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Stiffness and failure behaviour of folded sandwich cores under combined transverse shear and compression
Composites: Part A 38 (2007) 1288–1295 www.elsevier.com/locate/compositesa
Stiffness and failure behaviour of folded sandwich cores under combined transverse shear and compression M. Kintscher, L. Ka¨rger *, A. Wetzel, D. Hartung DLR, Institute of Composite Structures and Adaptive Systems, Structural Mechanics Section, Lilienthalplatz 7, 38108 Braunschweig, Germany Received 19 May 2006; received in revised form 14 November 2006; accepted 20 November 2006
Abstract For efficiently simulating the failure behaviour of sandwich structures made of stiff face sheets and a light-weight core, macroscopic material stiffness and strength values are essential. The investigated folded cores are made from Nomex paper coated with epoxy resin. Due to their channel-like structure, folded cores are air ventilated, which can help to reduce the danger of deterioration, which is a big advancement for applications in the aerospace industry. Folded core structures were tested under combined transverse compression and shear in order to get the stiffness values and the failure criterion under a multi-axial stress state. For this purpose a new test device was developed, which allows a simultaneous application of shear and compression loads. The test results are presented and discussed using a nonlinear description of the stiffness and failure behaviour of the folded core structure. Additionally, the results are compared to the stiffness and the failure behaviour of honeycomb cores. 2006 Elsevier Ltd. All rights reserved. Keywords: Sandwich core; B. Transverse cracking; C. Damage mechanics; D. Mechanical testing
1. Introduction Sandwich structures consist of a lightweight core and two outer face sheets of high stiffness. Therewith, they allow a very weight efficient shell design. While the thin face sheets act in an almost plane stress state, the main function of the core is to connect the face sheets and to transfer the transverse shear and normal stresses. Moreover, core structures may provide acoustic and heat insulation and act as energy absorbers. An additional advantage of folded core structures compared to honeycomb cores is the possibility of air ventilation to avoid deterioration caused by long term moisture exposure. To utilise this advantage, current research on folded core structures focuses on optimizing the geometry and the materials to achieve better mechanical properties and higher impact resistance, which are comparable to those of honeycomb cores.
*
Corresponding author. Tel.: +49 531 295 2295; fax: +49 531 295 2232. E-mail address: [email protected] (L. Ka¨rger).
1359-835X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2006.11.008
The advantages of sandwich structures are counteracted by their complex damage behaviour and their sensitivity to impact. Impact damage in sandwich structures can cause a significant strength and stability reduction. Therefore, various investigations have been made on impact behaviour of composite sandwich panels, and corresponding simulation tools have been developed. Ka¨rger et al. [1] analysed Nomex honeycomb sandwich panels in the context of the development of the fast damage tolerance FE tool CODAC. Nguyen et al. [2] conducted experimental impact tests on aluminium honeycomb sandwich panels and performed the impact analysis using an explicit FE code. To parametrically generate the finite element model for the honeycomb cores, the tool Sandmesh [3] was applied. Furthermore, Nguyen et al. used the tool Sandmesh for a FE mesh generation of folded structures. Low velocity impact was also investigated by Besant et al. [4] performing impact tests of aluminium honeycomb structures. Moreover, Besant et al. conducted combined transverse shear and compression tests and developed a quadratic failure criterion for aluminium honeycomb cores.
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
When sandwich structures are impacted, the core crushes and experiences a substantial stiffness reduction. To model the crushing behaviour of sandwich cores correctly, an appropriate description of its failure behaviour under combined out-of-plane shear and compression is needed. The quasi-static crushing behaviour of honeycomb under out-of-plane compression has been investigated frequently by many researchers and manufacturers. For example, Hong et al. [5] have studied aluminium honeycomb under compression dominant combined loading conditions. An indentation failure analysis of sandwich beams was performed by Petras and Sutcliffe [6], who developed a 2D-failure criterion for Nomex honeycomb. Mines and Birch [7] developed a new test rig to study the mechanical behaviour of Rohacel-51WF structural foam in a multiaxial stress state. In their work a linear relationship between compressive yielding and transverse shear stress is reported. A modified ASTM C-393 test method was used by Benderly and Putter [8] to generate controlled combinations of shear and compressive stress. They characterised the shear-compression failure envelope of Rohacel200WF structural foam under various temperatures and proposed a quadratic failure envelope. The failure of aluminium foam under multiaxial load was investigated by Gioux et al. [9], where the experimental data were compared to three yield criteria. In spite of the increasing application of sandwich structures in aerospace and transport vehicle design, the failure behaviour of sandwich cores under combined loading is not yet well investigated. So far, the authors are not aware of any literature regarding the stiffness interrelation between transverse shear and compression. In this paper, a methodology and a fixture construction for quasi-static, combined out-of-plane shear and compression tests on sandwich core materials are presented in Section 3. It is applied to folded core structures, which are described in Section 2. The main focus of the paper lays on the test results and their discussion. The test results acquired by the developed test facility are presented in Section 4. The stiffness and failure behaviour are discussed in Sections 5 and 6, respectively. As a reference, the folded core structures are compared to Nomex honeycomb cores with comparable density.
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folded geometries. Their structural properties can be varied by using different folding schemes. The Institute of Aircraft Design of the University of Stuttgart is currently developing and testing different manufacturing technologies and folding schemes in order to optimise structural properties. The core material used in this work was produced in Kazan, Russia and provided by Airbus Germany. It was folded from Nomex paper and coated by epoxy resin. Explicit material properties of the manufacturer were not available. The folded structure consists of cells formed by four connected plains in the shape of a parallelogram, cf. Fig. 1. The geometrical properties are provided in Table 1. The structural properties will be investigated in Section 4 and the following. For the combined shear and compression tests, the studied folded core specimens were bonded to steel face sheets with Epibond 1590. The face sheets were sandblasted and the amount of applied adhesive was relatively high to assure a good bonding of core and face sheets. However, by separating the specimens after testing, small local gaps in the bonding between core and face sheets were found. These voids were caused by imprecise manufacturing and variations in the core height. Although an influence of incomplete bonding on the test results could not directly be ascertained, the imprecise manufacturing is assumed to be the general reason for quite a large scatter. It should be mentioned that the quality of folded core structures manufactured by the University of Stuttgart has strongly improved. Not only a high geometric accuracy but also a
2. Material description and specimen set-up Folded structures are three-dimensional geometries folded from semi-finished sheets. They can be made of different materials such as metal or resin saturated Nomex paper. The Russian oil and gas distribution industry and the aircraft industry introduced folded structures in several noise reduction applications. Due to the possibility of air ventilation, folded structures are considered as core material for aerospace sandwich structure applications. Compared to honeycomb, folded structures are easily shapeable, which means that curvatures of small radius can be manufactured. There are numerous varieties of
Fig. 1. Geometry of the folded structure.
Table 1 Folded structure geometry properties Property Height, H Spreading, 2S Length, 2L Amplitude, V Density, q
Value 28 mm 35 mm 18 mm 33 mm 58 mkg3
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high-quality resin impregnation can be achieved by now. Due to the limited number of provided specimens, only the x-direction defined in Fig. 1 could be investigated in the here described testing program. 3. Test set-up Based on the test assembly proposed by Besant et al. [4] a test device was developed to apply combined out-of-plane shear and compressive loading to the specimen. The new test device is used to apply a constant shear deformation. Subsequently, the compressive loading is realised by the static test facility Zwick 1484. An overview of the test set-up is given in Fig. 2. The test device is schematically shown in Fig. 3. To assure a balanced application of the shear load to the specimen, a roll (1) and a steel towing rope (2) are used in combination with a double-core specimen. The relocatable roll construction is fixed on the base plate. The shear load is applied by a screw jack (3) mounted opposite to the roll construction. The fine thread (4) allows a fine adjustment of the shear load. To position the roll construction exactly, an adjusting screw (5) can be used. The shear load data is captured by a load cell (6) mounted to the screw jack. The shear deformation is measured by displacement transduc-
Fig. 2. Zwick 1484 and test set-up.
ers (7) as shown schematically in Fig. 3. A vertical displacement of the face sheets, which occurs due to compression, is allowed by the hinge bearing the screw jack (3) in an elongated hole. To assure a stiffness much higher than the tested core material, the face sheets of the double-core specimens are made of steel. Additional experimental tests with a ‘‘dummy’’ core made of two aluminium blocks showed that the stiffness of the test device is very high in comparison to the stiffness of the real core. Consequently, the displacement measurements in the tests were assured to be primarily caused by the core structure and not by the test device. Furthermore, several shear-compression tests were conducted with additional displacement transducers at different locations to check the uniformity of the transverse normal and the transverse shear deformation. It was also observed that failure did not start systematically from one and the same edge or corner of the specimen. Consequently, failure initiation only depended on possible material inhomogeneities, it was random and was not influenced by edge effects. In this way the operational reliability of the test device could be approved [10]. The geometry of the tested double-core specimens is given in Fig. 4. Note that the height of the specimen is limited by the diameter of the roll in order to avoid transverse forces. However, specimens with heights in the approximate range of the roll diameter ±5 mm can be tested without provoking considerable error, since the transverse force component is negligible in this case. An additional margin for variable core heights is given by changing the thickness of the steel plate. The dimensions of the studied specimen cores were chosen with 150 mm · 135 mm to keep boundary effects negligibly small. Dependent on the core structure, alternative dimensions are possible, i.e. for cores with finer cell dimensions smaller specimens can be used. The experimental data of the combined transverse shear and compression tests were captured by a data acquisition system (DAS) connected to a PC, as shown in Fig. 5. Since oscillations in force–time and displacement–time histories had been recognised during pretests, a low-pass filter was used. The total vertical displacement of the compressive loading was measured by the internal DAS of the test machine Zwick and additionally by a linear variable displacement transducer (LVDT) W20TK HBM. The separate vertical displacements of the lower and upper core were measured by additional LVDTs. The shear displacement of the upper core was measured by an LVDT between the middle plate and the upper face sheet. To calculate the shear displacement of the lower core, the total shear displacement of both cores was captured by a further LVDT. In Fig. 6 the measuring set-up is displayed with a honeycomb specimen, which was used for reference tests. The diagonal positioning of two vertical displacement transducers on the top of the specimen provides an indication of unintentional inclinations of the specimen. Each shear-compression test started with applying a certain static transverse shear load via the screw jack. When a constant shear load was reached, the quasi-static
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
Fig. 3. Shear load fixture.
Fig. 4. Specimen – side view, length in mm.
Fig. 5. Schematic data acquisition.
Fig. 6. Positions of LVDT’s at the specimen.
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compressive load was successively applied by the test facility Zwick. To avoid an amplification of possible small initial inclinations of the upper face sheet and to reduce nonlinearities at the beginning of the compressive loading a self-adjusting compression plate was used. It was adjusted and fixed before applying the shear load. In this way the double core specimens were tested by different combinations of shear and compression loads, controlled by the variable initial shear load. The results are described in Section 4. 4. Test results Thirteen folded core structures were tested under combined transverse shear and compressive loading. Furthermore, a couple of pure compression and pure shear tests were conducted. Note that the focus of the here presented investigations lays on folded structures and on the mechanical behaviour under combined transverse shear and compressive loads. Results of tests on honeycomb cores will only be used for reference. An overview of the combined shear-compression and pure compression test results is shown by the compression stress–strain curves in Fig. 7. The displayed values assigned to the stress–strain curves denote the initial transverse shear stress at the beginning of the test. Note that the shear load decreases with increasing compressive loading, cf. discussion in Sections 5 and 6. For a clearer arrangement, the curves are displayed with an arbitrary offset in the axis of abscissa. The first three curves result from pure compression tests and show the unaffected compression stiffness. With increasing shear load, a decreasing compression strength and compression stiffness is observed. The non-linear behaviour at the beginning of the compressive loading is presumably the effect of closing gaps between compression plate, specimen and support. Additional non-linear effects are observed, if shear loads larger
than 7 kN are initialised. At this point, local coating damages started to occur, which slightly weakened the core already prior to applying the compressive load. 5. Stiffness behaviour The compression stiffness of the studied folded cores can be deduced from the slopes of the linear regions of the stress–strain curves in Fig. 7. Although Fig. 7 shows a quite remarkable scatter, a correlation between initial shear load and compression stiffness can be found: The bigger the original shear deformation, the smaller is the residual compression stiffness. The reason for this phenomenon seems evident: Due to the initial shear deformation, the cell walls of the folded structure are deformed against their original position. Consequently, if the compressive load is applied, the inclined cell walls are less resistant and the compressive stiffness decreases. In the literature dealing with honeycomb cores and its material behaviour [4–6] such a stiffness interrelation between transverse shear and compression was never addressed. To assure the observed stiffness behaviour of the folded cores and to value it against the behaviour of comparable honeycomb core structures, an additional, similar test program was performed with honeycomb cores. The honeycombs, made of Nomex T722, had a similar density (64 kg/m2 compared to 58 kg/m2 of the folded core) and height (31 mm compared to 28 mm). Due to a more accurate fabrication of the honeycomb cores, the force and displacement values were measured with less scatter. Although the stiffness was found to be higher than those of the folded cores, the tendency was the same: Compression stiffness decreases with increasing initial shear deformation. The observed correlation between transverse shear and compression leads to a nonlinear stress–strain-relation. According to the experimental data the expression
0.6
transverse compression stress / MPa
0,06 MPa 0,1 MPa
0.5
0,12 MPa 0,16 MPa 0,17 MPa
0,0 MPa 0.4
0,22 MPa 0,25 MPa
0.3
0,27 MPa
0,35 MPa
0.2 0,38 MPa 0.1
0,35 MPa
0 0
0.01
0.02
0.03 0.04 0.05 0.06 0.07 transverse compression strain / 1
0.08
0.09
Fig. 7. Stress–strain curves of the specimens with different initial shear loads.
0.1
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
r3 ¼ C 33;nl ðe5 Þ e3
ð1Þ
is proposed, where r3 and e3 are the transverse normal stress and strain, respectively, and C33,nl(e5) is a nonlinear compression stiffness, which indicates the dependence of the transverse normal stress r3 on the transverse shear strain e5 = cxz. Eq. (1) represents a phenomenological approach, which is used to interpolate the experimental data points and which does not hold any physical justification. A best fit interpolation for the nonlinear compression stiffness can be found by performing a curve fitting in a C33,nl – e5 – diagram, cf. Fig. 8. Due to the large scatter of the test data of the studied folded cores, only a suggestion can be made for the nonlinear compression stiffness: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi e5 C 33;nl ðe5 Þ ¼ C 33;lin 1 a ð2Þ e5;crush with C33,lin being the linear material stiffness of pure transverse compression, e5,crush being the transverse shear strain of pure shear crushing, and a is an additional material parameter. The corresponding material properties of the studied folded and honeycomb cores are specified in Table 2. The shear behaviour in y-direction could not be studied yet due to the limited number of available folded core specimens. However, for developing a complete core stiffness model, further investigations are needed, where transverse shear loading is applied in the y- and in combined x–ydirections. In addition to the dependence of the transverse normal stiffness on shear deformation, the transverse shear stresses slightly decrease with increasing transverse normal loading. This behaviour can also be explained by the above described phenomenon of the deflected core structure: The slope of the cell walls redirects the applied compression force and, therewith, a force component in the direction of the original shear force appears. Consequently, the displacement controlled shear force decreases with increasing
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Table 2 Material parameters for defining the nonlinear compression stiffness C33,nl Core structure
C33,lin in
Folded cores Honeycombs
N mm2
2
2.248 · 10 3.148 · 102
55.0 156.0
r5 ¼ C 55;nl ðe3 Þ e5 ;
ð3Þ
where C55,nl (e3) is a nonlinear transverse shear stiffness. However, the effect of transverse shear stress reduction due to increasing transverse normal strain was found to be quite small. Therefore, the authors suggest to approximate the transverse shear stiffness simply by C 55;nl ðe3 Þ C 55;lin :
ð4Þ
6. Strength and failure criterion As Fig. 7 already indicates, a decrease of the compressive failure stress with increasing transverse shear load can be observed in the conducted tests. In Fig. 9 each of the data points represents the transverse compressive stress and the transverse shear stress at core failure of one test. The compressive stress is the maximum value of the recorded compression stress–strain curve in Fig. 7. Note that the corresponding transverse shear stress does not correspond to the initial shear load displayed in Fig. 7 but rather to the shear load remaining at the moment of maximum compression stress. This distinction has to be done due to the observed shear load decrease during the compression loading process. The strength values of the pure shear and compression tests are displayed on the ordinate and the abscissa, respectively.
transverse compression stiffness / MPa
50
40
30
20
10
0 0.005
2.5 0.5
normal deformation, which results in lower shear stresses. Theoretically, an expression similar to Eq. (1) could be used to describe this relation between transverse shear stresses r5 and transverse normal strains e3,
60
0
a
5,crush
0.01 transverse shear strain / 1
0.015
0.02
Fig. 8. Correlation between transverse normal stiffness and transverse shear strain.
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M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295 0.55 0.5
transverse shear stress / MPa
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
transverse compression stress / MPa
Fig. 9. Stresses at failure of a folded structure under rz–szx loading.
Again, the results scatter considerably. Anyway, for the obtained pairs of compression and shear stresses at failure a linear best fit interpolation of the test results seems reasonable, as proposed by Petras and Sutcliffe [6] for Nomex honeycombs. Accordingly, an approximate 2D failure criterion is proposed, which simply represents a linear interpolation of the data points: r3 ðÞ R3
þ
js5 j ¼ 1; R5
ð5Þ
where r3 and s5 are the current transverse compression and ðÞ shear stresses of a given stress state, and R3 and R5 are the compression and the shear strength. The proposed approximate 2D failure criterion (5) is only valid for compression. It is the simplest way to describe the interaction between transverse compressive and shear stresses. Even though this approximate 2D failure criterion is good enough for the design process, it might not be universally valid for all folded core structures and high-quality folded cores might lead to another approximation. Exemplarily, the reference tests with honeycomb cores resulted in a quadratic failure criterion, comparable to the one proposed by Besant et al. [4].
7. Conclusions In this paper, the stiffness and failure behaviour of folded core structures under combined transverse shear and compressive loading is investigated. For conducting the experimental test program, a test device has been designed and constructed to allow a simultaneous application of transverse shear and compression loads. By means of the new apparatus a limited number of double core specimens was tested by different combinations of shear and compression loads. The test results showed a substantial interaction between transverse shear and transverse compression for both, fail-
ure behaviour and stiffness of the studied folded core structure. It was found that the compression stiffness remarkably decreases with increasing initial shear deformation. To describe this nonlinear behaviour, an empirical interpolation function was proposed for the compression stiffness. Furthermore, a slight dependence of transverse shear stresses on transverse normal strains could be observed, which, however, was of small extent and was assumed to be negligible. Additional reference tests on honeycomb cores showed a similarly interrelated stiffness behaviour for combined shear and compressive loading as it has been observed for the investigated folded cores. As outlined for compression stiffness, the compressive failure stresses also decrease with increasing initial shear deformation. For the studied folded cores, the data points could be interpolated by a linear function, and a corresponding approximate 2D failure criterion was proposed. However, the test results of the folded cores showed a quite large scatter, which was likely to occur due to imprecise manufacturing. Folded core structures of advanced manufacturing technology might lead to a different failure criterion like, for example, a quadratic one, which could be observed in additional reference tests for honeycomb cores. Acknowledgements This work was funded by the Third National Aeronautical Research Program LuFo3. The authors are grateful to Airbus Germany for providing the folded core material. References [1] Ka¨rger L, Baaran J, Teßmer J. Rapid simulation of impacts on composite sandwich panels inducing barely visible damage. Compos Struct, in press. [2] Nguyen MQ, Jacombs SS, Thomson RS, Hachenberg D, Scott ML. Simulation of impact on sandwich structures. Composite Structures 2005;67:217–27.
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295 [3] Mudra C, Bestimmung mechanischer Kennwerte von faserversta¨rkten Faltwaben unter Verwendung der Methode der Finiten Elemente. Diplomarbeit, ILR TU Dresden; 2002. [4] Besant T, Davies GAO, Hitchings D. Finite element modelling of low velocity impact of composite sandwich panels. Compos: Part A 2001;32:1189–96. [5] Hong S-T, Pan J, Tyan T, Prasad P. Quasi-static crush behavior of aluminium honeycomb specimens under compression dominant combined loads. Int J Plasticity 2005;22:73–109. [6] Petras A, Sutcliffe MPF. Identation failure analysis of sandwich beams. Compos Struct 2000;50:311–8.
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[7] Mines RAW, Birch RS. The crush behaviour of Rohacell-51WF structural foam. Int J Solids Struct 2000;37:6321–41. [8] Benderly D, Putter S. Characterization of the shear/compression failure envelope of Rohacell foam. Polym Test 2004;23:51–7. [9] Gioux G, McCormack TM, Gibson LJ. Failure of aluminium foams under multiaxial loads. Int J Mech Sci 2000;42:1097–117. [10] Kintscher M, Ka¨rger L, Wetzel A, Goetting H-C. Versuchsprogramm – Kombinierte Druck-Schub-Versuche an Faltwabenkernen. IB 1312006/16, DLR, Institut fu¨r Faserverbundleichtbau und Adaptronik, Braunschweig; 2006.
Stiffness and failure behaviour of folded sandwich cores under combined transverse shear and compression M. Kintscher, L. Ka¨rger *, A. Wetzel, D. Hartung DLR, Institute of Composite Structures and Adaptive Systems, Structural Mechanics Section, Lilienthalplatz 7, 38108 Braunschweig, Germany Received 19 May 2006; received in revised form 14 November 2006; accepted 20 November 2006
Abstract For efficiently simulating the failure behaviour of sandwich structures made of stiff face sheets and a light-weight core, macroscopic material stiffness and strength values are essential. The investigated folded cores are made from Nomex paper coated with epoxy resin. Due to their channel-like structure, folded cores are air ventilated, which can help to reduce the danger of deterioration, which is a big advancement for applications in the aerospace industry. Folded core structures were tested under combined transverse compression and shear in order to get the stiffness values and the failure criterion under a multi-axial stress state. For this purpose a new test device was developed, which allows a simultaneous application of shear and compression loads. The test results are presented and discussed using a nonlinear description of the stiffness and failure behaviour of the folded core structure. Additionally, the results are compared to the stiffness and the failure behaviour of honeycomb cores. 2006 Elsevier Ltd. All rights reserved. Keywords: Sandwich core; B. Transverse cracking; C. Damage mechanics; D. Mechanical testing
1. Introduction Sandwich structures consist of a lightweight core and two outer face sheets of high stiffness. Therewith, they allow a very weight efficient shell design. While the thin face sheets act in an almost plane stress state, the main function of the core is to connect the face sheets and to transfer the transverse shear and normal stresses. Moreover, core structures may provide acoustic and heat insulation and act as energy absorbers. An additional advantage of folded core structures compared to honeycomb cores is the possibility of air ventilation to avoid deterioration caused by long term moisture exposure. To utilise this advantage, current research on folded core structures focuses on optimizing the geometry and the materials to achieve better mechanical properties and higher impact resistance, which are comparable to those of honeycomb cores.
*
Corresponding author. Tel.: +49 531 295 2295; fax: +49 531 295 2232. E-mail address: [email protected] (L. Ka¨rger).
1359-835X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2006.11.008
The advantages of sandwich structures are counteracted by their complex damage behaviour and their sensitivity to impact. Impact damage in sandwich structures can cause a significant strength and stability reduction. Therefore, various investigations have been made on impact behaviour of composite sandwich panels, and corresponding simulation tools have been developed. Ka¨rger et al. [1] analysed Nomex honeycomb sandwich panels in the context of the development of the fast damage tolerance FE tool CODAC. Nguyen et al. [2] conducted experimental impact tests on aluminium honeycomb sandwich panels and performed the impact analysis using an explicit FE code. To parametrically generate the finite element model for the honeycomb cores, the tool Sandmesh [3] was applied. Furthermore, Nguyen et al. used the tool Sandmesh for a FE mesh generation of folded structures. Low velocity impact was also investigated by Besant et al. [4] performing impact tests of aluminium honeycomb structures. Moreover, Besant et al. conducted combined transverse shear and compression tests and developed a quadratic failure criterion for aluminium honeycomb cores.
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
When sandwich structures are impacted, the core crushes and experiences a substantial stiffness reduction. To model the crushing behaviour of sandwich cores correctly, an appropriate description of its failure behaviour under combined out-of-plane shear and compression is needed. The quasi-static crushing behaviour of honeycomb under out-of-plane compression has been investigated frequently by many researchers and manufacturers. For example, Hong et al. [5] have studied aluminium honeycomb under compression dominant combined loading conditions. An indentation failure analysis of sandwich beams was performed by Petras and Sutcliffe [6], who developed a 2D-failure criterion for Nomex honeycomb. Mines and Birch [7] developed a new test rig to study the mechanical behaviour of Rohacel-51WF structural foam in a multiaxial stress state. In their work a linear relationship between compressive yielding and transverse shear stress is reported. A modified ASTM C-393 test method was used by Benderly and Putter [8] to generate controlled combinations of shear and compressive stress. They characterised the shear-compression failure envelope of Rohacel200WF structural foam under various temperatures and proposed a quadratic failure envelope. The failure of aluminium foam under multiaxial load was investigated by Gioux et al. [9], where the experimental data were compared to three yield criteria. In spite of the increasing application of sandwich structures in aerospace and transport vehicle design, the failure behaviour of sandwich cores under combined loading is not yet well investigated. So far, the authors are not aware of any literature regarding the stiffness interrelation between transverse shear and compression. In this paper, a methodology and a fixture construction for quasi-static, combined out-of-plane shear and compression tests on sandwich core materials are presented in Section 3. It is applied to folded core structures, which are described in Section 2. The main focus of the paper lays on the test results and their discussion. The test results acquired by the developed test facility are presented in Section 4. The stiffness and failure behaviour are discussed in Sections 5 and 6, respectively. As a reference, the folded core structures are compared to Nomex honeycomb cores with comparable density.
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folded geometries. Their structural properties can be varied by using different folding schemes. The Institute of Aircraft Design of the University of Stuttgart is currently developing and testing different manufacturing technologies and folding schemes in order to optimise structural properties. The core material used in this work was produced in Kazan, Russia and provided by Airbus Germany. It was folded from Nomex paper and coated by epoxy resin. Explicit material properties of the manufacturer were not available. The folded structure consists of cells formed by four connected plains in the shape of a parallelogram, cf. Fig. 1. The geometrical properties are provided in Table 1. The structural properties will be investigated in Section 4 and the following. For the combined shear and compression tests, the studied folded core specimens were bonded to steel face sheets with Epibond 1590. The face sheets were sandblasted and the amount of applied adhesive was relatively high to assure a good bonding of core and face sheets. However, by separating the specimens after testing, small local gaps in the bonding between core and face sheets were found. These voids were caused by imprecise manufacturing and variations in the core height. Although an influence of incomplete bonding on the test results could not directly be ascertained, the imprecise manufacturing is assumed to be the general reason for quite a large scatter. It should be mentioned that the quality of folded core structures manufactured by the University of Stuttgart has strongly improved. Not only a high geometric accuracy but also a
2. Material description and specimen set-up Folded structures are three-dimensional geometries folded from semi-finished sheets. They can be made of different materials such as metal or resin saturated Nomex paper. The Russian oil and gas distribution industry and the aircraft industry introduced folded structures in several noise reduction applications. Due to the possibility of air ventilation, folded structures are considered as core material for aerospace sandwich structure applications. Compared to honeycomb, folded structures are easily shapeable, which means that curvatures of small radius can be manufactured. There are numerous varieties of
Fig. 1. Geometry of the folded structure.
Table 1 Folded structure geometry properties Property Height, H Spreading, 2S Length, 2L Amplitude, V Density, q
Value 28 mm 35 mm 18 mm 33 mm 58 mkg3
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M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
high-quality resin impregnation can be achieved by now. Due to the limited number of provided specimens, only the x-direction defined in Fig. 1 could be investigated in the here described testing program. 3. Test set-up Based on the test assembly proposed by Besant et al. [4] a test device was developed to apply combined out-of-plane shear and compressive loading to the specimen. The new test device is used to apply a constant shear deformation. Subsequently, the compressive loading is realised by the static test facility Zwick 1484. An overview of the test set-up is given in Fig. 2. The test device is schematically shown in Fig. 3. To assure a balanced application of the shear load to the specimen, a roll (1) and a steel towing rope (2) are used in combination with a double-core specimen. The relocatable roll construction is fixed on the base plate. The shear load is applied by a screw jack (3) mounted opposite to the roll construction. The fine thread (4) allows a fine adjustment of the shear load. To position the roll construction exactly, an adjusting screw (5) can be used. The shear load data is captured by a load cell (6) mounted to the screw jack. The shear deformation is measured by displacement transduc-
Fig. 2. Zwick 1484 and test set-up.
ers (7) as shown schematically in Fig. 3. A vertical displacement of the face sheets, which occurs due to compression, is allowed by the hinge bearing the screw jack (3) in an elongated hole. To assure a stiffness much higher than the tested core material, the face sheets of the double-core specimens are made of steel. Additional experimental tests with a ‘‘dummy’’ core made of two aluminium blocks showed that the stiffness of the test device is very high in comparison to the stiffness of the real core. Consequently, the displacement measurements in the tests were assured to be primarily caused by the core structure and not by the test device. Furthermore, several shear-compression tests were conducted with additional displacement transducers at different locations to check the uniformity of the transverse normal and the transverse shear deformation. It was also observed that failure did not start systematically from one and the same edge or corner of the specimen. Consequently, failure initiation only depended on possible material inhomogeneities, it was random and was not influenced by edge effects. In this way the operational reliability of the test device could be approved [10]. The geometry of the tested double-core specimens is given in Fig. 4. Note that the height of the specimen is limited by the diameter of the roll in order to avoid transverse forces. However, specimens with heights in the approximate range of the roll diameter ±5 mm can be tested without provoking considerable error, since the transverse force component is negligible in this case. An additional margin for variable core heights is given by changing the thickness of the steel plate. The dimensions of the studied specimen cores were chosen with 150 mm · 135 mm to keep boundary effects negligibly small. Dependent on the core structure, alternative dimensions are possible, i.e. for cores with finer cell dimensions smaller specimens can be used. The experimental data of the combined transverse shear and compression tests were captured by a data acquisition system (DAS) connected to a PC, as shown in Fig. 5. Since oscillations in force–time and displacement–time histories had been recognised during pretests, a low-pass filter was used. The total vertical displacement of the compressive loading was measured by the internal DAS of the test machine Zwick and additionally by a linear variable displacement transducer (LVDT) W20TK HBM. The separate vertical displacements of the lower and upper core were measured by additional LVDTs. The shear displacement of the upper core was measured by an LVDT between the middle plate and the upper face sheet. To calculate the shear displacement of the lower core, the total shear displacement of both cores was captured by a further LVDT. In Fig. 6 the measuring set-up is displayed with a honeycomb specimen, which was used for reference tests. The diagonal positioning of two vertical displacement transducers on the top of the specimen provides an indication of unintentional inclinations of the specimen. Each shear-compression test started with applying a certain static transverse shear load via the screw jack. When a constant shear load was reached, the quasi-static
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
Fig. 3. Shear load fixture.
Fig. 4. Specimen – side view, length in mm.
Fig. 5. Schematic data acquisition.
Fig. 6. Positions of LVDT’s at the specimen.
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compressive load was successively applied by the test facility Zwick. To avoid an amplification of possible small initial inclinations of the upper face sheet and to reduce nonlinearities at the beginning of the compressive loading a self-adjusting compression plate was used. It was adjusted and fixed before applying the shear load. In this way the double core specimens were tested by different combinations of shear and compression loads, controlled by the variable initial shear load. The results are described in Section 4. 4. Test results Thirteen folded core structures were tested under combined transverse shear and compressive loading. Furthermore, a couple of pure compression and pure shear tests were conducted. Note that the focus of the here presented investigations lays on folded structures and on the mechanical behaviour under combined transverse shear and compressive loads. Results of tests on honeycomb cores will only be used for reference. An overview of the combined shear-compression and pure compression test results is shown by the compression stress–strain curves in Fig. 7. The displayed values assigned to the stress–strain curves denote the initial transverse shear stress at the beginning of the test. Note that the shear load decreases with increasing compressive loading, cf. discussion in Sections 5 and 6. For a clearer arrangement, the curves are displayed with an arbitrary offset in the axis of abscissa. The first three curves result from pure compression tests and show the unaffected compression stiffness. With increasing shear load, a decreasing compression strength and compression stiffness is observed. The non-linear behaviour at the beginning of the compressive loading is presumably the effect of closing gaps between compression plate, specimen and support. Additional non-linear effects are observed, if shear loads larger
than 7 kN are initialised. At this point, local coating damages started to occur, which slightly weakened the core already prior to applying the compressive load. 5. Stiffness behaviour The compression stiffness of the studied folded cores can be deduced from the slopes of the linear regions of the stress–strain curves in Fig. 7. Although Fig. 7 shows a quite remarkable scatter, a correlation between initial shear load and compression stiffness can be found: The bigger the original shear deformation, the smaller is the residual compression stiffness. The reason for this phenomenon seems evident: Due to the initial shear deformation, the cell walls of the folded structure are deformed against their original position. Consequently, if the compressive load is applied, the inclined cell walls are less resistant and the compressive stiffness decreases. In the literature dealing with honeycomb cores and its material behaviour [4–6] such a stiffness interrelation between transverse shear and compression was never addressed. To assure the observed stiffness behaviour of the folded cores and to value it against the behaviour of comparable honeycomb core structures, an additional, similar test program was performed with honeycomb cores. The honeycombs, made of Nomex T722, had a similar density (64 kg/m2 compared to 58 kg/m2 of the folded core) and height (31 mm compared to 28 mm). Due to a more accurate fabrication of the honeycomb cores, the force and displacement values were measured with less scatter. Although the stiffness was found to be higher than those of the folded cores, the tendency was the same: Compression stiffness decreases with increasing initial shear deformation. The observed correlation between transverse shear and compression leads to a nonlinear stress–strain-relation. According to the experimental data the expression
0.6
transverse compression stress / MPa
0,06 MPa 0,1 MPa
0.5
0,12 MPa 0,16 MPa 0,17 MPa
0,0 MPa 0.4
0,22 MPa 0,25 MPa
0.3
0,27 MPa
0,35 MPa
0.2 0,38 MPa 0.1
0,35 MPa
0 0
0.01
0.02
0.03 0.04 0.05 0.06 0.07 transverse compression strain / 1
0.08
0.09
Fig. 7. Stress–strain curves of the specimens with different initial shear loads.
0.1
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295
r3 ¼ C 33;nl ðe5 Þ e3
ð1Þ
is proposed, where r3 and e3 are the transverse normal stress and strain, respectively, and C33,nl(e5) is a nonlinear compression stiffness, which indicates the dependence of the transverse normal stress r3 on the transverse shear strain e5 = cxz. Eq. (1) represents a phenomenological approach, which is used to interpolate the experimental data points and which does not hold any physical justification. A best fit interpolation for the nonlinear compression stiffness can be found by performing a curve fitting in a C33,nl – e5 – diagram, cf. Fig. 8. Due to the large scatter of the test data of the studied folded cores, only a suggestion can be made for the nonlinear compression stiffness: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi e5 C 33;nl ðe5 Þ ¼ C 33;lin 1 a ð2Þ e5;crush with C33,lin being the linear material stiffness of pure transverse compression, e5,crush being the transverse shear strain of pure shear crushing, and a is an additional material parameter. The corresponding material properties of the studied folded and honeycomb cores are specified in Table 2. The shear behaviour in y-direction could not be studied yet due to the limited number of available folded core specimens. However, for developing a complete core stiffness model, further investigations are needed, where transverse shear loading is applied in the y- and in combined x–ydirections. In addition to the dependence of the transverse normal stiffness on shear deformation, the transverse shear stresses slightly decrease with increasing transverse normal loading. This behaviour can also be explained by the above described phenomenon of the deflected core structure: The slope of the cell walls redirects the applied compression force and, therewith, a force component in the direction of the original shear force appears. Consequently, the displacement controlled shear force decreases with increasing
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Table 2 Material parameters for defining the nonlinear compression stiffness C33,nl Core structure
C33,lin in
Folded cores Honeycombs
N mm2
2
2.248 · 10 3.148 · 102
55.0 156.0
r5 ¼ C 55;nl ðe3 Þ e5 ;
ð3Þ
where C55,nl (e3) is a nonlinear transverse shear stiffness. However, the effect of transverse shear stress reduction due to increasing transverse normal strain was found to be quite small. Therefore, the authors suggest to approximate the transverse shear stiffness simply by C 55;nl ðe3 Þ C 55;lin :
ð4Þ
6. Strength and failure criterion As Fig. 7 already indicates, a decrease of the compressive failure stress with increasing transverse shear load can be observed in the conducted tests. In Fig. 9 each of the data points represents the transverse compressive stress and the transverse shear stress at core failure of one test. The compressive stress is the maximum value of the recorded compression stress–strain curve in Fig. 7. Note that the corresponding transverse shear stress does not correspond to the initial shear load displayed in Fig. 7 but rather to the shear load remaining at the moment of maximum compression stress. This distinction has to be done due to the observed shear load decrease during the compression loading process. The strength values of the pure shear and compression tests are displayed on the ordinate and the abscissa, respectively.
transverse compression stiffness / MPa
50
40
30
20
10
0 0.005
2.5 0.5
normal deformation, which results in lower shear stresses. Theoretically, an expression similar to Eq. (1) could be used to describe this relation between transverse shear stresses r5 and transverse normal strains e3,
60
0
a
5,crush
0.01 transverse shear strain / 1
0.015
0.02
Fig. 8. Correlation between transverse normal stiffness and transverse shear strain.
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M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295 0.55 0.5
transverse shear stress / MPa
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
transverse compression stress / MPa
Fig. 9. Stresses at failure of a folded structure under rz–szx loading.
Again, the results scatter considerably. Anyway, for the obtained pairs of compression and shear stresses at failure a linear best fit interpolation of the test results seems reasonable, as proposed by Petras and Sutcliffe [6] for Nomex honeycombs. Accordingly, an approximate 2D failure criterion is proposed, which simply represents a linear interpolation of the data points: r3 ðÞ R3
þ
js5 j ¼ 1; R5
ð5Þ
where r3 and s5 are the current transverse compression and ðÞ shear stresses of a given stress state, and R3 and R5 are the compression and the shear strength. The proposed approximate 2D failure criterion (5) is only valid for compression. It is the simplest way to describe the interaction between transverse compressive and shear stresses. Even though this approximate 2D failure criterion is good enough for the design process, it might not be universally valid for all folded core structures and high-quality folded cores might lead to another approximation. Exemplarily, the reference tests with honeycomb cores resulted in a quadratic failure criterion, comparable to the one proposed by Besant et al. [4].
7. Conclusions In this paper, the stiffness and failure behaviour of folded core structures under combined transverse shear and compressive loading is investigated. For conducting the experimental test program, a test device has been designed and constructed to allow a simultaneous application of transverse shear and compression loads. By means of the new apparatus a limited number of double core specimens was tested by different combinations of shear and compression loads. The test results showed a substantial interaction between transverse shear and transverse compression for both, fail-
ure behaviour and stiffness of the studied folded core structure. It was found that the compression stiffness remarkably decreases with increasing initial shear deformation. To describe this nonlinear behaviour, an empirical interpolation function was proposed for the compression stiffness. Furthermore, a slight dependence of transverse shear stresses on transverse normal strains could be observed, which, however, was of small extent and was assumed to be negligible. Additional reference tests on honeycomb cores showed a similarly interrelated stiffness behaviour for combined shear and compressive loading as it has been observed for the investigated folded cores. As outlined for compression stiffness, the compressive failure stresses also decrease with increasing initial shear deformation. For the studied folded cores, the data points could be interpolated by a linear function, and a corresponding approximate 2D failure criterion was proposed. However, the test results of the folded cores showed a quite large scatter, which was likely to occur due to imprecise manufacturing. Folded core structures of advanced manufacturing technology might lead to a different failure criterion like, for example, a quadratic one, which could be observed in additional reference tests for honeycomb cores. Acknowledgements This work was funded by the Third National Aeronautical Research Program LuFo3. The authors are grateful to Airbus Germany for providing the folded core material. References [1] Ka¨rger L, Baaran J, Teßmer J. Rapid simulation of impacts on composite sandwich panels inducing barely visible damage. Compos Struct, in press. [2] Nguyen MQ, Jacombs SS, Thomson RS, Hachenberg D, Scott ML. Simulation of impact on sandwich structures. Composite Structures 2005;67:217–27.
M. Kintscher et al. / Composites: Part A 38 (2007) 1288–1295 [3] Mudra C, Bestimmung mechanischer Kennwerte von faserversta¨rkten Faltwaben unter Verwendung der Methode der Finiten Elemente. Diplomarbeit, ILR TU Dresden; 2002. [4] Besant T, Davies GAO, Hitchings D. Finite element modelling of low velocity impact of composite sandwich panels. Compos: Part A 2001;32:1189–96. [5] Hong S-T, Pan J, Tyan T, Prasad P. Quasi-static crush behavior of aluminium honeycomb specimens under compression dominant combined loads. Int J Plasticity 2005;22:73–109. [6] Petras A, Sutcliffe MPF. Identation failure analysis of sandwich beams. Compos Struct 2000;50:311–8.
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[7] Mines RAW, Birch RS. The crush behaviour of Rohacell-51WF structural foam. Int J Solids Struct 2000;37:6321–41. [8] Benderly D, Putter S. Characterization of the shear/compression failure envelope of Rohacell foam. Polym Test 2004;23:51–7. [9] Gioux G, McCormack TM, Gibson LJ. Failure of aluminium foams under multiaxial loads. Int J Mech Sci 2000;42:1097–117. [10] Kintscher M, Ka¨rger L, Wetzel A, Goetting H-C. Versuchsprogramm – Kombinierte Druck-Schub-Versuche an Faltwabenkernen. IB 1312006/16, DLR, Institut fu¨r Faserverbundleichtbau und Adaptronik, Braunschweig; 2006.