Functional description of fiber orientation in paperboard based on orientation tensors resulting from μ-CT scans

Modern μ -CT scans offer non-destructive three-dimensional microstructure analysis of various materials. Despite small density contrasts, this technology also accurately captures the complex network structure of paper and paperboard. It provides detailed insight into the fiber orientation distribution in paper, which was previously unattainable with existing measurement methods. The image analysis results are applicable for numerical fiber network models, and simulations based on these models can significantly improve our understanding of the microstructural influence on macrostructural paper properties, such as strength, stiffness, and curl tendency. This work presents a new method for investigating the microstructural fiber orientation in paperboard. Orientation tensors obtained from μ -CT scan image processing are extracted and evaluated. Based on the direction of the orientation tensor’s first eigenvector, the fiber orientation distribution is determined and then approximated by periodic and non-periodic probability density functions (PDFs). In this study, 40 commercial paperboard samples, each consisting of three plies, were analyzed. From a given set of commonly used PDFs, the best fitting ones have been identified based on their original location in the paper roll and on their ply. It was found that the von Mises PDF provided the most accurate representation of fiber orientation distribution in the middle ply, while the Elliptical PDF was the most suitable for the outer plies. Moreover, a more pronounced fiber orientation anisotropy was observed at the edges of the paper roll than in its center. The best PDFs and their function parameters are provided to allow for direct usage in numerical microstructure models of paperboard, thus enhancing their representativeness.