Energies 2021 , 14 , 1095
12of 14
Many challenges are still actual in the mechanics of corrugated cardboards and pack- aging due to the nonlinear material and the nonlinear/discontinuous geometry of the designs. Previously, the box strength was computed with the simplified formulas, which currently does not provide sufficient accuracy to the increasing needs of the packaging industry. This was proved by our recent series of publications, namely in [11,12,20,21]. 5. Conclusions In this study, the boxes made of corrugated cardboards with knife-cut perforations were analyzed. The box designs selected for the study represented the SRPs. Three types of perforations were considered, namely, 25 × 75, 50 × 50, and 75 × 25, in which the first value represents the percentage of the length of 10 mm, at which the knife cut the corrugated cardboard, and the second value represents the percentage of the length of 10 mm, at which the corrugated cardboard was intact. In the first part of the study, the series of top-to-bottom compression strength tests of boxes were conducted to determine their experimental ultimate loads. In the second part of the study, the analytical–numerical approach was proposed to take into consideration the different properties of perforations in modeling. In the third part of the study, the boxes with their peculiar design of perforations were modeled with simplified (McKee formula) and proposed the analytical–numerical approach. The tests conducted in the first part served to verify the modeling approach proposed in the second part of the study. In the third part of the study, it appeared that the approach proposed in the paper gave very low mean estimation error in comparison with the reference simplified (McKee formula) approach; the mean error was only a few percent. The McKee formula approach was presented to contrast the influence of the perforation on the estimation of the box ultimate load, according to the classical approach still widely used by the lab technicians. Thus, it can be concluded that the method presented in the study is a promising tool for determining the strength of perforated boxes, which are commonly used in the supply and sales market. 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 cardboard. The novelty of the presented work is the use of the analytical–numerical method, which finally takes into account the impact of perforation on the evaluation of the compressive strength of the SRP packaging. Supplementary Materials: The following are available online at https://www.mdpi.com/1996-107 3/14/4/1095/s1. In the TXT file, the computational results based on the method proposed, in which Figure 5 was generated are presented. In this file, the 1st and 2nd columns are k and r parameters; the 3rd column is the ECT value for particular cardboard quality; the 4th to 7th columns are critical loads of the i -th panel (obtained from FEM); the 8th to 11th columns are the reduction factors due to the in-plate aspect ratio of the box panel, γ i ,where i = { 1, 2, 3, 4 } and denotes the number of the panel. The 12th to 15th columns are the reduction factors, taking into account the ratio of the compressive strength of the plate with and without a perforation γ pi ,where i = { 1, 2, 3, 4 } and denotes the number of the panel. The 16th to 19th columns are the widths of the i -th panel of the box. Author Contributions: T.G. (Tomasz Garbowski): conceptualization, methodology, software, writing— original draft, writing—review and editing, supervision, project administration, funding acquisition; T.G. (Tomasz Gajewski): software, validation, formal analysis, investigation, writing—original draft, writing—review and editing, visualization; J.K.G.: writing—original draft, writing—review and editing, data curation, supervision, funding acquisition. All authors have read and agreed to the published version of the manuscript. Funding: The APC was funded by the Ministry of Science and Higher Education, Poland, grant from Poznan University of Technology; grant number 0612/SBAD/3567. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.
Made with FlippingBook Online newsletter maker