Delamination strength is an essential property for the creasing and folding operations of paperboard into boxes. Due to fixation during creasing, the paperboard suffers in-plane straining. In the present study, we aim to increase our understanding of how in-plane straining affects the delamination properties of paperboard. Samples of paperboard were first strained in in-plane tensile loading, both in the machine-direction and in the cross-direction. Afterward, the paperboard is loaded in the out-of-plane (ZD) direction. Three different grades of commercial paperboard from two major manufacturers were tested in a climate-controlled lab. The results showed similar results for all grades of paperboard, with the delamination strength and the out-of-plane stiffness decreasing virtually linearly with pre-straining. With about 5% plastic in-plane straining, the strength was reduced by about 20% and the stiffness decreased by more than 50% for all grades of paperboard. Normalizing the strength and the stiffness with their values without pre-straining reveals virtually the same relation for all grades of paperboard. If proven to be a general result, this will prove valuable in reducing the demand for experiments. Application: The results from this study are important for the understanding and modeling of creasing and folding of paperboard.

Paperboard packaging is made by processing board materials into sheets or rolls and shaping them through creasing, cutting, folding, and erecting. The conversion process generates residual moments at the folds that cause panel bulging. This study experimentally investigates how the bulging introduced during the converting processes influence the mechanical response of paperboard packages during point load testing within the elastic deformation range. The study shows that panel bulging may significantly affect packaging performance as-perceived strength and stiffness. Bulging, influenced by the board's basis weight, can affect the package performance even more than packaging stiffness. Point load tests in the elastic region were performed on empty packages (78 mm & times; 50 mm & times; 110 mm) with force applied at specific points along their long sides. The packages evaluated in this study were made of two identically processed materials of different grammages. The heavier material showed more pronounced bulging than the lighter one, leading to overlapping force-displacement curves for the packages, and to that, a lower force and stiffness may be measured at a certain indentation depth for the package of heavier material. This complicates material choice according to functional requirements. The results show that a highly bulged package might resemble one with less bulging of another material. According to the results, it is not certain that a higher grammage package shows a higher indentation force and stiffness than a lower grammage package when measured at a certain indentation. This indicates that optimizing the creasing and folding processes can be a way to enhance performance rather than simply increasing board weight. The study underscores the importance of controlling converting parameters, especially creasing and folding behavior. Well-performed creasing and folding gives a low residual momentum, little bulging, and a high stiffness and compression strength at point loading in the elastic region. Proper optimization can improve packaging performance and manual handling user-friendliness. Application: The results from this study are of significant importance for the package industry, especially in package design, as the results show that a lower grammage may give a higher stiffness, depending on loading position.

HybrixTM sandwich plates (Lamera AB, Gothenburg, Sweden) with metal face sheets could replace standard metal plates in many lightweight applications. Their composite core, which is crucial for the structural performance and the fracture behavior of the whole plate, consists of polymer fibers and binder, and a large amount of porosity. In this work, a novel micromechanical modeling approach for the fracture behavior of the composite core is presented, which could allow for a faster and improved design process for novel configurations of the plates. The modeling approach involves a novel method for the generation of virtual models for the complex microstructure of the core and our recently developed theoretical framework of an FFT-based computational homogenization scheme for cohesive zones. Furthermore, the parameters of the elastic–plastic material model including a non-local, ductile damage model were identified using microindentation experiments and mode I tests (Double Cantilever Beam). The novel modeling approach, along with the FFT-based homogenization scheme for cohesive zones, was also experimentally validated using mode III tests (Split Cantilever Beam) and a corresponding Finite Element simulation. 

Micro-CT analysis of experimentally creased and folded multilayer cardboards reveals insights into how the material deformation due to the creasing and folding process of cardboard impact the material concerning delaminations and position of broke particles. Delaminations were found in various locations and varied in size from just under a tenth of a millimeter to up to four times the thickness of the cardboard. The particles varied in size, ranging from a few micrometers to slightly larger than the cardboard thickness. Characteristic dimensions for the creased and folded cardboard were measured for selected cross sections. The differences in characteristic dimensions for the cross sections among the samples were typically a few hundredths of a millimeter. There are differences between cross-sections that are a few hundredths of a millimeter apart.

In packaging, the structural integrity of paperboard under complex stresses is essential.This study examines the delamination behavior of paperboard under normal andshear loading modes, which are the base for developing mixed-mode models. Four commercialpaperboard grades, sourced from fibers across three geographical regions, areinvestigated using Double Cantilever Beam (DCB) and Split Double Cantilever Beam(SDCB) tests, which are used to calibrate a cohesive zone model from the literature.This model introduces a shape parameter that governs the cohesive traction-separationrelationship, consistent across both normal and shear modes. Experimental findingssupport this approach, demonstrating that, while the shape parameter remains modeindependent,its numerical value varies uniquely for each paperboard quality.

BackgroundThe out-of-plane shear behavior of paperboards plays a critical role in converting processes such as creasing and folding. The recently proposed Split Double Cantilever Beam (SDCB) specimen has been used to characterize this behavior using a cohesive zone model, but its large size poses handling challenges.ObjectiveThis study aims to optimize the SDCB specimen configuration to improve manageability while maintaining the quality of experimental measurements.MethodsA design of experiments (DOE) approach and finite element analysis incorporating a mixed-mode interface model were used to analyze the influence of key specimen parameters. Shear reaction force and rotation relative to shear deformation were assessed to guide the optimization.ResultsA redesigned SDCB specimen was identified, achieving a 40% reduction in size and weight (retaining 60% of the original dimensions) without compromising the experimental quality. The optimized configuration maintained comparable measurement accuracy to the original design.ConclusionsThe proposed SDCB specimen redesign offers a more manageable experimental setup, enhancing usability in experimental studies while preserving the reliability of shear behavior characterization.

Cohesive Zone Models with finite thickness are widely used for the fracture mechanical modeling of material layers, e.g., adhesive layers. Within this approach, the whole layer is modeled as a cohesive zone. Moreover, computational homogenization techniques are crucial for the development of advanced engineering materials, which are often heterogeneous. Compared to the commonly used Finite Element Method (FEM), solvers based on the Fast Fourier Transform (FFT) are expected to reduce the computational effort needed for the homogenization. Originated from an existing method for the computational homogenization of cohesive zones using FEM, a novel FFT-based homogenization scheme for cohesive zone models is presented. Our implementation of the FFT solver uses a displacement-based Barzilai–Borwein scheme and a non-local ductile damage model for the fracture behavior. Finally, the practical application of the method is discussed using an adhesive layer and the core material of HybrixTM metal sandwich plates as examples. 

A cohesive interface model based on a master curve is proposed for the analysis of delamination in paperboard under various loading, unloading, and reloading conditions. The model is thermodynamically consistent and considers the effects of elasticity, plasticity, and damage. The proposed model is verified by comparing its predictions with experimental data obtained from multiple loading–unloading–reloading cycle experiments using a split double cantilever beam specimen. The results show that the model can predict the cyclic behavior of shear loading and provide insight into the damage evolution associated with different loading paths by analyzing the shear stress distribution in the fracture process zone. The model’s calibration process requires monotonic normal and shear loading data but only cyclic normal loading data. Additionally, the model accounts for the paperboard’s fiber–fiber friction and normal dilatation due to shear loading. In total, nine parameters are needed to calibrate the mode.

Cohesive Zone Models with finite thickness are widely used for the fracture mechanical modeling of layers of material, e.g., adhesives. Within this approach, the whole layer is modeled as a Cohesive Zone. Moreover, computational homogenization techniques are crucial for the development of advanced engineering materials, which are often heterogeneous. Compared to the classical Finite Element Method (FEM), computationally more efficient solvers based on the Fast Fourier Transform (FFT) are expected to reduce the computational effort needed for the homogenization. Originated from an existing method for the computational homogenization of Cohesive Zones using FEM, a novel FFT-based homogenization scheme for Cohesive Zone Models was developed. Our implementation of the FFT solver uses the Barzilai-Borwein scheme and a non-local ductile damage model for the fracture behavior. Finally, the method is applied to the core material of HybrixTM metal sandwich plates, and the good agreement with experimental results in opening mode I is shown. 

An experimental study to characterize properties controlling delamination of paperboard is presented. The normal and shear traction-separation laws are measured and evaluated using a double cantilever beam (DCB) and a split double cantilever beam (SCB) specimen. The DCB-experiments provides normal separation data in good agreement with results using alternative experimental techniques. From the measured data, both normal and shear fracture resistance data are obtained. A length parameter is introduced. The length parameter allows for the cohesive law to be obtained from a dimensionless master curve which is valid both for normal and shear loading. Taking advantage of the master curve, a mixed-mode potential is proposed. The mixed-mode potential is implemented as a user interface to a finite element code. As a final test, the experimental setups of the DCB and SCB specimens are simulated to validate the identified normal and shear properties.