Method for Calculating the Bending Stiffness of Honeycomb Paperboard.

The article presents continued considerations presented in a prior publication on the development of a model for calculating the bending stiffness BS of cellular honeycomb paperboards, applying the strength properties of paper raw materials used for the production of paperboard and the geometric parameters of cellular board. The results of BS calculations obtained by using the analytical model presented in the prior publication were significantly overestimated in relation to the value obtained by measurements. The calculation error in relation to the measurement value for the tested group of paperboards in the case of bending stiffness in the machine direction MD was within the range from 23% to 116%, and the average error was 65%, while in the cross direction CD, it was within the range from 2% to 54%, and the average error was 31%. The calculation model proposed in this work based on the physical properties of cellular paperboard reduces the error values for bending stiffness in both the machine and cross directions. The value of the average error for both main directions in the paperboard plane was 10%. The method enables more accurate determination of BS in the machine direction MD and in the cross direction CD at the paperboard design stage. In order to validate the proposed analytical model, the calculation results were compared with the results of BS laboratory measurements performed using the four-point bending method and, in order to expand the group of tested paperboards, with the measurement results presented in the prior article for cardboards with different raw material composition and different geometric parameters.

Bending Stiffness of Honeycomb Paperboard.

This article analyzes the influence of the initial deflection of the flat layers on the bending stiffness (BS) of honeycomb paperboards and presents two methods for its calculation. Both methods allow for the determination of BS in the main directions in the plane of the paperboard, i.e., the machine direction (MD) and the cross direction (CD). In addition, they have been verified by comparing the calculation results with the results of the BS measurements. The first method allowed for the calculation of the BS of cellular paperboard based on the mechanical properties of the paper used for its production. The second method allowed for the estimation of the BS of cellular paperboard based on the bending stiffness of other honeycomb paperboards with the same raw material composition and the same core cell size but with different thicknesses. In the first analytical method for the calculation of the bending stiffness of cellular paperboard, which does not include the deflections of the flat layers, the calculation results significantly differ from the measurement results, and they are overestimated. The second of the presented BS calculation methods allowed for a much more accurate assessment of paperboard's bending stiffness depending on its thickness.

Numerical and Experimental Study of Five-Layer Non-Symmetrical Paperboard Panel Stiffness.

This paper concerns the analysis of five-layer corrugated paperboard subjected to a four-point bending test. The segment of paperboard was tested to determine the bending stiffness. The investigations were conducted experimentally and numerically. The non-damaging tests of bending were carried out in an elastic range of samples. The detailed layers of paperboard were modelled as an orthotropic material. The simulation of flexure was based on a finite element method using Ansys® software. Several material properties and thicknesses of papers in the samples were taken into account to analyse the influence on general stiffness. Two different discrete models based on two geometries of paperboard were considered in this study to validate the experimental stiffness. The present analysis shows the possibility of numerical modelling to achieve a good correlation with experimental results. Moreover, the results of numerical estimations indicate that modelling of the perfect structure gives a lower bending stiffness and some corrections of geometry should be implemented. The discrepancy in stiffness between both methods ranged from 3.04 to 32.88% depending on the analysed variant.

The Strength of Egg Trays under Compression: A Numerical and Experimental Study.

This work concerns the analysis of egg packages subjected to compression. Experimental investigations were carried out to determine the curves of compression and maximum loads. To compare packages accessible on the market, several different shapes of egg packages were tested after being conditioned in air with a relative humidity of 50%. Several paper structures in stock were compressed. By validating the experiment results, numerical computations based on the finite element method (FEM) were executed. The estimations of a numerical model were performed with the use of the perfect plasticity of paper and with the assumption of large strains and deflections. Our own two structures of egg packaging were taken into account: basic and modified. The material of the packages was composed of 90% recovered paper and 10% coconut fibres. This paper involved the numerical modelling of such complex packaging. Moreover, our research showed that introducing several features into the structures of the packaging can improve the stiffness and raise the maximum load. Thanks to the application of ribs and grooves, the strength ratio and compression stiffness, in comparison to the basic tray, increased by approximately 23.4% and 36%, respectively. Moreover, the obtained indexes of modified trays were higher than the majority of the studied market trays.

Calculation of Honeycomb Paperboard Resistance to Edge Crush Test.

The article presents the method of calculating the edge crush test (ECT) of honeycomb paperboard. Calculations were made on the basis of mechanical properties of paper raw materials used for the production of cellular paperboard and geometrical parameters describing cellular paperboard. The presented method allows ECT calculation of honeycomb paperboard in the main directions in the paperboard plane; i.e., machine direction (MD) and cross direction (CD). The proposed method was verified by comparing the results of calculations with the results of ECT measurements of paperboard with different geometrical parameters made of different fibrous materials.

Flexural Damage of Honeycomb Paperboard-A Numerical and Experimental Study.

This paper presents an experimental and numerical analysis using the finite element method (FEM) of the bending of honeycomb-core panel. Segments of honeycomb paperboard of several thicknesses were subjected to four-point flexure tests to determine their bending stiffness and maximum load. Several mechanical properties of orthotropic materials were taken into account to account for the experimental results. The numerical analysis of the damage prediction was conducted by using well-known failure criteria such as maximum stress, maximum strain and Tsai-Wu. The present study revealed how to model the honeycomb panel to obtain curves close to experimental ones. This approach can be useful for modelling more complex structures made of honeycomb paperboard. Moreover, thanks to the use of variously shaped cells in numerical models, i.e., the shape of a regular hexagon and models with a real shape of the core cell, results of the calculation were comparable with the results of the measurements. It turned out that the increase of maximum loads and rise in stiffness for studied samples were almost either linearly proportional or quadratically proportional as a function of the panel thickness, respectively. On the basis of failure criteria, slightly lower maximum loads were attained in a comparison to empiric maximum loads.