Estimates of the Vigdergauz constants for regular triangular honeycombs

In this paper we study the effective elastic properties of regular triangular honeycombs. In particular we obtain some simple approximate formulae for the corresponding Vigdergauz constants with accuracy better than 1% for all densities.     

In-plane elastic constants and strengths of circular cell honeycombs

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.     

The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs

Four novel cylinder-ligament honeycombs are described, where each cylinder has 3 tangentially-attached ligaments to form either a hexagonal or re-entrant hexagonal cellular network. The re-entrant cylinder-ligament honeycombs are reported for the first time. The in-plane linear elastic constants and out-of-plane bending response of these honeycombs are predicted using finite element (FE) modelling and comparison made with hexagonal and re-entrant hexagonal honeycombs without cylinders. A laser-crafted re-entrant cylinder-ligament honeycomb is manufactured and characterized to verify the FE model. The re-entrant honeycombs display negative Poisson’s ratios and synclastic curvature upon out-of-plane bending. The hexagonal and ‘trichiral’ honeycombs possess positive Poisson’s ratios and anticlastic curvature. The ‘anti-trichiral’ honeycomb (short ligament limit) displays negative Poisson’s ratios when loaded in the plane of the honeycomb, but positive Poisson’s ratio behaviour (anticlastic curvature) under out-of-plane bending. These responses are understood qualitatively through considering deformation occurs via direct ligament flexure and cylinder rotation-induced ligament flexure.     

Transverse shear stiffness of thickness gradient honeycombs

This paper describes the transverse shear stiffness of a novel topology of gradient honeycomb structures. Opposite to classical honeycomb configurations, gradient honeycombs feature elements of their unit cells with a regular geometry variation across the whole honeycomb panel. The tessellation of the cells is not periodic, but is dictated by geometric constraints between adjacent units. Gradient honeycombs with wall thickness linearly increasing along the panel are described using experimental data and Finite Element models. The gradient behaviour of the cellular structure provides additional complexity, and the possibility of tailoring design properties, such as the stiffness per unit of weight. We observe a good agreement between the Finite Element and the experimental results, with maximum percentage errors <7% for the shear moduli of the honeycombs.     

Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading

Finite element models are developed for the in-plane linear elastic constants of a family of honeycombs comprising arrays of cylinders connected by ligaments. Honeycombs having cylinders with 3, 4 and 6 ligaments attached to them are considered, with two possible configurations explored for each of the 3- (trichiral and anti-trichiral) and 4- (tetrachiral and anti-tetrachiral) connected systems. Honeycombs for each configuration have been manufactured using rapid prototyping and subsequently characterised for mechanical properties through in-plane uniaxial loading to verify the models. An interesting consequence of the family of ‘chiral’ honeycombs presented here is the ability to produce negative Poisson’s ratio (auxetic) response. The deformation mechanisms responsible for auxetic functionality in such honeycombs are discussed.     

The transverse elastic properties of chiral honeycombs

This work describes the out-of-plane linear elastic mechanical properties of trichiral, tetrachiral and hexachiral honeycomb configurations. Analytical models are developed to calculate the transverse Young’s modulus and the Voigt and Reuss bounds for the transverse shear stiffness. Finite Element models are developed to validate the analytical results, and to identify the dependence of the transverse shear stiffness vs. the gauge thickness of the honeycombs. The models are then validated with experimental results from flatwise compressive and simple shear tests on samples produced with rapid prototype (RP)-based techniques.     

Theoretical and experimental studies of the instantaneous folding force of the polyurethane foam-filled square honeycombs

This paper presents a theoretical formula to predict the instantaneous folding force of a polyurethane foam-filled square column as a single unit of square honeycombs under axial loading. For this purpose, sum of the dissipated energy rate under folding deformations of the square column and the dissipated energy rate of polyurethane foam compression was equated to the work rate of the external force on the structure. The dissipated energy rate of compression and deformation of polyurethane foam was obtained by presenting a new deformation model and through the reduced volume ratio. The final formula obtained, reasonably predicts the instantaneous folding force of the polyurethane foam-filled square column. Finally, according to the calculated theoretical relation, the instantaneous folding force of the foam-filled square column was sketched versus the axial displacement and compared to the experimental results, which showed a good correlation.     

Fabrication process and electrical behavior of novel pressure-sensitive composites

A novel route was developed to fabricate a new pressure-sensitive composite by dispersing homogeneously conductive carbon particles in an insulating silicone rubber matrix. The composites showed a gradual change in electrical resistivity with applied pressure within percolation threshold region at a constant temperature. This type of gradual fall of resistivity with applied pressure is very important to fabricate pressure sensors. Various amounts of carbon particles were dispersed in a rubber matrix to understand the effect of volume fraction of conductive filler with applying external pressure on resistivity. A quantitative general effective media (GEM) theory was used to understand the resistivity of carbon–rubber composites system over a large range of volume fraction of carbon with applied pressure. The use of two different sizes of silicon rubber particles showed a significant effect in gradual fall of resistivity with applied pressure in the narrow range of percolation threshold. However, a large variation in resistivity from 1st measuring to 10th measuring was observed. A significant improvement in successive measuring of resistivity variation from 1st measuring to 10th measuring was observed when composites were fabricated in hexane solvent media. Finally, nano-sized Al₂O₃ was dispersed to control the resistivity variation upon successive measurement and to improve the mechanical properties of the composites. The material was suggested to use as unique materials as pressure sensors in practical applications mainly for robots.     

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.     

Flatwise buckling optimization of hexachiral and tetrachiral honeycombs

The flatwise compressive behaviour of tetrachiral and hexachiral honeycombs is analysed, using analytical and Finite Element simulations, both with explicit and implicit formulations. The tetrachiral and hexachiral cells are composed by cylinders connected by four and six tangent ligaments respectively. The ligaments act as mixed stiffeners-elastic foundations during flatwise compressive loading, providing different buckling mode shapes during deformation. The models are compared with experimental results obtained using RP-based honeycombs tested according to ASTM C 393-00 and ASTM C365-00.     

Influence of an Agatha flax fibre location in a stem on its mechanical,chemical and morphological properties

The mechanical properties of flax fibres are analysed as a function of their biochemical and morphological characteristics. The fibres, from the Agatha variety, have been selected from either the top, the middle or the bottom of the stems. The results of each analysis are discussed according to the position of the fibre in the stem and compared among themselves. Considering a flax fibre as a natural composite, this study underlines the complexity of its structure and shows that many parameters intervene in its deformation behaviour.     

Influence of single-walled carbon nanotubes on the effective elastic constants of poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) is one of the most extensively used thermoplastic polyesters out on the market, and it has been implemented in many forms. There has been limited work in the area of PET reinforced with single-walled carbon nanotubes (SWCNT) in mechanical properties. Nanocomposites based on PET with small contents of SWCNT were prepared by in situ polymerization. Elastic constants were determined by tensile tests performed on specimens instrumented with strain gauges. Assuming random orientation distribution of nanotubes, experimental Young’s modulus and Poisson’s ratio values were compared to some micromechanical models (Cox and Krenchel, Halpin–Tsai and Mori–Tanaka) which take into account orientation and aspect ratio of the nanotubes. However, the waviness of the nanotubes is a factor that influences the reinforcing efficiency.     

Effect of epoxy coatings on carbon fibers during manufacture of carbon fiber reinforced resin matrix composites

The changes in oxygen and nitrogen during manufacture of the carbon fiber reinforced resin matrix composites were measured using the X-ray photoelectron spectroscopy method. The effects of the change in oxygen and nitrogen on the strength of the carbon fibers were investigated and the results revealed that the change of the tensile strength with increasing heat curing temperature was attributed to the change in the surface flaws of the carbon fibers because the carbon fibers are sensitive to the surface flaws. The effect of the surface energy that was calculated using Kaelble’s method on the strength of the carbon fibers was investigated. Furthermore, the surface roughness of the carbon fibers was measured using atom force microscopy. The change trend of roughness was reverse to that of the strength, which was because of the brittle fracture of the carbon fibers.     

Experimental and theoretical analyses of mechanical properties of PP/PLA/clay nanocomposites

Compatibilized and non-compatibilized blends of polypropylene (PP) and poly(lactic acid) (PLA) with various compositions containing nanoclay particles were prepared by one step melt compounding in a twin screw extruder. Two nanocomposite systems with different matrices i.e. PP-rich (75/25 composition) containing Cloisite 15A and PLA-rich (25/75 composition) containing Cloisite 30B were selected for investigation of effect of nanoclays and n-butyl acrylate glycidyl methacrylate ethylene terpolymers (PTW) as compatibilizer on mechanical properties of PP/PLA/clay nanocomposites. Tensile and impact properties of the nanocomposite systems were investigated and correlated with their microstructures. Tensile modulus and strength of the blends were increased while elongation at break decreased by increasing PLA content. There was an irregular relationship between impact strength of the blends and PLA content. Several proposed models for blends and nanocomposites were used for prediction of tensile modulus of the samples. Most of the proposed models for blends could predict the tensile modulus of the blends successfully at low content of PLA. Another notable point was that most of the micromechanical models for nanocomposites fitted well to experimental values at low content of the clays and showed deviations at high clay loadings.     

Interface structure and bonding in abrasion circle friction stir spot welding: A novel approach for rapid welding aluminium alloy to steel automotive sheet

Aluminium alloy 6111-T4 and steel DC04 1 mm sheets have been successfully welded with a cycle time <1 s by “Abrasion circle friction spot welding”, a novel approach to joining dissimilar materials. This was achieved by using a probe tool translated through a circular path to abrade the steel sheet. It is shown that successful welds can be produced between these two weld members with a cycle time of less than one second, that exhibit very high failure loads and a nugget pullout fracture mode desired by industry. Transmission electron microscopy investigation of the joint interface revealed no intermetallic reaction layer. The weld formation mechanisms are discussed.     

Dielectric properties of chiral honeycombs – Modelling and experiment

Electromagnetic properties of mechanically chiral honeycomb structures are investigated. In extension to previous works on the subject, rigorous analysis is performed above the quasi-static frequency range. Theoretical considerations and full wave 3D electromagnetic simulations are conducted to prove that, for the honeycombs of interest, higher order harmonics due to structure periodicity are attenuated away from the panel surface at frequencies up to several GHz, which covers a number of popular ISM bands. As a consequence, only individual plane TEM waves are observable at practical locations of transmitters and receivers away from the panel. Under the same conditions, it is demonstrated that the structural chirality does not translate into chiral electromagnetic behaviour. In other words, orthogonal modes of the honeycomb scenarios are linearly polarised, and transformation of the electromagnetic energy into heat occurs purely as a result of classical conductivity or loss tangent, which are low for the low-density panels made of low-loss dielectric cores. This indicates that EMC or shielding characteristics can only be designed either by utilizing the phenomenon of wave reflections, or by equipping the panels with additional foils on surfaces or absorbing foams in air volumes. While precise measurements of final-sized honeycomb panels remain as a challenging task for further work, preliminary experiments have been performed showing good agreement with theoretical and computed predictions.     

Evaluation of the Micropolar elasticity constants for honeycombs

Summary The Micropolar and Lamè constants for a circular cell polycarbonate honeycomb are calculated using a finite element representation of the honeycomb microstructure. A hexagonally packed, circular cell, honeycomb sheet with a rigid circular inclusion was numerically analyzed under uniaxial tension. Micropolar Elasticity was found to be the best continuum representation of the discrete honeycomb. This conclusion was arrived at by matching the strain field in the discrete honeycomb with that predicted by a micropolar elastic continuum representation of the honeycomb. The minimum ratio of inclusion radius a to cell diameter d, for the honeycomb to be approximated accurately as a continuum was between 16 and 20. A radius of 20d and 32d showed a near perfect approximation to a continuum.     

Dynamic crushing strength of hexagonal honeycombs

Based on the repeatable collapsing mechanism of cells’ structure under dynamic crushing, an analytical formula of the dynamic crushing strength of regular hexagonal honeycombs is derived in terms of impact velocity and cell walls’ thickness ratio. It is consistent with the equation obtained from the shock wave theory that regards cellular material as continuum, in which the key parameter is approximately measured from the “stress–strain” curve of the cellular material. The effect of unequal thickness of cell walls on the honeycomb's dynamic crushing strength is discussed, and the result shows that the dynamic crushing strength of the hexagonal honeycomb with some double-thickness walls is about 1.3 times of that of the hexagonal honeycomb without double-thickness wall. All of the analytical predictions are compared with the numerical simulation results, showing good agreements.     

Applying the virtual fields method to determine the through-thickness moduli of thick composites with a nonlinear shear response

This paper presents a method allowing the simultaneous identification of parameters governing an orthotropic law with a nonlinear shear response. Such laws appear for instance through the thickness of thick laminated composites. The tested specimen is subjected to boundary conditions similar to those of a Iosipescu setup. The strain field in the central area is processed with the so-called virtual fields method, which is an application of the principle of virtual work with particular virtual fields. The method is simulated with data obtained from finite element calculations.     

Effect of a new additive on mechanical properties of hot-pressed silicon carbide ceramics

The mechanical properties and microstructure of SiC ceramics, hot pressed by simultaneously adding nano-SiC and oxides (MgO+Al₂O₃+Y₂O₃) or nitrate salts (Mg(NO₃)₂+Al(NO₃)₃+Y(NO₃)₃) as additives, were evaluated. The oxide additives system slightly influenced the mechanical properties of the ceramics, while the addition of nano-SiC lead to finer microstructure, and 5 vol.% nano-SiC changed the fracture mode from intergranular type to transgranular type. The ceramics with nitrate salts had fine, equiaxed grains with an average grain size larger than that of the system added oxides, thus inducing lower Viker’s hardness and flexural strength, while the presence of crystalline YAG phase improved the fracture toughness by 54.7%. Also, an observed increase in grain growth—with decreasing weight fraction of liquid and the grounded grain morphology in this system—confirmed a diffusion-controlled growth mechanism. Although the sample with the least amount of additives has the lowest relative density and largest grain size, its flexural strength did not drastically decrease. The influence of nano-SiC on the fracture toughness in the nitrate additive system was negligible.