Defence of doctoral thesis: Gustav Marin – Impact of paperboard deformation and damage mechanisms on packaging performance
KTH | RISE
Paper-based materials, such as paperboard, are commonly used as packaging materials. In addition to the fact that paper is renewable, there are also many other benefits of paperboard. From a mechanical point of view, paperboard has a high bending stiffness compared to its relatively low weight and high foldability, which are properties of significance in the design of packages. However, a distinct drawback of paperboard is its significant sensitivity to moisture. The moisture reduces the mechanical properties of the paperboard and consequently reduces the performance of the package. This thesis addresses the impact of paperboard deformation and damage mechanisms on packaging performance, with the characterization of the material properties as a starting point. Initially, the relations between moisture and different mechanical properties on a continuum material level were investigated. Then, experimental testing and finite element (FE) simulations were applied to evaluate these relations at the packaging design level.
In Paper A, a material characterization was performed on five commercial paperboards with different basis weights, from the same producer. Five types of mechanical tests to characterize the paperboards material properties were performed:
- In-plane tensile test,
- Out-of-plane tensile test,
- Short-span Compression Test (SCT),
- Two-point folding,
- Double-notch shear test.
All tests were performed at several levels of relative humidity (RH). Linear relations between the mechanical properties normalized with their respective value at 50 % RH and moisture ratio were found.
Paper B examined whether the linear relationships discovered in Paper A are also valid for other paperboard series. Therefore, this study investigated 15 paperboards from four producers at the same RH levels as in Paper A. The paperboards were chosen to be different in furnish and construction, where four recycled boards were included. Here, the in-plane stiffnesses, strengths and SCT values were evaluated as a function of moisture. When the investigated paperboards’ moisture ratios were also normalized, all paperboards followed a linear master curve between normalized mechanical property and normalized moisture ratio. Additionally, a bilinear elastic-plastic in‑plane model was developed to predict the stress-strain relation of an arbitrary paperboard at an arbitrary moisture level without requiring mechanical testing except at standard conditions (50% RH, 23 °C).
In Paper C, the master curve developed in Paper B was used to estimate material input parameters for simulating a Box Compression Test (BCT) at different moisture levels by using an orthotropic material model with a stress-based failure criterion, i.e., a relatively simple material model with few input parameters. The result showed that it was possible to accurately predict the load-compression curve of a BCT when accounting for moisture. Furthermore, it was concluded that modeling the creases’ mechanical properties is vital for capturing the stiffness response of the package. Here, a measurable approach for reducing the creases’ mechanical properties was suggested, based on a folding test to obtain the relative creasing strength (RCS) and a short-span tensile test to obtain the relative tensile strength (RTS). It should be emphasized that the model does not include any fitting parameters. All input data is based on measured values. Due to the importance of creases, the RCS and RTS ratios were investigated further in Paper D. When evaluated against normative shear strength during creasing, the RCS and RTS values together formed a creasing window, where the RTS values corresponded to in-plane cracks (upper limit) and the RCS values corresponded to delamination damage (lower limit). It was observed that both the lower and upper limits exhibit linear relations as functions of shear strain.
Since creases have an evident effect on the packaging performance from a stacking point of view, it was interesting to investigate a load case exposing the package to shear. Therefore, an additional load case was investigated in Paper E: torsion of paperboard packages, where the experimental data was accurately predicted. Additionally, the effect of bending stiffness was investigated by developing two FE models. Model 1 (used in Paper C) treated the paperboard as a homogeneous material, and Model 2 considered the paperboard a three-ply laminate structure. No significant effect was noted, and it was concluded that the strength has a more significant effect on the BCT than the bending stiffness. It should also be mentioned that there were no problems with cracks when the paperboards were creased and mounted to packages used in Papers C and E. This correlates to the creasing window developed in Paper D since the creasing depth used for the packages is located within the creasing window.
To conclude, the primary procedure in this thesis is developing an easy-to-use model with few material parameters that demonstrably can predict the load-deformation curves for two different load cases. The purpose of the model is not to be used for the precise prediction of failure loads but to gain knowledge about damage mechanisms during the testing procedures. A clear advantage of this approach is that the model can be used to either change the package’s geometry or perform a parametric study on the ingoing material parameters. This can also be varied for each ply separately, which helps converters and paperboard producers. It has also been shown that the model can account for different moisture levels if the master curve developed within this thesis is applied. Finally, it should be emphasized again that the model does not include any fitting parameters. All input data is based on measured values.