Energies 2021 , 14 , 3203
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layers. The main task of which is to increase the load capacity and stiffness in the CD, but most importantly, to keep the flat layers at an appropriate distance from each other, which allows obtaining significantly increased bending stiffness in both directions. The optimal corrugated board should be characterized by maximum strength and stiffness, and at the same time be light and cheap to produce. In assessing the quality of corrugated board, the compressive or tensile and flexural or torsional stiffnesses/strengths are important; the former due to the load-bearing capacity, while the latter due to the resistance to loss of stability. The maximum stiffness or strength can be obtained by selecting the appropriate materials for the individual layers and/or by selecting the appropriate geometry (wave height and period) for the corrugated layers. There are hundreds of papers on the market with different grammages and mechanical properties, produced in a different proportion of virgin to recycled fibers. This gives an enormous number of combinations of possible layer arrangements and layer geometry of the corrugated cardboard, which does not stop producers from constantly trying to find the best solution. Unfortunately, their efforts may be wasted if the carefully designed quality of the corrugated cardboard does not achieve the assumed strength parameters after production, i.e., converting processes. Before corrugated board becomes a typical transportation box, or a color, branded shelf-ready box (SRP) or a display-ready box it goes through a number of converting processes, e.g., printing, lamination, die-cutting, etc. All these processes cause crushing of the corrugated layers, which in turn leads to a reduction of strength and stiffness of the material and therefore affects the performance of structures made of corrugated boards. The deterioration of the mechanical properties can be observed in all crucial laboratory test results, e.g., four-point bending test, torsional test, shear test, edge crush test, etc. Even though, the degraded stiffnesses and strengths could easily be measured by cutting specimens from the converted cardboard, this is rarely done in practice. Typically, this effect is accounted for by adding safety factors to the equations that estimate the load capacity of the package. Since the middle of the last century, scientists and engineers have tried to find robust and simple tools for estimating the strength of corrugated board boxes. Among them the analytical tools [1–10] are the simplest, but unfortunately less precise and limited only to the typical box structures. Numerical models of corrugated board packaging [11–16], although much more precise, require specific knowledge and a full set of material parameters to correctly simulate the behavior of the box. In the finite element-based tools, a procedure called homogenization [17–25] is very often used, which allows for significant time savings in the analysis and at the same time guarantees the correct behavior of simplified models. This is especially important when the computational models are complex (they consist of many layers of cardboard) or the analysis concerns geometries with complex shapes, such as cardboard furniture [26]. In our previous works, we presented analytical-numerical methods [27–29] for as- sessing the strength of corrugated board boxes, which allow to obtain quick and accurate results for the packaging with different geometries (ventilation/hand holes [28] and per- forations [29]). In order to properly estimate the strength of a corrugated box, special attention should be paid to transverse shear properties [30–32]. This is because the decrease in this material parameter significantly affects the load-bearing capacity of the package. In general, any deteriorated stiffness (i.e., flexural, torsional or transversal) and the strength of the corrugated board can be readily implemented in any estimation method. The only requirement is to determine the relationship between the amount of damage (stiffness and strength degradation) and the amount of physical crushing of the cardboard. The article presents the results of the research on the crushing of various single-walled corrugated boards. In the first step, the relationship between intentionally induced crushing with very high accuracy to different types of corrugated boards and the measured loss of stiffness in various laboratory tests was checked. Since the crushing of the sample takes place in the thickness direction, the greatest decrease in bending and twisting stiffness (due to the reduction of the corrugated board thickness and, therefore, a significant reduction of
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