The present study investigates torsional and compressive loading of a paperboard package. Finite element (FE) analyses simulating the tests were performed to improve understanding of the stresses and deformations in the paperboard during loading. A simple experimental characterization of the necessary material properties could be performed to represent the multi-ply paperboard as a single-ply structure. The results from the single-ply model were compared with a laminate model, and the differences between the models were small. Comparing experimental and FE simulations of box compression and torsion showed that the FE models could accurately predict the response curves. However, in the simulations, there was an overprediction of the maximum compressive force and maximum torque, which was expected since geometrical imperfections and the heterogeneous internal structure of the material were not accounted for in the material model or the FE model. Local yield lines formed at the onset of non-linearities in the package load–displacement curves. Therefore, the strength of the paperboard affects the maximum compressive strength and maximum torque, and the bending stiffness of the paperboard only had a minor effect. When a first local maximum was reached, the number of FE that reached the failure stress increased exponentially. The simulations also showed that box compression was not an effect of package height, but higher packages had a lower maximum torque. © 2022 The Authors. 

Creasing is an essential process to convert paperboards into packages since it enables folding along well-defined lines. The creasing process relies on purpose-made damage that is initiated in the paperboard structure: delamination. However, creasing might also cause in-plane cracks, which must be avoided. In this laboratory study, three paperboards were creased at six different depths, respectively. Two mechanical tests were performed to characterize the creases at standard climate (23°C and 50% RH): 2-point folding, to examine the bending force and short-span in-plane tensile test to evaluate the strength. The results were normalized with the values for the uncreased boards, which gave the relative strength ratios: relative creasing strength (RCS) and relative tensile strength (RTS). When the relative strengths were evaluated against the normative shear strains, a creasing window was formed. This window has an upper limit given by the RTS values, corresponding to the in-plane cracks, and a lower limit given by the RCS values, corresponding to the delamination damage initiated in the paperboard during creasing. It was observed that both the RCS and RTS values exhibit a linear relation against normative shear strain. From this, it was concluded that performing tests at two creasing depths might be sufficient to estimate the lower, and upper, limits for the creasing window in future studies. Finally, the effect of moisture was investigated by creasing, folding and tensile testing at 23°C and 90% RH, which showed that moisture had no clear effect on the RCS or the RTS values. 

Finite element (FE) analyses can be used as a powerful tool in the package design process to study for instance stress and strain fields that arise during loading. An orthotropic linear elastic material model with a stress-based failure criterion was used to simulate box compression tests (BCTs) of a paperboard package in the FE solver LS-Dyna. Physical experiments were performed at 50%, 70%, and 90% relative humidity (RH). The input parameters required for the simulations were calculated based on material characterization at standard climate (50% RH and 23°C) and a linear relation between mechanical material properties and moisture ratio established in earlier studies. The result showed that it was possible to accurately predict the load–compression curve of a BCT when moisture was accounted for. Furthermore, it was found that modelling of the mechanical properties of the creases are important for capturing the stiffness response of the package. To conclude, it was possible to predict the box compression strength and the linear stiffness response prior to the peak in the load–compression response at relevant moisture levels, by using the previously established linear relationship between moisture ratio and material properties. In addition to the moisture ratio at the preferred moisture level, the only material properties required were the in-plane strengths and stiffnesses, and the out-of-plane shear moduli at standard climate. 

To verify a linear relation between normalized mechanical property and moisture ratio, in-plane tensile tests were performed on four types of paperboard from different manufacturers. Tensile properties were normalized with respect to the property at standard climate (50 % RH, 23 °C). Short-span Compression Tests were also performed to investigate if the relation was linear also for in-plane compression. The tests were performed at different relative humidity (20, 50, 70 and 90 % RH) but with constant temperature (23 °C) in MD and CD, respectively. The linear relation was confirmed for the normalized mechanical properties investigated. In fact, when also the moisture ratio was normalized with the standard climate, all paperboards coincided along the same line. Therefore, each mechanical property could be expressed as a linear function of moisture ratio and two parameters. Moreover, an in-plane bilinear elastic-plastic material model was suggested, based on four parameters: Strength, stiffness, yield strength and hardening modulus, where all parameters could be expressed as linear functions of moisture ratio. The model could predict the elastic-plastic behavior for any moisture content from the two parameters in the linear relations and the mechanical properties at standard climate.

Five commercial multiply folding boxboards made on the same paperboard machine have been analyzed. The paperboards were from the same product series but had different grammage (235, 255, 270, 315, 340 g/m2) and different bending stiffness. The paperboards are normally used to make packages, and because the bending stiffness and grammage varies, the performance of the packages will differ. Finite element simulations can be used to predict these differences, but for this to occur, the stiffness and strength properties need to be determined. For efficient determination of the three-dimensional properties in the machine direction (MD), cross direction (CD), and Z direction (ZD), it is proposed that the paperboard should be characterized using in-plane tension, ZD-tension, shear strength profiles, and two-point bending. The proposed setups have been used to determine stiffness and strength properties at different relative humidity (20,% 50%, 70%, and 90% RH), and the mechanical properties have been evaluated as a function of moisture ratio. There was a linear relation between mechanical properties and moisture ratio for each paperboard. When the data was normalized with respect to the standard climate (50% RH) and plotted as a function of moisture ratio, it was shown that the normalized mechanical properties for all paperboards coincided along one single line and could therefore be expressed as a linear function of moisture ratio and two constants. Consequently, it is possible to obtain the mechanical properties of a paperboard by knowing the structural properties for the preferred level of RH and the mechanical property for the standard climate (50% RH and 23°C).

Packages made of five folding box boards made on the same paperboard machinehave been analysed. The paperboards were from the same product series but had different grammage (235, 255, 270, 315, 340 g/m2) and different bending stiffness. Thepaperboards are normally used to make packages, and since the bending stiffnessand grammage varies the packages performance will be different. In this study, twodifferent load cases were defined and Box Compression Tests (BCT) were performedat different levels of relative humidity (30, 50, 70, 90 % RH) and were evaluated as afunction of moisture ratio.The result showed a linear relation between the box compression strength and themoisture ratio. In addition, when the data was normalized with the measurements forthe standard climate (50 % RH) and was evaluated as a function of moisture ratio, theresult indicated that the normalized box compression strength for all the paperboardsand both of the load cases could be expressed as a linear function of moisture, dependent of two constants a and b.Consequently, the study indicates that it is possible to estimate the Box compressionstrength at different climates of a package made of paperboard, by knowing the boxcompression strength for the standard climate (50 % RH and 23 °C) and the constantsa and b.

Torsional loading with combined out-of-plane compressive loading has been studied for its viability in measurement of out-of-plane shear properties. Paperboards of two qualities were evaluated, namely paperboard A, which was a multiply, while paperboard B was a single ply. Both paperboards were produced on commercial paperboard machines. A total of 24 samples were prepared, 12 of each quality, which were tested under four different load levels. Three different out-of-plane compressive load levels were tested in addition to test without compressive load. Results have been presented from the successful tests in terms of torque versus angle of torsion and shear stress versus shear strain plots. It has been demonstrated that the technique was suitable for out-of-plane shear measurements. An order of magnitude agreement in the values of the properties was obtained in the torsional test method and the rigid block shear tests. Results indicated a possible stable post-peak response in shear loading at sample sizes that would provide material properties comparable with that of a homogeneous test. The torsional setup offered benefit of ease of applying out-of-plane axial loads, both in compression and tension.

A finite element framework has been proposed that can be used to simulate both empty paperboard packages and package filled with plastic granulates. A gable top package was made of a commercial paperboard, and material properties needed in the material model were determined. Two simulations were performed, a drop test and a compression test. By comparison between experimental and numerical results, the deformation mechanisms at impact could be identified and correlated to material properties. When the package was filled with granulates, different mechanisms was activated compared with an empty package. The granulates contribute to bulging of the panels, such that the edges became more load bearing compared with the panels. When the edges carried the loads, the importance of the out-of-plane properties also increased, and local failure initiation related to delamination was observed. Comparison between experimental and numerical impact forces shows that there are still important things to consider in the model generation, eg, variation of properties within the package, which originate both from material property variations, and the loading history, eg, during manufacturing and handling.

 A finite element framework has been proposed that can be used to simulateboth empty paperboard packages and package filled with plastic granulates. A Gabletop package was made of a commercial paperboard, and material properties neededin the material model was determined. Two simulations were performed, a drop testand a compression test. By comparison between experimental and numerical results,the deformation mechanisms at impact could be identified and correlated to materialproperties. When the package was filled with granulates different mechanisms wasactivated compared to an empty package. The granulates contribute to bulging ofthe panels, such that the edges became more load bearing compared to the panels.When the edges carried the loads the importance of the out-of-plane properties alsoincreased, and local failure initiation related to delamination was observed. Comparison between experimental and numerical impact forces show that there are still important things to consider in the model generation, e.g. variation of properties withinthe package, which originate both from material property variations and the loadinghistory, e.g. during manufacturing and handling.

Research has been undertaken to characterise the in-plane and out-of-plane stiffness and strength properties of paperboards to enable data for use in determining constitutive parameters needed in finite element simulations. Paperboards with different bending stiffness were analysed, using five folding box boards of varying grammage (235, 255, 270, 315 and 340gsm). The stiffness and strength properties were determined at different relative humidity (RH), namely, 20, 50, 70 and 90%. As well as in-plane tensile test and out-of-plane tensile test, the short-span compression test (SCT) was carried out, together with bending stiffness test and double-notch shear test. The results revealed a linear relation between mechanical properties and moisture ratio for each paperboard. When the data were normalised with data for the standard climate (50% RH) and investigated as a function of moisture ratio, it was determined that the normalised mechanical properties for all paperboards coincided along one single line. Thus they could be expressed as a linear function of moisture ratio and two constants. It has been concluded that by knowing the structural properties for the preferred level of RH and the mechanical property for the standard climate, the mechanical properties of a paperboard could be obtained.