 491 - 502 (2021). doi:10.1515/npprj-2020-0092, Large deformations under in-plane compression of paperboard appear in forming processes like hydroforming, pressforming and deep drawing, but the mechanisms of deformation have not been studied on a micromechanical level. A constrained in-plane compression test is presented. This test allows for in-plane compression, buckling, wrinkling and compaction. The constrained compression test is realized using a DEBEN CT-500 in-situ tester for laboratory microtomography and synchrotron microtomography. Experiments with five different materials spanning from laboratory handsheets to commercially available multi-layered paperboards are performed. Image processing is used to observe the local out-of-plane fiber orientation and compaction. A phenomenological investigation of the deformation behavior of these materials is presented. Delamination is found to be the primary mechanisms of failure in the multi-layered boards. Furthermore, a porous network structure, created by using long and minimally refined softwood fibers, is found to facilitate the formation of uniform wrinkles and compaction., Published by Walter de Gruyter GmbH, Boston

This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration me...

The anisotropic properties and pressure sensitivity are intrinsic features of the constitutive response of fiber network materials. Although advanced models have been developed to simulate the complex response of fibrous materials, the lack of comparative studies may lead to a dubiety regarding the selection of a suitable method. In this study, the pressure-sensitive Hoffman yield criterion and the Xia model are implemented for the plane stress case to simulate the mechanical response under a bi-axial loading state. The performance of both models is experimentally assessed by comparison to bi-axial tests on cruciform-shaped specimens loaded in different directions with respect to the material principal directions. The comparison with the experimentally measured forces shows the ability of the Hoffman model as well as the Xia model with shape parameter k ≤ 2 to adequately predict the material response. However, this study demonstrates that the Xia model consistently presents a stiffer bi-axial response when k ≥ 3 compared to the Hoffman model. This result highlights the importance of calibrating the shape parameter k for the Xia model using a bi-axial test, which can be a cumbersome task. Also, for the same tension-compression response, the Hill criterion as a special case of the Hoffman model presents a good ability to simulate the mechanical response of the material for bi-axial conditions. Furthermore, in terms of stability criteria, the Xia model is unconditionally convex while the convexity of the Hoffman model is a function of the orthotropic plastic matrix. This study not only assesses the prediction capabilities of the two models, but also gives an insight into the selection of an appropriate constitutive model for material characterization and simulation of fibrous materials. The UMAT implementations of both models which are not available in commercial software and the calibration tool of the Xia model are shared with open-source along with this work.

The influence of strain during drying is known to have a large effect on its mechanical properties like tensile strength, Young’s modulus and hygroexpansion. In this study we investigate free and restrained dried paper and investigate the relation between the paper microstructure and its mechanical properties. The first part of the work investigates the development of the mechanical properties as well as paper internal stresses and strains (elastic-, inelastic- and hygrostrain) at different moisture contents during the drying process. Emphasis is put on the changes of hygrostrains and the paper hygroexpansion coefficient during drying. One main finding was that in constrained drying the drying stresses are considerably below the yield stress and, as a consequence, the deformations are mainly inelastic (creep) and only marginally elastic. In the second part we are analyzing the microstructure of free and restrained dried sheets by X-ray microtomography ($$\mu$$μ-CT). From the$$\mu$$μ-CT analysis relevant network parameters such as number of contact points, fiber bond area, free fiber length and fiber curl were extracted. Also a novel method to investigate the interface angle of the fibers in the vicinity of the bond sites was established. The results showed that the major difference from the drying procedure manifests itself in the out-of-plane curl of the fibers. Statistically number of contact points, bond area and in-plane curl were not different whereas in-plane curl and free fiber length were different. The interface angle appears to be slightly affected by the drying procedure but is overall very low.

The tensile tests of individual bleached softwood kraft pulp fibers and sheets, as well as the micro-mechanical simulation of the fiber network, suggest that only a part of the elongation potential of individual fibers is utilized in the elongation of the sheet. The stress-strain curves of two actual individual pulp fibers and one mimicked classic stress-strain behavior of fiber were applied to a micromechanical simulation of random fiber networks. Both the experimental results and the micromechanical simulations indicated that fiber bonding has an important role not only in determining the strength but also the elongation of fiber networks. Additionally, the results indicate that the shape of the stress-strain curve of individual pulp fibers may have a significant influence on the shape of the stress-strain curve of a paper sheet. A large increase in elongation and strength of paper can be reached only by strength-ening fiber-fiber bonding, as demonstrated by the experimental handsheets containing starch and cellulose microfi-brils and by the micromechanical simulations. The key conclusion related to this investigation was that simulated uniform inter-fiber bond strength does not influence the shape of the stress-strain curve of the fiber network until the bonds fail, whereas the number of bonds has an influence on the activation of the fiber network and on the shape of the whole stress-strain curve.

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 can only be performed along the axis of the fiber and are associated with problems of enforcing restraints. Alternative indirect approaches, such as micro-mechanical modeling, can help but yield results that are not fully decoupled from the model assumptions. Here, we compare these methods with nanoindentation as a method to extract elastic material constants of the individual fibers. We show that both the longitudinal and the transverse elastic modulus can be determined, additionally enabling the measurement of fiber properties in-situ inside a sheet of paper such that the entire industrial process history is captured. The obtained longitudinal modulus is comparable to traditional methods for larger indents but with a strongly increased scatter as the size of the indentation is decreased further.

This paper presents and experimentally validates an augmented Kalman filter extended with a fixed-lag smoother for solving joint state and input estimation problems. Sparse acceleration measurements from a truck side skirt excited by road-induced vibrations from a vibration test track are analysed. The system model is obtained experimentally from an operational modal analysis, reducing modelling errors and avoiding the need for a finite element model and it serves itself as a numerical model. The motion of the truck component is estimated and the results are compared to those of a joint input-state estimation filtering algorithm, in addition to the actual measured motion. Both algorithms are tuned according to a novel process based on minimal a priori information concerning the system states and inputs. The focus of this work is to assess the robustness, performance, and tuning of the algorithms. Two sensor configurations are studied: one where the number of response measurement sensors is high compared to the number of estimated motions and participating modes, and another where the number of response measurements is reduced. Both algorithms perform very well within the first configuration. With a reduced number of response measurements, the fixed-lag smoother is superior to the joint input-state filter in capturing the individual motion of each position on the side skirt.

A number of problems associated with dimensional stability of paper products have to do with hygroexpansion in response to changes in humidity or moisture content. The main underlying mechanism of hygroexpansion in paper is the effect of the change of fiber cross-sections transferred through fiber bonds. In fact, the transverse expansion of fibers can be an order of magnitude greater than the longitudinal expansion. Addressing such problems using modeling on the microscale is associated with large computational costs since both the bonds and the fibers need to be resolved. We present a method for modeling the hygro or thermal expansion of interconnected fiber networks modeled with beam elements and connected through beam-to-beam contact. Being a line structure, beams can only support pointwise contact, which poses a challenge for modeling the force transfer induced by the deformation of the cross-sections at the contact point. The idea of implementing the stress transfer is to use a concurrent multiscale approach in which the bond level is resolved in detail using the configuration of the fibers and the computed strains are passed over to the beam elements. We verify and prove the applicability of this approach by comparing it with continuum models. We demonstrate the advantage of using this approach in terms of its tremendous saving in time. The use of beam models for modeling the hygro- or thermal expansion of fiber networks enables considering relevant sizes in the problems involving dimensional stability, in particular those associated with embedded inhomogeneities. We will show the applicability of the model by providing insights into published experimental observations on the hygroexpansion properties of paper products. Finally, we will demonstrate that the use of a 2D model to simulate the inter-fiber bonds in a network, not only leads to underestimation of out-of-plane deformations, but also to overestimation of the contribution of the transverse deformation of fibers to the in-plane dimensional change of the network.

Refining (i.e., mechanical beating of pulp) is a common procedure that is used in paper-making to improve the mechanical properties of the final product. The improvements caused by refining are mainly attributed to increased density and to a better bonding between fibers. In this work, we study how various mechanisms that can be triggered by refining affect the tensile behavior of the sheets. Consequently, we use direct numerical simulations of fiber networks. We relate our finding to the experimental measurements that we conducted on handsheets. We have found that fibrillar fines with size distributions below the resolution of modern state-of-the art pulp characterization tools have a substantial contribution to the increased strength and stiffness of the sheets.

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.

The stochastic variations in the structural properties of thin fiber networks govern to a great extent their mechanical performance. To assess the influence of local structural variability on the local strain and mechanical response of the network, we propose a multiscale approach combining modeling, numerical simulation and experimental measurements. Based on micro-mechanical fiber network simulations, a continuum model describing the response at the mesoscale level is first developed. Experimentally measured spatial fields of thickness, density, fiber orientation and anisotropy are thereafter used as input to a macroscale finite-element model. The latter is used to simulate the impact of spatial variability of each of the studied structural properties. In addition, this work brings novelty by including the influence of the drying condition during the production process on the fiber properties. The proposed approach is experimentally validated by comparison to measured strain fields and uniaxial responses. The results suggest that the spatial variability in density presents the highest impact on the local strain field followed by thickness and fiber orientation. Meanwhile, for the mechanical response, the fiber orientation angle with respect to the drying restraints is the key influencer and its contribution to the anisotropy of the mechanical properties is greater than the contribution of the fiber anisotropy developed during the fiber sheet-making., 12 pages, 14 figures

To model fiber failures in random fiber networks, we have developed an elastoplastic Timoshenko beam finite element with embedded discontinuities. The method is based on the theory of strong discontinuities where the generalized displacement field is enhanced by a jump. The continuum mechanics formulation accounts for a fracture process zone and a bulk material while retaining traction continuity across the discontinuity. The additional degrees of freedom that are associated with the discontinuity are represented by a midpoint node, which is statically condensed to enable the implementation in commercial software through the user element interface . We propose a quasi-brittle fracture model, where the failure-related deformation is uncoupled from the plastic deformation in the bulk material. To retain the positive definite finite element stiffness matrix of the bulk material, we neglect the fracture-related softening of the discontinuity and employ a modified Newton iteration in the strain softening domain. Our implementation facilitates the integration into commercial finite element software and examples illustrate the robustness of the method. The FORTRAN source code is freely available to benchmark our model. We show that fiber failures contribute to the nonlinear stress–strain response of paper. Together with fiber–fiber bond failures, they can potentially explain the nonlinear stress–strain response of paper and nanopaper.

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

We investigate the suitability of three-dimensional Voronoi structures in representing a large strain macroscopic compressive response of nanofibrillar cellulose foams and understanding the connection between the features of the response and details of the microstructure. We utilise Lloyd’s algorithm to generate centroidal tessellations to relax the Voronoi structures and have reduced polydispersity. We begin by validating these structures against simulations of structures recreated from microtomography scans. We show that by controlling the cell face curvature, it is possible to match the compressive response for a 96.02 % porous structure. For the structures of higher porosity (98.41 %), the compressive response can only be matched up to strain levels of 0.4 with the densification stresses being overestimated. We then ascertain the representative volume element (RVE) size based on the measures of relative elastic modulus and relative yield strength. The effects of cell face curvature and partially closed cells on the elastic modulus and plateau stress is then estimated. Finally, the large strain response is compared against the two-dimensional Voronoi model and available experimental data for NFC foams. The results show that compared to the two-dimensional model, the three-dimensional analysis provides a stiffer response at a given porosity due to earlier self-contact.

High-porosity, three-dimensional wood fiber networks made by foam forming present experimentally accessible instances of hierarchically structured, athermal fiber networks. We investigate the large deformation compression behavior of these networks using fiber-resolved finite element analyses to elucidate the role of microstructures in the mechanical response to compression. Three-dimensional network structures are acquired using micro-computed tomography and subsequent skeletonization into a Euclidean graph representation. By using a fitting procedure to the geometrical graph data, we are able to identify nine independent statistical parameters needed for the regeneration of artificial networks with the observed statistics. The compression response of these artificially generated networks and the physical network is then investigated using implicit finite element analysis. A direct comparison of the simulation results from the reconstructed and artificial network reveals remarkable differences already in the elastic region. These can neither be fully explained by density scaling, the size effect nor the boundary conditions. The only factor which provides the consistent explanation of the observed difference is the density and fiber orientation nonuniformities; these contribute to strain-localization so that the network becomes more compliant than expected for statistically uniform microstructures. We also demonstrate that the experimentally manifested strain-stiffening of such networks is due to development of new inter-fiber contacts during compression.

The reactor pressure vessel (RPV) of a nuclear reactor is one of the key safety barriers preventing radioactive environmental releases during a severe accident. One of the promising strategies of severe accident management (SAM) is to retain the molten core having continuous decay heat inside the RPV by natural water cooling of the external vessel surface. The feasibility of such a strategy relies on complex safety analyses including accurate prediction of vessel thermo-mechanical behavior which can be assessed by mechanical stresses and strains. In this paper, we present the stress–strain response of an ablated RPV of a Nordic boiling water reactor (BWR) to dynamic thermomechanical loads set by expanding volumetrically heated molten pool inside the RPV cooled by water at the external surface. MELCOR 2.2.9541 severe accident code is used to simulate the in-vessel behavior and provides the input conditions for dedicated structural analysis of the RPV using ANSYS® Mechanical APDL 19.2. A creep model of the SA533B1 vessel steel is validated against uniaxial creep tests carried out by INEL (Idaho National Engineering Laboratory) and creep tests performed at CEA (French Alternative Energies and Atomic Energy Commission) as part of the OLHF (OECD Lower Head Failure) Project. Two generic severe accident scenarios are considered: (i) Station Blackout (SBO) and (ii) Station Black-out and Loss-of-coolant Accident (SBO + LOCA). In both scenarios, we found that the RPV has maintained structural integrity considering two failure criteria: stress-based and strain-based.

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.

The possibility of predicting the fatigue life of vehicle components based on sparse in-service vibration measurements enables an optimization of the maintenance and utilization of a vehicle fleet. This paper presents a novel methodology for fatigue damage prediction based on strain fields estimated from sparse vibration measurements on a dynamic structure together with a finite element model. The strain is estimated with a fixed-lag Kalman smoother, which is based on a state-space model derived from a modal description of the finite element model. The methodology is demonstrated with a full-scale laboratory experiment of a vehicle component subjected to road- induced vibrations where both strains and accelerations were measured. Fatigue damage is computed from the estimated strains, and verification of the accuracy of the predicted damage showed good results. The proposed methodology was then followed when the outcome of a full-scale vibration fatigue rig test of the component was predicted. The computed damage predicted the same failure locations as the ones which occurred during the rig test. The good correlation between the numerically computed damage and the outcome of the fatigue rig test indicates that the methodology presented in this paper has a high potential in predicting fatigue damage.

Good runnability of paper web is an important factor for improving performance of printing process. Printing nips cause web tension variations which are known to affect web runnability. However, ra ...

The tensile response of dense fiber-based materials like paper or paperboard is mainly dependent of the properties of the fibers, which store most of the elastic energy. In this paper, we investigate the influence of geometrical and material parameters on the mechanical response of the pulp fibers used in paper manufacturing. We developed a three-dimensional finite element model of the fiber, which accounts for microfibril orientation of cellulose fibril, and the presence of lignin in the secondary cell wall. The results showed that the change in the microfibril orientation upon axial straining is mainly a geometrical effect, and is independent of the material properties of the fiber, as long as the deformations are elastic. Plastic strain accelerates the change in microfibril orientation and thus makes it material-dependent. The results also showed that the elastic modulus of the fiber has a non-linear dependency on microfibril angle, with elastic modulus being more sensitive to the change of microfibril angle around small initial values of microfibril angles. Based on numerical results acquired from a 3D fiber model supported by available experimental evidence, we propose an anisotropic-kinematic hardening plasticity model for a fiber within a beam framework. The proposed fiber model is capable of reproducing the main features of the cyclic tensile response of a pulp fiber, such as stiffening due to changing microfibril angle. The constitutive model of the fiber was implemented in a finite-element model of the fiber network. By using the fiber network model, we estimated the level of strain that fiber segments accumulate before the typical failure strain of the entire network is reached.

With the goal of partial or complete replacement of plastic components with paper-based products, 3D paper structures have seen a growing interest in industrial applications: from packaging to more complex daily life objects. However, the extensibility of paper has become a key issue within this context and is the main factor determining the formability of these products and determining the depth of the achievable shapes. The most effective way to increase paper’s stretch potential is by subjecting the moist paper web to a compaction process, which can be achieved through an extensible unit that is located in the drying section of a paper machine, where the network experiences in-plane compression in the machine direction (MD), under out-of-plane lateral constraints. The objective of this work is to clarify the mechanisms governing the compression process and to evaluate the influence of various parameters on the final material properties to optimize the industrial production of extensible paper. The system operation has been simulated realistically and shows that paper experiences a compressive state passing through the nip, with plastic strains in MD direction being of the same order of the applied speed difference, which was expected experimentally in optimal conditions of compaction. Starting from an initial reference case, a sensitivity study has been performed to identify and address the following factors that may affect the compression state: (a) friction coefficients; (b) indentation level; (c) speed difference; and (d) rubber properties. The analysis of the numerical results gives an insight into the mechanisms governing the compaction operations and allows a better comprehension of the features controlling the process outcome.

There is a growing interest in applications for nanofibrillated cellulose based materials owing to their exceptional mechanical properties. Nanofibrillated cellulose (NFC) foam is one such derivative which has potential applications in a wide array of fields. Here, we characterise the mechanical properties of two particular high porosity NFC foams (98.13 and 98.96 %) prepared by a freeze drying process. We evaluate their behaviour in uni-axial and bi-axial compression with cyclic loading. The secondary loading cycles reveal complete irreversible damage of the microstructure, with the secondary loading path being characterised by near zero plateau stress. In force controlled tests, negligible hysteresis corroborates the idea that there is no energy dissipation owing to near complete microstructural damage. Furthermore, we observe no indications of preferential orientation of the microstructure in these tests. The stress responses in mutually perpendicular directions are seen to be identical, within statistical considerations. We then utilise the “pseudo-elastic” model developed and adopt it to the case of highly compressible Ogden strain energy formulation with a modified neo-Hookean for the unloading, with a view of fitting a continuum hyperelastic model to the experimental data. The material parameters obtained from uni-axial data are seen to be insufficient to describe the more general bi-axial deformation. The parameters obtained from the bi-axial test describe uni-axial deformation up to stretches of ~0.5 but overestimate the stress levels beyond that point.

Nano Fibrillar Cellulose (NFC) is fast emerging as a biomaterial with promising applications, one of which is cellular foam. The inner structure of the foam can take various shapes and hierarchical ...

We apply image analysis methods based on micro-computed tomography (μCT) to extract the parameters that characterize the structure and bonding parameters in the fiber network of paper. The scaling and variational properties of μCT images are examined by analyzing paper structural properties of two 1 × 1 mm2 test pieces, which have been cut out from a low-grammage handsheet. We demonstrate the applicability of the methods for extracting the free fiber length, fiber cross-sectional data, the distances between the fibers, and the number of fiber-to-fiber bonds, which are the key properties required for the adequate representation of the network in numerical models. We compare the extracted connectivity data with the early reported analytical estimations and conclude that the number of contacts in three-dimensional networks is controlled by the fiber aspect ratio. In addition, we compare the cross-sectional data with those measured by the fiber morphology characterization tools and estimate the fiber shrinkage from completely wet to dry state to be nearly 20%. QC 20160613

A finite element model for 3D random fiber networks was constructed to simulate deformation and failure behavior of networks with dynamic bonding/debonding properties. Such fiber networks are ubiquitous among many living systems, soft matters, bio-materials, and engineering materials (papers and non-woven). A key feature of this new network model is the fiber–fiber interaction model that is based on AFM measurements from our earlier study. A series of simulations have been performed to investigate strain localization behavior, strength statistics, in particular, the variations of strength, strain-to-failure and elastic modulus, and their size dependence. Other variables investigated are fiber geometries. The result showed that, in spite of its disordered structure, strength and elastic modulus of a fiber network varied very little statistically, as long as the average number of fibers in the simulated specimen and the degree of fiber orientation are kept constant. However, strain-to-failure showed very significant statistical variations, and thus more sensitivity to the disordered structures.

We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

Nanopaper is a transparent film made of network-forming nanocellulose fibers. These fibers are several micrometers long with a diameter of 4–50 nm. The reported elastic modulus of nanopaper often falls short of even conservative theoretical predictions based on the modulus of crystalline cellulose, although such predictions usually perform well for other fiber composite materials. We investigate this inconsistency and suggest explanations by identifying the critical factors affecting the stiffness of nanopaper. A similar inconsistency is found when predicting the stiffness of conventional paper, and it is usually explained by the effects introduced during drying. We found that the effect of the drying cannot solely explain the relatively low elastic modulus of nanopaper. Among the factors that showed the most influence are the presence of non-crystalline regions along the length of the nanofibers, initial strains and the three-dimensional structure of individual bonds.

Interfiber friction in paper exists in fiber suspensions, fiber flocs, and fiber networks. The interfiber friction force is, therefore, important both in papermaking and in the use of paper. The objective of this research is to develop a methodology using atomic force microscopy (AFM) for the direct measurement of the friction force between pulp fibers. Different factors such as AFM scanning velocity, contact area, and fiber surface roughness were investigated. The results show that AFM is an effective tool for measuring micro-scale interfiber friction forces. Both AFM scanning velocity and fiber surface roughness affect the measured results. The coefficient of friction increases, but the initial adhesion force decreases, with increasing fiber surface roughness.

Paper is a composite of fibers, air and additives where the fiber/fiber joints keep the network structure together. A study was undertaken to establish the link between the properties of the contact zone between fibers and paper performance under mechanical loading. The contact zone between fibers was investigated using light microscopy. A staining technique was developed for evaluating the influence of surface charge on fiber/fiber joint strength. The joint strength was linearly correlated with paper tensile strength and with the average amplitude of the acoustic events measured by acoustic emission testing. The fiber surface conformability was improved by changing the surface charge. This resulted in increased fiber/fiber joint strength as the relative contact area became larger. Increasing the molecular adhesion in the contact zone with the aid of strength additives also improved the fiber/fiber joint strength.

Fiber/fiber joints were analyzed using finite element analysis in order to characterize the influence of fiber and contact region properties on the stress— strain behavior of a single fiber/fiber cross. The output of the models was validated by comparison with experimental load—deformation curves. The contact zone of the fiber/fiber joint was studied with respect to the appearance of the contact zone, the contact area, and the contact pattern; the work of adhesion of the contact areas was also considered. It was shown that the two-dimensional appearance of the contact zone had little influence on the stress—strain behavior of the fiber/fiber cross under tensile loading. The maximum stress and hence the fiber/fiber joint strength was, however, affected by the degree of contact. It was concluded that knowledge of the material behavior of the contact zone (such as local plastic behavior), and of chemical effects (such as work of adhesion) are needed to predict the fiber/fiber joint strength.

Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation and retention which is consistent with all field observations. This paper first reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding fluting. The fluting formation has been considered as a post-buckling phenomenon which has been analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with the ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale hygro-strain variations, which in turn are caused by the moisture variations created during fast convection (through-air) drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, but that high drying temperatures promote inelastic (irreversible) deformations in paper and this may itself preserve fluting.

In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid-solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called ''edge-flutter'' is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.

An experimental investigation is performed and analyzed in order to examine the onset and evolution of damage processes in thin isotropic paper sheets made of mechanical pulp. A microscopy technique has been used to estimate the relative fraction of bond and fibre breaks. It has been found that the active damage mechanism is bond failure, hence supporting the assumption of an isotropic scalar valued damage variable.All experiments have been performed by simultaneous with the mechanical loading monitoring the acoustic emission activity. Three different experimental setups have been designed offering the possibility to analyze the influence of stress gradients, as well as different levels of the ratios between the in-plane normal stresses, on the onset of damage. It is concluded that stress gradients in the paper specimens have a large influence on the onset of damage. When stress gradients are present a non-local theory has to be used in the analysis. In this way compliance with an isotropic damage criterion is achieved. The characteristic length, determining the gradient sensitivity, has been found to be of the same order of magnitude as some average fibre length.To study the evolution of the damage processes, wide and short specimens have been loaded in tension resulting in stable damage processes. With the assumptions made regarding the mechanical behavior of the paper material after onset of damage, the damage and the cumulative number of acoustic events curve correlates very well. The experimentally obtained data is used to determine material parameters in a proposed damage evolution law. It is found that the assumed damage evolution law can, for isotropic paper materials with bond rupture as the prevalent failure mechanism, be further simplified as only one specific material dependent damage evolution parameter has to be determined in experiments.

A major structural component of the cell is the actin cytoskeleton, in which actin subunits are polymerised into actin filaments. These networks can be cross-linked by various types of ABPs (Actin Binding Proteins), such as Filamin A. In this paper, the passive response of cross-linked actin filament networks is evaluated, by use of a numerical and continuum network model. For the numerical model, the influence of filament length, statistical dispersion, cross-link compliance (including that representative of Filamin A) and boundary conditions on the mechanical response is evaluated and compared to experimental results. It is found that the introduction of statistical dispersion of filament lengths has a significant influence on the computed results, reducing the network stiffness by several orders of magnitude. Actin networks have previously been shown to have a characteristic transition from an initial bending-dominated to a stretching-dominated regime at larger strains, and the cross-link compliance is shown to shift this transition. The continuum network model, a modified eight-chain polymer model, is evaluated and shown to predict experimental results reasonably well, although a single set of parameters cannot be found to predict the characteristic dependence of filament length for different types of cross-links. Given the vast diversity of cross-linking proteins, the dependence of mechanical response on cross-link compliance signifies the importance of incorporating it properly in models to understand the roles of different types of actin networks and their respective tasks in the cell.