Experimental and theoretical analysis of in-plane cohesive testing of paperboard

Tryding, Johan; Marin, Gustav; Nygårds, Mikael; Mäkelä, Petri; Ferrari, Giulio

doi:10.1177/1056789516630776

Cited by 15 publications

(12 citation statements)

References 17 publications

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“…1(a). The samples were mounted in a custom-built tensile test device using specially designed grips as described in Tryding et al [3], see Fig. 1(c).…”

Section: Sample Preparation and In-plane Tensile Testsmentioning

confidence: 99%

“…In general terms, the angles of the MD strain streaks (close to 45°) could indicate both ductile deformation behaviour and brittle shear failure. Tryding et al [3] showed that the stable sample length parameter, that depends on the elastic modulus and the post-peak slope of the global stress-displacement response, can be used as an indicator of if a paperboard sample behaves in a more ductile-or a more brittle-like manner. The stable length differs between samples tested in MD and CD and the diagonal strain field patterns in the MD-tested samples in this study might, together with the global force-displacement response, therefore indicate a more brittle behaviour compared to the CDtested samples.…”

Section: Strain Field Patterns -An Indication Of Deformation Mechanismsmentioning

confidence: 99%

“…In-plane tensile tests of paperboards (ISO 1924-3) show a typical macromechanical behaviour of an initial linear phase (elasticity) followed by non-linear hardening (plasticity) until failure occurs with a drop in stress to zero. A gradually descending postpeak behaviour, that can be described as cohesive failure, is present in short samples [2,3]. However, despite a relatively well-understood macro-mechanical behaviour of papers and paperboards, challenging aspects of these materials is their anisotropic nature, through thickness heterogeneity and variability at the microscale.…”

Section: Introductionmentioning

confidence: 99%

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3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

et al. 2021

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Background Experimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D. Objective The main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples. Methods X-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions. Results The results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination. Conclusions In-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

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“…1(a). The samples were mounted in a custom-built tensile test device using specially designed grips as described in Tryding et al [3], see Fig. 1(c).…”

Section: Sample Preparation and In-plane Tensile Testsmentioning

confidence: 99%

Section: Strain Field Patterns -An Indication Of Deformation Mechanismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

et al. 2021

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“…An additional challenge is the calibration of these models. The classical experimental tests that can be conducted to measure the delamination resistance of paper and board include the Scott bond test [80,119], the z-directional testing based on lamination techniques [9,79], the Y-peel test [94], and the short-span uniaxial tension tests [243]. The aforementioned procedures are useful for the out-of-plane tensile response.…”

Section: Modeling Of Paperboard Laminatesmentioning

confidence: 99%

A Review of Recent Trends and Challenges in Computational Modeling of Paper and Paperboard at Different Scales

Simon

2020

Arch Computat Methods Eng

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Paper and paperboard are widely used in packaging products. The material behavior of paper and paperboard is very complex because different scales need to be considered in order to describe all relevant effects and phenomena. In particular, at least three scales can be distinguished: the fiber scale, network scale, and sheet scale. Since it is extremely challenging to measure the material behavior experimentally on all of these scales simultaneously, computational modeling of these materials has gained importance in recent years. This work aims at giving a systematic review of the numerical approaches and obtained results published in recent years. Focus is set on both the recent trends and achievements as well as challenges and open questions.

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“…Other works dealing with the out-of-plane elastoplastic deformation behaviour of paper can be found in Stenberg et al, 7 Nygards et al, 8 and Li et al 9 In these works, it is assumed that the in-plane and out-of-plane stress components are only allowed to independently drive the in-plane and out-of-plane inelastic deformation, respectively. Also, some authors describe the response of the paper by continuum damage models, see Isaksson et al, 10 Zechner et al, 11 and Tryding et al 12 A major drawback of the non-quadratic modelling approach is a slow rate of convergence as the edges of the yield surface become sharper. A possibility to overcome this problem is to describe the in-plane anisotropic behaviour of the material by means of a multisurface plasticity model.…”

Section: Introductionmentioning

confidence: 99%

A comparative study of a multi-surface and a non-quadratic plasticity model with application to the in-plane anisotropic elastoplastic modelling of paper and paperboard

Bedzra

Reese

et al. 2018

Journal of Composite Materials

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In this paper, a three-dimensional anisotropic multi-surface model for the in-plane elastoplastic deformation of paper and paperboard is developed. The model is based on the concept of structural tensors. It employs three different yield functions and parameterised consistency conditions for three different loading scenarios. The evolution of the yield surface with plastic strain is described by multiple hardening variables. Furthermore, the evolution equations are integrated using the unconditionally stable backward Euler method. Also, the internal variables are updated using a particular form of the elastic predictor/plastic corrector algorithm. The constitutive model is calibrated from a set of simple uniaxial tension tests performed in various directions of the material and is validated against loading in other directions. Additionally, the predictive capability as well as the numerical performance of the constitutive model is accessed against an existing non-quadratic plasticity model. Finally, the applicability of the constitutive model is demonstrated by performing a tensile test on a paperboard with a hole.

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Experimental and theoretical analysis of in-plane cohesive testing of paperboard

Cited by 15 publications

References 17 publications

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

A Review of Recent Trends and Challenges in Computational Modeling of Paper and Paperboard at Different Scales

A comparative study of a multi-surface and a non-quadratic plasticity model with application to the in-plane anisotropic elastoplastic modelling of paper and paperboard

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