materials
Article Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections Tomasz Garbowski 1, * and Anna Knitter-Pia˛tkowska 2
1 Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznan´ , Poland 2 Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan´ , Poland; anna.knitter-piatkowska@put.poznan.pl * Correspondence: tomasz.garbowski@up.poznan.pl Abstract: Bending stiffness (BS) is one of the two most important mechanical parameters of corrugated board. The second is edge crush resistance (ECT). Both are used in many analytical formulas to assess the load capacity of corrugated cardboard packaging. Therefore, the correct determination of bending stiffness is crucial in the design of corrugated board structures. This paper focuses on the analytical determination of BS based on the known parameters of the constituent papers and the geometry of the corrugated layers. The work analyzes in detail the dependence of the bending stiffness of an asymmetric, five-layer corrugated cardboard on the sample arrangement. A specimen bent so that the layers on the lower wave side are compressed has approximately 10% higher stiffness value. This is due to imperfections, which are particularly important in the case of compression of very thin liners. The study showed that imperfection at the level of a few microns causes noticeable drops in bending stiffness. The method has also been validated by means of experimental data from the literature and simple numerical finite element model (FEM). The obtained compliance of the computational model with the experimental model is very satisfactory. The work also included a critical discussion of the already published data and observations of other scientists in the field.
Citation: Garbowski, T.; Knitter-Pia˛tkowska, A. Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections. Materials 2022 , 15 , 663. https:// doi.org/10.3390/ma15020663
Keywords: bending stiffness; analytical solution; imperfections; corrugated board; thin-walled structures
1. Introduction A sign of the present times is the constant pursuit of the purchase of various merchan- dise, and thus the need for their packaging and safe transport, both in traditional forms of sale and e-commerce. The foremost desirable characteristics of the packaging are naturally adequate strength in relation to light weight and, in the interest of the natural environment, reusable, recyclable and biodegradable. Corrugated cardboard packaging perfectly meets all the above-mentioned requirements. Going further, the popularity of this type of pack- ages is associated with the intensive development of a separate branch of industry and research. In view of the laws governing the free market, manufacturers strive for the most cost-effective solutions while maintaining the appropriate load-bearing capacity of card- board packaging. The scientists, who have been developing for many years new methods to determine the material properties of the corrugated cardboard [1,2] and are constantly trying to understand the nature of the packaging performance, through numerous studies, involving a variety of techniques, are here to help. The task is challenging mainly due to the layered structure of the corrugated cardboard with two characteristic in-plane directions of orthotropy associated with the mechanical strength of the paperboard—the machine direction (MD) perpendicular to the main axis of the fluting and parallel to the paper- board fiber alignment, and cross direction (CD) which is parallel to the fluting. Moreover, there are a number of factors that reduce the strength of a cardboard itself or corrugated cardboard packaging, the impact of which has been analyzed and is still is the subject of investigation, e.g., [3] in particular time and storing conditions [4,5], stacking load [6–8],
Academic Editor: Alexey Smolin
Received: 29 December 2021 Accepted: 14 January 2022 Published: 16 January 2022
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Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
Materials 2022 , 15 , 663. https://doi.org/10.3390/ma15020663
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