Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mechanical Tests of Corrugated Cardboard
2.2. Coefficient of Determination and Estimation Error
2.3. Numerical–Analytical Approach for Modeling Crushing
- Building the initial geometry of the intact corrugated cardboard (Stage a);
- Defining the shape of the crushed corrugated cardboard by a numerical–analytical approximation (Stage a–b);
- Building the material stiffness matrix using the geometry of crushed corrugated cardboard (Stage c–d);
- Homogenizing the structure to a single layered composite with effective properties according to the method presented by Garbowski and Gajewski [31] (Stage d–e);
- Computing packaging compressive strength for simple flap boxes with various dimensions via an analytical formula proposed by Garbowski et al. [23], using composite properties acquired in the previous stage (Stage f).
3. Results
3.1. Experimental Study
3.2. Modeling Crushing in Estimating Compressive Strength of Packaging
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Layers | ||||||
---|---|---|---|---|---|---|
(MPa) | (MPa) | (-) | (MPa) | (MPa) | (MPa) | |
liners | 3326 | 1694 | 0.34 | 859 | 429.5 | 429.5 |
fluting | 2614 | 1532 | 0.32 | 724 | 362 | 362 |
Crushing Level, (%) | Parameter (-) | Parameter (-) |
---|---|---|
0 | 1.11 | 0.0238 |
5 | 1.39 | 0.0091 |
10 | 1.68 | 0.0028 |
15 | 2.04 | 0.0006 |
20 | 2.49 | 0.0001 |
25 | 3.13 | 0 |
30 | 4.09 | 0 |
35 | 5.65 | 0 |
40 | 8.58 | 0 |
45 | 15.54 | 0 |
50 | 45.98 | 0 |
Cardboard Index | THK2 * | ECT * | BNT-MD * | BNT-CD * | SST-MD * | SST-CD * | TST-MD * | TST-CD * |
---|---|---|---|---|---|---|---|---|
BC-480 | 0.000 | 0.302 | 0.591 | 0.956 | 0.989 | 0.993 | 0.566 | 0.954 |
BC-580 | 0.014 | 0.304 | 0.898 | 0.917 | 0.976 | 0.998 | 0.704 | 0.877 |
EB-560 | 0.000 | 0.000 | 0.981 | 0.727 | 0.989 | 0.965 | 0.726 | 0.888 |
EB-670 | 0.000 | 0.000 | 0.915 | 0.770 | 0.988 | 0.957 | 0.695 | 0.931 |
Cardboard Index | BNT * | SST * | TST * |
---|---|---|---|
BC-480 | 0.951 | 0.995 | 0.949 |
BC-580 | 1.000 | 0.996 | 0.987 |
EB-560 | 0.892 | 0.994 | 0.982 |
EB-670 | 0.859 | 0.993 | 0.974 |
Cardboard Index | |
---|---|
BC-480 | 0.977 |
BC-580 | 0.967 |
EB-560 | 0.941 |
EB-670 | 0.930 |
0% Crushing | 10% Crushing | 20% Crushing | 30% Crushing | |
---|---|---|---|---|
19,514 | 17,598 | 15,751 | 14,006 | |
14,326 | 12,759 | 11,273 | 9876 | |
3438 | 3094 | 2763 | 2453 | |
5629 | 5069 | 4517 | 3993 | |
77.3 | 52.1 | 39.5 | 30.5 | |
237.0 | 211.7 | 187.6 | 164.7 | |
ECT (kN/m) | 8.0 | 7.6 | 7.2 | 6.8 |
Box Dimensions | Box Compressive Strength Due to Crushed Cardboard | |||||
---|---|---|---|---|---|---|
b (mm) | c (mm) | a (mm) | 0% Crushing (N) | 10% Crushing (N) | 20% Crushing (N) | 30% Crushing (N) |
500 | 500 | 500 | 6001 | 5613 | 5227 | 4848 |
500 | 1000 | 500 | 6933 | 6490 | 6049 | 5616 |
300 | 900 | 500 | 5805 | 5433 | 5064 | 4701 |
250 | 1000 | 500 | 5894 | 5516 | 5141 | 4772 |
200 | 1000 | 500 | 5685 | 5320 | 4958 | 4602 |
600 | 900 | 500 | 7132 | 6676 | 6223 | 5777 |
500 | 500 | 750 | 6177 | 5773 | 5373 | 4979 |
500 | 1000 | 750 | 6469 | 6052 | 5638 | 5230 |
300 | 900 | 750 | 5378 | 5031 | 4686 | 4347 |
250 | 1000 | 750 | 5367 | 5021 | 4679 | 4341 |
200 | 1000 | 750 | 5156 | 4824 | 4494 | 4170 |
600 | 900 | 750 | 6686 | 6256 | 5828 | 5406 |
500 | 500 | 1000 | 6001 | 5613 | 5227 | 4848 |
500 | 1000 | 1000 | 6257 | 5854 | 5453 | 5059 |
300 | 900 | 1000 | 5295 | 4952 | 4611 | 4276 |
250 | 1000 | 1000 | 5218 | 4880 | 4545 | 4215 |
200 | 1000 | 1000 | 5004 | 4680 | 4358 | 4042 |
600 | 900 | 1000 | 6646 | 6218 | 5793 | 5373 |
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Gajewski, T.; Garbowski, T.; Staszak, N.; Kuca, M. Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes. Energies 2021, 14, 4321. https://doi.org/10.3390/en14144321
Gajewski T, Garbowski T, Staszak N, Kuca M. Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes. Energies. 2021; 14(14):4321. https://doi.org/10.3390/en14144321
Chicago/Turabian StyleGajewski, Tomasz, Tomasz Garbowski, Natalia Staszak, and Małgorzata Kuca. 2021. "Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes" Energies 14, no. 14: 4321. https://doi.org/10.3390/en14144321
APA StyleGajewski, T., Garbowski, T., Staszak, N., & Kuca, M. (2021). Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes. Energies, 14(14), 4321. https://doi.org/10.3390/en14144321