energies
Article Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Perforations
Tomasz Garbowski 1 , Tomasz Gajewski 2 and Jakub Krzysztof Grabski 3, *
1 Department of Biosystems Engineering, Poznan University of Life Sciences, Wojska Polskiego 50, 60-627 Poznan´, Poland; tomasz.garbowski@up.poznan.pl 2 Institute of Structural Analysis, Poznan University of Technology, Piotrowo Street 5, 60-965 Poznan´ , Poland; tomasz.gajewski@put.poznan.pl 3 Institute of Applied Mechanics, Poznan University of Technology, Jana Pawła II Street 24, 60-965 Poznan´ , Poland * Correspondence: jakub.grabski@put.poznan.pl Abstract: This paper presents a modified analytical formula for estimating the static top-to-bottom compressive strength of corrugated board packaging with different perforations. The analytical framework is based here on Heimerl’s assumption with an extension from a single panel to a full box, enhanced with a numerically calculated critical load. In the proposed method, the torsional and shear stiffness of corrugated cardboard, as well as the panel depth-to-width ratio is implemented in the finite element model used for buckling analysis. The new approach is compared with the successful though the simplified McKee formula and is also verified with the experimental results of various packaging designs made of corrugated cardboard. The obtained results indicate that for boxes containing specific perforations, simplified methods give much larger estimation error than the analytical– numerical approach proposed in the article. To the best knowledge of the authors, the influence of the perforations has never been considered before in the analytical or analytical–numerical approach for estimation of the compressive strength of boxes made of corrugated paperboard. The novelty of this paper is to adopt the method presented to include perforation influence on the box compressive strength estimation.
Citation: Garbowski, T.; Gajewski, T.; Grabski, J.K. Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Perforations. Energies 2021 , 14 , 1095. https://doi.org/10.3390/en14041095 Academic Editor: Jos é A.F.O. Correia Received: 31 December 2020 Accepted: 18 February 2021 Published: 19 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 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/).
Keywords: corrugated board; McKee formula; buckling; orthotropic panels; laboratory tests; box strength; crease; perforation
1. Introduction Shelf-ready packaging (SRP) is playing an increasingly important role in the modern industry, including the supply and sales market. The main task of SRP is to ensure safe transportation and storage of products in packaging and then putting them directly on shelves without unpacking individual goods. Application of SRP leads to the reduction of costs related to the work of employees and helps to save time. Therefore, tedious unpacking of products on the shelf has been reduced to a few seconds. The SRPs are made of corrugated cardboard with different perforations, which enable easy separation of the lower part of the packaging, called the tray, and the upper part of the packaging, called the cover. On the other hand, perforations can significantly influence the mechanical strength of boxes made of corrugated paperboards [1]. It reduces the integrity of the wall. Thus, the final compression strength of the box would also decrease. In this paper, the strength of boxes with perforations is investigated. Performing physical experiments allows for the design and development of paper- board or corrugated cardboard boxes, to ensure their proper mechanical strength. It strictly depends on two characteristic in-plane directions of the corrugated cardboard. They are related to fluting; the first direction, called machine direction (MD), is perpendicular to the main axis of it and parallel to paperboard fiber alignment. The second one, called cross direction (CD), is parallel to the fluting.
Energies 2021 , 14 , 1095. https://doi.org/10.3390/en14041095
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