Tray forming operation of paperboard: A case study using implicit finite element analysis

Abstract

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.

The Effect of Ply Properties in Paperboard Converting Operations: A Way To Increase Formability

“…The criterion states that the Tsai-Wu index should be below 1 to avoid failure. A detailed discussion about the Tsai-Wu index evaluation can be found in Lindberg and Kulachenko (2021). In Fig.…”

“…the tensile stresses in MD and CD for each ply. The numerical model developed and used for this study is a sub-model of the model used in Lindberg and Kulachenko (2021), where the lower critical area was successfully identified in the simulations of the full tray forming operation. The simulations in this study were performed with the finite element solver Ansys 2019R1 in a quasi-static regime using an implicit time-integration method.…”

“…With such simulations, the impact of the paperboard properties on the risk of failure during forming operations can be assessed. The current study is a continuation of the work performed in Lindberg and Kulachenko (2021), where the tray forming operation was simulated using an implicit non-linear finite element (FE) model using a single-ply approach. In contrast to the previous study, where the difference between the boards can be seen already on the sheet level, the boards considered here have similar properties, but still show of differences in performance.…”

“…At the time of the study, however, only Board B had no reported problems at the customer end. In Lindberg and Kulachenko (2021), the tensile tests showed observable differences between the two boards on the sheet level, with Board B having higher stress and strain to failure in the paperboard machine direction (MD) and the cross-machine direction (CD), but somewhat lower stress and strain to failure in the 45-direction. The FE-model in that study predicted that the observed differences on the sheet level can explain the performance degradation in Board A.…”

“…For this, a three-ply FE sub-model was built where the plies were modeled with their individual material properties and thicknesses. The model is a submodel of the model in Lindberg and Kulachenko (2021). The sub-model is simulating the area constituting the critical lower corner in the tray forming process, see Fig.…”