The transverse and longitudinal elastic constants of pulp fibers in paper sheets

Czibula, Caterina; Brandberg, August; Cordill, Megan J.; Matković, Aleksandar; Глушко, Олександр; Czibula, Chiara; Kulachenko, Artem; Teichert, Christian; Hirn, Ulrich

doi:10.1038/s41598-021-01515-9

Cited by 12 publications

(8 citation statements)

References 42 publications

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“…2. According to previous experimental studies (Michaela et al 2013;Caterina et al 2021;Tristan et al 2019) and referring to the simulation data of Borodulina et al (2018), the tensile modulus of bers was mainly concentrated in the range of 10-30 GPa. We selected the ber elastic modulus E for 30 GPa, tangential modulus E tan for 10 GPa and yield stress σ s for 150 MPa.…”

Section: Selection Of Model Parametersmentioning

confidence: 88%

Influence mechanism of paper mechanical properties: numerical simulation and experimental verification based on a fiber network

Sun

Wei

et al. 2023

Preprint

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As a kind of renewable material that is widely available, paper is applicable in various fields. However, the research on its properties focuses mainly on macro mechanical properties, which ignores the micro theory based on the interface of paper. In essence, paper is a microscopic network made up of interrelated fibers. In this paper, a comprehensive experimental and computational study was conducted on the mechanical properties of the fiber and the fiber network, with consideration given to the impact of microstructure. A beam-spring model was established by using the beam fiber network. Then, simulations were performed on exemplary fiber network samples to demonstrate the impact of fiber microparameters on their mechanical properties, such as the force-elongation curve and strength. It was revealed through mechanical experiments that the tensile strength in the Z-direction (fiber bond strength) had a more significant impact on the properties of paper than the zero spacing tensile index (fiber strength), which is highly consistent with the result of modeling. All the simulation results were validated by performing experimental measurement. Finally, computational insights were gained into the pattern of interfiber bond damage on different fiber microlevels. To sum up, the proposed beam-spring model was demonstrated as applicable to predict the response from the fiber networks of paper materials.

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Section: Selection Of Model Parametersmentioning

confidence: 88%

Influence mechanism of paper mechanical properties: numerical simulation and experimental verification based on a fiber network

Sun

Wei

et al. 2023

Preprint

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“…The UKP fibres exhibit—compared to CTMP and CP—a very low absolute value for the modulus as presented in Fig. 8 c. These fibres have been subject to investigations before and there their mean longitudinal modulus was four times higher, though they exhibited considerable scattering [ 31 ]. Still, these fibres also exhibit rate-dependent behaviour.…”

Section: Discussionmentioning

confidence: 99%

The effect of the strain rate on the longitudinal modulus of cellulosic fibres

2022

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The longitudinal stiffness of cellulosic fibres plays an important role in the mechanical performance of many products these fibres are used for. Especially, the fibres’ viscoelastic properties are having an influence on the product performance.In this work, tensile testing at different strain rates was performed on single fibres to investigate the rate dependence of their moduli. Four different fibre types were tested: chemi-thermomechanical softwood pulp (CTMP), bleached chemical softwood pulp (CP), unbleached softwood kraft pulp (UKP), and viscose (VIS). For each fibre sample, ten strain rates ranging from 0.113% s−1 to 800% s−1 were applied. The rate-dependent modulus $$E_{r}$$ E r of each fibre at each strain rate was calculated by linearly fitting the stress–strain curves. By obtaining the values of the normalized modulus, a slope value per decade was calculated to quantify the rate dependence. To exclude possible plastic and relaxation effects, two additional experiments were used: a force-controlled loading–unloading experiment and a reverse rate protocol.All cellulosic fibres tested exhibited rate-dependent behaviour with a log-linear relationship between loading rate and modulus. For each tenfold increase in loading rate we found an increase in modulus up to nearly 20%—depending on the fibre type. Viscose fibres exhibit the highest rate dependence, whereas chemical softwood pulp fibres exhibit the lowest.

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“…Using Equation 4, the sheet-scale expansion can directly be predicted, upon inserting the experimentally obtained fiber swelling properties, i.e. ll and tt , assuming a free fiber length of ∼ 50% (Wernersson et al, 2014;Borodulina et al, 2016;Urstöger et al, 2020), and adopting the fiber stiffness characteristics from literature with ν lt = ν tl equal to 0.022 (Magnusson and Östlund, 2013;Brandberg et al, 2020;Czibula et al, 2021). E t /E l is different for FD and RD, HW and SW fibers (Jentzen, 1964), therefore a range of values for E t /E l between 6 and 11 is studied here, covering the relevant range of values found in literature (Magnusson and Östlund, 2013;Brandberg et al, 2020;Czibula et al, 2021).…”

Section: Inter-fiber Bond Modelmentioning

confidence: 99%

Transient hygro- and hydro-expansion of freely and restrained dried paper: the fiber-network coupling

Vonk¹,

Spreuwel²,

Anijs³

et al. 2023

Preprint

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The transient dimensional changes during hygro-expansion and hydro-expansion of freely and restrained dried, softwood and hardwood sheets and fibers is monitored, to unravel the governing micro-mechanisms occurring during gradual water saturation. The response of individual fibers is measured using a fullfield global digital height correlation method, which has been extended to monitor the transient hydroexpansion of fibers from dry to fully saturated. The hygro-and hydro-expansion is larger for freely versus restrained dried and softwood versus hardwood handsheets. The transient sheet-scale hydro-expansion reveals a sudden strain and moisture content step. It is postulated that the driving mechanism is the moisture-induced softening of the so-called "dislocated regions" in the fiber's cellulose micro-fibrils, unlocking further fiber swelling. The strain step is negligible for restrained dried handsheets, which is attributed to the "dislocated cellulose regions" being locked in their stretched configuration during restrained drying, which is supported by the single fiber hydro-expansion measurements. Finally, an inter-fiber bond model is exploited and adapted to predict the sheet-scale hygro-expansion from the fiber level characteristics. The model correctly predicts the qualitative differences between freely versus restrained dried and softwood versus hardwood handsheets, yet, its simplified geometry does not allow for more quantitative predictions of the sheet-scale hydro-expansion.

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The transverse and longitudinal elastic constants of pulp fibers in paper sheets

Cited by 12 publications

References 42 publications

Influence mechanism of paper mechanical properties: numerical simulation and experimental verification based on a fiber network

Influence mechanism of paper mechanical properties: numerical simulation and experimental verification based on a fiber network

The effect of the strain rate on the longitudinal modulus of cellulosic fibres

Transient hygro- and hydro-expansion of freely and restrained dried paper: the fiber-network coupling

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