sandwich structures with folded core: mechanical modeling and ...

SEICO 09 SAMPE EUROPE 30th. International Jubilee Conference and Forum

SANDWICH STRUCTURES WITH FOLDED CORE: MECHANICAL MODELING AND IMPACT SIMULATIONS SEBASTIAN HEIMBS EADS Innovation Works, 81663 Munich, Germany SEBASTIAN KILCHERT German Aerospace Center (DLR), 70569 Stuttgart, Germany SEBASTIAN FISCHER Universität Stuttgart, Institut für Flugzeugbau, 70569 Stuttgart, Germany MICHAEL KLAUS RWTH Aachen University, Department of Aerospace and Lightweight Structures, 52062 Aachen, Germany EMMANUEL BARANGER LMT-Cachan (ENS Cachan/CNRS/UPMC/PRES UniverSud Paris), 61 Av. du Président Wilson, F-94235 Cachan Cedex, France

SUMMARY Within the research project CELPACT innovative sandwich core structures are investigated with respect to their impact energy absorption behavior. Among them are folded cores, made by folding sheet materials to a three-dimensional zigzag structure. One important issue - besides the development of efficient manufacturing processes and the determination of their mechanical behavior - is to investigate, how such core structures can be modeled within a finite element (FE) analysis, since such numerical tools play an increasingly important role in aircraft engineering. The model development of various foldcore types on the mesoscale unit cell level, the homogenized macroscale level and a combined multiscale level using different commercial FE codes is presented in this paper. Modeling issues like cell wall material modeling or imperfection modeling are discussed. Finally, these models are adopted for impact simulations and residual strength investigations. The numerical results were found to be in good correlation to experimental data.

1. INTRODUCTION Foldcores are an innovative generation of cellular core structures for sandwich composites. They are made by folding sheet materials to a three-dimensional structure with their design and cell wall material depending on the specific application, allowing for tailored compression, shear or energy absorption properties with a wide range of possible configurations [1, 2]. In the European project CELPACT [3] the mechanical and impact behavior of three different types of foldcore structures is investigated: x x

Discontinuously produced folded cores made of 0.35 mm thick prepreg sheets of unidirectional carbon fiber/epoxy resin (CFRP, Fig. 1a) Continuously produced folded cores made of 0.35 mm thick prepreg sheets of random aramid fiber/phenolic resin (AFRP, Fig. 1b)

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x

Continuously produced folded cores made of 0.1 mm thick aluminum foil EN AW-1050A (Fig. 1c).

Their manufacturing and experimentally determined mechanical behavior under compression and shear loads is described in [4], their impact behavior in [5]. In the following study the development of finite element (FE) models of these folded composite cores is presented. Such models allow for a detailed analysis of failure modes and cell wall deformation mechanisms under transverse loads, making them an efficient tool for the design of sandwich structures under transient loads. Modeling approaches on different levels of detail as well as the application of these models for impact simulations and residual strength investigations are presented in this paper. a)

b)

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Figure 1: Folded sandwich core structures: a) CFRP, b) AFRP and c) aluminum.

2. UNIT CELL MODELS (MESOSCALE MODELS) 2.1 Unit cell geometry The first modeling approach is on the mesoscale unit cell level with a detailed representation of the cell wall structure using shell elements. Such models are adequate for impact simulations or can be used for geometrical optimization studies. The basis of such models is the repetitively arranged unit cell, which is defined by a specified set of independent geometric parameters (Fig. 2). In order to be able to easily generate folded core meso-models of different geometries with preprocessing tools (e.g. ANSYS and PATRAN), parametric models were developed using the respective command languages [6]. J

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a Figure 2: s Geometric parameters of foldcore unit cells with a) simple zigzag configuration or b) with additional cell wall ‘s’ at front folding edge. 2.2 Cell wall material modeling The cell wall material modeling of the folded core structure has a strong influence on the correct representation of the unit cell’s collapse and fracture behavior under Session 5B

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transverse compression or shear loads. A large effort was therefore put into the experimental determination of the respective material’s properties [4]. The cell wall material of the CFRP foldcore was modeled with the orthotropic composite material model in LS-DYNA, based on the failure law by Chang/Chang, using experimentally determined material data. In case of the AFRP foldcore, experiments showed different elastic properties for tensile, bending and compressive loads, resulting from an inhomogeneous cell wall material composition with the aramid fibers distributed close to the neutral axis and pure phenolic resin in the outer regions (Fig. 3). The pure resin regions could take up to 50% - 60% of the entire cell wall thickness. The inhomogeneous cell wall material was modeled with the PAM-CRASH code on basis of a multilayer shell element approach and an elastic material model with damage [7]. An inner shell layer covers the material behavior of an aramid fiber/phenolic resin composite and the outer layers the pure phenolic resin. The corresponding material parameters were determined in base material tests. Also for the aluminum foldcore cell wall material tests were conducted and the data were incorporated into a bilinear elastic-plastic material model. Resin

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Figure 3: Micrographs of the front folding edge of an AFRP foldcore with a detailed view on the random fiber and resin distribution.

2.3 Imperfection modeling Since in reality cellular structures exhibit geometrical imperfections that affect the buckling load of the single cell walls and the whole structure’s strength, a uniform mesoscale model without imperfections will always lead to an overestimation of stiffness and strength properties. In this study, several different approaches to account for imperfections in the FE models were investigated. One way is to include the geometrical imperfections in the mesh on a global basis by randomly distorting the core’s geometry prior to meshing or on a local basis by randomly modifying all nodes’ coordinates (‘node-shaking’) [6]. While a perfect foldcore structure tends to buckle uniformly in each repeating unit cell, a distorted structure shows slightly different buckling patterns in each cell and thus avoids discrepancies resulting from uniform behavior. Another approach is the optical scanning of the real geometrical imperfections [8]. In this work the system ATOS by the manufacturer Gom was used, a threedimensional digitizer, which applies the principle of triangulation. The sample is scanned from top, which allows to scan the complete sample at once. However, it is not possible for the digitizer to capture the lower edges of the foldcore (Fig. 4a). The raw scanning data had to be processed in order to obtain a surface that can be used for meshing (Fig. 4b). Session 5B

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a)

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Figure 4: a) Raw data from three-dimensional digitizing and b) processed geometry and c) FE model.

In a further approach the folding process was simulated in order to capture the geometrical imperfections resulting from the manufacturing process. Fig. 5a depicts the folding pattern marked on a plane paper sheet before folding. The left pattern is the ideal one, while the right pattern exhibits a distortion. A node has been moved 0.25 mm in both in-plane directions. This order of magnitude corresponds to measured values of the real specimen. The folding process was simulated using ABAQUS Standard. The deformed geometry for the distorted pattern is shown in Fig. 5b. Only the new node coordinates, not the resulting strain state were used to build the final meso-model. a)

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Distortion

Figure 5: a) Ideal and distorted folding patterns, b) resulting folded geometry for distorted pattern.

2.4 Validation In order to validate the mesoscale unit cell models, transverse compression and shear tests were simulated and the results were compared to experimental data [4]. The stress-strain curves of folded cores loaded in compression and shear first show a linear elastic behavior. As soon as the cell walls start to buckle, the curves become nonlinear and drop steeply when the cell walls collapse. In case of the ductile AFRP or aluminum foldcore, the cells are folded, while they are crushed in the CFRP foldcore. At large strains the compressive stress-strain curve increases as the collapsed structure is densified, while the shear stress-strain curve drops to zero due to tearing of the paper faces. Generally, the stress-strain curves in Fig. 6, showing the compression and shear test results from a PAM-CRASH simulation of the AFRP foldcore, indicate a good correlation between simulation and experiment, in particular for the core buckling/collapse behavior. It was observed that buckling of the paper planes and edges initiates at similar strain states for both experiment and simulation. Also the occurrence of ruptures, which were observed mainly at the folding edges, was in good correlation. Session 5B

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Figure 6: Comparison of simulation and experiment: Stress-strain behavior of AFRP foldcore a) in compression and b) in shear.

3. HOMOGENISED MODELS (MACROSCALE MODELS) Although mesoscale unit cell models are beneficial for local investigations like impact loadings, they are numerically too expensive to be used solely in FE models of large-scale sandwich structures. Therefore, a macroscale modeling approach with a homogenized cellular foldcore was investigated as well. The basic idea of this homogenization was to develop a constitutive law for continuum solid elements, so that the mechanical behavior of these solid elements is equal to the effective mechanical behavior of the foldcore structure. Only global behavior can be represented with this approach, no local phenomena. In most commercial codes like LS-DYNA or PAM-CRASH there are material models existing for this purpose. The input of these models are the foldcore’s six independent effective stress-strain curves, three for normal stresses and three for shear stresses in all three material directions, which were determined numerically using the mesoscale model. In general, the mechanical behavior for in-plane and transverse normal and shear stresses is treated as fully uncoupled.

4. MULTI-MODEL COUPLING (MULTISCALE MODELS) The multi-model coupling (MMC) approach combines the mesoscale unit cell model with the homogenized model and may be an efficient technique for impact simulations on large-scale sandwich structures. Typically, the detailed model is limited to the impact zone, where nonlinear effects like buckling and damage occur, and the homogenized model, which primarily covers the elastic foldcore behavior, is used in the surrounding sandwich areas around the impact zone (Fig. 7). Each submodel may run at different time steps within the explicit calculation, which are determined by the individual smallest element size. The performance of the multiscale model depends strongly on the interface between mesoscale and homogenized model. A constraint or contact formulation can be used, which is able to transfer forces and moments. The suitability of the respective interface to cover the correct global sandwich structure’s stiffness was checked by 3-point-bending simulations and a global modal analysis. Session 5B

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a)

b)

Figure 7: Multi-model coupling of a) CFRP foldcore sandwich and b) AFRP foldcore sandwich with unit cell model under the impact zone and homogenized model in the surrounding.

Besides such a multiscale modeling approach, multiscale computational strategies are investigated within the CELPACT project. Those aim at solving the problem at the microscale, which exhibits a huge number of degrees of freedom. Domain decomposition methods [9] can be used in order to decrease the computational cost associated with such huge nonlinear numerical problems. Within the CELPACT project, mixed domain decomposition methods are studied following the work of [10] on geometrical nonlinear problems.

5. IMPACT SIMULATIONS The models described in the previous chapters have been used for low velocity impact simulations with a rigid spherical impactor hitting a foldcore sandwich panel. For this purpose, CFRP skin plates were added to the foldcore models and connected by contact formulations. The skins were modeled with multi-layered shell elements (according to the lay-up used in the experiments) and orthotropic composite material models with damage laws by Chang/Chang (LS-DYNA) and Ladevèze (PAM-CRASH). Various parameter studies were conducted, in which the influence of element size, the impact position, the plate size, the loading rate and the influence of friction on the sliding interfaces has been evaluated. The main results were the element size having a large influence on the simulation results and the impact location and friction having a negligible effect. The simulation results are in acceptable agreement with the experimental force and energy plots with some discrepancies arising from the added complexity of the model with the skin damage modeling, skin/core bonding and contact modeling (Fig. 8). The impact load is limited to a very local area of the sandwich structure. The impacted foldcore cell as well as the neighboring cells on both sides are stressed. Any further cells and the respective skin areas are unstressed, resulting from the high stiffness of the core. The predominant failure mode of the upper skin is matrix tensile failure initiated in and propagating from the bottom ply as well as delaminations. Damage in the skin laminate is initiated at a much lower energy level as in the core structure. Session 5B

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Figure 8: Low velocity impact models and comparison of force-displacement and energy-displacement curves of the low velocity impact loadings for a) AFRP foldcore sandwich (400 J impact) and b) CFRP foldcore sandwich (30 J impact).

6. RESIDUAL STRENGTH ANALYSIS The damage inside the skin, core or the skin/core bonding of an impacted sandwich structure may lead to a significant reduction of the structure’s compression and bending strength [11]. To avoid expensive and time-consuming test programs (impact tests, 4-point bending tests and compression after impact (CAI) tests), numerical simulations may be useful to estimate the residual strength after impact. Therefore, a procedure was investigated to simulate low velocity impact tests as well as the residual strength tests (i.e. 4-point bending or CAI tests) of the predamaged sandwich structures. The data resulting from impact simulations with LSDYNA, especially the residual deformations and damage in the skins and core were used to establish ‘pre-damaged’ models for nonlinear static residual strength simulations of 4-point bending tests after impact as well as CAI tests with ABAQUS Standard. Compared to results achieved with non-impacted sandwich plates, a severe strength reduction was observed even for very low impact energies (Fig. 9). a) 50

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Figure 9: Force-displacement diagrams for a) 4-point bending and b) CAI after 5 J impact. Session 5B

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7. CONCLUSIONS The mechanical modeling of folded sandwich core structures for finite element analyses on mesoscale, macroscale and multiscale level was investigated. The material modeling of the cell walls has proven to be an important issue for unit cell models, especially in case of inhomogeneous resin-impregnated fibrous paper materials. Also an adequate representation of the geometrical imperfections of the cellular structure is essential for a realistic simulation of cell wall buckling, folding and fracture phenomena under transverse compression and shear loads. Multi-model coupling methods as the combination of detailed unit cell models and homogenized models were found to be an efficient solution to simulate local loadings on largescale foldcore sandwich structures. This could be verified for low velocity impact loads on foldcore sandwich panels, where the simulation results in terms of impact damage, force and energy levels were in good correlation to experimental data. All in all, the numerical models have proven to be a useful tool for the designer of foldcore sandwich structures in the analysis of foreign object impact damage. However, the reliability of the simulation necessitates a detailed knowledge of the cell wall material characteristics and the imperfections in the structure.

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[11]

Khaliulin V.I., Batrakov V.V., Menyashkin D.G.: On structural and manufacturing capabilities of folded structures for use in sandwich panels, SAMPE Europe International Conference, Paris, 2007, pp. 141-148. Klett Y., Drechsler K., Kolax M., Wentzel H., Kehrle R.: Design of multifunctional folded core structures for aerospace sandwich applications, 1st CEAS European Air and Space Conference, Berlin, 2007, pp. 903-908. Johnson A.F.: Novel structural core sandwich materials for aircraft applications: CELPACT project overview, SAMPE Europe International Conference, Paris, 2009. Fischer S., Heimbs S., Kilchert S., Klaus M., Cluzel C.: Sandwich structures with folded core: manufacturing and mechanical behavior, SAMPE Europe International Conference, Paris, 2009. Lampeas G., Johnson A.F., Mines R.A.W., Klaus M., Siviour C.R.: The impact performance of sandwich structures with innovative cellular metal and folded composite cores, SAMPE Europe International Conference, Paris, 2009. Heimbs S., Middendorf P., Kilchert S., Johnson A.F., Maier M.: Experimental and numerical analysis of composite folded sandwich core structures in compression, Applied Composite Materials, 14(5-6), 2007, pp. 363-377. Kilchert S., Johnson A.F., Voggenreiter H.: FE modeling of phenolic resin impregnated aramid paper adopted in foldcore sandwich cores, 9th International Conference on Computational Structures Technology, Athens, 2008. Fischer S., Drechsler K.: Aluminum foldcores for sandwich structure application, CELLMET2008, Cellular Metals for Structural and Functional Applications, 2nd International Symposium, Dresden, 2008. Ladevèze P., Loiseau O., Dureisseix D.: A micro-macro and parallel computational strategy for highly heterogeneous structures, International Journal for Numerical Methods in Engineering, 52(1-2), 2001, pp.121-138. Cresta P., Allix O., Rey C., Guinard S.: Nonlinear localization strategies for domain decomposition methods: application to post-buckling analyses, Computer Methods in Applied Mechanics and Engineering, 196(8), 2007, pp. 1436-1446. Göttner W., Klaus M., Reimerdes H.-G.: Bending strength of sandwich panels with different cores after impact, 16th European Conference of Fracture, Greece, 2006.

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