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Laminated paperboard and paper is widely used in packaging products. Its out-of-plane properties play a crucial role in converting paperboard to a carton through the creasing and folding process. The aim of this study is to describe the out-of-plane mechanical response with an elastic-plastic model based on the observed experimental behavior. The model was derived from a thermodynamic framework and was based on the multiplicative split of the deformation gradient in the context of hyperelasticity. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the plastic behavior. The model considers both material densification and internal friction effects, which were observed experimentally. According to the experimental behavior, a quadratic yield locus under pure shear loading was assumed in the model. Finally, the model was validated with a cylinder compression test and found to capture the highly anisotropic, elastic-plastic behavior accurately. [ABSTRACT FROM AUTHOR]

Laminated paperboard and paper is widely used in packaging products. It generally exhibits highly anisotropic and nonlinear mechanical behavior. The aim of this study is to describe the in-plane material behavior with an orthotropic elastic-plastic model based on the observed experimental behavior. A structural tensor-based approach was applied to model the elastic deformation, while a multi-surface based yield criterion was adopted to describe the yield behavior. The model incorporated nonlinear kinematic and isotropic hardening to capture the anisotropic hardening effect. In the experiment, the compressive yield stress was found to be insensitive to the previous tensile deformation. The proposed model could capture this compression yield stress preserving effect under reverse loading, which in turn reduced the required material parameters as expected. With the material parameters calibrated from a set of simple uniaxial tests in various directions, the model was shown to predict the stress-strain behavior for other orientations satisfactorily. The model was further validated with experiments under complex loading conditions and found to capture the highly anisotropic, elastic-plastic behavior accurately. [ABSTRACT FROM AUTHOR]

A paper web produced under industrial conditions always exhibits an anisotropy in its mechanical properties measured in the machine and cross directions. Proper and fast information about current paper anisotropy would significantly increase the efficiency of web quality control systems and allow to produce paper with greater precision. The main objective of the work presented was to determine the possibility of measurement of paper anisotropy. The method proposed is based on the image analysis of the orientation and location of special markers -- luminescent fibres -- which were introduced to the structure of the paper. Studies have shown that the method of image analysis provides a detection of fibres with a satisfactory level of efficiency, thus allowing accurate examination of the anisotropy of the paper samples analysed. On the basis of experiments, it was also found that the method of image analysis proposed allows to detect fibres with an accuracy appropriate for the problem under consideration. The invention presented has already been registered in a Patent Office as submission no. P.411294. [ABSTRACT FROM AUTHOR]

An in-plane elasto-plastic material model and a hygroexpansivity-shrinkage model for paper and board are introduced in this paper. The input parameters for both models are fiber orientation anisotropy and dry solids content. These two models, based on experimental results, could be used in an analytical approach to estimate, for example, plastic strain and shrinkage in simple one-dimensional cases, but for studies of the combined and more complicated effects of hygro-elasto-plastic behavior, a numerical finite element model was constructed. The finite element approach also offered possibilities for studying different structural variations of an orthotropic sheet as well as buckling behavior and internal stress situations under local strain differences. A few examples are presented of the effect of the anisotropy and moisture streaks under stretching and drying conditions on strain differences and buckling. The internal stresses were studied through a case in which the drying of different layers occurred at different stages. Both the anisotropy and moisture streaks were capable of rendering the buckling of the sample visible. The permanency of these defects highly depends on several process stages and tension conditions of the sheet, as demonstrated in this paper. The application possibilities of the hygro-elasto-plastic model are diverse, including investigation into several phenomena and defects appearing in drying, converting and printing process conditions. [ABSTRACT FROM AUTHOR]

Abstract: The rheological nature of paper or board is usually treated either as elasto-plastic or as viscoelastic depending on the studied paper making process or behavior in converting and end use. In this paper we study several stress–strain curve models and the determination of material parameters from an elasto-plastic point of view. Finally, a suitable approach for all stress–strain curves measured from 180 strips is constructed using a linear function for an elastic region and a nonlinear function for a strain hardening region. This model determines a proportional limit (elastic limit) and gives fairly elegant dependencies between material/fitting parameters and two important factors of mechanical properties of paper: dry solids content and anisotropy. In this paper the dependency of a plastic strain on dry solids content and anisotropy is estimated using the introduced stress–strain curve model. Correspondingly, the model can be used to estimate many other mechanical behaviors, for example, the tension differences arising from non-uniform moisture content of the paper web profile. However, the main target of this study is to produce competent parameters based on modeled stress–strain curves for further construction of a material model. This elasto-plastic material model will be utilized in out-of-plane deformation and fracture models. [Copyright &y& Elsevier]

Abstract: In this paper a simplified network model for mechano-sorptive creep is presented, which is a further development of an earlier paper [Strömbro, J., Gudmundson, P., 2008. Mechano-sorptive creep under compressive loading – a micromechanical model. International Journal of Solids and Structures 45 (9), 2420–2450.]. It is assumed that the anisotropic hygroexpansion of the fibres leads to large stresses at the fibre bonds when the moisture content changes. The resulting stress state will accelerate creep if the fibre material obeys a constitutive law that is non-linear. Fibre kinks are included in order to capture experimental observations of larger mechano-sorptive effects in compression than in tension. Moisture dependent material parameters and anisotropy in the fibre distribution have been introduced. Theoretical predictions based on the model are compared to experimental results for an anisotropic paper both under tensile and compressive loading at varying moisture content and it is found that the important features in the experiments are captured by the model. Different kinds of drying conditions have also been examined. [Copyright &y& Elsevier]

Abstract: Two-dimensional axially moving materials have a wide range of industrial applications such as papers, plastics and composites in producing lines, power transmission and conveyor belts, etc. In many of these instances, the moving material is not isotropic, but is a single-layer orthotropic material or consists of several orthotropic layers. In this article, free vibration of axially moving symmetrically laminated plates subjected to in-plan forces is studied by classical plate theory. This category includes symmetric cross-ply and angle-ply laminates and anisotropic plates. Firstly, an exact method is developed to analyze vibration of multi-span traveling cross-ply laminates, and then a semi-analytical finite strip method is extended for moving symmetric laminated plates in general, with arbitrary boundary conditions. By the finite strip method intermediate elastic or rigid supports can also be added to the model of the moving plate. The supports may be in the form of point, line or local distributed supports. [Copyright &y& Elsevier]

Abstract: A void network model, named Pore-Cor, has been used to study the permeation of an ink solvent into paper coating formulations coated onto a synthetic substrate. The network model generated anisotropic void networks of rectangular cross-sectional pores connected by elliptical cross-sectional throats. These structures had porosities and mercury intrusion properties which closely matched those of the experimental samples. The permeation of hexadecane, used as an analogue for the experimental test oil, was then simulated through these void structures. The simulations were compared to measurements of the permeation of mineral oil into four types of paper coating formulation. The simulations showed that the inertia of the fluid as it enters void features causes a considerable change in wetting over a few milliseconds, a timescale relevant to printing in a modern press. They also showed that in the more anisotropic samples, fast advance wetting occurred through narrow void features. It was found that the match between experimental and simulated wetting could be improved by correcting the simulation for the number of surface throats. The simulations showed a more realistic experimental trend, and much greater preferential flow, than the traditional Lucas–Washburn and effective hydraulic radius approaches. [Copyright &y& Elsevier]