Realistic Fe simulation of foldcore sandwich structures
- Sebastian Fischer^{1}Email author
https://doi.org/10.1186/s40712-015-0041-z
© Fischer. 2015
Received: 13 April 2015
Accepted: 29 June 2015
Published: 18 July 2015
Abstract
Background
Foldcore is an origami-like structural sandwich core which is manufactured by folding a planar base material into a three dimensional structure. The manufacturing technology is open to a variety of base materials and also a range of unit cell geometries is feasible. This results in a wide spectrum of mechanical properties which can be achieved by foldcores.
Methods
Mechanical characterisation of foldcores by testing is therefore costly. So FE simulation is required to reduce testing effort. A modelling method for foldcores which allows realistic simulation is developed and presented within this paper.
Results
The modelling method is validated by comparison with experiments. The test cases are compression tests and shear tests. Stiffness and strength is evaluated from experiment and simulation. Comparison shows very good correlation.
Conclusions
The presented method is able to simulate the mechanical properties of foldcores and is therefore a valuable tool for further product development.
Keywords
Foldcore Mechanical properties Finite element analysis (FEA) Mechanical testingBackground
Sandwich structures generally exhibit an excellent bending stiffness at low weights. The bending stiffness to weight ratio of a panel can be increased by several magnitudes if a monolithic structure is substituted by a sandwich structure. On the other hand, sandwich structures suffer several drawbacks, which limit their use in certain applications. For example in a passenger aircraft, sandwich structures are only used in secondary structures. Secondary structures are characterized by the fact that their failure does not lead to a catastrophic damage to the aircraft. Typical secondary structures are for example flaps, radomes, and nacelle structures. An exception is the fuselage of the Premier Beechcraft I, where sandwich structures are applied.
These disadvantages mentioned above are among others the vulnerability to impact loads which may cause debonding of the face sheet from the core and the problem of humidity accumulation in closed-cell sandwich cores. Novel folded sandwich core materials—fold-core—can solve the problem of humidity accumulation by featuring an open cellular design which enables ventilation of the foldcore (Miura 1972; Miura 1975; Zakirov et al. 2005; Zakirov et al. 2006; Kolax 2004; Kehrle & Kolax 2006; Hachenberg et al. 2003). So, the foldcore is an interesting alternative sandwich core material to foam cores and honeycomb. To unlock the potential of mechanical properties and help designing the foldcore’s unit cell to specific needs, simulation methods have to be used. A modelling method which allows realistic simulation is presented in this paper.
The foldcore concept
A range of base materials is usable for the manufacturing process. Typical base materials are thin metal foils, plastic foils, or resin-impregnated paper-like materials compounded from synthetic or natural fibres.
Another way of adjusting the foldcore to specific needs is variation of the base material. The range is from cheap materials like cardboard over metal foils and plastic foils up to high-performance materials like fibre-reinforced materials (Grzeschik et al. 2011; Kilchert et al. 2008; Fischer & Drechsler 2009; Fischer et al. 2009; Fischer & Drechsler 2008).
Due to the variability in unit cell geometry and base material, characterization of the foldcore mechanical properties by mechanical testing is expensive. So, simulation methods are needed to support product development.
Simulation of foldcore structures
Little literature is available on simulation of foldcores. An extensive overview of available literature is given in (Heimbs 2013) which is recommended for further reading. Here, a few of these are picked out to demonstrate modelling methods.
Usually, the meso-structure of the foldcore is considered when finite element (FE) models of the core are set up. This means that the cell walls of the foldcore are meshed with appropriate finite elements. Mostly conventional shell elements are used for this purpose. The meso-structure of a foldcore or a honeycomb can be considered as a thin-walled structure, so shell elements are efficient. Using continuum (solid) elements would lead to a large number of elements and long calculation times.
These meso-models can be used to calculate any given load case. Recent studies dealt with simulation of impact load cases (Heimbs et al. 2008; Heimbs et al. 2007). For impact simulation, it is important to capture the crushing behaviour and energy absorption. So, a material model for the cell wall material with a realistic failure model is needed. A detailed modelling of details of the foldcore like geometric imperfections or the bond line in contrast is here not necessary. But these details drive stiffness and strength properties of the foldcore which will be discussed later.
Similar modelling is widely used for honeycomb structures like presented in Hohe (2003), Chawla et al. (2003), Aminanda et al. (2007), and Aktay et al. (2007). As both are thin-walled structures when regarding the meso-structure, similar effects occur during stressing these structures like buckling of the cell walls and crushing and rupture of the cell wall material. So, when working on foldcores, it is reasonable to adopt simulation methods which were developed for honeycombs.
For the design engineer, the most important mechanical properties of a sandwich core material are stiffness and strength. Recent studies focussed on impact behaviour and achieved excellent results in terms of crushing behaviour and energy absorption. But these models typically overpredict initial stiffness of the core and also strength which is defined as peak stress. So, still a modelling method is needed which allows exact prediction of strength and stiffness.
In this study, a modelling method is presented which is able to predict stiffness and strength parameters of foldcores. Influencing variables on the foldcore mechanical properties are quantified, and modelling methods are presented which can cope with those influences. The modelling method is validated on test cases. Performed tests are flatwise compression and transverse shear (ASTM C273/C273M–11A 2011; ASTM C365/C365M–11 2011). These tests are typically performed to characterize sandwich core materials.
Unit cell and base material
Base material data
Material | E (MPa) | t (mm) | ν (−) | σ _{y} (MPa) | σ _{u} (MPa) | ε _{F} (−) | ρ (kg/m^{3}) |
---|---|---|---|---|---|---|---|
Aluminium EN AW-1050A | 68,628 | 0.1 | 0.306 | 108.3 | 148.1 | 0.0969 | 2,583 |
Dimensions of the unit cell
Geometry | H (mm) | L (mm) | S (mm) | V (mm) | ρ _{specific} (1/mm) | ρ (kg/m^{3}) |
---|---|---|---|---|---|---|
182 | 12 | 6.28 | 8.84 | 8.84 | 0.193 | 54 |
Methods
Building a finite element model which includes all relevant details of the foldcore is the basis for realistic simulation. Besides material data and the unit cell geometry, there are further effects which have to be considered. These are geometric imperfections of the foldcore, the bonding to the face sheets, and the folding edges (Fischer 2012).
General
This is done in order to avoid different boundary conditions between sample and model. A meso-model of the foldcore is used which uses conventional shell elements. Continuum elements are used for the face sheets. Load introduction is done with a rigid element. Details of the meso-model are given in the next sections. The commercial FE software Abaqus/Explicit is used for all simulations in this study. The element size in noncritical areas is 0.4 × 0.4 mm. The mesh is refined in the edges to an element size of 0.1 × 0.2 mm. The mesh refinement is performed with quadrangular elements; no triangular elements are used in the model. An elastic-plastic isotropic material model with isotropic hardening and a ductile failure criterion is used. Geometrically and physically nonlinear simulations are carried out.
Imperfections
Geometric imperfections are found to be a main influence on the behaviour of the foldcore. These imperfections occur during manufacturing of the foldcore in the folding process. In theory, the material is only folded around the folding edges and the surfaces between those edges stay plane. This would work out if the edges were hinges and would have no bending stiffness. In reality, those edges have, dependent on the foregoing embossing process and on the base material itself, some bending stiffness. That is why the surfaces do not stay perfect plane but become curved. This affects stiffness and buckling load of the foldcore and is therefore an influence on mechanical properties and has to be considered.
Different methods to cope with imperfections are presented in literature. One method to impose random imperfections is node shaking or a random deviation in material properties (Kilchert 2013; Heimbs 2008). Another method is superposing the ideal geometry with the first buckling mode for instance (Rejab & Cantwell 2013). The method proposed here is scanning a sample and using the original geometry as basis for the model (Fischer 2012).
Folding edges
Another influence on the mechanical properties of the foldcore is the behaviour of the edges. During the folding process, they are stressed and can be a weak point of the foldcore.
The edges on top and bottom of the core running in the W-direction of the core are not critical. They are bonded to the face sheets and stabilized by the glue. The edges in the L-direction are free and have to be considered in the model.
In this study, residual stresses are eliminated by a heat treatment. So, they do not have to be considered. If residual stresses were not eliminated, they could be taken in account by using modified material models for instance.
When loading a foldcore, stress concentrations are located inside the edges. So, if the material in the edges is degraded, this is an influence on the global mechanical properties of the foldcore. What happens in this case is that plasticization occurs at reduced loads in the edges. This leads to buckling in the faces and to a reduced strength as buckling is the first failure mechanism of the core. The failure mechanism stays the same but strength is reduced. In the case discussed here, strength is reduced by 13 % under compressive load while stiffness is not affected significantly.
Bonding to face sheets
The last important influence on the mechanical behaviour is the bonding to the face sheets. The bonding defines the strength against debonding. But also the stiffness and strength of the core in flatwise compression and transverse shear are influenced by the bonding.
The fillet could be considered by modelling it with solid elements. This would be realistic but would also bring in additional degrees of freedom which mean additional computational effort. Also, the modelling itself could be expensive if we think of foldcore models based on scanned geometries.
Thickness of composite shell elements
Row 1 (mm) | Row 2 (mm) | Row 3 (mm) | Row 4 (mm) | ||
---|---|---|---|---|---|
Layer 1 | Adhesive | 0.043735 | 1.4462 | 0.28185 | 0.50597 |
Layer 2 | Aluminium | 0.1 | 0.1 | 0.1 | 0.00001 |
Layer 3 | Adhesive | 0.043735 | 1.4462 | 0.28185 | 0.50597 |
Results and discussion
The modelling details described above are assembled in finite element models which are used to calculate the flatwise compression test and the transverse shear test in order to validate the modelling.
Comparison of test and simulation
Test | Modulus/strength | Experiment | FEM | ||
---|---|---|---|---|---|
Minimum | Maximum | Mean | |||
Compression | E _{Z} (MPa) | 16 | 58 | 34 | 35 |
σ _{Z} (MPa) | 0.49 | 0.77 | 0.63 | 0.67 | |
Shear L | G _{L} (MPa) | 148 | 183 | 160 | 166 |
τ _{L} (MPa) | 0.63 | 0.65 | 0.64 | 0.66 | |
Shear W | G _{W} (MPa) | 159 | 276 | 202 | 224 |
τ _{W} (MPa) | 0.63 | 0.67 | 0.66 | 0.74 |
The failure modes observed in the experiments are qualitatively the same for compression and shear. The first failure mode is buckling of the cell faces. The main mechanism which drives buckling is plasticization of the folding edge. If this happens, the “clamping” of the faces gets weaker and the critical buckling load of the faces is decreased. Buckling defines the peak stress of the stress-strain curve. At this point, there is no rupture in the material.
The second failure mechanism is the rupture of the folding edge. This happens after reaching peak stress leading to a significant drop in the stress level. The further course of the stress-strain curve is defined by further rupture in the edges, folding of the faces, and compaction.
Six specimens are used for every performed test. As shown in Table 4, there is a large scatter in the experiments. This is due to sample manufacturing; the folding process for these samples is done manually, leading to unequal quality of samples. Automatic production of samples in constant quality is a development target in ongoing research.
These tests are recalculated with the methods described above. An elastic-plastic material model with a ductile failure criterion is used. Material data is given in Table 1. All samples have the same unit cell geometry (tpye 182); the dimensions of the unit cell are given in Table 2.
As seen in “Imperfections,” “Folding edges,” and “Bonding to face sheets,” the new modelling approach does not change the qualitative mechanical behaviour of the foldcores much. But the quantitative comparison to experimental values was improved. So, with this modelling method developed here, it is possible to simulate strength and stiffness with high accuracy.
Conclusions
A modelling method for realistic simulation of foldcores has been elaborated. The influences on mechanical properties of foldcores were investigated and modelling approaches were set up. These influences are geometrical imperfections, the folding edges, and the bond line.
The modelling method was validated by comparison with experiments. Compression tests and shear tests were used as test cases. The models were able to predict test results with little deviation.
Declarations
Acknowledgements
Parts of this work were part of the EU project CELPACT within the Sixth Framework Programme of the European Commission (Contract AST5-CT-2006-031038, 2006–2009). The author gratefully acknowledges the funding of the research activities.
Authors’ Affiliations
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