Characterization of in‐plane load bearing of a honeycomb paperboard

The in‐plane bearing capacity of the face layer and core layer of a honeycomb paperboard is limited and unstable. However, a combination of the face layer and core layer of the honeycomb paperboard protects cardboard from small‐load buckling instability and provides sufficient stiffness and bearing strength. In the study, the platform theory models of the machine direction and cross direction are established based on plastic deformation, plastic energy dissipation, and the energy conservation theory. Additionally, the marginal pressure strength in the machine direction and cross direction are deduced by combining the practical application of the honeycomb paperboard. A comparison of theoretical and experimental data indicates that the two are in good agreement. Therefore, the theoretical results of the study provide a theoretical basis for the scientific and reasonable selection of important parameters of honeycomb paperboards with different strength requirements.     

Experimental Characterisation and Numerical Modelling of Hexagonal Honeycomb Cellular Solids under Multi‐axial Loading

Abstract: Cellular solids are becoming increasingly popular for sandwich core and energy‐absorbing applications in many automotive and other transportation structures. This paper investigates experimentally and numerically the strength and post‐failure energy absorption of a popular hexagonal aluminium honeycomb material under multi‐axial loading conditions. For the experimental work, an improved Arcan test apparatus is used so that interaction of multi‐axial compression and shear loading on failure and crushing may be studied; optical measuring methods are used to extract deformation data. In addition, experimental work to characterise the material with pre‐deformation in the in‐plane directions has also been conducted. This experimental work provides input for computational modelling of the material and two alternative modelling approaches have been investigated. First, a three‐dimensional anisotropic, elastic–plastic model, with coupling of loading components is used to represent the material at the macro‐level and, second, a meso‐modelling approach using a fine shell representation of the thin‐walled honeycomb cellular structure is applied. For practical analysis of large‐scale structures, the former approach is computationally efficient and can reasonably treat the most important failure and crush characteristics of the material. However, for more accurate analysis, particularly in the case of complex non‐proportional loading, the meso‐shell model may provide a more realistic solution.     

Critical buckling load of paper honeycomb under out‐of‐plane pressure

Two out‐of‐plane buckling criteria for paper honeycomb are proposed by analysing the structure properties and the collapse mechanism of paper honeycomb: these are based on the peeling strength and ring crush strength of the chipboard wall. Taking into account the orthotropic, initial deflection and large deflection properties of the chipboard wall, the two new mechanical models and the calculation methods are developed to represent the out‐of‐plane critical load of paper honeycomb. Theoretical calculations and test results show that the models are suitable for describing the collapse mechanism of paper honeycomb. The peeling strength and ring crush strength determine the critical buckling load of paper honeycomb in different stretch phases. The out‐of‐plane critical buckling load can be predicted when the two models are integrated. Copyright © 2005 John Wiley & Sons, Ltd.     

梯度铝蜂窝夹芯板的力学行为

梯度分层铝合金蜂窝板是一种有效的吸能结构,本工作在梯度铝蜂窝结构的基础上根据梯度率的概念,通过改变蜂窝芯层的胞壁长度,设计了4种质量相同、梯度率不同的铝蜂窝夹芯结构。通过准静态压缩实验,并结合非线性有限元模拟准静态及冲击态下梯度铝蜂窝夹芯结构的变形情况及其力学性能,分析对比了相同质量下梯度铝蜂窝夹芯结构在准静态下的变形模式以及冲击载荷下分层均质蜂窝结构和不同梯度率的分层梯度蜂窝结构的动态响应和能量吸收特性。结果表明:在准静态压缩过程中,铝蜂窝梯度夹芯板的变形具有明显的局部化特征,蜂窝芯的变形为低密度优先变形直至密实,层级之间的密实化应变差随芯层密度的增大而逐渐减小;在高速冲击下,梯度蜂窝板并非严格按照准静态过程中逐级变形直至密实,而是在锤头冲击惯性及芯层密度的相互作用下整体发生的线弹性变形、弹性屈曲、塑性坍塌及密实化;另外,在本工作所设计的梯度率中,当梯度率为γ₁=0.0276时,梯度蜂窝夹芯板的吸能性达到最好,相较于同等质量下的均质蜂窝夹芯板,能量吸收提高了10.63%。     

泡沫填充蜂窝材料动态力学性能的物质点法模拟

为了研究泡沫填充蜂窝材料(FFH)在动态加载下的力学响应和吸能效果,采用物质点法建立了FFH的细观物质点模型。泡沫细观物质点模型的应力-应变曲线与理论模型和实验结果吻合较好,FFH细观物质点模型的变形失效模式与实验结果一致。研究发现,填充泡沫和蜂窝分别通过塑性变形和屈曲变形吸能,填充泡沫对蜂窝吸能效果增强效应显著。获得了填充泡沫密度和加载应变率对FFH变形损伤和吸能效果的影响。填充泡沫密度增加,FFH动态力学性能提高,吸能总量增加,蜂窝吸能增加。填充泡沫增强了蜂窝的屈曲强度,促进蜂窝抵抗更多的变形。FFH的应力-应变曲线对加载应变率敏感,其吸能效果受加载应变率一定程度的影响,但总量变化不超过15%。吸能总量和组分吸能比例由FFH整体结构决定,与加载应变率无关。      

Non‐uniform plastic deformation of micron scale objects

Significant increases in apparent flow strength are observed when non‐uniform plastic deformation of metals occurs at the scale ranging from roughly one to ten microns. Several basic plane strain problems are analysed numerically in this paper based on a new formulation of strain gradient plasticity. The problems are the tangential and normal loading of a finite rectangular block of material bonded to rigid platens and having traction‐free ends, and the normal loading of a half‐space by a flat, rigid punch. The solutions illustrate fundamental features of plasticity at the micron scale that are not captured by conventional plasticity theory. These include the role of material length parameters in establishing the size dependence of strength and the elevation of resistance to plastic flow resulting from constraint on plastic flow at boundaries. Details of the finite element method employed in the numerical analysis of the higher order gradient theory will be discussed and related to prior formulations having some of the same features. Copyright © 2003 John Wiley & Sons, Ltd.     

Crush dynamics of square honeycomb sandwich cores

Square honeycombs are effective as cores for all‐metal sandwich plates in that they combine excellent crushing strength and energy absorption with good stiffness and strength in out‐of‐plane shear and in‐plane stretch. In applications where sandwich plates must absorb significant energy in crushing under intense impulsive loads, dynamic effects play a significant role in the behaviour of the core. Three distinct dynamic effects can be identified: (i) inertial resistance, (ii) inertial stabilization of webs against buckling, and (iii) material strain‐rate dependence. Each contributes to dynamic strengthening of the core. These effects are illustrated and quantified with the aid of detailed numerical calculations for rates of deformation characteristic of shock loads in air and water. A continuum model for high rate deformation of square honeycomb cores is introduced that can be used to simulate core behaviour in large structural calculations when it is not feasible to mesh the detailed core geometry. The performance of the continuum model is demonstrated for crushing deformations. Copyright © 2005 John Wiley & Sons, Ltd.     

纸木蜂窝板面外静态压缩有限元仿真分析

目的 探究纸木蜂窝板的压溃模式和单个蜂窝单元的变形失效模式,为纸木蜂窝板内部失效机制提供一定的理论基础。方法 通过有限元仿真模拟,分析面外静态压缩得到变形云图、应力–应变云图和应力–应变曲线。结果 纸木蜂窝板的受压过程分为4个阶段,应力集中分布在蜂窝芯层,最外侧的蜂窝最早出现变形且变形较大,随后中间区域的蜂窝逐步变形增大。蜂窝芯层在受压时存在至多1个应力峰,蜂窝壁弯曲折叠了1～2次,产生了1～2个塑性铰,并在此过程中吸收能量。结论 纸木蜂窝板的压溃失效趋势为由外侧蜂窝向内部蜂窝,由单层壁向双层壁,由最弱的压溃点向其余位置。     

Structure and Mechanical Properties of AFS Sandwiches Studied by in‐situ Compression Tests in X‐ray Microtomography

Al foam core / Al alloy skins sandwiches have potential for application in light weight structures. Recently, the foaming processes have improved and large, thick and 3D‐shape panels can be produced using the precursor technology. The microstructure of an AFS sandwich is analysed in this paper at a microscale and a mesoscale using X‐ray tomography and conventional SEM analysis. The main deformation mechanism of the core under compression is also studied thanks to in situ test. It is shown that the foam first present plastic buckling and then walls rupture. This is well correlated to the microstructure of the constitutive material of the core.     

冲击载荷作用下火工分离保护装置的建模与分析

为了模拟空间火工分离保护装置冲击载荷下的动力学特性,首先,建立了该保护装置的简化模型,计算得到火工分离体的初速度,推导了装置的冲击变形和变形能公式;保护装置分别采用2A12、TC4、蜂窝夹层材料,建立三种材料的多线性本构模型,采用显式动力学求解步分析其冲击响应特性,分析可知,蜂窝夹层材料具有最佳的能量吸收特性,2A12的能量吸收特性介于蜂窝夹层材料和TC4之间,其塑性变形量适中;应变能释放和冲击碰撞的耦合分析可知,应变能占比小,体现为振荡衰减的过程,结构的冲击响应特性主要由碰撞冲击导致;试验表明,该火工分离保护装置的瞬态动力学过程与分析一致,局部最大应力为302MPa,冲击响应谱最大值为3242g,满足有效载荷的可靠解锁分离要求。     

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.     

疲劳振动对蜂窝纸板缓冲性能影响

为探究蜂窝纸板在不同程度疲劳振动下缓冲特性的变化规律,通过对多种湿度环境下处理的纸板进行不同程度的疲劳振动,再进行准静态压缩试验,并借助Matlab软件得到其应力-应变曲线、缓冲系数与湿度、振动次数关系曲线、塑性形变及能量吸收曲线。结果表明,随着振动次数和相对湿度的不断增加,材料的承载能力、剩余屈服力、缓冲效果、吸能特性都随之减弱,且随应变大小而有所不同。振动后的蜂窝纸板与振前相比各项性能都有响应减弱,此研究可以为产品不同环境条件和物流情况下的缓冲包装设计提供理论依据。     

CFRP圆形胞元蜂窝芯层面外剪切模量

为了减少卫星的热变形,将碳纤维增强树脂基复合材料（CFRP）材料圆管周期排布获得新型圆形胞元蜂窝芯层。考虑无论是Ressiner理论还是商业有限元软件ABAQUS,层合板计算热变形时,芯层的面外剪切模量均很重要,因此对CFRP圆形胞元蜂窝芯层的面外剪切进行了研究。分别从应力与应变的角度基于能量等效原理求出圆形胞元蜂窝芯层的面外剪切模量公式。以T300/环氧材料的工程常见铺层为例,比较基于ABAQUS软件计算所得剪切模量仿真解与公式计算所得理论解,其最大误差仅为10.4%,证实公式对于CFRP材料的适用性。同时用（±45°）₂铺层的T300/环氧芯层完成双剪试验,试验结果与理论结果误差为24.1%,与前人研究的铝蜂窝面外剪切模量理论解与试验解的误差相近。最后通过仿真手段证实,24.1%的误差对整体夹层结构影响较小,说明公式具有良好的工程应用价值。为以后CFRP圆形胞元蜂窝芯层的设计提供重要基础。     

Deformation and failure of blast-loaded metallic sandwich panels—Experimental investigations

Metallic sandwich panels with a cellular core such as honeycomb have the capability of dissipating considerable energy by large plastic deformation under impact/blast loading. To investigate the structural response of sandwich panels loaded by blasts, a large number of experiments have been conducted, and the experimental results are reported and discussed in this paper. Quantitative results were obtained based on the measurement in the tests by a ballistic pendulum with corresponding sensors, and then the deformation/failure modes of specimen were classified and analysed systematically. The experimental programme was designed to investigate the effects on the structural response of face-sheet and core configurations, i.e. face-sheet thickness, cell size and foil thickness of the honeycomb, and mass of charge. The experimental data were then compared with the predicted data from finite element simulations, and the results show a good agreement between the experimental and computational studies.     

304不锈钢消音蜂窝钎焊工艺、组织及力学性能分析

采用镍基BNi2钎料钎焊制备了304不锈钢消音蜂窝,对蜂窝芯体与面板钎焊界面组织和蜂窝的力学性能进行了分析和测试,并研究了钎焊热循环次数对钎焊界面组织和蜂窝拉伸力学性能的影响,为实际工程应用确定未焊合缺陷补焊次数提供了依据。液态钎料的毛细作用使钎料沿蜂窝芯箔材表面铺展并与箔材发生显著的元素扩散反应,蜂窝芯与面板之间的钎缝由Ni、Cr、Si等互溶而成的Ni基固溶体组织组成,未生成脆性共晶组织或金属间化合物。钎料中的B和Si元素显著扩散于面板材料中,形成钎料-面板反应区,因B元素的沿晶界快速扩散效应,面板侧组织呈现晶界元素渗入特征。随着钎焊次数增加,钎料对母材的溶解和晶界渗透增加,钎焊界面组织发生显著变化。制备的304不锈钢消音蜂窝拉脱强度为7.21MPa,呈现板/芯界面附近蜂窝芯破坏特点,多次钎焊时蜂窝拉脱强度呈下降趋势。制备的304不锈钢消音蜂窝平压、侧压和弯曲力学性能测试过程均经历弹性变形、塑性变形和失稳三个阶段,强度值分别为5.67MPa、33.85MPa和105.87MPa,平压和弯曲失效模型为蜂窝失稳,侧压破坏除蜂窝失稳外,发生穿孔面板与蜂窝芯体剥离的现象。鉴于多次钎焊热循环对蜂窝拉脱强度的不利影响,建议304不锈钢蜂窝钎焊缺陷的最大补焊次数为一次。     

Single‐camera special stereo‐digital image correlation applied for accurate virtual fields method identification

A single‐camera special stereo‐DIC (SS‐DIC) is proposed for accurate virtual fields method (VFM) identification. The single‐camera SS‐DIC allows accurate surface 3D deformation measurements using a single colour camera and a specially designed colour separation device. It not only effectively eliminates the unavoidable out‐of‐plane movement/rotation due to unideal in‐plane loading but also delivers uniformly distributed measurement points that brings great simplicity and convenience for internal virtual work calculation in VFM. In addition, since only a single camera is used for stereovision, the proposed SS‐DIC system requires no complicated synchronisation devices. The effectiveness and practicality of the proposed method are evaluated by heterogeneous deformation experiments of a holed aluminium alloy and 304 stainless steel plate. Combined with a high‐speed colour camera, the proposed method is expected to be a simple and practical method for the calibration of material constitutive model under intermediate and high strain rate conditions using VFM.     

纸蜂窝夹芯复合板材静态缓冲性能研究

目的为了新型纸蜂窝夹芯复合板材在运输包装中的推广应用,对新型泡状纸蜂窝夹芯复合板和纸蜂窝夹芯复合平板的缓冲性能和吸能特性进行研究。方法主要通过静态压缩实验,研究不同芯高的纸蜂窝结构类板材的应力-应变曲线、总能量吸收图、单位体积能量吸收图和缓冲系数-应变曲线,分析结构和芯高对板材静态压缩性能的影响。结果数据表明同种芯高的板材,纸蜂窝夹芯复合平板的应力峰值稍高;纸蜂窝夹芯复合平板的能量吸收、单位体积能量吸收最好;泡状纸蜂窝夹芯板由于泡结构的作用,缓冲性能大大增强。结论纸蜂窝夹芯复合平板的平压强度最好,而泡状纸蜂窝夹芯复合板的缓冲性能优于同等结构的蜂窝纸板,2种板材都有很好的应用前景。     

An integration procedure based on multi‐surface plasticity for plane stress plasticity: Theoretical formulation and application

An integration procedure designed to satisfy plane stress conditions for any constitutive law initially described in 3D and based on classical plasticity theory is presented herein. This method relies on multi‐surface plasticity, which allows associating in series various mechanisms. Three mechanisms have ultimately been used and added to the first one to satisfy the plane stress conditions. They are chosen to generate a plastic flow in the 3 out‐of‐plane directions, whose stresses must be canceled (σ₃₃,σ₁₃, and σ₂₃). The advantage of this method lies in its ease of use for every plastic constitutive law (in the general case of the non‐associated flow rule and with both nonlinear kinematic and isotropic hardening). Method implementation using a cutting plane algorithm is presented in its general framework and then illustrated by the example of a J2‐plasticity material model considering linear kinematic and isotropic hardening. The approach is compared with the same J2‐plasticity model that has been directly derived from a projection of its equations onto the plane stress subspace. The performance of the multi‐surface plasticity method is shown through the comparison of iso‐error and iso‐step contours in both formulations, and lastly with a case study considering a hollow plate subjected to tension. Copyright © 2014 John Wiley & Sons, Ltd.     

蜂窝芯层创新结构及成型性

目的设计一款增强型蜂窝芯层创新结构。方法通过平板粘合尺寸决定新增芯层在六边形蜂窝胞元中的形状,选取直线肋板结构为研究对象,对比创新结构与常规结构的面外承载性能,在现有蜂窝芯层加工工艺的基础上,对此蜂窝芯层的成型工艺及参数进行分析研究。结果新结构可实现平板状粘合,当胞元内粘合尺寸为胞元边长的0.625倍时,在蜂窝孔内形成直线肋板结构,分布均匀,创新结构比常规结构的平台应力提高了315.74%,同时针对该结构改进设计了半自动及全自动粘合工艺方法。结论创新结构科学稳定,承载性能得到显著提高,芯层粘合工艺改动小,能为扩充夹层板材结构及成型工艺提供参考。     

A non‐linear interface element for 3D mesoscale analysis of brick‐masonry structures

This paper presents a novel interface element for the geometric and material non‐linear analysis of unreinforced brick‐masonry structures. In the proposed modelling approach, the blocks are modelled using 3D continuum solid elements, whereas the mortar and brick–mortar interfaces are modelled by means of the 2D non‐linear interface element. This enables the representation of any 3D arrangement for brick‐masonry, accounting for the in‐plane stacking mode and the through‐thickness geometry, and importantly it allows the investigation of both the in‐plane and the out‐of‐plane responses of unreinforced masonry panels. A co‐rotational approach is employed for the interface element, which shifts the treatment of geometric non‐linearity to the level of discrete entities, and enables the consideration of material non‐linearity within a simplified local framework employing first‐order kinematics. In this respect, the internal interface forces are modelled by means of elasto‐plastic material laws based on work‐softening plasticity and employing multi‐surface plasticity concepts. Following the presentation of the interface element formulation details, several experimental–numerical comparisons are provided for the in‐plane and out‐of‐plane static behaviours of brick‐masonry panels. The favourable results achieved demonstrate the accuracy and the significant potential of using the developed interface element for the non‐linear analysis of brick‐masonry structures under extreme loading conditions. Copyright © 2010 John Wiley & Sons, Ltd.