Compression Response of Composite Cushioning Materials in Series by Virtual Parameter Methods

With the assumption that the constitutive relationship of every single cushioning layer is known in advance, this paper presents virtual parameter methods for predicting compressive responses of composite cushioning materials in series (i.e. multi‐layered cushioning materials). In the proposed methods, a derivative term is introduced to transform nonlinear algebraic equations for characterizing compressive behaviours of the composite cushioning materials into explicit differential equations under quasi‐static loadings. Introducing a first or second order derivate term is equivalent to introducing a virtual damping or virtual mass to the cushioning system. It is found that the solutions with the virtual parameter methods will diverge if the order of the introduced derivative term is higher than two, and the virtual parameter (i.e. the coefficient of the introduced derivative) must be larger than zero if first or second order derivative is used. The analytical results indicate that the terms associated with the virtual parameter in the predicted responses are a monotonically decreasing function of the virtual parameter if the latter is nonnegative. To trade off between prediction precision and computation convergence speed, an analytical process is developed for estimating the range of the virtual parameter. Then a scheme for jointly predicting the compressive response and optimizing the virtual parameter is proposed. For comparison, both simulations and quasi‐static compressive tests have been carried out on layered foam and corrugated paperboard structures, which correspond to materials without and with negative stiffness zone in the stress–strain curves, respectively. The results show that the predicted responses obtained using the proposed method match the experimental data very well. Moreover, unlike the Newton–Raphson iteration method, the proposed methods are able to capture the progressive buckling phenomenon for multi‐layered corrugated paperboard subjected to quasi‐static loading condition. Copyright © 2015 John Wiley & Sons, Ltd.     

瓦楞夹层结构动态力学性能评估

以典型的瓦楞夹层结构--瓦楞纸板为例,本文研究了不同应变率下的A、B、C、E型多层瓦楞纸板的力学性能。结果表明由于变形机制的不同造成动态平台应力值比静态平台应力值有明显的增加。本文采用中等应变率下评估动态应力的Cowper-Symonds方程与试验数据相结合,构建了一个综合考虑结构参数和应变率效应的多层瓦楞纸板的动态平台应力的预测方程。结果表明：随着应变率的增加,多层瓦楞纸板的平台应力明显增加;经过标准化后的方程能够较全面的用于多层瓦楞纸板的动态平台应力的预测,同时,该方程对于其他材质的瓦楞夹层结构的力学性能的研究有重要的参考价值。     

A theoretical and experimental study on corrugated paperboard crushing under quasi‐static loadings

This paper presents 2 mathematical models to predict the initial peak stress and the plateau stress of corrugated paperboard which is simplified and regarded as the orthotropic plate under longitudinal compression. The resultant stress‐strain curve exhibits initial stiffening stage and a long plateau stage, where the initial peak stress determining the edgewise crush resistance of the board and most impact energy will be absorbed by the long plateau stage. By analyzing the elastic buckling of the board wall, a model of predicting the initial peak stress was obtained, while the plateau stress model was developed based on the gradual process of compression for corrugated board and energy conservation principle. Moreover, experiments were carried out to corroborate the presented model by comparing the predicted value with that by experiments, showing overall good agreement. It can be concluded that the proposed models can be applied for design of corrugated containers and cushioning packaging by corrugated paperboard.     

Influence of Low‐Intensity Repeated Impacts on Energy Absorption and Vibration Transmissibility of Honeycomb Paperboard

Packaging products in logistics typically will receive multiple low‐intensity repeated impacts, fewer moderate to high‐intensity impacts and vibration. As a result of low‐intensity repeated impacts, local buckling and fold will be formed in honeycomb paperboard, and its cushioning performance will be weakened. This paper investigates the influence of low‐intensity repeated impacts on the cushioning performance of honeycomb paperboard. The low‐intensity repeated impacts with dropping height 5 cm were conducted at first. Then, the moderate‐intensity impact with dropping height 80 cm and vibration experiment were, respectively, conducted. The results show: (a) honeycomb paperboard absorbs the energy produced by low‐intensity repeated impacts through layer upon layer folding of honeycomb structure. The highest buckling peak turns up in low‐intensity impact, followed by a series of buckling in intact honeycomb paperboard. However, the buckling is not obvious in repeated impacts; (b) the load carrying capacity of honeycomb paperboard after low‐intensity repeated impacts declines significantly. Three deformation stages are observed in the load–displacement curve. Most of impact energy is absorbed in the plateau stage. The absorbed energy of damaged honeycomb paperboard under moderate‐intensity impact decreases with the increasing of low‐intensity impact repetitions; and (c) the low‐intensity repeated impacts have an obvious influence on the resonance frequency of packaging product and stiffness of honeycomb paperboard. To confirm vibration properties of product using honeycomb paperboard cushioning, it should be considered in a designing process that honeycomb paperboard changes soften more in logistics. Copyright © 2016 John Wiley & Sons, Ltd.     

逐层交错对瓦楞纸板静态缓冲性能的影响

目的 研究在逐层交错的方式下,交错角度对瓦楞纸板静态缓冲性能的影响。方法 将单瓦楞纸板以逐层交错的方式粘合,制得0°,30°,45°,60°,90°等5种角度的试样,通过平压试验和侧压试验,研究交错角度对瓦楞纸板承载性能和吸能性能的影响。结果 交错角度对试样的密实化应变影响较小;在侧压试验中,交错角度在0°~45°之间时,试样的侧压强度和比吸能随着角度的增大而减小;交错角度在45°~90°之间时,随着角度的增大,试样的侧压强度和比吸能先增大后减小;在平压试验中,交错角度对试样的平均抗压强度和比吸能影响较小。结论 交错角度对瓦楞纸板侧压缓冲性能影响较大,对平压缓冲性能影响较小。     

Enhancement of cushioning performance with paperboard crumple inserts

This paper introduces a novel approach to using multi‐layered corrugated paperboard to provide improved protection against severe mechanical shocks and drops. Conventionally, cushion design requires the determination of the maximum expected shock levels or drop heights as well as their probability of occurrence. These are usually determined from statistical analysis of original field measurements or published drop height distribution data. With this approach, it is acknowledged that the cushioning element will provide adequate protection for statistically likely events but not for extreme, statistically unusual, events. A multi‐layer cushioning system made entirely of corrugated paperboard, designed to extend the cushioning protection range to include these extreme events, has been investigated. The main feature of the cushion is the inclusion of a corrugated paperboard crumple element designed to provide the necessary energy absorption for high compression stress levels. The effect of the complex deceleration produced by the crumple element on the product is analysed by means of the shock response spectrum. Experiments have shown that the paperboard crumple insert dramatically extends the protection range of the cushioning system by generally lowering the shock response spectrum, thus extending the cushion curve static load range. This results in a significant increase in the allowable drop height for a limited number of extreme events. Although this approach may be extended to a combination of conventional cushioning materials, the benefits of providing product protection with recyclable paperboard material are significant. Copyright © 2005 John Wiley & Sons, Ltd.     

立式瓦楞复合纸板静态压缩试验与有限元分析

目的对立式瓦楞复合纸板的静态压缩过程进行试验研究和有限元分析,研究不同楞型立式瓦楞复合纸板的力学性能。方法制作A楞、AB楞、B楞等3种不同立式瓦楞复合纸板试样,进行静态压缩实验,得到其压缩应力-应变曲线;建立3种楞型的立式瓦楞复合纸板有限元模型,进行静力学分析,得到其压缩应力-应变曲线,并与实验结果进行对比分析。结果试验和有限元分析均显示立式瓦楞复合纸板的静态压缩过程与蜂窝纸板的静态压缩过程类似,包括弹性阶段、屈服阶段、平台阶段、密实化阶段,试验和有限元分析所得到的压缩应力-应变曲线相吻合。纸板的峰值应力和平台应力与楞型有关,且随着楞高的增大而减小。结论通过试验研究和有限元分析方法得到了不同楞型立式瓦楞复合纸板的静态压缩性能,对该新型材料的应用有重要参考价值。     

蜂窝-瓦楞复合纸板的面外承载及静态缓冲性能研究

通过静态压缩试验,测定了蜂窝纸板、蜂窝-瓦楞复合纸板的静态缓冲特性曲线,讨论了蜂窝-瓦楞双面复合纸板的静态压缩变形过程,并分析了复合层数和瓦楞楞型对蜂窝-瓦楞复合纸板的面外承载性能和静态缓冲性能的影响。结果表明,蜂窝-瓦楞复合纸板的面外承载能力明显低于未经复合的蜂窝纸板;蜂窝-瓦楞复合纸板在低应力阶段的缓冲性能明显优于蜂窝纸板,但在高应力阶段与蜂窝纸板的缓冲性能基本一致。     

层合方式和压缩方向对层合瓦楞纸板压缩性能的影响

目的研究层合方式和压缩方向对层合瓦楞纸板压缩性能的影响。方法通过静态压缩对平齐式和交错式等2种层合瓦楞纸板的3个方向进行实验,得到相应的应力-应变曲线,运用能量效率法对其峰应力、平均抗压强度、总吸能和比能量吸收进行对比分析。结果 2种层合方式的瓦楞纸板在x,y,z方向的应力-应变曲线走势大致相似,峰应力、平均抗压强度、总吸能和比能量吸收均为x方向最大,y方向次之,z方向最小。在x,y,z各个方向上,平齐式层合瓦楞纸板的峰应力、平均抗压强度、总吸能和比能量吸收均高于交错式层合瓦楞纸板。结论不同层合方式和压缩方向对层合瓦楞纸板压缩性能的影响较大,设计重型缓冲包装时可以优先选择平齐式层合瓦楞纸板的x方向,可以更好地达到提高缓冲效果和节约材料的目的。     

0945型瓦楞纸板衬垫缓冲防振性能试验

目的研究0945型瓦楞纸板衬垫三角形支座底部支撑点位置对其缓冲防振性能的影响。方法以0945型衬垫三角形支座的底部支撑点与边缘的水平距离为结构参数,采用B楞瓦楞纸板制作5种0945型衬垫试样,利用静、动态压缩试验、随机振动试验分析衬垫的缓冲防振性能。结果应力-应变曲线表明,当底部支撑点与边缘的距离为40 mm时,衬垫的最大应力达到78 k N;当该距离为0时,衬垫的单位体积应变能达到35.67 k J/m3。最大加速度-静应力曲线表明,40 mm时衬垫的最大加速度最小。随机振动功率谱密度曲线表明,距离为0时,衬垫的功率谱密度峰值最小。结论 0945型瓦楞纸板衬垫三角形支座为直角三角形时,垂直边能承受较大载荷,产生较小变形,不易塌陷,缓冲防振性能最好。     

蜂窝纸板与瓦楞纸板组合结构缓冲特性研究

通过试验测试了瓦楞纸板、蜂窝纸板及其组合结构的缓冲特性曲线,并将组合结构与另外两种材料的曲线特征进行比较,结果表明,组合结构兼具有两者的优点,对于小幅荷载和较大载荷都有良好的缓冲能力.     

瓦楞纸板缓冲结构的缓冲性能影响因素研究

瓦楞纸板在缓冲包装中应用极为广泛,其结构对其缓冲性能有很大的影响。设计了内三角形、外三角形、正方形、正方形复合结构,通过静态压缩实验,绘制了其应力-应变曲线。分析比较了内外折叠情况、缓冲结构的角度、支座的形状以及斜撑等因素对缓冲性能的影响。研究表明,内三角结构的缓冲性能优于外三角结构;支座倾斜角度60°的结构具有较好缓冲性能;设计的缓冲结构中,最佳缓冲结构为正方形复合结构。研究结果对瓦楞纸板缓冲结构的设计及应用提供了参考。     

Structure design of reinforced honeycomb paperboard core and characterization of its out‐of‐plane bearing strength

Honeycomb paperboard's out‐of‐plane bearing performance is one of the important properties in packaging field application. Further improvement of its bearing performance has important value in engineering practice. In this paper, a honeycomb core structure was designed, and the bonding dimension and manufacturing process were designed. The mechanism of out‐of‐plane quasi‐static compression deformation of reinforced honeycomb paperboard was analyzed by experiments. The theoretical model of out‐of‐plane platform stress was constructed by applying the plastic deformation, plastic energy dissipation and energy conservation theory. The results show that the improved structure can be mechanically bonded in a flat state with less technological changes. Under the same honeycomb core material and core size parameters, the bearing strength of the improved structure increases by an average of 3.9 times to conventional structure. In order to meet the same compressive strength requirement, the improved structure can reduce the performance requirements of honeycomb core material or increase the core size compared with the conventional structure. When the honeycomb core cell is larger, the tension on the core layer required for the production process is reduced. The theoretical and experimental data are in good agreement with each other, and the relative errors are all less than 13%.     

EPE棱跌落缓冲性能试验研究

目的对EPE棱跌落的缓冲性能进行试验研究,验证现有棱跌落当量面积计算方法的局限性,并探索动态当量面积的计算方法。方法通过动态冲击试验研究,对比棱线接触、V台接触和纸箱包装棱部冲击等3种接触方式对当量面积大小的影响程度,以及构成棱部缓冲结构中边长、棱长与缓冲作用的关系。结果 3种接触方式动态冲击试验获得的最大加速度-静应力曲线族表明:在构成的棱部缓冲结构中,在相同当量面积条件下,棱长的增加会降低冲击接触应力和加速度;边长变化对实际应用中缓冲效果的影响不显著。结论现有当量面积计算方法无法作为可靠的缓冲设计依据。在棱跌落冲击状态下,棱垫的边长变化较棱长对缓冲性能有更大的影响。     

折叠型双瓦楞纸板衬垫动态缓冲特性的试验研究

试验研究了3种折叠型双瓦楞纸板衬垫结构在跌落高度分别为30cm、60cm、90cm 3种条件下的动态缓冲特性,采用3次多项式曲线拟合法获得了峰值加速度-静应力曲线的经验公式和特征系数.这些研究工作对折叠型双瓦楞纸板衬垫在运输包装中的应用具有良好的参考价值.     

纸夹芯和泡沫复合层状结构的静态缓冲吸能特性研究

针对由发泡聚乙烯（EPE）、瓦楞纸板、蜂窝纸板组成的复合层状结构的包装防护作用,通过实验对比分析了这类结构的横向静态压缩变形特征和缓冲吸能特性。结果表明,这类结构在压缩初始阶段和最后阶段主要表现为EPE的力学性能,而在中间阶段为瓦楞纸板、蜂窝纸板的力学性能。复合层状结构的弹性模量、总吸能、行程利用率均高于EPE,而单位体积变形能则由于试样厚度增加幅值不同,并未表现出与总吸能一致的变化规律。比吸能随着压缩应变增大而增加,几乎不受压缩速度的影响,其中EPE与蜂窝纸板复合层状结构的比吸能均大于EPE与瓦楞纸板复合结构。在应力水平较小时,EPE与瓦楞纸板复合层状结构的能量吸收效率大,然而在应力水平较大时,EPE与蜂窝纸板复合的能量吸收效率大。     

层合瓦楞纸板结构沿瓦楞方向的准静态压缩性能研究

试验研究了层合瓦楞纸板结构沿瓦楞方向的准静态压缩性能。研究结果表明:该结构准静态压缩载荷-变形曲线可分为2段——线弹性段和褶皱化变形段;楞型不同、厚度相同的样品,其准静态压缩最大值与瓦楞纸板的边压强度完全相关;楞型相同、厚度不同的样品,随着厚度的增加静态压缩最大值逐渐降低,厚度对载荷最大值所对应的变形值的影响不大。     

Energy absorption diagrams of paper honeycomb sandwich structures

It is very important to evaluate the cushioning properties of paper honeycomb sandwich structures for optimizing pack design. The energy absorption diagram is one method to characterize the cushioning properties of materials. In this paper, we investigate energy absorption and develop energy absorption diagrams for paper honeycomb sandwich structures. Based on static compression experiments, the compressive stress–strain curve is simplified into three sections: linear elasticity, plateau and densification. By considering the factors associated with the structure of paper honeycombs, the energy absorption model is obtained and characterized by the thickness‐to‐length ratio of the honeycomb cell wall. Both theory and experiment show that the compression energy absorption capability increases with the increasing thickness‐to‐length ratio of the honeycomb cell wall, and a good agreement is achieved between the theoretical and experimental energy absorption curves. The proposed method to develop an energy absorption diagram for paper honeycomb sandwich structures can be used to characterize the cushioning properties and optimize the structures of paper honeycomb sandwiches. Copyright © 2008 John Wiley & Sons, Ltd.     

B楞瓦楞纸板本构模型及其应用

瓦楞纸板因其可降解及优良的缓冲性能,常用于运输包装中。用万能试验机得到了B楞瓦楞纸板的静态应力-应变曲线,再用最小二乘法拟合出了此纸板的静态本构关系。然后,根据所拟合的曲线,计算出了B楞瓦楞纸板的缓冲系数-最大应力曲线。最后,给出了一个B楞瓦楞纸板的承载算例。     

蜂窝纸板动态缓冲特性曲线测试分析

通过动态压缩试验，测试4种厚度蜂窝纸板的最大加速度-静应力曲线，研究蜂窝纸板的动态缓冲特性，获得蜂窝纸板的最大加速度-静应力曲线的特征系数和经验公式，为蜂窝纸板在缓冲包装设计中的推广应用提供了基本数据。