纸蜂窝压缩密实化应变评估

分析纸蜂窝压缩密实化应变对纸蜂窝吸能特性评估的重要性,引入纸蜂窝压缩瞬时相对密度的概念,从理论上建立纸蜂窝压缩密实化应变评估方程,并做了不同结构参数的纸蜂窝准静态压缩试验,试验结果表明纸蜂窝胞壁厚度、边长和纸蜂窝的拉伸率等结构因素对压缩密实化应变均有一定的影响:纸蜂窝压缩密实化应变随胞壁的厚度δ的增大而减小;随蜂窝胞元边长ι的增大而增大:随蜂窝胞壁厚跨比δ/ι的增大而减小;随其拉伸率γ的增大,先增大后减小,在拉伸率为1时,其压缩密实化应变达最大值;纸蜂窝结构因素对其压缩密实化应变的影响与文中的理论公式是相符的,纸蜂窝的密实化应变与其相对密度近似呈反比例关系,当纸蜂窝的瞬时相对密度为0.39左右时,纸蜂窝压缩趋于密实化.将该评估方程用于五层瓦楞纸板的压缩密实化过程评估表明它也可用于其他结构形式纸蜂窝材料的压缩密实化应变评估,具有一定的普适性.     

Effects of defects on in-plane properties of periodic metal honeycombs

The effects of missing or fractured cell walls on in-plane effective elastic stiffness and initial yield strength of square and triangular cell metal honeycombs are investigated using finite element analysis. Due to the change of localized deformation mode, the in-plane properties of defected honeycombs can differ significantly from those of intact metal honeycombs, depending on cell type and stress state. First, the effect of the size of a statistical volume element of honeycomb cells with randomly removed cell walls is explored by using different numbers of cells with 5% of walls removed, subject to periodic boundary conditions. The size of a representative volume element (statistically homogeneous) is determined for each considered in-plane property. Next, the effective in-plane properties of square cell and triangular cell honeycombs are, respectively, calculated as a function of increasing number density of randomly removed cell walls. Finally, the sensitivities of axial compressive effective properties of these honeycombs to missing cell walls are compared with that of a previously analyzed hexagonal cell honeycomb. The results indicate that some in-plane properties sharply diminish with defect density, while others exhibit more gradual decay. In compression, the effective elastic stiffness and initial yield strength of triangular cell honeycombs are least sensitive to defects among those considered.     

Size effects in ductile cellular solids. Part I: modeling

In the mechanical testing of metallic foams, an important issue is the effect of the specimen size, relative to the cell size, on the measured properties. Here we analyze size effects for the modulus and strength of regular, hexagonal honeycombs under uniaxial and shear loadings. Size effects for indentation of a honeycomb are evaluated using finite element analysis. Finally, the results for honeycombs are extrapolated to foams. The results are compared with data for metallic foams in the following, companion paper.     

Effective mechanical and transport properties of cellular solids

We utilize two different approaches, homogenization theory and discrete network analyses, to study the mechanical and transport properties of two-dimensional cellular solids (honeycombs) consisting of either hexagonal, triangular, square or Voronoi cells. We exploit results from homogenization theory for porous solids (in the low-density limit) to establish rigorous bounds on the effective thermal conductivity of honeycombs in terms of the elastic moduli and vice versa. It is shown that for hexagonal, triangular or square honeycombs, the cross-property bound relating the bulk modulus to the thermal conductivity turns out to be an exact and optimal result. The same is true for the cross-property bound linking the shear or Young's modulus of the triangular honeycomb to its conductivity. For low-density honeycombs, we observe that all of the elastic moduli do not depend on the Poisson's ratio of the solid phase. The elastic-viscoelastic correspondence principle enables us to conclude that all of the viscoelastic moduli of honeycombs in the low-density limit are proportional to the complex Young's modulus of the solid phase. Such structures have real Poisson's ratios and the loss tangent is the same for any load.     

Effects of concentrated rigid inclusions defects on the in-plane impact behavior of hexagonal honeycombs

Hexagonal honeycombs have exhibited significant advantages in energy absorption and they are increasingly used as absorbers under crush conditions. The in-plane crushing process of imperfect hexagonal honeycombs with concentrated rigid inclusions defects is simulated using finite element simulations. In each case, a constant velocity is applied to an impact plate which then crushed the honeycomb. Simulation results indicate that the defect location has a great influence on the deformation modes, especially at low and moderate velocity. After analyzing the apparent reflection about dynamic response at the impact end, the respective influences of local fraction of inclusions and foil thickness (relative density) on the crushing plateau stress on account of the crushing velocity are further discussed. Furthermore, the energy absorption capacity under constant velocity loading is studied. Due to the distribution of the concentrated rigid inclusions defects, the energy absorption can be controlled effectively.     

Modelling fatigue damage accumulation in two-dimensional Voronoi honeycombs

Trabecular bone, a porous, cellular type of bone found at the ends of the long bones and within the vertebrae, is subject to cyclic compressive loading resulting from the activities of daily living. Such fatigue loading can result in fracture, especially in vertebrae of patients with osteoporosis. As an initial step in understanding compressive fatigue of trabecular bone we previously used finite-element analysis to model the progressive damage and failure of a simple, two-dimensional hexagonal honeycomb. In this study, the analysis is extended to a random, Voronoi honeycomb. Bending of the cell walls induces tensile stresses even when the overall loading is compressive. The cell walls are assumed to have a distribution of crack lengths in their tensile zones. The cracks are assumed to grow according to a Paris law and fail when the cracks reach 75% of the cell wall thickness. Failed cell walls are removed from the structure, the stress distribution recalculated and the next increment of fatigue loading are simulated. The Young's modulus of the honeycomb is calculated after each cell wall failure. Overall failure of the Voronoi structure is assumed to occur when the modulus is reduced by 5%; further loading reduces the modulus sharply. The slope of the S–N curve for the Voronoi honeycomb is the same as that for the hexagonal honeycomb. The model suggests that a random honeycomb is more sensitive to fatigue than a regular one.     

The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids

The utility of unit cell models that assume periodic microstructures may be limited when applied to cellular materials that have non-periodic microstructures. We analyzed the effects of non-periodic microstructure and defects on the compressive failure behavior of Voronoi honeycombs using finite element analysis. Our results indicate that the non-periodic arrangement of cell walls in random Voronoi honeycombs (with cells approximately uniform in size) results in higher strains in a small number of cell walls compared to periodic, hexagonal honeycombs. Consequently, the Voronoi honeycombs were approximately 30% weaker than periodic, hexagonal honeycombs of the same density. The strength difference between the Voronoi and periodic honeycombs depended slightly on density, due to density-dependent interactions between failure modes (i.e. plastic collapse and elastic buckling). Defects, introduced by removing cell walls at random locations, caused a sharp decrease in the effective mechanical properties of both Voronoi and periodic honeycombs (e.g. a 10% reduction in density due to defects caused a 60% reduction in the strength of Voronoi honeycombs). The sensitivity to defects was comparable for thin-walled, elastomeric honeycombs (relative density 0.015) and for thicker walled, plastic honeycombs (relative density 0.15). The properties degraded to zero when 35% of the cell walls were removed, consistent with the percolation limit for a two-dimensional network of hexagonal cells. When four or more adjacent cell walls were removed, the localized band of cell collapse passed through the defect site and the effective strength and modulus were reduced, indicating that even those defects which have a negligible effect on density can alter the failure pattern as well as the effective properties of honeycombs with cells of approximately equal size and strength.     

Crashworthiness analysis on alternative square honeycomb structure under axial loading

Hexagonal metal honeycomb is widely used in energy absorption field for its special construction. However, many other metal honeycomb structures also show good energy absorption characteristics. Currently, most of the researches focus on hexagonal honeycomb, while few are performed into different honeycomb structures. Therefore, a new alternative square honeycomb is developed to expand the non-hexagonal metal honeycomb applications in the energy absorption fields with the aim of designing low mass and low volume energy absorbers. The finite element model of alternative square honeycomb is built to analyze its specific energy absorption property. As the diversity of honeycomb structure, the parameterized metal honeycomb finite element analysis program is conducted based on PCL language. That program can automatically create finite element model. Numerical results show that with the same foil thickness and cell length of metal honeycomb, the alternative square has better specific energy absorption than hexagonal honeycomb. Using response surface method, the mathematical formulas of honeycomb crashworthiness properties are obtained and optimization is done to get the maximum specific energy absorption property honeycomb. Optimal results demonstrate that to absorb same energy, alternative square honeycomb can save 10% volume of buffer structure than hexagonal honeycomb can do. This research is significant in providing technical support in the extended application of different honeycomb used as crashworthiness structures, and is absolutely essential in low volume and low mass energy absorber design.     

A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar structure with non-uniform strut morphology is developed. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square honeycombs, and 3D hexagonal and rhombic cellular materials of rod-like columnar structure. The effective elastic constants are determined taking account of bending, axial, and shear deformations of the struts. Unlike the theoretical work of other investigators for 2D honeycombs, considering bending, axial and shearing deformations of struts, the present model not only produces transverse isotropy for regular hexagonal columnar structure but also provides a consistent Poisson's ratio when applied to a square honeycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plane elastic constants of 2D and 3D structures (excluding the in-plane shear modulus of rhombic structures) and the out-of-plane shear moduli of 3D structures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the presence of taper increases values of the effective Young's and shear moduli for which the bending compliance is dominant, but decreases those for which the axial compliance is dominant. It is found that the effective elastic properties of cellular materials are dependent not only on the relative density but also on strut morphology both in cross-section geometry and its variation along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating the effective elastic properties of cellular materials.     

Elastic collapse of honeycombs under out-of-plane pressure

A theoretical scheme is developed to analyze the initial elastic buckling of hexagonal honeycombs with walls of equal or unequal thickness and of square or triangular honeycombs under out-of-plane pressure. The computing results obtained by using this scheme are in good agreement with experimental data.     

Elastic moduli and plastic collapse strength of hexagonal honeycombs with plateau borders

The theoretical analysis for the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders is proposed and presented here. The variation of cell edge thickness in real honeycombs is taken into account in deriving their elastic moduli and plastic collapse strengths. A repeating element, composed of three cell edges connected at a vertex with Plateau borders of constant radius of curvature and width, is employed to calculate the elastic moduli and plastic collapse strength of hexagonal honeycombs. Results suggest that both the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders depend on their relative density and the volume fraction of solid contained in the Plateau border region. Meanwhile, effects of solid distribution on the elastic moduli and plastic collapse strength of hexagonal honeycombs are investigated, providing a guideline for the optimal microstructure design of honeycombs.     

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular hon-eycomb structures with both positive and negative Poisson's ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.     

In-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs with dual imperfections

The in-plane elastic modulus, Poisson's ratio and plastic collapse strength of regular hexagonal honeycombs with dual imperfections of non-straight and variable-thickness cell edges were theoretically derived from a model of curved cell edges with Plateau borders. Finite element analyses (FEA) on the stiffness and strength of regular hexagonal honeycombs with dual imperfections were also performed and then compared to the theoretical modeling. Both analytical and numerical results indicate that the in-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs with dual imperfections depend on their relative density, the solid distribution in cell edges and the curvature of cell edges. Meanwhile, the effects of dual imperfections on the in-plane elastic moduli and plastic collapse strength of regular hexagonal honeycombs are more drastic as compared to those of each single imperfection. Also, it is found that the normalized in-plane elastic modulus and plastic collapse strength of regular hexagonal honeycombs with dual imperfections are approximately equal to the products of those with each single imperfection.     

Plastic deformation modes of regular hexagonal honeycombs under in-plane biaxial compression

A limit analysis approach is employed to identify the plastic deformation modes of regular hexagonal honeycombs with relatively large wall-thickness-to-length ratios under in-plane biaxial compression. An infinite block of honeycomb material is considered and a representative block consisting of four hexagonal cells is defined when assuming the kinematic admissibility of the modes and a periodic repeatability of the representative block in both spatial directions. In general, three plastic collapse modes are found to be preferable depending on the direction of loading, and in some particular cases they are similar to the modes that occur elastically under stress or strain controlled in-plane biaxial compression. It is shown that the critical forces at the onset of the plastic collapse depend on the assumed constraints for the deformation of the representative block. The results obtained from the theoretical analysis and the numerical simulations are compared and discussed.     

气凝胶填充金属蜂窝夹层结构隔热性能试验与模拟

在1300℃温度和30 min保温时间的条件下,使用Nb基钎料对铌合金进行钎焊来成形铌合金蜂窝。对铌合金蜂窝与气凝胶填充铌合金蜂窝进行加热试验,测定了热面与冷面的瞬态温度。在与实际试验条件基本保持一致的情况下,建立了金属蜂窝与气凝胶填充金属蜂窝的有限元模型,并对不同几何参数的蜂窝进行传热模拟,分析了蜂窝芯格壁厚、芯体高度、芯格内径对隔热性能的影响,并以此总结出蜂窝的隔热机理。研究结果表明：气凝胶可有效地提高蜂窝隔热性能;芯格壁厚越小,芯体高度越大,蜂窝隔热性能越好;填充气凝胶时,芯格内径越大隔热性能越好,蜂窝芯空腔时,芯格内径越大,隔热性能越差。     

指数率流体热弹流润滑分析

应用多重网格技术,求得了指数率非牛顿流体线接触热弹流润滑的数值解,分析了油膜压力、厚度和温度等随流变指数、速度参数、滑滚比及载荷参数的变化关系,并与相同工况下的等温解进行了比较。结果表明,随着流变指数的增加,油膜厚度和温度、入口处的当量粘度、最小膜厚、中心膜厚和最大温升均增大,而油膜压力和摩擦因数的变化较小。指数率流体弹流润滑问题的热效应不可忽略;与压缩功项相比,油膜能量方程中的热耗散项对温度的影响最大。同时,无量纲速度参数、滑滚比和载荷参数等均影响热弹流润滑特性。     

胞元尺寸对六边形聚氨酯蜂窝结构泊松比和吸收能量的影响

采用有限元模型对热塑性聚氨酯弹性体蜂窝结构的压缩过程进行了模拟,并用试验进行验证.采用该模型研究了胞元凹角、宽度和壁厚对蜂窝结构泊松比和吸收能量的影响.结果表明:该模型能较准确地模拟蜂窝结构的压缩过程,试验和模拟峰值应力的相对误差在10％以内;凹角为负时,蜂窝结构具有负泊松比性质,其吸收能量较凹角为正的蜂窝结构的大;胞...     

The out-of-plane properties of honeycombs

Honeycombs are often used as cores in sandwich panels. The honeycomb cores carry the normal and shear loads in the surfaces perpendicular to the axis of the hexagonal prisms. Honeycombs are particular strong in this out-of-plane direction. In this paper, the collapse behaviour under both shear and simple compression in the out-of-plane direction is analyzed. Buckling, debonding and fracture are identified as possible collapse mechanisms. The modelling work is checked by extensive experiments on a wide range of Nomex honeycombs. Good agreements are found between the model and the data.     

铝蜂窝夹芯板低速动态冲击响应研究

为研究不同结构参数对质量相同、强度不同的两种铝蜂窝夹芯板低速动态冲击响应的影响，建立了铝蜂窝夹芯板受半球型落锤低速冲击的数值模型，并将有限元计算结果与试验结果进行对比，检验了模型的可靠性。在此基础上，对比研究了不同上下铝板厚度和不同蜂窝芯壁厚对两种铝蜂窝夹芯板在低速冲击下吸能效果的影响。结果表明：在质量相同的情况下，强度小、高度大的夹芯板在低速冲击下力-位移曲线更易出现双峰模式，增加蜂窝芯壁厚或是上下铝板厚度都会使第一次的峰值力增加，第二次峰值力降低；强度小、高度大的夹芯板蜂窝芯在低速冲击中吸能占比更多，强度大、高度小的则是上层铝板吸收的能量更多，前者的质量、体积比吸能更高；铝蜂窝夹芯板质量比吸能和体积比吸能与壁厚边长比、板厚芯高比均呈幂次关系。     

管轴压成形失稳起皱力学过程的研究

管轴压成形的先进性、优势及成形过程的成功实施受到变形区开裂和传力区起皱等失稳因素的制约,为此采用理论解析与试验相结合的方法,对失稳起皱的力学过程、影响因素及影响规律进行了研究,并给出了失稳判据,以实现稳定成形时变形参数的取值范围的确定。研究表明:成形过程的失稳起皱受到几何参数、材料参数及摩擦边界条件的共同作用。其中,模具圆角曲率半径是决定性因素,并且存在一个最大和最小圆角半径区域使成形过程顺利进行而不发生失稳起皱;增大管坯材料硬化指数,减小相对厚度及接触面的摩擦,有利于减少失稳的发生。对牌号为5052,原始管平均直径d_0=31.0mm,41.0mm铝管的应用表明所提出的判据是可靠实用的。