Finite element and experimental investigation on the effect of repetitive shock in corrugated cardboard packaging 829
Table 5. Number of shocks for unlimited endurance fatigue. Acceleration (g) Shock duration (ms) Experimental shock number Numerical shock number 5 49.8 >1000 1740 12 20.1 >1000 600 10 25.0 >1000 1273 13 17.1 >1000 420 6 59.4 >1000 1505 7 80.8 >1000 1160 13 48.7 >1000 140
5. Conclusion In present work, the effect of shock fatigue on corrugated cardboard boxes was estimated by vibration table and finite element methods. The damage boundary curve of the studied box, that define its fragility based on its sensitivity to acceleration and the velocity change that occurs during shock, was constructed using both methods. To efficiently simulate the mechanical behavior of a corrugated cardboard box, we proposed an elastoplastic homogenization model to replace a corrugated-core sandwich panel by a homogeneous plate. The proposed model performs satisfactorily in static and dynamic loading. Experimental characterization can be time-consuming and expensive. We have showed that it is possible to estimate DBC of the package using finite element method with good precision. This technique can easily be applied to other packaging. However, the physical testing is still needed to validate the final design. Author Contributions V.D. Luong carried out the simulations; A.-S. Bonnin and J.-B. Nolot conducted the experiments and analyzed the experimental results; D. Erre designed the experiments and analyzed the experimental results; F. Abbès and B. Abbès developed the mathematical modeling and examined the theory validation. The manuscript was written through the contribution of all authors. All authors discussed the results, reviewed, and approved the final version of the manuscript. Conflict of Interest The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this article.
Funding The authors received no financial support for the research, authorship, and publication of this article.
References [1] Goodwin, D., Young, D., Protective packaging for distribution , DEStech Publications, Lancaster, PA, USA, 2011. [2] Newton, R.E., Fragility Assessment Theory and Practice , Monterey Research Laboratory, Inc., California, 1976. [3] Burgess, G.J., Product fragility and damage boundary theory, Packaging Technolgy and Science , 1(1), 1988, 5– 10. [4] Kipp, W.I., Developments in testing products for distribution, Packaging Technology and Science , 13(3), 2000, 89– 98. [5] Kitazawa, H., Saito, K., Ishikawa, Y., Effect of difference in acceleration and velocity change on product damage due to repetitive shock, Packaging Technology and Science , 27(3), 2014, 221-230. [6] Horiguchi, S., Saito, K., Test method for enhanced mechanical shock fragility statistics accuracy, Packaging Technology and Science , 32(4), 2019, 199-210. [7] Luong, V.D., Abbès, F., Abbès, B., Duong, P.T.M., Nolot, J.-B., Erre, D., Guo, Y.-Q., Finite element simulation of the strength of corrugated board boxes under impact dynamics, In: Nguyen-Xuan H., Phung-Van P., Rabczuk T. (eds) Proceedings of the International Conference on Advances in Computational Mechanics 2017, ACOME 2017, Lecture Notes in Mechanical Engineering , 2018, 369-380. [8] Li, H., Chen, A., Duan, N., Dropping Shock Characteristics of the Suspension Cushioning System with Critical Components, Shock and Vibration , 2017, 2017, 3164294. [9] Song, S., Duan, N.-N., Chen, A.-J., Application of variational iteration method for dropping damage evaluation of the suspension spring packaging system, Abstract and Applied Analysis , 2014, 2014, 385404. [10] Biancolini, M.E., Brutti, C., Numerical and experimental investigation of the strength of corrugated board packages, Packaging Technology and Science , 16(2), 2003, 47‐60. [11] Biancolini, M.E., Brutti, C., Porziani, S., Corrugated board containers design methods, International Journal of Computational Materials Science and Surface Engineering , 3(2-3), 2010, 143‐163. [12] Han, J., Park, J.M., Finite element analysis of vent/hand hole designs for corrugated fibreboard boxes, Packaging Technology and Science , 20(1), 2007, 39‐ 47. [13] Fadiji, T., Coetzee, C., Opara, U.L., Compression strength of ventilated corrugated paperboard packages: numerical modelling, experimental validation and effects of vent geometric design, Biosystems Engineering , 151, 2016, 231‐247. [14] Duong, P.T.M., Abbès, B., Li, Y.M., Hammou, A.D., Makhlouf, M., Guo, Y.-Q., An analytic homogenization model for shear torsion coupling problems of double corrugated core sandwich plates, Journal of Composite Materials , 47(11), 2013, 1327–1341. [15] Hammou, A.D., Duong, P.T.M., Abbès, B., Makhlouf, M., Guo, Y.-Q., Finite element simulation with a homogenization model and experimental study of free drop tests of corrugated cardboard packaging, Mechanics & Industry , 13(3), 2012, 175–184. [16] Abbès, B., Guo, Y.-Q., Analytic homogenization for torsion of orthotropic sandwich plates: application to corrugated cardboard, Composite Structures , 92(3), 2010, 699–706. [17] Talbi, N., Batti, A., Ayad, R., Guo, Y.-Q., An analytical homogenization model for finite element modeling of corrugated cardboard, Composite Structures , 88(2), 2009, 280–289. [18] Nordstrand, T., Carlsson, L.A., Allen, H.G., Transverse shear stiffness of structural core sandwich, Composite Structures , 27(3), 1994, 317–329. [19] Garbowski, T., Marek, A., Homogenization of corrugated boards through inverse analysis, An International Conference on Engineering and Applied Sciences Optimization, M. Papadrakakis, M.G. Karlaftis, N.D. Lagaros (eds.) , Kos Island, Greece, 4-6, June 2014. [20] Rabczuk, T., Kim, J. Y., Samaniego, E., Belytschko, T., Homogenization of sandwich structures, International Journal for Numerical Methods in Engineering , 61, 2004, 1009–1027. [21] Anitescu, C., Atroshchenko, E., Alajlan, N., Rabczuk, T., Artificial Neural Network methods for the solution of second order boundary value problems, Computers, Materials and Continua , 59(1), 2019, 345-359. [22] Hill, R., A theory of the yielding and plastic flow in anisotropic metals, Proceedings of The Royal Society , 193, 1948, 111–128. [23] Hoffman, O., The brittle strength of orthotropic materials, Journal of Composite Materials , 1(2), 1967, 200–206. [24] Tsai, S.W., Wu, E.M., A general theory of strength for anisotropic materials, Journal of Composite Materials , 5(1), 1971, 58–80.
Journal of Applied and Computational Mechanics, Vol. 7, No. 2, (2021), 820-830
Made with FlippingBook Ebook Creator