Effective In-plane Properties Research Articles

Elastic properties of honeycombs with spline curve cell walls

In the ideal models, cell walls of honeycomb structures are perfect flat sheets or straight lines (viewed from out-of-plane projection), whereas most of the real honeycomb products contain curved cell walls due to the widely employed manufacturing processes. Moreover, some honeycomb products are made intentionally to have corrugated cell walls for an enhanced out-of-plane stability or an increase of structural stiffness. In the presented study, a relative new modeling method for the nonlinear cell walls of honeycomb structures is used. The method makes use of Bezier spline functions to describe the curved cell walls. Energy method and Castigliano's theorem are used to formulate the force-displacement relationship of a single cell wall, and the homogenized stiffness matrix is derived based on the proper boundary conditions of the cell walls. Analytical and experimental verification shows that the proposed model is very accurate and versatile in predicting the mechanical responses of different honeycomb geometries. Parametric studies are conducted, analytically and numerically, to examine the influence of the spline cell wall geometries on the honeycomb's effective in-plane properties and the out-of-plane stability. The study leads to the recommendation of a cell wall design strategy for maximizing the out-of-plane buckling resistance of honeycomb structures.

Developing a homogenization approach for estimation of in-plan effective elastic moduli of hexagonal honeycombs

In this research, a computational technique is developed for determining effective in-plane properties of hexagonal core honeycombs utilizing homogenization multi-scale technique based on averaging theorems. Purposely associated with engineering constants, specialized unit cells under appropriate boundary conditions are elaborated for two well-known configurations of uniform cell wall thickness and doubled thickness vertical cell walls hexagonal honeycombs. Constant boundary element method (CBEM) are employed for discretizing the boundary integral form of equivalent stress and strain equations and avoiding dependency to the mesh density and elements type selection challenges at cell walls intersection. Comparing with available experimental data for uniform cell wall thickness hexagonal honeycombs, the proposed method validated for a wide range of relative densities. Then comparing with well-defined existing analytical methods which have been previously validated experimentally, the verification of proposed method is done for uniform cell wall thickness and double thickness vertical cell walls. The results show that the proposed methods can present a well approximation of in-plane engineering constants for relative densities lower than 0.3 and also can be applied to higher relative densities by defining proper unit cells where available analytical methods encounter with significant inability.

Simplified Method for Predicting Overall Thermomechanical Properties of Cracked Composite Laminates

Predictive method of overall thermomechanical properties of symmetric composite laminates with matrix cracks in multiple plies is presented. A general 2 n-ply symmetric cracked laminate is divided into n - 1 cracked sublaminates. Each sublaminate containing obliquely-crossed matrix cracks is analyzed using a two-dimensional shear-lag model and its effective in-plane properties are calculated. Application of lamination theory to the n - 1 sublaminates with effective properties results in estimation of overall properties of the cracked laminate. Effectiveness of this simplified method is verified by comparing with available FE results. Finally, this article shows the applicability of this predictive method to energy release rate analysis associated with matrix cracking.

Two-scale analysis of a filament-wound cylindrical structure and application of periodic boundary conditions

A two-scale numerical approach to predict the effective in-plane properties of helical filament-wound thin-walled cylindrical tubes is provided. A meso-scale repeated unit cell (RUC) model for a filament-wound tube is established according to the manufacturing process, in which cross-overs, undulations and overlaps of fibre bundles are described using a bottom-up solid modelling technique. An approach to implement the general periodic boundary conditions in a finite element analysis scheme is also presented. As an application example, the effective in-plane elastic constants of glass fibre/epoxy filament-wound tubes are predicted and the influences of the number of the winding circuits and the shape of the fibre bundles are analyzed and discussed. In addition, the stress/strain distribution in the RUC is obtained which provides the essential information on the stress/strain concentration due to fibre cross-over/undulation/overlap. This then indicates the location where damage will initiate.

Effective properties for plain weave composites through-thickness reinforced with carbon nanotube forests

Abstract In this paper, an analytical approach is proposed to study the elastic properties of plain weave unit cells with reinforcing single-walled carbon nanotube forests of different growing patterns on the warp and weft carbon yarns. For the carbon nanotube-reinforced polymer matrix in which the carbon fibers are embedded, its properties can be evaluated using a modified rule of mixture. A numerical study using the present analytical approach reveals that for the cases considered, only a small increase in the nanotube volume fraction can result in a remarkable increase in the out-of-plane Young’s modulus and a slight increase in the out-of-plane shear modulus but a decrease in the out-of-plane Poisson’s ratios for the plain weave composite. The existence of carbon nanotube forests does not significantly affect the effective in-plane properties of plain weave composites. It is also noted from the present numerical study that the effective properties of plain weave composites with nanotube forest reinforcement are closely related to the nanotube volume fraction, growing or distribution patterns, but slightly affected by the orientations of carbon nanotubes.

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.