Numerical modelling of honeycomb core crush behaviour

Abstract

In this work several numerical techniques for modelling the transverse crush behaviour of honeycomb core materials were developed and compared with test data on aluminium and Nomex™ honeycomb. The methods included a detailed honeycomb micromechanics model, a homogenised material model suitable for use in FE code solid elements, and a homogenised discrete/finite element model used in a semi-adaptive numerical coupling (SAC) technique. The micromechanics model is shown to be suitable for honeycomb design, since it may be used to compute crush energy absorption for different honeycomb cell sizes, cell wall thicknesses and cell materials. However, the very fine meshes required make it unsuitable for analysis of large sandwich structures. The homogenised FE model may be used for such structures, but gives poor agreement when failure is due to core crushing. The SAC model is shown to be most appropriate for use in structural simulations with extensive compression core crushing failures, since the discrete particles are able to model the material compaction during local crushing.

Introduction

Composite sandwich construction consists of a lightweight core material sandwiched between two stiff facings. There are essentially two different classes of cores, namely foams and honeycombs, with a wide range of materials and properties within each type. Composite facings are commonly made of laminated fibre reinforced plastics. In terms of structural analysis, sandwich structures are efficient shell structures under transverse and bending loads compared with monolithic composite shells, since with a small additional weight of core shell bending stiffness and strength are significantly increased.

Sandwich structural concepts for aerospace applications were first employed in mass production during the Second World War in a military multipurpose aircraft, the de Havilland Mosquito. Its wings and fuselage were constructed in sandwich shells with plywood skins and balsa wood core [1]. Since then the application of polymeric composite sandwich structures in the aerospace industry has been continuously increasing as new fibre types, resin systems, adhesives, new lightweight core materials and advanced manufacturing techniques have been developed and introduced into the market. In aircraft structures, sandwich materials may be used in ailerons, spoilers, passenger floors and numerous nacelles and fairings. The latest commercial aeroplane projects of Airbus and Boeing, the A380 and the 787, respectively, show the evolutionary growth in the use of composites materials. The main structure of Airbus A380 includes 25% of carbon fibre reinforced plastic (CFRP) structures, compared to 15% in the Airbus A340 launched in 2002.

A critical loading case in aircraft structures is impact from birds, hailstones and foreign objects and the designer needs reliable methods for predicting impact damage in wing and fuselage components. Structural sandwich components have low resistance to high-velocity impact due to the thin outer composite skins and the highly deformable cores. Most common damage mechanisms in composites, such as matrix cracking, debonding and fibre failure, may appear individually or interact, resulting in complex skin failure modes under impact. After fracture of the skin, the impacting object may damage and penetrate into the core. If impact speed is low, sandwich panels may respond by bending and little damage occurs if the kinetic energy of the impacting object is accommodated by the elastic strain energy level of the panel. At higher impact velocities a critical condition is reached when local contact stress exceeds local strength, leading to laminate bending failure, core/skin interface delamination and core compression strength failure [2]. Core deformation and failure are therefore decisive factors for the energy absorption capability of sandwich panels [3].

Among core materials, honeycomb materials have been widely used in aerospace applications. Numerous studies have been conducted to understand the mechanical response of honeycomb structures under different loadings. The mechanical properties of honeycomb structures under transverse loads were investigated both analytically and experimentally by Gibson and Ashby [4]. Wu and Jiang [5] focussed on the investigation of the crushing phenomena of honeycomb structures under both quasi-static and dynamic loading conditions considering the effects of cell dimension, material strength and number of cells under loading. They investigated the honeycomb specimens with cell size of 3.2 and 4.7 mm and recommend the use of honeycomb structures with small cell size and low core height made of high-strength material for higher energy absorption under quasi-static and impact loading conditions. Yamashita and Gotoh [6] studied the quasi-static compression response of aluminium honeycomb in the thickness direction. They investigated the effect of the cell shape and the foil thickness on crush behaviour. The numerical investigation showed that the cyclic buckling mode takes place in every case and that the crush strength is higher for the smaller cell angle and also increases with the foil thickness. However, when the crush strength is evaluated with respect to the net cross section of the material part only, it attains the maximum value when the cell shape is a regular hexagonal.

In vehicle crash tests, moving or stationary deformable barriers made of metal honeycombs are extensively used to represent second crashed vehicle. When honeycomb barriers are crushed, the deformation patterns and the macroscopic stress distributions are non-uniform and complex. Therefore, constitutive description of honeycombs under multi-axial loading conditions is required. Hong et al. [7] investigated the influence of shear stress on the quasi-static crush behaviour of aluminium honeycomb specimens under compression dominant combined loads. The experimental results indicated that the energy absorption rate depends on the ratio of the shear stress to the compressive stress and on the in-plane orientation angle. Petras and Sutcliffe [8] investigated the mechanical response of sandwich beam consisting of glass fibre reinforced plastic laminate skins and Nomex™ aramid paper honeycomb core. They described a failure mode map for skin and sandwich core under three-point-bending. They showed that the failure mode and load depend on the ratio of skin thickness to span length and honeycomb relative density. Beside quasi-static analysis also numerical and complementary experimental studies on the performance of sandwich structures under different velocities were conducted. Goldsmith et al. [9] focussed on the perforation characteristics of cellular sandwich plates under transverse impact. They found that the ballistic limit of sandwich plates was not significantly affected by the type, cell size or wall diameter of composite, as the principal mechanism resisting perforation was piercing the facing plates. Thus, identical skins produced the same ballistic limit regardless of core type. Horrigan and Aitken [10] investigated the soft impact on Nomex™ honeycomb-cored sandwich panels. They employed the finite element method for numerical simulation of the impact behaviour of the honeycomb core. They observed in impact tests that soft bodies impacting on Nomex™ honeycomb-cored sandwich caused a shallow crushing of the core. Contrarily, hard bodies caused deeper and severe damage. They additionally modelled the impact cases and obtained a good agreement between experimental and numerical results. Meo et al. [11] investigated a low-velocity impact event on a Nomex™ honeycomb-cored sandwich. The numerical model they proposed gave good agreement concerning the calculation of dent depth and area of delamination. Aktay et al. [3] investigated high-velocity impact on both PEI and Nomex™ honeycomb-cored sandwich panels. They obtained good agreement with the experimental results. The Element Elimination Technique (EET) was used for the crushing failure of Nomex™ honeycomb. They pointed out the difficulties using EET. This technique is based on removing the finite elements on reaching a threshold stress or strain value. Considering the case of impact, the failed material is contained mostly in the impact damage zone and contributes to the damage resistance even after the initial failure. Since EET progressively removes the damaged elements from the impact zone, it cannot model realistic impact load cases. Additionally, small increments in the element elimination threshold may change the impact failure mode completely, leading to wrong numerical results.

The common point of the abovementioned works is the modelling of honeycomb structure using homogenised models. Since the crushing strength of honeycomb structures is highly dependent on geometry and core material properties, some investigations considered a micromechanical model approach. Chawla et al. [12] investigated the relationship between the crushing behaviour of aluminium honeycomb structure and simulation parameters, such as element size, effect of adhesive bonding between the neighbouring cells, variation in impact velocity and material model. They obtained good agreement between numerical and experimental results. This study indicated that such a numerical model considering micromechanics can be used to study the effect of other parameters such as overall size, cell size, foil thickness, thickness of honeycomb, number of complete cells and material properties. Nguyen et al. [13] simulated the impact response of sandwich structures with both honeycomb and folded core. They pointed out that several modelling approaches can be adopted for impact analysis of honeycomb sandwich structures. One standard approach is to use 3-D solid elements to model the sandwich core and 2-D shell elements for the face sheets. This method requires the homogenised material properties for the core to be determined through mechanical testing. While this methodology can be used to accurately predict impact damage, there is still the need for mechanical testing for each individual core type. A more advanced approach is to explicitly model the honeycomb core and face sheets using shell elements. This involves modelling each core cell with shell elements, so the final model is an accurate and detailed representation of the real geometry, which could be very time-consuming. A three-dimensional shell model for both core configurations was generated. Good results were obtained although they identified the structural and dynamic behaviour of these materials to be sensitive to the selection of the internal core geometry, which has a direct relation to extent of damage in the folded core and face sheets