Strength Of Honeycomb Research Articles

Response of Honeycombs Subjected to In-Plane Shear

Study on the response of honeycombs subjected to in-plane shear helps establish the constitutive relations for honeycombs and shed light on the mechanics of cellular materials. The present study explores the nonlinear elastic response of honeycombs under in-plane shear by analyzing the large deflection of cell walls in a unit cell. Governing equations are established which relate the macroscopic response of honeycombs to the deflection of cell walls. Solving these equations, the behavior of regular honeycombs under in-plane shear along horizontal (X) and vertical (Y) directions was investigated. It is found that the response of regular honeycombs under in-plane shear depends on the nondimensional shear stress which is a parameter combining the thickness-to-length ratio of cell walls, the Young's modulus of base materials, and macroscopic shear stress. Lateral shrinking is a distinctive characteristic for honeycombs under in-plane shear, which should be taken into account when establishing constitutive relations and performing simple shear experiments. Expressions for predicting the shear strength of honeycombs are formulated in this paper. It is noted that the normalized shear strength of regular honeycombs depends on two ratios: the thickness-to-length ratio of cell walls and the ratio of Young's modulus to yield strength of base materials, and the former has a dominant effect. By comparing honeycombs with cell walls of uniform thickness against honeycombs with vertical cell walls of double thickness, it is found that doubling the thickness of vertical cell walls of honeycombs increases their shear strength along horizontal (X) direction nearly twice, but does not improve the shear strength that much along the vertical (Y) direction.

Experimental and numerical studies on the crush resistance of aluminum honeycombs with various cell configurations

Commercial aluminum honeycombs with various cell configurations are experimentally tested to study the influence of cell number and central angle on the out-of-plane crush resistance of the structures. The boundary effect is found to have significant impact on the crush strength of the structure when the number of cells is small and the central angle is observed to get a difference less than 10% in the strength of the honeycombs. Numerical analyses based on whole honeycomb model and Y-shaped element model are carried out to simulate the crush and deformation process of the specimens. The adhesive bonding of the double thickness foil is considered in the simulation and the numerical results show good agreement with the experimental data and theoretical predictions. Finally, the reason for the small influence of central angle on the out-of-plane strength of honeycombs is investigated and the interaction effect between wall thickness and central angle is believed to account for it.

Analyses on the dynamic strength of honeycombs under the y-directional crushing

Based on the cells’ collapse mechanisms revealed from the numerical simulations, analytical models are established to deduce the crushing strength of the honeycombs along the y-direction with wide range of impact velocity, which express crushing strength as a function of the impact velocity, the cell size, the cell-wall angle, and the mechanical properties of the base material. The analytical predictions are in good agreement with the numerical simulation results. The optimal cell-wall angle of the honeycomb is analytically obtained as about 45°, which provides a theoretical confirmation on the finding from the numerical simulations. Moreover, a dynamic sensitivity index is proposed to quantitatively evaluate the sensitivity of the honeycombs’ crushing strength to the impact velocity, which is expressed as a function of the cell-wall angle and the honeycomb’s relative density. It is shown that the dynamic sensitivity of the honeycomb is reversely proportional to the honeycomb’s relative density, while the crushing strength of the honeycomb with β=45° is the least sensitive to the impact velocity.

Quasi-Static Crush Behavior of Aluminum Hexagonal Honeycomb with Perforated Cell Walls

The crush behavior of aluminum hexagonal honeycomb with perforated cell walls under out-of-plane quasi-static loadings was experimentally investigated. The honeycomb specimens with different heights were compressed in axial direction under displacement control. There are four sequential deformation stages during compression: linear elasticity, buckling, crushing and densification state. The performances of hexagonal honeycombs with perforated cell walls were compared with those of imperforated hexagonal honeycombs with the same sizes. The results show that the perforated holes weaken the strength of honeycombs markedly and the strength of honeycomb decreases with the specimen height.

In-plane elastic constants and strengths of circular cell honeycombs

Abstract The in-plane elastic modulus, Poisson’s ratio, brittle crushing strength and plastic yielding strength of honeycombs with hexagonally packed circular cells are analyzed theoretically. The resulting theoretical expressions are compared with the numerical results obtained from a series of finite element analyses for circular cell honeycombs with various relative densities, leading to a good correlation. It is also found that the in-plane mechanical properties of circular cell honeycombs are significantly affected by the ratio of cell-wall thickness to cell radius. Though the elastic constants along the two principal directions of circular cell honeycombs are the same, the brittle crushing strength and plastic yielding strength along the two principal directions are not identical. Furthermore, the in-plane mechanical properties of circular cell honeycombs are compared to those of regular hexagonal honeycombs with straight and uniform-thickness cell walls to evaluate their microstructural efficiency.

Crushing strength of honeycombs with various cell wall angles

The effects of cell wall angle on the in‐plane impact behaviours of hexagonal honeycombs are studied by finite element method simulations. The cell wall angle varies from 15 to 75° while a regular hexagonal honeycomb possesses a cell wall angle of 30°. Three different impact velocities 10, 60 and 100 m s−1 are involved. The crushing strengths of honeycombs with various cell wall angles but the same density are compared. The results show that the crushing strength of honeycombs is enhanced with increasing impact velocities for both x directional impact and y directional impact. The crushing strength ratio of y directional impact to x directional impact is sensitive to cell wall angle at lower impact velocities, while it approaches 1 for various cell wall angles at a high impact velocity of 100 m s−1. The cell shape has significant influence on the crushing strength of honeycombs in both x directional impact and y directional impact at low impact velocities, in which the crushing strength can be diminished to only 10% of that of the regular honeycomb. However, this influence is weakened sharply with increasing impact velocity. Comparatively, the influence of cell shape on the x directional crushing strength is more significant than that in the y direction.

Impact behavior of honeycombs under combined shear-compression. Part II: Analysis

In this paper, a numerical virtual model of honeycomb specimen as a small structure is used to simulate its combined shear-compression behavior under impact loading. With ABAQUS/Explicit code, the response of such a structure made of shell elements is calculated under prescribed velocities as those measured in the combined shear-compression tests presented in Part I of this study. The simulated results agree well with the experimental ones in terms of overall pressure/crush curves and deformation modes. It allows for the determination of the separated normal behavior and shear behavior of honeycomb specimen under dynamic combined shear-compression. It is found that the normal strength of honeycombs decreases with increasing shearing load. Quasi-static calculations were also performed and a significant dynamic strength enhancement found in experiments was validated again in the numerical work. A crushing envelope in normal strength vs. shear strength plane was obtained on the basis of these simulations.

Crushing Strength of Aluminum Honeycomb with Thinning Cell Wall

To evaluate the crash safety of automobiles, various collision tests are performed by the auto industry. In the offset frontal collision test and the side collision test, the target is an aluminum honeycomb material which has thinning cell walls. In this study, based on the analyses of the shock absorption mechanism, a new crushing strength formula is proposed. First, load-displacement curves obtained from compression tests in quasi-static condition showed an almost linear relation between a thinning rate of cell walls and a crushing strength. Second, based on Wierzbicki's theory, a new formula was proposed, which can estimate a crushing strength of a honeycomb material with thinning wall. In addition, a correcting equation which considered an elastic deformation was also proposed. Third, parametric analyses were carried out with a FE model which can simulate a delamination between cell walls. The results obtained from the theory and FEM almost corresponded to each other for a wide range of the thinning rate. Fourth, impact tests were carried out, in which the weight was dropped freely at the speed used for the automobile tests. Those results almost agreed well with the sum of the theoretical crush strength and the inside air pressure.

The effects of foam filling on compressive response of hexagonal cell aluminum honeycombs under axial loading-experimental study

In this paper the effects of foam filling of honeycomb panels on their plastic behavior and mechanical properties are studied experimentally. Five types of Al 5052-H39 honeycombs in bare and foam filled conditions are subjected to quasi-static axial compressive loading. The panels are selected so that the effects of parameters such as the cell size, the cell walls thickness and the panel thickness on the mean crushing strength, energy absorption capacity and the wavelength of the folds could be investigated. Tests show that foam filling of panels increases their mean crushing strength and energy absorption capacity up to 300% and the less the honeycomb density the greater the effect of foam filling. Furthermore, mean crushing strength of foam filled panels is larger than the sum of the mean crushing strengths of bare honeycomb and foam alone. The wavelength of folds and densification strain in foam filled panels are smaller than those of bare honeycombs. These tests also showed that unlike the theoretic formula the panel thickness influences the mean crushing strength of honeycomb.

Quasistatic deformation and failure modes of composite square honeycombs

Carbon fibre epoxy matrix composite honeycombs have been fabricated by slotting, assembling and adhesively bonding composite laminate sheets with various fibre architectures. Their out-of-plane compressive and in-plane shear responses were measured as a function of relative density, ratio of the cell height to width and the number of cells in the specimen. The measurements indicate that the response is relatively insensitive to the ratio of the cell height to cell width and number of cells in the specimen but is strongly dependent on the laminate type and fibre orientation. For example, the compressive strength of the honeycombs made from 0 90 laminates with fibres aligned with the compression direction was greater than that of honeycombs made from a woven material with fibres at ±45 . However, the shear strengths exhibited the opposite trend. These differences were attributed to a change in failure mode. In compression the honeycombs failed by either elastic buckling or plastic microbuckling while in shear the two main failure modes were elastic buckling or shear failure of the composite sheet material. Analytical models are derived for these collapse modes and used to predict the strength of the honeycomb structure. The predicted strengths are substantially higher than the measurements due to the presence of manufacturing imperfections in the honeycombs that are not accounted for in the analytical models. A limited finite element (FE) investigation is also reported to quantify the effects of imperfections on the compressive strength of the composite honeycombs. The measurements and analytical predictions reported here indicate that composite cellular materials such as honeycombs reside in a gap in the strength versus density material property space, providing new opportunities for lightweight, high strength structural design.

Cellular Metals Manufacturing

Open cell, stochastic nickel foams are widely used for the electrodes and current collectors of metal – metal hydride batteries. Closed cell, periodic aluminum honeycomb is extensively used for the cores of light, stiff sandwich panel structures. Interest is now growing in other cell topologies and potential applications are expanding. For example cellular metals are being evaluated for impact energy absorption, for noise and vibration damping and for novel approaches to thermal management. Numerous methods for manufacturing cellular metals are being developed. As a basic understanding of the relationships between cell topology and the performance of cellular metals in each application area begins to emerge, interest is growing in processes that enable an optimized topology to be reproducibly created. For some applications, such as acoustic attenuation, stochastic metal foams are likely to be preferred over their periodically structured counterparts. Nonetheless, the average cell s ize, the cell size standard deviation, the relative density and the microstructure of the ligaments are all important to control. The invention of more stable processes and improved methods for on-line control of the cellular structure via in-situ sensing and more sophisticated control algorithms are likely to lead to significant improvements in foam topology. For load supporting applications, sandwich panels containing honeycomb cores are much superior to those utilizing stochastic foams, but they are more costly than stochastic foam core materials. Recently, processes have begun to emerge for making open cell periodic cell materials with triangular or pyramidal truss topologies. These have been shown to match the stiffness and strength of honeycomb in sandwich panels. New cellular metals manufacturing processes that use metal textiles and deformed sheet metal are being explored as potentially low cost manufacturing processes for these applications. These topologically optimized systems are opening up new multifunctional applications for cellular metals.

Effects of solid distribution on the elastic buckling of honeycombs

The elastic buckling strengths of honeycombs depend on their relative density, cell geometry and the elastic modulus of solid cell edges. In this study, we consider the effect of the distribution of solid between three cell edges and a vertex on elastic buckling using a semi-analytical integral-equation approach. At first, the geometry of three cell edges connected at a vertex with Plateau borders is analyzed and then employed to represent a repeating element for regular hexagonal honeycombs. The bending moments, rotational angle and the stiffness of a rotational spring corresponding to the constraint from inclined adjacent cell edges are derived for the vertical cell edge within the repeating element. Consequently, the elastic buckling strength of regular hexagonal honeycombs can be numerically obtained. Moreover, the effects of the distribution of the solid on the elastic buckling strengths of regular hexagonal honeycombs are presented and evaluated.

Effect of inclusions and holes on the stiffness and strength of honeycombs

A finite element study has been performed on the effects of holes and rigid inclusions on the elastic modulus and yield strength of regular honeycombs under biaxial loading. The focus is on honeycombs that have already been weakened by a small degree of geometrical imperfection, such as a random distribution of fractured cell walls, as these imperfect honeycombs resemble commercially available metallic foams. Hashin–Shtrikman lower and upper bounds and self-consistent estimates of elastic moduli are derived to provide reference solutions to the finite element calculations. It is found that the strength of an imperfect honeycomb is relatively insensitive to the presence of holes and inclusions, consistent with recent experimental observations on commercial aluminium alloy foams.

Behavior of intact and damaged honeycombs: a finite element study

The Young’s moduli, the elastic buckling strength and the plastic collapse strength of regular honeycombs with defects consisting of missing cells in the structure were analyzed using the finite element method. The behavior of intact honeycombs was first analyzed; the results of this numerical study are consistent with those of previous analyses. The effect of single, isolated defects of varying sizes and the effect of the separation distance between two defects on the elastic and plastic behaviors were then analyzed. Single, isolated defects reduce the modulus and strength. The elastic buckling strength of a honeycomb with a defect normalized by the intact strength decreases directly with the ratio of the minimum net cross-sectional area normalized by the intact cross-sectional area. The plastic collapse strength of a honeycomb with a defect normalized by the intact strength decreases less rapidly than the ratio of the minimum net cross-sectional area normalized by the intact cross-sectional area. Two closely spaced, separate defects interact to reduce the elastic buckling strength of a honeycomb; at a separation distance of about ten cells separate defects act independently. The separation distance between two defects has little effect on the Young’s modulus or the plastic collapse strength of a honeycomb. The finite element analysis allows localization behavior to be studied: we find that the localization strain decreases with increasing t/ l .

Properties of a Submicron-Honeycomb thin film

ABSTRACTA method has been developed of separating the porous film produced by anodizing aluminium from its substrate. Such films have a honeycomb morphology with pores that open at both surfaces. They are composed of essentially anhydrous alumina doped with acid anion from the anodizing electrolyte, and are electron diffraction insensitive. A geometrical model has been developed that describes how the pore morphology is determined by the anodizing voltage. Using this model, expressions are derived that relate cell dimensions to voltage-determined parameters and bulk properties such as porosity.The flexural modulus and tensile strength of honeycombs have been modelled by considering bending moments experienced by the cell walls. Thus, the properties were expressed in terms of cell dimensions. Here, the anodic film and honeycomb models are combined. These are used to analyze the mechanical properties of the films as determined by the anodizing parameters. A critical crack size is predicted and compared with the results of microstructural examinations. Good agreement is shown. Assumptions behind these findings and the implications arising are discussed.