This study addresses the question of how the difference in mechanical properties of the individual layers in a multi-ply commercial paperboard affects the outcome of the tray-forming operation. Two commercially produced paperboards with nearly identical mechanical properties when conventionally tensile tested were considered. These boards are produced on different machines with the same target grammage and density. Despite the similar mechanical properties, their performance in a given tray-forming operation was drastically different, with one of the boards showing an unacceptable failure rate. To investigate the difference seen during converting operations, a detailed multi-ply finite element model was built to simulate the converting operation. The present model considers a critical area of the paperboard known to exhibit failures. To derive the constitutive relations for each ply in the sub-model, both boards were split to single out individual plies which were then tensile tested. Including the properties of individual plies revealed large differences between the boards when it comes to the distribution of the properties in the thickness direction. In particular, the top plies differed to a large extent. This is attributed to the difference in refining energies for the plies. The results from the three-ply sub-model demonstrated the importance of including the multi-ply structure in the analysis. Weakening of the top ply facing the punch by using lower refining energy considerably increased the risk of failure of the entire board. These results suggest that there is room for optimizing the board performance by adjusting the refining energy at the ply level.

The possibility to perform advanced forming operations of initially plane paperboard paves the way to making products like food trays, plates, cups and other containers as a part of shifting towards a circular bioeconomy. As a part of the ongoing efforts of expanding the product range using paperboard, we performed analyses of the forming operation using simulations. An implicit non-linear finite element model is built to more accurately than previous studies simulate the tray forming process of paperboard. Two different commercial paperboards are investigated. The use of an implicit solver enabled the inclusion of the creasing pattern into the geometry of the paperboard blank resolving the formation of wrinkles during forming. The material data is extracted from tensile test curves of the investigated paperboards and was fitted accurately using Hill's plasticity with difference in tension and compression accounted for with subsequent failure evaluation. The results showed that the inclusion of the creases in the geometry is vital for getting a correct shape of the formed tray and important for decreasing the risk of failure. The results also showed that friction has a big impact on the formed shape and hence on the stress levels, and therefore supports the means of lowering friction between the blank holder and the blank during the tray forming operation. A stochastic approach is proposed to determine the probability of failure for the boards. The performed failure evaluation is consistent with the field observations. The developed approach enables more precise simulations of paperboard tray forming.