J. Appl. Comput. Mech., 7(2) (2021) 820-830 DOI: 10.22055/JACM.2020.35968.2771
ISSN: 2383-4536 jacm.scu.ac.ir
Finite Element and Experimental Investigation on the Effect of Repetitive Shock in Corrugated Cardboard Packaging
Viet Dung Luong 1 , Anne-Sophie Bonnin 2 , Fazilay Abbès 1 , Jean-Baptiste Nolot 2 , Damien Erre 2 , Boussad Abbès 1
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
Received December 05 2020; Revised December 26 2020; Accepted for publication December 27 2020. Corresponding author: B. Abbès (boussad.abbes@univ-reims.fr) © 2020 Published by Shahid Chamran University of Ahvaz
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: Packaging, Shock test, Fatigue, Finite element simulation, Elastoplastic model.
1. Introduction Corrugated cardboard boxes are designed to protect products from hazards of the distribution, transportation, and storage environment so that the products can be shipped to consumers without damage. When packaged products are shipped, they may encounter many dynamic events such as drops, impacts, compressions, vibrations…etc. during handling and transportation which might cause damage to the product. Shocks are one of the most severe factors that cause damage to products. The intensity of a given shock is characterized by its acceleration level or amplitude, and the duration over which the shock takes place [1]. Another important characterization of a shock pulse is the velocity change, which is represented by the area under the acceleration amplitude versus time curve. The damage boundary curve (DBC) is widely used to determine the shock damage of a product based on its sensitivity to acceleration and velocity change [2]. DBCs were applied to evaluate repetitive‐shock‐induced damage [3-5]. Test procedure to determine DBC usually requires the use of a programmable shock machine, which can vary the amplitude, duration and velocity change parameters of repeated impacts [6-9]. In our study, a test procedure is proposed using a vibration table to generate shocks of various shapes and intensities to construct the DBC of a corrugated cardboard box. Finite element (FE) modelling of corrugated cardboard has been an area of extensive research in static analysis. Biancolini et al. [10-11] developed equivalent material models of corrugated cardboard using a homogenization approach to predict the eigenvalue buckling load, and ultimate compression load from nonlinear static analyses of boxes. Han and Park [12] and Fadiji et al. [13] investigated the effects of vent design on compression strength using FE simulations on ventilated corrugated cardboard boxes. FE modelling of corrugated cardboard packages is fastidious, and the meshing generates heavy models which increases CPU time. In order to deal with this, researchers developed homogenization models that replace 3D structural models with a single-layered shell model. The proposed homogenization methods generally deal only with elastic properties [14-18], while for the description of nonlinear behavior of corrugated cardboard also plasticity must be considered [7, 19]. Rabczuk et al. [20] proposed a homogenization method for sandwich structures based on the equivalence of the continuum stored energy density function and a discrete energy associated to a representative core cell considering material nonlinearities including buckling of the core. They applied this homogenization to different types of cores under dynamic loading and in fluid–structure interaction examples. Recently, Anitescu et al. [21] proposed a method based on artificial neural networks (ANN) and an adaptive collocation strategy that can be applied for such problems. To model the orthotropic plastic behavior of paperboard, the common plasticity models used for are Hill [22], Hoffman [23], Tsai and Wu [24], Xia et al. [25], Mäkelä and Östlund [26], Harrysson and Ristinmaa [27]. Since corrugated cardboard consists of flat paperboard layers (linerboards) distanced by sine-shaped layer (fluting), the determination of effective elastoplastic
Published online: December 28 2020
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