1. Introduction {#sec1-materials-13-01706}
===============

Honeycomb board is manufactured on the basis of fibrous materials, most often from coniferous trees. Due to the spatial structure, it has low specific weight and good strength properties \[[@B1-materials-13-01706],[@B2-materials-13-01706]\]. Its advantages also include recyclability; excellent energy absorption properties; and insulation, thermal, and acoustic properties \[[@B3-materials-13-01706]\]. Honeycomb paper cores are used in many multilayer and packaging products and they successively replace this type of plastic or aluminium products due to the lower manufacturing cost and lower specific weight. This organic and biodegradable raw material is gaining great popularity in various industries. It is used as a fillings for doors, countertops, furniture boards, partition walls in construction, and sandwiched multilayer structures in the aviation and automotive industries \[[@B4-materials-13-01706],[@B5-materials-13-01706],[@B6-materials-13-01706],[@B7-materials-13-01706]\]. The production and use of honeycomb paper panels in the furniture industry are developing rapidly in Europe \[[@B8-materials-13-01706]\]. The demand for lighter furniture elements is increasing, which is contributing to lower transport costs and easier assembly, alongside the reduction of formaldehyde emissions, which is also an important issue in the modern world \[[@B9-materials-13-01706]\].

In the packaging industry, cellular paperboard is used to produce large-size boxes and their fillings. In most applications, in which cellular paperboard is treated as a construction material, it carries compressive loads caused by forces acting in its plane. To assess strength at this type of load, its edge crush test, *ECT,* can be used. In a certain direction along the paperboard plane, the *ECT* value is defined as the maximum compressive force transferred by the crushed paperboard until it is destroyed, related to the length of the side of the sample perpendicular to the direction of the force.

This indicator is particularly useful in cases wherein the strengths of panels with large values of panel thickness in the direction of load application are considered. This indicator is of decisive importance in, e.g., determining the resistance of boxes to the static pressure of boxes.

The study of cellular paperboard was carried out by Wen \[[@B10-materials-13-01706]\], who compared the results of measuring 5 mm thick cellular paperboard with the results of corrugated board. The comparison concerned both *ECT* edge crushing resistance in both directions in the paperboard plane, and the *FCT* flat crushing test.

Chen et al. \[[@B11-materials-13-01706]\] presented studies on lightweight multilayer panels with different honeycomb core structures made of paper, and wood cladding composite. By using experimental tests and finite element modelling methods, the authors presented the impacts of the construction parameters of honeycomb and the properties of the core material and cladding on the mechanical properties of light laminated panels.

Borsellino and Di Bella \[[@B12-materials-13-01706]\] conducted tests of laminates with different core structures at different load methods, including resistance to edge crushing of the paper honeycomb. The purpose of the work was based on experimental research to assess the relationship between stresses and deformations at uniform compressive static load.

Smardzewski et al. \[[@B13-materials-13-01706]\] conducted a study to determine the effect of a rectangular cellular paper core on the mechanical properties of three-layer furniture panels.

Smardzewski and Prekrat \[[@B14-materials-13-01706]\] presented modelling of mechanical properties of cellular wooden panels with a paper honeycomb core. The subjects of the study were the thin panels of a paper honeycomb with hexagonal cells. The research was carried out using numerical models; the results of numerical calculations were compared with the results of experimental measurements. As a result of the research, it was confirmed that the cores of cellular wood panels show strong orthotropic properties.

The authors of the work decided to develop a simple method for determining the *ECT* of honeycomb boards and to verify them in experimental studies. Another verification method was to develop complex numerical models in the finite element method (FEM), which should still be compared with experimental research.

Despite the fact that the literature provides information on *ECT* of honeycomb boards, none of the presented studies presents a simple, analytical method for determining the value of the edge crush resistance of cellular cardboard.

The purpose of the work is to present mathematical relationships that allow calculating the resistance of honeycomb paperboard to edge crushing in the machine and cross directions, based on its geometric parameters and mechanical properties of the materials from which it was made.

Cellular paperboard consists of two outer layers and a honeycomb core (see [Figure 1](#materials-13-01706-f001){ref-type="fig"}).

The geometrical parameters describing the cellular paperboard are:

*D*---diameter of the circle inscribed in the regular hexagon determined by the contact lines of the cell walls with cover layer, defined as the cell mesh size;

*h*---core height;

*H*---paperboard thickness.

The length of the regular hexagon's side can be determined from Equation (1) using parameter *D* given by the paperboard manufacturer (see [Figure 2](#materials-13-01706-f002){ref-type="fig"}):$$a = D/\sqrt{3}$$

Cellular cardboard has the characteristics of orthotropic bodies. This is due to the core structure and the distribution of mechanical properties of the flat layers, which is characteristic of orthotropic bodies. In the plane of cellular paperboard, two main directions of orthotropy can be distinguished. The first one coincides with the direction of manufacture and it is called machine direction, *MD*. The second main direction, perpendicular to the machine direction, is referred to as cross direction, *CD*. The main directions of the *CD* and *MD* of the paperboard coincide with the main directions of the paper used for the flat layers of the *CD~O~* and *MD~O~* paperboard (see [Figure 1](#materials-13-01706-f001){ref-type="fig"}). In the case of a paperboard core, the machine direction of the paper used for the *MD~R~* core is parallel to the height of the core and the cross direction *CD~R~* is perpendicular to the height of the core.

The proposed method for determining the resistance of honeycomb paperboard to edge crushing is based on the stability of thin-walled isotropic \[[@B15-materials-13-01706],[@B16-materials-13-01706],[@B17-materials-13-01706],[@B18-materials-13-01706]\] and orthotropic plates \[[@B19-materials-13-01706],[@B20-materials-13-01706],[@B21-materials-13-01706],[@B22-materials-13-01706],[@B23-materials-13-01706]\]. The formulas for calculating *ECT* presented in the article were developed in detail in \[[@B24-materials-13-01706],[@B25-materials-13-01706],[@B26-materials-13-01706]\].

2. Materials and Methods {#sec2-materials-13-01706}
========================

Sixteen honeycomb paperboards with different geometrical parameters and made of different fibrous materials were tested, and 4 types of paper used for their production.

The following papers are used in the remainder of the article:T135---testliner, 135 g/m^2^ basis weight;T160---testliner, 160 g/m^2^ basis weight;T200---testliner, 200 g/m^2^ basis weight;F140---fluting, 140 g/m^2^ basis weight.

[Table 1](#materials-13-01706-t001){ref-type="table"} presented material constants of the papers.

The honeycomb paperboard markings contain information about their material composition according to the following record (material of the first cover layer/core material/material of the second cover layer). For example: honeycomb paperboard with the core made of T160 paper and two cover layers of T135 paper has the mark T135/T160/T135.

To identify each paperboard, thickness *H*, the diameter of the circle inscribed in the regular hexagon of the core *D* cells, and the markings of the paper from which it was made, are provided.

To avoid the impact of climatic conditions on the results of strength tests of papers and boards, the testing pieces were conditioned before the test in accordance with PN-EN 20187: 2000 \[[@B27-materials-13-01706]\], and the tests were carried out in an air-conditioned room with the same climatic conditions as during the conditioning of the testing pieces; i.e., temperature 23 ± 1 °C and relative air humidity 50% ± 2%.

In the case of paper from which paperboard was made, the basis weight was measured in accordance with PN-EN ISO 536: 2012 \[[@B28-materials-13-01706]\], thickness in accordance with PN-EN ISO 534: 2012 \[[@B29-materials-13-01706]\], and the Young's modulus in machine and cross directions was determined based on a tensile test at constant speed stretching performed in accordance with PN-EN ISO 1924-2: 2010 \[[@B30-materials-13-01706]\].

*ECT* measurements were made using a universal Zwick testing machine (Ulm, Germany) with a load range up to 20 kN using the tooling shown in [Figure 3](#materials-13-01706-f003){ref-type="fig"}. The tooling consists of two square plates of 144 cm^2^ each. Both plates are rigidly attached to the lower frame of the machine, and the upper to the movable traverse (see [Figure 3](#materials-13-01706-f003){ref-type="fig"}a). Supporting blocks (see [Figure 3](#materials-13-01706-f003){ref-type="fig"}b) were used to test cardboard with small thickness, maintaining the tested piece in a vertical position until reaching the initial force.

One-hundred-millimetre squared tested pieces were crushed; only for paperboard less than 10 mm thick were the tested pieces reduced to 50 mm to protect against global buckling.

Before starting the measurement, the tested piece was subjected to a 10 N initial force. During the measurements, the plates approached each other at a speed of 12.5 mm/min.

The measurements were carried out in two main directions in the plane of the paperboard; and on their basis its resistance to edge crushing in the machine direction *ECT~MD~* and cross direction *ECT~CD~* was determined respectively. The result of the determination in each direction is given as the average value obtained after testing ten pieces.

The *ECT* value was calculated from the equation:$$ECT = \frac{F}{l},~kN/m$$ where: *F*---value of destructive force, kN;*l*---length of the loaded edge of the tested piece, m.

Calculation Methodology
-----------------------

The resistance of cellular board, both in the machine direction and in the cross direction, was calculated as the sum of loads carried by the core and both cover layers:$$ECT_{MD} = ECT_{RMD} + ECT_{OMD}$$ $$ECT_{CD~} = ECT_{RCD} + ECT_{OCD}$$ where: *ECT~RCD~* and *ECT~OCD~*---edge crushing resistance towards *CD*, core and both cover layers, respectively,*ECT~RMD~* and *ECT~OMD~*---resistance to edge crushing in the *MD* direction of core and both cover layers, respectively.

It was assumed that the calculation model of the resistance to edge crushing of the core will describe the destruction of a repeating element of the paperboard core structure. The *ABCE* periodic cell was separated from the honeycomb core structure (see [Figure 4](#materials-13-01706-f004){ref-type="fig"}).

It has been assumed that the cross-section of the core cell with a plane parallel to the cover layer has the shape of a regular hexagon with side *a*.

[Figure 5](#materials-13-01706-f005){ref-type="fig"} shows the dimensions of the periodic cell.

The dimensions of the periodic cell can be determined from the equation:$$CE = AB = 2 \cdot a + 2 \cdot a~ \cdot \cos\gamma$$ $$AC = BE = 2 \cdot a~ \cdot \sin\gamma$$

In the case of a regular hexagon cell that has been taken into account in the calculations, the angle *γ* is 60°. It was assumed that only single-thickness walls are responsible for cell destruction in the *ECT* test, *t~R~* marked in black in [Figure 4](#materials-13-01706-f004){ref-type="fig"}. The double walls *t~R~*, which are formed by gluing two layers of core material marked in red in [Figure 4](#materials-13-01706-f004){ref-type="fig"}, are not damaged, as observed in preliminary *ECT* tests of honeycomb panels.

The load schemes used to calculate the *Q* forces transmitted through the periodic core cell in the *MD* and *CD* directions are illustrated in [Figure 6](#materials-13-01706-f006){ref-type="fig"}.

The maximum *Q~MD~* and *Q~CD~* forces transferred by the periodic core cell in the *MD* and *CD* direction were calculated from:$$Q_{MD~} = 2~ \cdot S~ \cdot \sin\gamma$$ $$Q_{CD~} = 2~ \cdot S~ \cdot \cos\gamma$$ where: *S*---maximum force transmitted during compression in the cross direction of the core material by a wall of a single thickness.

The force *S* can be determined from the following relationship:$$S = \alpha~ \cdot ~t_{R}~ \cdot h~ \cdot ~\sigma_{cr}$$ where: *t~R~*---thickness of paper used for core production;*h*---core thickness of cellular paperboard;*σ*~cr~---critical stress;*α*---coefficient of elastic restoration of a single cell wall.

The α factor is respectively:$$\alpha = 1.0~~gdy~~\frac{a}{h} > 1.0$$ $$\alpha = 3.41 - 1.41\frac{a}{h}~~gdy~~0.2 \leq \frac{a}{h}~ \leq 1.0$$ $$\alpha = 1.0~~gdy~~0.1 < \frac{a}{h} < 0.2~$$

Critical stress *σ*~cr~ can be determined from the equation:$$\sigma_{cr} = \frac{\pi^{2~} \cdot ~{t_{R}}^{2}}{12~ \cdot ~h^{2}}\sqrt{E_{RMD} \cdot E_{RCD}}\left\lbrack {\eta + 2 + \frac{1}{\eta}} \right\rbrack$$ where:$$\eta = \left( \frac{h}{a} \right)^{2} \cdot \sqrt{\frac{E_{RCD}}{E_{RMD}}}$$

Substituting Equation (14) into Equation (13) gets:$$\sigma_{cr} = \frac{\pi^{2}~ \cdot ~t_{R}^{2}}{12~ \cdot ~h^{2}}~ \cdot ~\sqrt{E_{RMD}~ \cdot ~E_{RCD}~} \cdot ~\left\lbrack {2 + \left( \frac{h}{a} \right)^{2}~ \cdot ~\sqrt{\frac{E_{RCD}}{E_{RMD}}} + \frac{1}{\left( \frac{h}{a} \right)^{2}~ \cdot ~\sqrt{\frac{E_{RCD}}{E_{RMD}}}}} \right\rbrack$$ where: *E~RCD~*, *E~RMD~*---Young's paper moduli used to produce the cellular paperboard core in cross and machine directions, respectively.

Many studies are devoted to a detailed discussions of Equations (13) and (14), as presented by Kołakowski et al. \[[@B24-materials-13-01706],[@B25-materials-13-01706],[@B26-materials-13-01706]\].

The *ECT~RMD~* and *ECT~RCD~* core crush test was calculated from the relationship:$$ECT_{RMD} = \frac{Q_{MD}}{AB} = \frac{\alpha~ \cdot ~t_{R~}~ \cdot ~h~ \cdot ~\sigma_{cr}~ \cdot \sin\gamma}{a~ \cdot ~\left( {1 + cos~\gamma} \right)}$$ $$ECT_{RCD} = \frac{Q_{CD}}{AC} = \frac{\alpha~ \cdot ~t_{R~}~ \cdot ~h~ \cdot ~\sigma_{cr}~ \cdot \cos\gamma}{a~ \cdot ~sin~\gamma}$$

The resistance of two honeycomb board cover layers to *ECT~OMD~* and *ECT~OCD~* edge crushing was determined from the following equation:$$ECT_{OMD} = \beta_{OMD}\  \cdot \ \frac{2\  \cdot \ \pi^{2}\  \cdot \ t_{o}^{3}}{3\  \cdot \ \left( {a + 2\  \cdot a\  \cdot cos\gamma} \right)^{2}}\  \cdot \ \sqrt{E_{OMD} \cdot E_{OCD}}$$ $$ECT_{OCD} = \beta_{OCD}~ \cdot ~\frac{\pi^{2}~ \cdot ~t_{o}^{3}}{6~ \cdot ~\left( {~a~ \cdot sin\gamma} \right)^{2}}~ \cdot ~\sqrt{E_{OMD} \cdot ~E_{OCD}}$$ where: *E~OCD~, E~OMD~*---Young's moduli of paper used to produce cover layers of cellular paperboard in cross and machine directions, respectively;*t~o~*---the thickness of the paper used for flat layers of cellular paperboard;*β~OMD~*, *β~OCD~*---elastic support coefficients, determined experimentally.

It should be taken into account that *E~OMD~ ≠ E~OCD~*, and this implies that *β~OMD~* *≠ β~OCD~*.

The *β~OMD~* factor is assumed as a function of the *a/h* ratio:$$\frac{a}{h} \leq 0.6~ \cdot \sqrt[4]{\frac{E_{OMD}}{E_{OCD}}}~~to~~\beta_{OMD} = 1.1~ \cdot ~\sqrt[4]{\frac{E_{OMD}}{E_{OCD}}}$$ $$\frac{a}{h} > 0.6~ \cdot \sqrt[4]{\frac{E_{OMD}}{E_{OCD}}}~~to~~\beta_{OMD} = \left\lbrack {1.1 + 0.3~ \cdot ~\left( \frac{a}{h} \right)} \right\rbrack \cdot ~\sqrt[4]{\frac{E_{OMD}}{E_{OCD}}}$$

The coefficient *β~OCD~* is constant, and it is:$$\beta_{OCD} = \left\lbrack {1.5 + 0.6\left( \frac{a}{h} \right)} \right\rbrack \cdot \sqrt[4]{\frac{E_{OCD}}{E_{OMD}}}$$

The cellular board's resistance to edge crushing in the machine direction *ECT~MD~* and cross direction *ECT~CD~* can be determined from the Equations (23) and (24), obtained after substituting Equations (16) and (18) into Equations (3) and (17), and Equation (19) to Equation (4):$$ECT_{MD} = ECT_{RMD} + ECT_{OMD} = \alpha \cdot ~\frac{t_{R} \cdot ~h~ \cdot \sigma_{cr~} \cdot sin\gamma~}{a~ \cdot \left( {1 + cos\gamma} \right)} + \beta_{OMD} \cdot \frac{2~ \cdot ~\pi^{2}~ \cdot ~t_{o}^{3}}{3~ \cdot ~\left( {a + 2~ \cdot a~ \cdot cos\gamma} \right)^{2}}~ \cdot \sqrt{E_{OMD} \cdot ~E_{OCD}}$$ $$ECT_{CD} = ECT_{RCD} + ECT_{OCD} = \alpha \cdot ~\frac{t_{R} \cdot ~h~ \cdot \sigma_{cr~} \cdot cos\gamma~}{a~ \cdot sin\gamma} + \beta_{OCD} \cdot \frac{\pi^{2}~ \cdot ~t_{o}^{3}}{6~ \cdot ~\left( {a~ \cdot sin\gamma} \right)^{2}}~ \cdot \sqrt{E_{OMD} \cdot ~E_{OCD}}$$

3. Results and Discussion {#sec3-materials-13-01706}
=========================

Theoretical *ECT* values in the machine direction *ECT~MD~* and cross direction *ECT~CD~* were calculated based on the results of measurements of the properties of the materials used for the production of cellular paperboards and the geometrical parameters of the boards.

[Table 2](#materials-13-01706-t002){ref-type="table"} and [Table 3](#materials-13-01706-t003){ref-type="table"} summarise the results of *ECT* measurements and calculations in both main directions.

[Figure 7](#materials-13-01706-f007){ref-type="fig"} and [Figure 8](#materials-13-01706-f008){ref-type="fig"} show a comparison of measurement results and calculations of cellular board resistance to edge crushing in the machine and cross directions.

In almost all cases examined, the differences between the measured and calculated *ECT* values are within the variability of the results of measurements and calculations. For two honeycomb paperboards, the minimum calculation value is greater than the maximum value obtained from measurements by less than 1.2%.

The largest discrepancy between the measured and calculated values was in the *MD* direction: 20% of the actual *ECT~MD~* value and in the *CD* direction 24%. The largest *ECT~MD~* discrepancy was found in the case of cardboard with mesh size *D* = 15 mm, thickness *H* = 60 mm, made of T200 and F140 papers. The largest discrepancy between the calculated and measured *ECT~CD~* values was in the case of paperboard with mesh size *D* = 15 mm, thickness *H* equal to 30 mm, made of T200 and F140 papers. The mean value of the discrepancy between the measured and calculated *ECT* values in all the cases examined was 11% of the actual value in both *MD* and *CD*.

[Figure 9](#materials-13-01706-f009){ref-type="fig"} summarizes the *ECT* measurements of paperboard with the same mesh size made of the same materials.

In both cases, at low core heights, up to 20 mm, there is an increasing tendency for greater edge crush resistance as the cardboard thickness increases. Then, the *ECT* value remains at the same level. This is due to the fact that as the value of the *a/h* decreases, the influence of the core on the *ECT* of the paperboard decreases, striving for a constant value.

[Figure 10](#materials-13-01706-f010){ref-type="fig"} shows *ECT* values of cardboard with the same geometrical parameters made of various raw fibres.

The measurement results illustrated in [Figure 10](#materials-13-01706-f010){ref-type="fig"} show the effect of physical properties of the papers on the *ECT* of cellular board. The use of a paper with a higher basis weight, and thus higher thickness and better mechanical properties, causes a significant increase in the *ECT* value in both machine and cross directions.

[Figure 11](#materials-13-01706-f011){ref-type="fig"} and [Figure 12](#materials-13-01706-f012){ref-type="fig"} show *ECT* values of paperboard made from the same raw materials of the same thickness, differing in mesh size.

The very large decrease in *ECT* of cellular board visible in [Figure 11](#materials-13-01706-f011){ref-type="fig"} and [Figure 12](#materials-13-01706-f012){ref-type="fig"} is associated with a decrease in the force transmitted by the cover layers, which buckle more easily with an increase in mesh size.

The relationships between the individual parameters used to calculate *ECT* and its value show a consistent nature with the mathematical relationships presented in Equations (23) and (24); e.g., an increase in cardboard thickness causes an increase in *ECT* value, while an increase in mesh size causes a decrease in *ECT* value.

The big impact on the differences between the real values of edge crush resistance and the values calculated in theoretical way result from the fact that the paperboard was produced in different periods of time, and during the production of the core, the papers are unwound simultaneously from several turns, and thus for their production, materials from various supplies are used, the mechanical properties of which may differ significantly. It happens that the actual values of mechanical properties differ by up to 20% from the nominal values given in the specification. In addition, switching machines for the production of paperboard of a different thickness can cause a different degree of stretching of the core or a different arrangement of the cell wall gluing lines, and thus the deviation of the dimensions and shape of the cell from the cells shaped like a hexagon, which is the shape adopted in the mathematical description. Very often during production, the core is slightly crushed, which also has a significant impact on the value of edge crush resistance \[[@B31-materials-13-01706]\].

During the tests, no global buckling of paperboard samples was found. Shibao Wen \[[@B10-materials-13-01706]\], who tested much thinner (and thus more vulnerable to global buckling) cellular cardboard with a thickness of about 5 mm did not find this phenomenon.

4. Conclusions {#sec4-materials-13-01706}
==============

The proposed method allows one to calculate the *ECT* of cellular paperboard both in machine and cross directions on the basis of the paperboard's geometric parameters and the mechanical properties of materials used for its production. It is much easier and much faster in practical application than numerical methods such as the finite element method or the finite difference method. In the examined range of *a/h* values in each of the main directions in the board plane, the theoretically calculated values differed from real values by an average of 11% of the actual value, and the maximum difference that occurred in the cross direction was 24%. Considering that the mechanical properties of raw materials and the geometrical parameters of paperboard can differ significantly from the nominal values assumed during the calculations, the obtained calculation accuracy can be considered satisfactory. In the future, the authors plan to compare the results obtained with the proposed calculation method and the results obtained by numerical calculations. However, they do not expect significant differences in the accuracy of the calculations due to the fact that the calculation errors result from the variability of strength properties of materials and heterogeneity of the geometry of the core due to changes in the parameters of the production process.

Conceptualization, Z.K., W.S., and G.K.-F.; methodology, Z.K., G.K.-F., and W.S.; conceived and designed the experiments G.K.-F. and W.S.; prepared the materials and samples, G.K.-F.; performed the experiments as part of her doctoral thesis, G.K.-F.; processed and collated the results, G.K.-F., All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

The authors declare no conflict of interest.

![Cellular paperboard parameters.](materials-13-01706-g001){#materials-13-01706-f001}

![Cell mesh parameters.](materials-13-01706-g002){#materials-13-01706-f002}

![Instrumentation for the edge crush test (*ECT)*: (**a**) measuring instrumentation; (**b**) test sample supported by support blocks.](materials-13-01706-g003){#materials-13-01706-f003}

![*ABCE* periodic cell extracted from the paperboard core.](materials-13-01706-g004){#materials-13-01706-f004}

![Dimensions of the periodic core cell.](materials-13-01706-g005){#materials-13-01706-f005}

![Load diagrams used to calculate *Q* forces: (**a**) in machine direction (*MD)*, (**b**) towards cross direction (*CD)*.](materials-13-01706-g006){#materials-13-01706-f006}

![Resistance of honeycomb paperboard to edge crushing in the machine direction.](materials-13-01706-g007){#materials-13-01706-f007}

![Resistance of honeycomb paperboard to edge crushing in the cross direction.](materials-13-01706-g008){#materials-13-01706-f008}

![Results of *ECT~MD~* and *ECT~CD~* measurements of paperboard with 15 mm mesh diameter, made of T135 paper.](materials-13-01706-g009){#materials-13-01706-f009}

![Results of *ECT~MD~* measurements of cardboard with a 15 mm mesh diameter, made of various raw materials.](materials-13-01706-g010){#materials-13-01706-f010}

![*ECT* of paperboard with thickness *H* = 20 and different mesh sizes, made of paper T200/F140/T200.](materials-13-01706-g011){#materials-13-01706-f011}

![*ECT* of paperboard with thickness *H* = 30 and different mesh sizes, made of T200/F140/T200 papers.](materials-13-01706-g012){#materials-13-01706-f012}

materials-13-01706-t001_Table 1

###### 

Material constants of the papers are presented.

  --------------------------------------------------------------------------------------------------------------------------------
  Symbol   Paper Thickness\   Young's Modules of Paper in Cross Direction (GPa)   Young's Modules of Paper in Machine Direction\
           (mm)                                                                   (GPa)
  -------- ------------------ --------------------------------------------------- ------------------------------------------------
  T135     0.204              1.8                                                 5.3

  T160     0.209              2.3                                                 4.9

  T200     0.263              2.3                                                 5.7

  F140     0.203              2.1                                                 5.5
  --------------------------------------------------------------------------------------------------------------------------------

materials-13-01706-t002_Table 2

###### 

*ECT* measurement results: means of ten measurements and standard deviations.

  --------------------------------------------------------------------------------------------------------------------------------
  Symbol           *D*\   *H*\   *ECT~MD~*\   Max\         Min\         SD~MD~\   *ECT~CD~*\   Max\         Min\         SD~CD~\
                   mm     mm     N/m          *ECT~MD~*\   *ECT~MD~*\   N/m       N/m          *ECT~CD~*\   *ECT~CD~*\   N/m
                                              N/m          N/m                                 N/m          N/m          
  ---------------- ------ ------ ------------ ------------ ------------ --------- ------------ ------------ ------------ ---------
  T135/T135/T135   15     8      2005         2159         1794         159       2067         2392         1906         187

  T135/T135/T135   15     10     2235         2468         2061         115       2326         2429         2208         97

  T135/T135/T135   15     15     2207         2362         2000         84        2389         2630         2110         215

  T135/T135/T135   15     20     2270         2713         1854         306       2447         2629         2034         188

  T135/T135/T135   15     28     2182         2390         1972         187       2387         2781         2058         258

  T135/T135/T135   15     30     2358         2630         1982         336       2457         2866         2016         340

  T135/T160/T135   15     25     2138         2496         1900         182       2204         2337         2100         103

  T135/T160/T135   15     35     2369         2555         2081         188       2454         2586         1897         182

  T135/T160/T135   15     70     2464         2844         2136         217       2409         2608         2039         196

  T200/F140/T200   15     20     2930         3706         2550         321       3334         3724         3005         391

  T200/F140/T200   15     30     2953         3177         2834         110       3355         3569         2887         238

  T200/F140/T200   15     50     2843         3264         2623         247       3281         3403         2894         103

  T200/F140/T200   15     60     2370         2608         2203         170       2745         3210         2223         314

  T200/F140/T200   21     20     1691         1901         1562         157       1872         2042         1691         159

  T200/F140/T200   25     30     1378         1538         1169         118       1487         1665         1406         122

  T200/F140/T200   25     40     1433         1891         1227         191       1417         1790         1089         276
  --------------------------------------------------------------------------------------------------------------------------------

materials-13-01706-t003_Table 3

###### 

*ECT* calculation results.

  --------------------------------------------------------------------------------------------------------------
  Symbol           *D*\   *H*\   *ECT~MD~*\   Max\         Min\         *ECT~CD~*\   Max\           Min\
                   mm     mm     N/m          *ECT~MD~*\   *ECT~MD~*\   N/m          *ECT~C~*~D~\   *ECT~CD~*\
                                              N/m          N/m                       N/m            N/m
  ---------------- ------ ------ ------------ ------------ ------------ ------------ -------------- ------------
  T135/T135/T135   15     8      1989         2434         1692         2200         2675           1928

  T135/T135/T135   15     10     2373         2897         2033         2554         3105           2240

  T135/T135/T135   15     15     1932         2353         1675         2207         2679           1956

  T135/T135/T135   15     20     1942         2363         1697         2163         2624           1929

  T135/T135/T135   15     28     2111         2564         1859         2286         2771           2051

  T135/T135/T135   15     30     2166         2631         1911         2334         2828           2096

  T135/T160/T135   15     25     2436         2968         2080         2625         3191           2285

  T135/T160/T135   15     35     2856         3476         2442         3010         3656           2615

  T135/T160/T135   15     70     2004         2439         1712         2111         2563           1844

  T200/F140/T200   15     20     3265         3780         2803         4040         4665           3485

  T200/F140/T200   15     30     3539         4106         3028         4171         4828           3584

  T200/F140/T200   15     50     2742         3165         2374         3261         3756           2830

  T200/F140/T200   15     60     2864         3309         2474         3355         3869           2905

  T200/F140/T200   21     20     1654         1915         1421         2136         2464           1845

  T200/F140/T200   25     30     1166         1350         1002         1460         1686           1261

  T200/F140/T200   25     40     1209         1402         1037         1461         1690           1259
  --------------------------------------------------------------------------------------------------------------
