Influence of inhomogeneities on the tensile and compressive mechanical properties of paperboard

Abstract: The in-plane properties of paperboard have always been of interest to paper scientists. The reason for this is that they play a significant role for the usability of the paperboard in converting and end-use. Tensile properties are crucial when the board is fed through printing and converting machines at high speeds. While compressive properties are essential in the later use, e.g. in packages. Inhomogeneities affect both the compressive and tensile properties. For the tensile properties, it is the inherent heterogeneity of the paperboard that might cause problems for the board-maker, especially in the design of more advanced paperboard packages. Varying material properties, through the thickness of the paperboard, are on the other hand frequently used by the board-makers, when they wish to achieve high bending stiffness with low fiber usage. It is of interest to know how this practice affects the local compressive properties. Papers A and B aims to adress this, while Papers C, D and E focus on in-plane heterogeneities and their effect on the paperboard's behavior.The first paper, Paper A, investigates the mechanism that causes failure in the short span compression test (SCT). Three different multiply paperboards, chosen to have distinctly different through-thickness profiles were examined. The boards were characterized and the data was used to simulate SCT. The simulation was conducted with a finite element model consisting of layers of continuum elements with cohesive interfaces in-between. From the model it was concluded that the main mechanism for failure in SCT is delamination due to shear damage.The second paper, Paper B, was a continuation of Paper A. The effect of the through-thickness profiles on the local compression strength was examined for five paperboards. It was concluded that the local compression is governed by in-plane stiffness and through thickness delamination. The delamination damage was in turn dependent on the local transverse shear strength and in-plane stiffness gradients. Furthermore, it was concluded that the pre-delamination mechanisms were essentially elastic.In the third paper, Paper C, the tensile test is investigated with focus on sample size and strain distributions. Multiply paperboards were examined with varying sample sizes using digital image correlation (DIC). Different strain behavior was found for different sample sizes, which was dependent on the length to width ratio of the sample and was caused by activation of local zones with high strainability in the sample. These zones were of constant size and therefore occupied different amounts of the total sample area.The fourth paper, Paper D, focuses on the local strain zones seen in Paper C and how they were affected by creping. The thermal response in paper was studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of streaks with increased temperature could be observed. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Due to the fibrous network structure, paper has an inhomogeneous microstructure, called formation. It could be shown that the formation was the cause of the inhomogeneous deformation in paper. Finite element simulations were used to show how papers with different amount of homogeneity would deform. Creped papers, where the strain at break has been increased, were analyzed. For these papers it was seen that an overlaid permanent damage was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.In the fifth and final paper, Paper E, the virtual field method (VFM) was applied on DIC-data from Paper C. This was done to demonstrate the ability of different VFM-formulations for characterization of paperboard stiffness heterogeneity. The specimen was divided into three subregions based on the axial strain magnitude. VFM-analysis showed that the subregions had stiffnesses and Poisson's ratio's that varied in a monotonically decreasing fashion, with the stiffness differences between subregions increasing with applied tensile stress. The results suggested that high stiffness regions provide only marginal improvement of the mechanical behavior.