PAPERmaking! Vol8 Nr2 2022

Materials 2022 , 15 , 663

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Figure 10. BS calculated by a theoretical model for all 6 boards in which only flat layers are active (blue bars) and by two numerical models where corrugated layers are included in the calculation (red bars) or are excluded from the calculation (yellow bars). Table4. The bending stiffness computed by the numerical model with included fluting with different number of periods. FEM-2–a model with two periods (see Figure 9a), FEM-4–a model with four periods (see Figure 9b).

BS (Nm)

Name

FEM-1

FEM-2

FEM-3

FEM-4

Board1 Board2 Board3 Board4 Board5 Board6

8.187

8.198

8.160

8.160

12.129

12.135

12.069

12.069

8.213 8.322

8.231 8.332

8.182 8.292

8.182 8.293

11.983

11.991

11.926

11.926

9.652

9.669

9.625

9.626

In the next step, the influence of imperfection amount on the bending stiffness in the analytical model was analyzed. The results for the parameter k ranging from 2 to 4 are shown in Figure 11. The selected value of k = 2.3 is marked on all graphs along with corresponding BS values for both case EB and BE. The selected value of k gives the best agreement between the results obtained with the proposed model and the available experimental data. Because the presented analytical model takes into account the initial imperfections of compressed segments in the corrugated board, thus allows to distinguish between the bending stiffness of the corrugated board whether the E wave or the B wave is compressed. The bending stiffness not only decreases with the increase of the initial imperfection, but also the BS difference between the EB and BE increases as the imperfections increase (see Figure 12). In other words, as the initial imperfections increase, the bending stiffness of the sample in the EB configuration (compression on the B wave side) decreases faster than the bending stiffness of the sample in the BE configuration.

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