The characterization and modeling of the out-of-plane behavior of fiber-based materials is essential for understanding their mechanical properties and improving their performance in various applications, especially in the forming process. Despite this, research on paper and paperboard has mainly focused on its in-plane behavior rather than its out-of-plane behavior. However, for accurate material characterization and modeling, it is critical to consider the out-of-plane behavior. In particular, delamination occurs during forming processes such as creasing, folding, and deep drawing. In this study, three material models for paperboard are presented: a single all-material continuum model and two composite models using different cohesion methods. The two composite models decouple in-plane and out-of-plane behavior and consist of continuum models describing the behavior of individual layers and cohesive interface models connecting the layers. Material characterization experiments are performed to derive the model parameters and verify the models. The models are validated using three-point bending and bulge tests and show good agreement. A case study is also conducted on the application of the three models in the simulation of a deep drawing process with respect to wrinkle formation. By comparing the simulation results of wrinkle formation in the deep drawing process, the composite models, especially the cohesive interface composite model, show greater accuracy in replicating the experimental results, indicating that a single continuum model can also be used to represent wrinkles.

The evaluation of wrinkles in deep-drawn fiber-based materials is crucial for the assessment of product quality and the optimization of manufacturing processes. Wrinkling is a common phenomenon in the deep-drawing process and is caused by tangential compressive stresses on the flanges of the blank. This phenomenon is particularly prevalent for fiber-based materials with high tensile depths and can seriously affect the appearance and mechanical properties of the final product. The objective of this study is to identify the key process parameters affecting wrinkling and to deepen the understanding of their roles and interactions using wrinkle data for deep-drawn paper products. Image analysis techniques are employed, supported by a specially constructed darkroom platform to ensure uniform light intensity for capturing photographs. An automated program is developed for the detection and evaluation of wrinkle characteristics and distribution, which allows the free choice of the region to be detected and the representation of the wrinkle geometry not limited by the number. To enhance the precision of this program, the ellipticity is initially rectified for products without flanges, specifically cup-shaped deep-drawn products. The ellipticity is caused by the pronounced springback effect of the paperboard. The approach is employed to investigate the impact of material properties, blank holder force, drawing depth, drawing clearance, and punch speed on wrinkling formation after the deep-drawing process. The findings reveal that the blank holder force and drawing clearance are critical factors in wrinkle formation, with higher blank holder force generally leading to increased wrinkle numbers.

This study investigates how moisture preconditioning and thermal parameters affect the stretchability of paper in 3D forming, with the goal of extending geometric forming limits and enhancing process stability. Multidimensional tensile tests were performed on FibreForm Duo (310 g/m²) using a hemispherical punch. Key variables included water bath dwell time, punch temperature, and contact time, simulating industrial conditions in high-speed packaging. A short duration of water bath immersion (1–3 s) led to rapid moisture uptake (−20%), resulting in significantly improved formability. Compared to unconditioned samples, the maximum stretch increased by up to 3.5 percentage points. The process window identified (3.03 s dwell time; 70 °C punch temperature; 1.08 s contact time to punch) yielded a predicted stretch of 16.5%, representing a notable expansion of the material’s geometric forming capacity. Regression analysis (R² = 0.8946) confirmed the strong statistical significance of all parameters.

This study presents a novel transmission-based method for characterizing local structural features, including the grammage, thickness, and fiber orientation, of paper materials. Some non-destructive techniques, such as micro-computed tomography ($\mu$-CT), microscopy, and radiation-based methods, are costly, time-consuming, and lack the ability to provide comprehensive local structural information within a single measurement. The proposed method utilizes a single light transmission measurement to assess local grammage and thickness through histogram matching with reference data obtained via $\beta$-radiography and profilometry. The same light transmission images are also used to determine local fiber orientation, employing image analysis techniques. The structure tensor method, which analyzes gradients of light transmission images, provides detailed insight into the local fiber orientation. The results show that thickness and grammage measurements are independent of which side of the paper is evaluated, while the fiber orientation distribution varies between the front and back sides, reflecting differences in fiber arrangement due to manufacturing processes. Various distribution functions are compared, and the Pearson Type 3, log-normal, and gamma distributions are found to most accurately describe the grammage, thickness, and fiber orientation distributions. The study includes a variety of paper types, ensuring a robust and comprehensive analysis of material behavior, and confirms that the method can effectively infer the inhomogeneous features from a single light transmission measurement.

The temperature of the tools and the moisture content of the material play a significant role in the 3D forming of paperboard in terms of the degree of forming and the quality of the formed part. It is known that different forming mechanisms act within the paperboard in different areas of the deep drawing tools during the deep drawing of paperboard and that the success of the forming process is also based on a dynamic interaction between material moisture and tool surface temperature. However, it has not yet been investigated how the forming parameters can be influenced by an individually adjustable temperature for the individual tool areas and how they influence the complex interaction with the moisture content of the paperboard during the forming process. Due to the inhomogeneity of the natural fiber network of paperboard, rapid and directed temperature changes of the tools are also of interest in order to be able to react quickly to variations of material properties in order to prevent frequent process failure within a continuous production. In this paper, test tools with individually controllable heating zones were developed and the use of different heating technologies to improve the rate of temperature change was analyzed. These tools were used to investigate the influence of temperature in the individual sections of the deep drawing process and how the moisture content can be specifically controlled during the process. It was found that with modern heating technology, the deep-drawing tools can be tempered significantly faster and that a temperature difference between the blank holder zone and the drawing cavity zone has a positive influence on the formability and the fixation of the shape of the part produced. This effect was further enhanced by the fact that, thanks to the temperature tailored tool, it was possible to work with a very high moisture content of the paperboard.

Deep drawing is a common process for shaping paperboard packages. To improve performance, the paperboard is kept in a room with high humidity before treatment. The surfaces of forming tools that come into contact with the paperboard are heated. A control problem for heating moist paperboard, with evaporation from the pore surface, is considered in this paper. Micro-CT images of three different paperboards are taken, segmented, and parameterized with respect to the specific pore surface in terms of the pore surface per pore volume, pore volume fraction, fiber thickness, average surface contact area between fibers, and unsupported fiber length. Simple averaging formulas are provided to compute the effective coefficients in the coupled water-diffusion and heat-transfer problem with a phase transition. The model is validated by experimental measurements and offers an opportunity for optimal heating control to simultaneously ensure compliance of the paperboard layer, leading to small delamination at its boundary, thereby avoiding folding.