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It was evident the greatest risk for failure often was within the middle ply. Moreover, if the density is lowered, the risk of failure due to insufficient middle ply density increases. Hence by having good control of the densities in the differ- ent plies it would be possible to balance where the weakest point in the through-thickness direction should be located, and how much stronger the outer plies need to be for optimal performance. Hence, it is not the strength of the individual ply that is important, it is the relation to the other plies that gives optimal performance. While it could be concluded that an efficient way to increase the bending stiffness of a paperboard was to decrease the density of the middle ply. When the density is decreased from 500 to 400 kg/m 3 the bending stiffness increase about 50%. However, the analysis also show that this will result in a 20% drop in ZD strength. The drop in ZD strength will also affect the maximum bending moment that the paperboard can carry, which in turn will affect the box compression. Hence, lightweight will reduce quality of the paperboard, which is not acceptable. An alternative approach is then to work with the strength profile in the through-thickness direction. Instead, it would be possible to work with the density gradient in the paper- board, which can be controlled by drainage of the paper- board during production. The analysis done here showed that it would be advantageous to increase the strength of the lower part of the middle ply to increase the maximum bending moment of the paperboard. In addition, the orien- tation of the different plies can be utilized to optimize the paperboard performance; the plies can be oriented more or less in the MD to minimize the largest stresses that arise in the through-thickness direction. Acknowledgements The work has been financed by internal resources from BillerudKorsnäs, for which the author is grateful. BillerudKorsnäs acknowledge the possibility offered to publish results within the sci- entific community. Funding Open access funding provided by Royal Institute of Technology. Data availability This manuscript has no additional data available.
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