Materials 2022 , 15 , 663
5of 17
while the corrected B-flute height is:
h ∗ 2 = h 2 + 0.5 t 2 + 0.5 t 3 + t 5 .
(3)
Figure 4. Thickness of all corrugated board layers and axial distance between liners in the computa- tional model. Table 3 summarizes the thicknesses of all corrugated cardboard layers for six boards and the calculated distances between liners (i.e., corrected heights of the corrugated layers), according to Equations (2) and (3).
Table3. Thickness of individual layers of corrugated board and height of corrugated layers.
Thickness ( μ m)
Height (mm)
Mode ID
h * 1
* 2
Liner 1
FluteE
Liner 2
FluteB
Liner 3
h
Board1 Board2 Board3 Board4 Board5 Board6
142 185 142 142 185 142
164 227 199 177 199 177
126 177 126 139 177 164
164 199 139 177 199 177
146 186 146 146 186 186
1.498 1.608 1.523 1.518 1.580 1.530
2.880 2.961 2.855 2.899 2.961 2.930
As already mentioned, the measured thicknesses of the constituent papers (see Table 3) and the geometry of the corrugated layers (see Table 2) were taken from [29]. 2.3. Bending Stiffness of Assymetric Corrugated Board with Imperfections It is assumed in this study that only liners are involved in bending in the MD, which means that fluting has only the role of supporting the liners in the correct position. There- fore, their tensile/compression and bending stiffnesses are negligible. In order to derive the model, first, all liners were segmented between the supporting wave crests in the corrugated layer (see Figure 5). Preliminary geometric imperfections were included in the compressed segments, which reduced the stiffness of these elements. These assumptions allow to capture the difference in BS depending on the sign of a bending moment in the asymmetric boards. Since the five-layer corrugated board consists of three liners, three different segment lengths can be distinguished: L 1 and L 3 correspond to the E and B wave periods, respec- tively. On the other hand, the length L 2 can reach the maximum value of p 1 (where p 1 is a lower wave period, see Figure 3). However, usually every second segment is divided into two sections by the crest of wave B, indicated by L 2 on Figure 5. Therefore, the average length equal to 2/3 p 1 was adopted in the middle liner for further analyses.
Made with FlippingBook - Online magazine maker