Prediction of bending strength of long corrugated boxes

Long corrugated boxes were supported at both ends and bent by a concentrated force applied at the middle. Boxes with different lengths, cross‐sectional shapes, flute directions and board strengths were tested, using a standard compression tester with a fixed platen in accordance with ASTM D‐642. An equation was developed to relate compression strength to the various properties of the box. The correlation coefficient R² for the fit to actual data was about 0.4. Boxes having the flutes run around the box had a 20% higher compression strength than with horizontal flutes. The most significant factor was found to be the board edge crush strength. The results suggest that failure of boxes in bending is due to localized crushing at the point of application of the load, rather than whole‐box collapse. Copyright © 2001 John Wiley & Sons, Ltd.     

The effect of pallet top deck stiffness on the compression strength of asymmetrically supported corrugated boxes

During unitized shipment, the components of unit loads are interacting with each other. During floor stacking of unit loads, the load on the top of the pallet causes the top deck of the pallet to bend, which creates an uneven top deck surface resulting in uneven or asymmetrical support of the corrugated boxes. This asymmetrical support could significantly affect the strength of the corrugated boxes, and it depends on the top deck stiffness of the pallet. This study is aimed at investigating how the variations of pallet top deck stiffness and the resulting asymmetric support affect corrugated box compression strength. The study used a scaled-down unit load compression test on quarter-scale pallet designs with different deckboard thicknesses using four different corrugated box designs. Pallet top deck stiffness was determined to have a significant effect on box compression strength. There was a 27%–37% increase in box compression strength for boxes supported by high-stiffness pallets in comparison with low-stiffness pallets. The fact that boxes were weaker on low-stiffness pallets could be explained by the uneven pressure distribution between the pallet deck and bottom layer of boxes. Pressure data showed that a higher percentage of total pressure was located under the box sidewalls that were supported on the outside stringers of low-stiffness pallets in comparison with high-stiffness pallets. This was disproportionately loading one side of the box. Utilizing the effects of pallet top deck stiffness on box compression performance, a unit load cost analysis is presented showing that a stiffer pallet can be used to carry boxes with less board material; hence, it can reduce the total unit load packaging cost.     

Digital image correlation analysis of vertical strain for corrugated fiberboard box panel in compression

This work was aimed at examining the overall contributions to displacement of panels of compressed boxes, such as panel compression strain and flap and crease displacements. 3D digital image correlation (DIC) was used to analyse motion of side panels of corrugated fiberboard regular slotted containers. The vertical displacement and the vertical component of strain of the panel face during box compression test were examined. Measuring displacements of the whole compressed box with DIC enables measurement of the in‐plane compression of a panel in isolation from the horizontal fold or crease zone displacement, without having to test tube sections of the box to infer or extract the in‐plane panel compression behaviour. Detailed study of two box designs in three representative test cases was presented, which in future could be extended to other box designs. At peak load, the in‐plane compression of the panels, calculated from the average vertical component of the strain along the right edge of the long panel of the box, was 3% to 6% of total crosshead displacement for the test cases. At peak load, the portion of the box compression associated with bottom box flaps or crease zone crushing was 48% to 59% of total crosshead displacement for the different cases. The analysis showed that the majority of the vertical displacement of the box occurred in the top and bottom creased folds and that these folds are responsible for the low apparent in‐plane stiffness of a box.     

压痕形状对瓦楞纸箱抗压强度影响的试验

目的 在不同形状的压痕条件下,对瓦楞纸箱进行抗压试验,研究纸箱的变形情况和抗压能力。方法 首先设计无压痕纸箱、一字型压痕箱、八字型压痕箱以及菱形压痕箱;其次将各种压痕形状下的纸箱,利用纸箱抗压试验机进行空箱抗压实验,记录各自的最大压溃力;最后对实验数据进行分析,明确抗压强度与压痕形状的关系。结果 不同压痕形状对瓦楞纸箱的抗压强度有不同程度的影响,其中菱形影响最大。菱形压痕通过阻碍纸箱变形趋势可提高瓦楞纸箱的抗压强度。结论 在瓦楞纸箱侧板上通过施加阻碍纸箱工字型变形的压痕（如菱形压痕）,可以增加瓦楞纸箱的抗压强度,对瓦楞纸箱的生产设计具有参考意义。     

Application of beam on elastic foundation to the interaction between a corrugated box and pallet deckboard

Corrugated boxes are ubiquitous in shipping and warehousing logistics. In physical distribution, corrugated boxes are often shipped in a unit load form where the interaction between the components determines the effectiveness and safety of the overall system. When lower stiffness pallets are used to support the corrugated boxes, the compression strength of boxes is reduced due to the uneven support conditions caused by the deforming top deckboards of the pallet. In this study, a modification of the principle of beam on elastic foundation was used to predict the effect of pallet deck stiffness on the performance of a corrugated box. In the model, the corrugated box acts as the elastic foundation, and the deckboard is represented as the beam. Pallet deck stiffness, pallet connection stiffness, and package stiffness are required model inputs. The resulting model was capable of predicting the normalized distribution of forces along the boxes' length sidewall but was not capable of predicting the compression strength of the box at failure.     

大长宽比对纸箱抗压能力影响的研究与分析

对获取纸箱抗压能力的3种主要技术手段:试验测试方法、经典公式计算方法和计算机仿真模拟方法的优缺点进行了对比分析。选择0201型BC楞瓦楞纸箱为对象,分别采取试验测试和经典公式计算,在纸板材料、纸箱高度、周长相同的条件下,对长宽比从1～3范围变化的纸箱抗压能力进行了计算和测试。结果表明:长宽比从1变化到3时,纸箱的抗压强度先升再降;当长宽比为1.6左右时,抗压强度达到最大值。试验结果和利用经典抗压能力计算结果的对比分析表明,计算结果均较大地偏离了试验结果。由于不能充分考虑到纸板加工质量、纸箱成型工艺、温湿度及其它因素的影响,经典抗压能力计算公式均是偏保守的。     

Mechanical Behavior of a Partially Encased Composite Girder with Corrugated Steel Web: Interaction of Shear and Bending

The synergistic use of partially encased concrete and composite girders with corrugated steel webs (CGCSWs) has been proposed to avoid the buckling of corrugated steel webs and compression steel flanges under large combined shear force and bending moment in the hogging area. First, model tests were carried out on two specimens with different shear spans to investigate the mechanical behavior, including the load-carrying capacity, failure modes, flexural and shear stress distribution, and development of concrete cracking. Experimental results show that the interaction of shear force and bending moment causes the failure of specimens. The bending-to-shear ratio does not affect the shear stiffness of a composite girder in the elastic stage when concrete cracking does not exist, but significantly influences the shear stiffness after concrete cracking. In addition, composite sections in the elastic stage satisfy the assumption of the plane section under combined shear force and bending moment. However, after concrete cracking in the tension field, the normal stresses of a corrugated web in the tension area become small due to the “accordion effect,” with almost zero stress at the flat panels but recognizable stress at the inclined panels. Second, three-dimensional finite-element (FE) models considering material and geometric nonlinearity were built and validated by experiments, and parametric analyses were conducted on composite girders with different lengths and heights to determine their load-carrying capacity when subjected to combined loads. Finally, an interaction formula with respect to shear and flexural strength is offered on the basis of experimental and numerical results in order to evaluate the load-carrying capacity of such composite structures, thereby providing a reference for the design of partially encased composite girders with corrugated steel webs (PECGCSWs) under combined flexural and shear loads.     

瓦楞纸箱强度的静态仿真分析及试验研究

选用某B型单瓦楞纸箱,将其切割成3段,对各段分别进行抗压试验,以探讨各段对整个纸箱强度的贡献度。考虑瓦楞纸箱的材料非线性和几何非线性,采用ANSYS有限元分析软件对纸箱上段和中段以及整个纸箱进行抗压试验仿真分析,以得到纸箱各段和整个纸箱的压缩变形结果、压溃力和压溃位移。结果表明:仿真分析结果与抗压试验结果基本一致,从而验证了所建模型的可行性,且纸箱的强度基本上取决于横向皱褶。     

瓦楞纸箱抗压强度的研究进展

目的综述国内外对瓦楞纸箱抗压强度的研究进展,探讨瓦楞纸箱的发展趋势。方法以查阅文献等形式,了解国内外瓦楞纸箱抗压强度的研究现状。论述对瓦楞纸箱力学性能的研究,讨论抗压强度经验公式的修订、抗压强度影响因素及提高方法。结论抗压强度的研究为瓦楞纸箱生产企业和包装设计者提供了必要的实验数据。轻量化、定量化、节约资源和降低成本等是瓦楞纸箱科学发展的要求,也为全球瓦楞纸箱的发展指明了方向。     

Effect of Pallet Deckboard Stiffness on Corrugated Box Compression Strength

The packaging industry has long considered pallets to be rigid structures. However, in a unit load, the weight of the product produces compressive forces that are distributed across the pallet causing the top deckboards to deflect. Corrugated paperboard boxes are highly susceptible to changing support conditions; therefore, the deckboard deflection directly impacts the vertical compression strength of the box. Therefore, the objective of this study is to evaluate the effect of pallet deckboard stiffness on the vertical compression strength and deflection of corrugated paperboard boxes. Additional treatments included gaps between the deckboards and location of the box relative to the pallet stringers. Copyright © 2016 John Wiley & Sons, Ltd.     

Estimation of the compression strength of corrugated fibreboard boxes and its application to box design using a personal computer

Many papers have been published on the compression strength of corrugated fibreboard boxes, using such formulae as Kellicut's equation and McKee's equation for the calculation. These equations, however, require known values of the strength of linerboard or corrugated fibreboard, they do not include the influence of moisture content and they are inadequate in the case of wrap-around boxes. The present author measured the mechanical properties of a large number of fibreboard boxes, and has derived a statistical formula useful for estimating the compression strength of a box based on its specifications — grade of corrugated fibreboard, size of box, type of box, printed area and moisture content. The calculation gives fairly good agreement with experimental results. The estimation technique has further been converted into a personal computer program, which renders the design of corrugated fibreboard boxes an easier task.     

瓦楞纸箱的有限元建模及屈曲分析

建立了瓦楞纸箱的有限元模型并进行了屈曲分析,计算了该瓦楞纸箱的临界载荷和屈曲模态.将临界载荷与利用凯利卡特公式计算的抗压强度进行了对比.分析结果表明,利用有限元的方法计算的瓦楞纸箱临界屈曲载荷与凯利卡特公式计算抗压强度非常接近.因此利用屈曲分析计算瓦楞纸箱的抗压强度是一种可行的方法.     

Corrugated Box Compression—A Literature Survey

The past 130+ years of research into the production of corrugated packaging has produced a tremendous wealth of information about the structural dynamics of corrugated boxes in use and in failure. Most of the studies in this area were published in the journals of the paper industry. However, much of the current work on corrugated fiberboard packaging now comes from individuals with a focus on corrugated packaging as a whole rather than on the corrugated paper or structures that comprise the packaging material. Because of the difficulty in accessing or identifying some of the previous art, more recent studies may tread ground well covered by others decades earlier. This review focuses on the process of box compression and the utility of box compression testing, bringing previous work back to the fore to provide useful background for current studies. It examines the conditioning and testing process in detail, discusses the state of the art in compression estimation, and explores various parameters that affect box compression strength that are not captured in most current industry models. It also looks at how box compression results are related to field performance of boxes in unit loads. In the process, it identifies many areas for fruitful new research. Copyright © 2013 John Wiley & Sons, Ltd.     

Some experimental aspects of the compression behaviour of boxes made up of G‐flute corrugated boards

The load‐bearing capacity of boxes made up of thin‐walled G‐flute corrugated boards was investigated by performing monotonic and cyclic compression tests on boxes of various geometries. Results provided a large experimental database on the influence of the box dimensions and compression velocities on buckling parameters such as critical load and the corresponding critical axial deformation. Cyclic loading tests permitted the detection of the onset of an irreversible strain state, which could be related to damage initiation and propagation in the microstructure of the panels of boxes. Moreover, main differences, which could be observed between G‐flute corrugated boards and folding boards, were emphasized. Finally, the ability of some usual modelling approaches to predict the critical load of boxes was discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of load history on the performance of corrugated fibreboard boxes

This paper investigates the effect of load histories (static and dynamic) on the compression strength and shock absorption properties of corrugated fibreboard boxes. Experiments were set up in the laboratory to simulate compressive forces and drops that occur during normal transportation of packaged products. The results show that static compression forces (not to failure) do not have significant influence on the compressive strength or shock absorption of corrugated boxes, and that dynamic compression forces do have a significant influence on these performance factors. This study was limited to one box size and style and suggests that more extensive research be undertaken to determine the effects of previous loading histories on a broad range of box configurations.     

冷冻食品包装用瓦楞纸箱结构设计研究

根据冷冻食品用瓦楞纸箱在冷库中易出现的塌箱现象,介绍了塌箱原因。从瓦楞纸箱结构设计的角度,研究了提高瓦楞纸箱抗压强度的方法。实验数据分析表明:按照纸板理论边压强度的1.25倍进行配纸,所得到的瓦楞纸板抗压强度可满足储运环境要求;此外,将常用02型箱型改为套合型箱型,也可明显提高纸箱的抗压强度。     

基于ANSYS Workbench 的瓦楞纸箱抗压性能仿真研究

建立了瓦楞纸箱的有限元模型并进行了结构修正,应用ANSYS Workbench有限元分析软件对纸箱结构模型进行了屈曲分析,从而求得了瓦楞纸箱的抗压强度,最后通过抗压试验进行了验证。有限元分析结果与试验结果比较接近,验证了模型的有效性。     

瓦楞纸箱自锁底结构的设计与分析

目的以奶品瓦楞纸箱的自锁底结构为研究对象,研究不同自锁底结构的力学特性。方法以奶品礼箱为对象,设计6种不同自锁底结构、3种不同尺寸的18种瓦楞纸箱,根据国家标准,分别进行空箱抗压实验与95 cm的跌落实验。结果空箱抗压实验结果显示,18种自锁底箱体能够承受的最大压力在1133~1437 N之间,其中2片粘合翼均在侧面板上的X2-0结构能够承受的最大压力最大,达到了1437N;X2-5结构能够承受的最大压力接近X2-0结构,达到1421 N。6种不同自锁底结构的底面跌落数据显示,底面跌落时最大加速度均在51~59 m/s2之间,其中X2-0结构纸箱的薄弱角缩进尺寸最小,为11mm。结论对比了不同缩进量的6种自锁底结构的抗压和跌落试验结果,X2-5型具有较大的抗压性能和耐冲击性能。     

Experimental and numerical performance of corrugated fibreboard at different orientations under four‐point bending test

This paper presents experimental work, finite element (FE) model, and analytical solution for predicting the four‐point bending on C‐flute corrugated fibreboard (CFB) when oriented at different angles. The angles of the CFB samples used in this research study were 0° (cross‐machine direction) and 30°, 45°, 60°, and 90° (machine direction). The CFB was assumed as an orthotropic shell element in the FE model and was validated by comparing the bending stiffness, maximum bending force, and failure formation from the experimental test. It was found in the experiment that the 90° sample had the highest bending stiffness with the lowest maximum bending force while the 0° sample had the opposite. An interesting finding was that the 30° and 45° samples improve the bending stiffness than does 0° without significantly affecting the maximum bending force. Both the FE model and analytical solution predicted the bending stiffness trend of the board from 0° to 90° with good agreement compared with experimental results. The maximum bending force in the FE model showed reasonable agreement with the experimental findings. The failure regions on the samples showed similar patterns in both experiments and the FE model. The accurate response in the FE model justify that it is a good tool to predict the bending behaviour of CFB.     

不同铺层方式下连续玻璃纤维/聚丙烯复合材料波纹夹芯板的力学性能

制备了多种铺层方式的连续玻璃纤维/聚丙烯（GF/PP）复合材料波纹夹芯板,并研究了GF/PP复合材料波纹夹芯板的平压性能和弯曲性能。结果显示:面板相同时,增加芯板厚度可大大增加夹芯板整体的平压性能;芯板相同时,面板的铺层方式对夹芯板的平压性能有一定影响,且面板含有0°和90°铺层的波纹夹芯板具有最高的平压模量,为59.55 MPa,而单纯增加面板厚度对提升波纹夹芯板的平压性能影响不大;面板铺层方式对弯曲性能具有较大影响,面板为0°铺层的波纹夹芯板具有最高的横向弯曲模量,为783.66 MPa,面板为90°铺层的波纹夹芯板具有最高的纵向弯曲模量,为732.09 MPa;面板为单向铺层（0°或90°铺层）时,会使夹芯板另一方向（纵向或横向）的弯曲性能形成短板。