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Structural MechanicsISRN LUTVDG/TVSM--03/1015--SE (1-129)ISBN 91-628-5563-8 ISSN 0281-6679BASIC TESTING AND STRENGTHDESIGN OF CORRUGATED BOARDAND CONTAINERSDoctoral Thesis byTOMAS NORDSTRANDCopyright Tomas Nordstrand, 2003.Printed by KFS i Lund AB, Lund, Sweden, February 2003.For information, address:Division of Structural Mechanics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden.Homepage:

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ABSTRACTPackaging serves a lot of purposes, and would be hard to do without. Packagingprotects the goods during transport, saves costs, informs about the product, andextends its durability. A transport package is required to be strong and lightweight inorder to be cost effective. Furthermore, it should be recycled because ofenvironmental and economical concerns. Corrugated board has all of these features.This thesis is compiled of seven papers that theoretically and experimentally treat thestructural properties and behaviour of corrugated board and containers duringbuckling and collapse. The aim was to create a practical tool for strength analysis ofboxes that can be used by corrugated board box designers. This tool is based on finiteelement analysis.The first studies concerned testing and analysis of corrugated board in three-pointbending and evaluation of the bending stiffness and the transverse shear stiffness. Thetransverse shear stiffness was also measured using a block shear test. It was shownthat evaluated bending stiffness agrees with theoretically predicted values. However,evaluation of transverse shear stiffness showed significantly lower values than thepredicted values. The predicted values were based on material testing of constituentliners and fluting prior to corrugation. Earlier studies have shown that the flutingsustains considerable damage at its troughs and crests in the corrugation process andthis is probably a major contributing factor to the discrepancy. Furthermore, the blockshear method seems to constrain the deformation of the board and consistentlyproduces higher values of the transverse shear stiffness than the three-point-bendingtest. It is recommended to use the latter method.Further experimental studies involved the construction of rigs for testing corrugatedboard panels under compression and cylinders under combined stresses. The paneltest rig, furnishing simply supported boundary conditions on all edges, was used tostudy the buckling behaviour of corrugated board. Post-buckling analysis of anorthotropic plate with initial imperfection predicted failure loads that exceed theexperimental values by only 6-7 % using the Tsai-Wu failure criterion. It wasconfirmed, by testing the cylinders that failure of biaxially loaded corrugated board isnot significantly affected by local buckling and that the Tsai-Wu failure criterion isappropriate to use.A method for prediction of the top-to-bottom compression strength of corrugatedboard containers using finite element analysis was developed and verified by a largenumber of box compression tests. Up to triple-wall corrugated board isaccommodated in the finite element model. The described FE-method for predictingthe top-to-bottom compressive strength of corrugated containers has been used as thebasic component in the subsequent development of a user-friendly computer-basedtool for strength design of containers.Keywords: analysis, bending, box, buckling, collapse, compression, corrugation,corrugated board, crease, design, experiment, failure criterion, fluting, finite elementmethod, liner, local buckling, packaging, panel, paper, stiffness, strength, test method,transverse shear

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CONTENTSPART I: INTRODUCTION AND SUMMARYPAGE1General remarks1Background and earlier work3Aim of present work4General assumptions and limitations in present work5Summary of contents and major conclusions5Concluding remarks and future research6Presented papers7Acknowledgements8References9PART II: APPENDED PAPERSPAPER 1: T. Nordstrand, H. G. Allen and L. A. Carlsson, "Transverse Shear Stiffnessof Structural Core Sandwich", Composite Structures, No. 27, pp. 317-329,1994.PAPER 2: T. Nordstrand and L.A. Carlsson, "Evaluation of Transverse Shear Stiffnessof Structural Core Sandwich Plates", Composite Structures, Vol. 37, pp.145-153, 1997.PAPER 3: T. Nordstrand, "On Buckling Loads for Edge-Loaded Orthotropic Platesincluding Transverse Shear", SCA Research, Box 716, 851 21 Sundsvall,Sweden. To be submitted to Composite Structures.PAPER 4: T. Nordstrand, "Parametrical Study of the Post-buckling Strength ofStructural Core Sandwich Panels", Composite Structures, No. 30, pp. 441451, 1995.PAPER 5: T. Nordstrand, "Analysis and Testing of Corrugated Board Panels into thePost-buckling Regime", SCA Research, Box 716, 851 21 Sundsvall,Sweden. To be submitted to Composite Structures.PAPER 6: P. Patel, T. Nordstrand and L. A. Carlsson, "Local buckling and collapse ofcorrugated board under biaxial stress", Composite Structures, Vol. 39, No.1-2, pp. 93-110, 1997.PAPER 7: T. Nordstrand, M. Blackenfeldt and M. Renman, "A Strength PredictionMethod for Corrugated Board Containers", Report TVSM-3065, Div. ofStructural Mechanics, Lund University, Sweden, 2003.

Part IIntroduction and Summary

INTRODUCTION AND SUMMARYGeneral remarksIn 2001 the European transport packaging market had an estimated value ofapproximately 20 billion. Corrugated board represented 62 per cent of this market value[1]. A transport package is required to be strong and lightweight in order to be costeffective. Furthermore, it should be recycled because of environmental and economicalconcerns. Corrugated board has all of these features. In its most common form, viz.single-wall board, two face sheets, called liners, are bonded to a wave shaped web calledfluting or medium, see Figure 1. The resulting pipes make the board extremely stiff inbending and stable against buckling in relation to its weight [1]. Consequently, thestrength of the wood fibres in the board is also utilised in an efficient way. The flutingpipes are oriented in the cross-direction (y, CD) of board production, see Figure 1. Theorientation of the board in-line with production is called machine-direction (x, MD).Orientation through the thickness of the board is denoted Z-direction (z, ZD). Thisdefinition of principal directions is also used for the constituent paper sheets.z, ZDy, CDX, MDFigure 1. Single-wall corrugated board.In area, about 80 per cent of corrugated board production is single-wall board. The restis produced for more demanding packaging solutions that require double or triple-wallboard, illustrated in Figure 2.z, ZDy, CDX, MDFigure 2. Double and triple-wall corrugated board.The profile of a corrugated web in Figure 3 is characterised by a letter, A, B, C, E or F,specified in Table 1 [1]. Also listed in Table 1 are the take-up factors which quantify thelength of the fluting per unit length of the board. For example, one metre of corrugatedboard with B-flute requires a 1.32 m long piece of paper prior to corrugation.1

hcz, ZDy, CDX, MDλλFigure 3. The geometry of a corrugated web.As seen in Table 1 the tallest core profile is A-flute, which is used in board for heavyduty boxes. B and C-flute are used for the most common board grades. The E and Fflutes are small and consequently used in board for smaller boxes, e.g. perfumepackages, where appearance and printability are important [1].Table 1. Flute profiles.ProfileWavelength, λ (mm)Flute height, hc (mm)Take-up factor, 3.2- corrugator is a set of machines in line, designed to bring together liner and medium toform single, double or triple-wall board. This operation is achieved in a continuousprocess, see Figure 4.The reels of liner and medium are fed into the corrugator. The medium is conditionedwith heat and steam and fed between large corrugating rolls forming fluting. In theSingle Facer, starch adhesive is applied to the tips of the flutes on one side and the innerliner is glued to the fluting. The fluting with one liner attached to it is called single-faceweb and travels along the machine towards the Double Backer where the single-faceweb is bonded to the outer liner and forms corrugated board. The corrugated board isthen cut and stacked.Double BackerCorrugated boardSingle FacerLinerMachine direction MDFlutingLinerMediumFigure 4. Manufacture of corrugated board.2

The first corrugators were built in the US at the start of the last century. However, upuntil 1920, the majority of products shipped via railroads, for example, were packed inwooden crates. The corrugated box was relatively new and few had any experience intransporting them. In order to avoid liability for damage while shipping items incorrugated boxes, railroads in the US established a standard known as Rule 41. Rule 41was an important step in opening up the market for corrugated board packaging. Lateron, during World War II, corrugated board packaging was called upon to deliver rationsand other war material to all corners of the earth. This contributed to the establishmentof corrugated board globally. After the war the market grew rapidly, and the range ofsizes and capabilities of corrugated boxes grew to fit the myriad of new productsdeveloped. Recently, the combination of a plastic bag inside a corrugated board box(bag-in-box) has resulted in many new opportunities, including the latest trendpackaging of wine.Corrugated board is permeable to moisture and absorbs water. This will reduce itsstrength and stiffness. However, it can be made both water and grease proof.Many package styles and design options are possible, but often an international standardof box styles [2], the FEFCO-code, is used in specifying a design. One of the mostcommon box styles is the regular slotted container (RSC) denoted FEFCO 0201, seeFigure 5. The box size is specified by LxWxH, i.e. length of the longest side panel,width of the shortest side and height. The flap size is half of the width. In the logisticschain in Sweden a transport package is usually adjusted to the EUR-pallet. Thus thelength and width of an RSC are usually uniform divisions of the pallet size (1200x800mm), e.g. 300x200 mm or 600x400 mm.CreaseFlapW/2HLWLHWSide panelW/2LWFigure 5. A regular slotted container, code FEFCO 0201.RSC:s are produced with an in-line Slotter-Folder-Gluer, which in one operationcreases, cuts, folds and glues the blank into its final shape. The RSC is then palletisedand ready to be shipped flat to the customer.Background and earlier workSeveral experimental studies have been conducted on the compression strength ofcorrugated board containers [3,4]. The most common failure mode for a corrugated boxloaded in top-to-bottom compression is post-buckling deflection of its side panels,3

followed by biaxial compressive failure of the board in the highly stressed corner regionsof the box. Local instabilities of the liners and fluting may also interact with the failureprogression [5-8]. A detailed finite element analysis of a corrugated board panel hasshown that local buckling of one of the liners may occur before actual material failure [9].This can also be observed visually just prior to compression failure of panels and boxes[10]. However, for shallow boxes and boxes with high board bending stiffness incomparison to the box perimeter, failure is often caused by crushing of the creased boardat the loaded edges instead of collapse during buckling [11].When considering the compression of panels in a box it is recognised that the flaps,attached to the panels through the creases at top and bottom edges, introduce aneccentricity in the loading [12, 13]. Furthermore, the top and bottom edges normally havea much lower stiffness than the interior of the panel due to the creases. It has beenconcluded that the low stiffness prevents a redistribution of the stresses to the corners ofthe box and consequently reduces the box compression strength.Several previous investigations have involved finite element analysis of corrugated board.Peterson [14] developed a finite element model to study the stress fields developed in acorrugated board beam under three point loading. Pommier and Poustius studied bendingstiffnesses of corrugated board using a linear elastic finite element code [15]. Pommierand Poustius also developed a linear elastic finite element model for prediction ofcompression strength of boxes [16]. Likewise a linear elastic finite element model of acorrugated board panel for prediction of compression strength was developed by Rahman[17].Patel developed a linear elastic finite element model in a study of biaxial failure ofcorrugated board [18]. The model was used to predict buckling patterns of a circular tubesubjected to different loading conditions. In an investigation by Nyman, local buckling ofcorrugated board facings was studied numerically through finite element calculations[19].Little published work is available on the use of non-linear constitutive models forprediction of strength of corrugated board structures. However, a non-linear model ofcorrugated board was developed by Gilchrist, Suhling and Urbanik [20]. In their model,both material and geometrical non-linearities were included, in-plane and transverseloadings of corrugated board were examined. Bronkhorst and Riedemann [21] andNordstrand and Hagglund [22] have developed non-linear finite element models forcorrugated board configurations. These investigations generated predictions forcompressive creep of a box and time-dependent sagging of a corrugated board tray.Aim of present workThis project was initiated with the objective of developing a design method based onfundamental engineering mechanics to predict the stren