Finite Element and Experimental Investigation on the Effect of ‎Repetitive Shock in Corrugated Cardboard Packaging

Document Type : Research Paper

Authors

1 MATIM, University of Reims Champagne-Ardenne, UFR SEN, Campus Moulin de la Housse, 51100 Reims, France

2 ESIReims, University of Reims Champagne-Ardenne, Esplanade Roland Garros, 51100 Reims, France

Abstract

The primary concern of the current study is estimating the repetitive shock induced damages leading to cumulative fatigue on corrugated cardboard boxes experimentally and numerically. Repetitive shock tests were performed on boxes using a vibration table to construct a Damage Boundary Curve (DBC). To computationally determine this curve, a finite element approach is proposed using an elastoplastic homogenization model for corrugated cardboard. The proposed model was implemented in the finite element software ABAQUS. Thanks to adopted model simplifications, a box can be easily and reliably modelled as a homogenized structure. A calibration method is used to compute a set of effective parameters in homogenized model in order to keep its behavior qualitatively and quantitatively close to the response of a full structural model. For verification, the identified model is used to simulate the box compression test. To replicate the experimental tests, simulations of successive repetitive shock pulses are carried with the proposed model for oligocyclique and limited endurance fatigue. To reduce computational costs, we propose a simple method for unlimited endurance fatigue by extrapolating a trend line after some training cycles. The proposed method shows good agreement with experimental results.

Keywords

Main Subjects

[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.
[25] Xia, Q.S., Boyce, M.C., Parks, D.M., A constitutive model for the anisotropic elastic-plastic deformation of paper and paper board, International Journal of Solids and Structures, 39(15), 2002, 4053-4071.
[26] Mäkelä, P., Östlund, S., Orthotropic elastic-plastic material model for paper materials, International Journal of Solids and Structures, 40(21), 2003, 5599-5620.
[27] Harrysson, A., Ristinmaa, M., Large strain elasto-plastic model of paper and corrugated board, International Journal of Solids and Structures, 45(11-12), 2008, 3334–3352.
[28] Karafillis, A.P., Boyce, M.C., A general anisotropic yield criterion using bounds and a transformation weighting tensor, Journal of the Mechanics and Physics of Solids, 41(12), 1993, 1859–1886.
[29] Abaqus v. 6.19 documentation, Dassault Systemes Simulia Corporation, 2016.
[30] Poloni C., Pediroda, V., GA coupled with computationally expensive simulations: tools to improve efficiency, In Genetic Algorithms and Evolution Strategies in Engineering and Computer Science, John Wiley and Sons, England, 1997.
[31] Spicer, D., Cook, J., Poloni C., Sen P., EP20082 Frontier: Industrial MultiObjective Design Optimisation, In Proceedings of the 4th European Computational Fluid Dynamics Conference (ECCOMAS 98), John Wiley and Sons, England, 1998.