Flexural behaviour of a polymeric foam/glass-fibre composite: FE modelling and experimental testing

Transcription

1 Flexural behaviour of a polymeric foam/glass-fibre composite: FE modelling and experimental testing G. Belingardi, M. P. Cavatorta & L. Peroni Department of Mechanical Engineering, Politecnico di Torino, Italy Abstract The paper describes the experimental testing and FE modelling of sandwich beams under bending loads. The faces are made of glass fibres in epoxy resin. The core is a polymeric foam, with a net of resin walls perpendicular to the faces having a pitch of about 30 mm. Flexural tests were run on the face and core materials and the sandwich structure. For the sandwich, failure occurred due to core shear cracking. Simulation of flexural tests was run up to formation of the first crack within the core. 2D and 3D models of the sandwich beam were implemented. At first, models were validated by comparison with Pagano analytical elasticity theory and Swanson experimental and FEM data. Then, FE models were run to simulate the flexural test on the face and core materials and the sandwich. Comparison with experimental data was made on the value of specimen deflection at failure and of the strain measured in some experimental tests by means of strain gauges. For the sandwich, the model correctly predicted the area of crack formation within the core. In a second part of the work, alternative solutions for the resin-foam core were examined. Three types of foam were selected. Foams with increasing densities obviously exhibit greater mechanical properties. However, modelling showed that by increasing the core density other failure modes become possible, like face indentation. Finally, models were run to investigate the influence on flexural response of the experimentally observed scattering of the mechanical properties for face and core materials and of face thickness and resin wall position. The scattering of experimental results was then discussed. Keywords: composite sandwich, flexural behaviour, FE modelling, mechanical tests.

2 4 High Performance Structures and Materials II 1 Introduction Sandwich structures are known to provide high stiffness to weight ratio under bending loads. In particular, sandwich plates with a soft core, i.e. a core made of foam or a non-metallic light honeycomb, are largely used for their highly efficient structure. Although extensively used in design practice, the classical sandwich theory is known to significantly underestimate vertical displacements of the sandwich [1]. In addition, in the case of soft-core sandwich beams, the theory fails to accurately predict the bending deformation under concentrated loads because of the inability to model the core indentation phenomenon. Also illustrated in [2], the flexibility of the low strength core affects the overall behaviour of the sandwich plate and leads to high stress concentrations in terms of peeling stresses, bending moments and shear forces at the edges of the sandwich plate and in the vicinity of localized concentrated loads. In particular, soft-core sandwich structures are shown [3] to experience pronounced non linear displacements near active or reactive point loads before the constitutive materials exceed the elastic limit or failure criterion. In the case of soft-core sandwich structures, the simplifying assumption of an antiplane core cannot be adopted. To provide a proper stress field solution, a three-dimensional analysis is required. In the literature, both numerical and analytical solutions have been considered. Swanson and Kim [4] have performed a comparison of the high order theory for sandwich beams with elasticity and FE analyses finding good correlation. Further examination has been carried out by Swanson [5] by comparing the response of orthotropic sandwich plates to concentrated loading with the three-dimensional elasticity solution of Pagano [6,7] and with the high order sandwich theory of Frostig and Baruch [8]. The comparison has revealed good agreement excluding the maximum strains of the face-sheets and the interface shear stresses. In [3], four-point flexure tests run on a PVC foam core sandwich demonstrate that a non linear higher order theory is to be used to correctly predict localization of maximum peeling stresses. However, a linear high-order analysis allows to correctly estimate vertical displacements. Literature solutions are limited to the case where all boundaries are simply supported. Only very recently Lovinger and Frostig [2] have proposed an analytical two-dimensional solution of the stress and distribution fields for a general scheme of loads. In general, the implementation of FE analysis is found to be problematic. To meet the compatibility requirements between the sandwich layers requires the use of three-dimensional solid elements to model both the core and the facesheets. Taking into account the variation of stresses throughout the core height requires several elements through the thickness of the core. A realistic FE sandwich plate model requires a mesh with a large number of nodes and elements. In the present paper, a 3D finite element model of a foam core sandwich beam under bending loads is presented. Validation of the FE model has been conducted in two ways. At first, the model was validated with literature data both

3 High Performance Structures and Materials II 5 referring to analytical models and FE models. The second validation has been conducted by a comparison with experimental results. Simulation of flexural tests is run for the face sheet and the core materials as well as for the sandwich beam. For the latter, numerical simulation is run up to formation of the first crack within the core. Material data to be input into the FE model were obtained through a calibration testing program [9]. The FE model is then used to investigate the influence of the foam core density on the sandwich flexural behaviour and mode of failure. Finally, scattering of experimental data is discussed. 2 Experimental testing The selected material is a glass fibre epoxy composite/foam sandwich structure. The face sheets are made of a few layers of glass fibres in epoxy resin, covered by a ply of fabric and one of gelcoat. The stacking sequence is characterized by the overlapping of four plies with fibre orientation [random/ 45/+45/0 2 ]. As indicated, the 0 ply has a thickness that is twice that of the other plies. In the face sheets, the stacking sequence is repeated twice. A 60 kg/m 3 linear PVC foam (H60) was used as the core. A net of resin walls perpendicular to the external laminates are present within the foam with a pitch of about 30 mm. Four point flexure tests were run on simple 15 x 210 mm beam-like samples for the face sheets and sandwich structure [10]. The testing fixture was mounted on a servo-hydraulic testing machine with maximum loading capacity of 100 kn. The hydraulic actuator was electronically controlled in order to perform constant velocity tests. Signals of the force applied by the actuator and of the actuator stroke were acquired in time with an appropriate sampling rate. Figure 1: Flexural response of sandwich beams: specimen fixture and dynamics of specimen failure.

4 6 High Performance Structures and Materials II For a few tests, three grid rosette gauges were bonded to the specimen top and bottom faces. The six strain gauge signals were monitored at the same frequency used for monitoring of the load and the stroke signal. In the testing fixture the cylindrical bearings have a 20 mm diameter. For tests on the face material, the distance between the bearings was fixed to 37 mm for the upper bearings and to 135 mm for the bottom bearings. For tests on the sandwich structure, the distance between the upper bearings was set to 33 mm while the distance between the bottom bearings to 156 mm. For the face sheets, two series of static bending tests were run at different velocity of the hydraulic actuator (0.2 mm/s; 20 mm/s). Results showed no significant strain-rate effect for the material. For most tests, damage occurred at the top lamina, where fibres are in tension. For a few tests, a significant damage also occurred at the bottom lamina, where fibres are in compression. For the sandwich structure, the dynamics of specimen failure was quite reproducible from test to test (Figure 1): after a phase of elastic bending, a first fracture in the foam occurs at a 45 angle followed almost immediately by a second fracture in the foam symmetrical to the first fracture. Afterwards, a series of minor fractures at a 45 angle can be observed in the foam. At last separation of the foam from the sandwich faces takes place. The dynamics of this last phase was on the contrary quite random. The difference in fracture behaviour after the first two symmetrical fractures is most likely responsible for the high data scattering which becomes more significant after the elastic phase and increases with increasing of the stroke (Figure 2). A new fracture in the foam corresponds to a steep load decrease in the load-stroke curve. For the sandwich specimens, no significant damage was observed to occur within the face sheets, with the exception of a few specimens for which high values of the stroke were reached and some damage was observed to occur close to the contact region with the top bearings Stroke (mm) Figure 2: Data scattering for load-stroke curves for flexure tests run on sandwich specimens. Results are drawn on 10 tests.

5 High Performance Structures and Materials II 7 3 FE modelling 2D and 3D models of the sandwich beam were implemented. The software code is ANSYS. Initially, a 2D model of the beam was created reproducing the material, load and constraint conditions of Swanson experimental and FEM data [11]. 8-node-plane elements were used. The foam was modelled as isotropic; for the face sheets two models were implemented as in the original article [11]: one in which the composite sheets were modelled as orthotropic and one in which the sheets were modelled as isotropic. No significant difference between the two models was found for specimen deflection and strain distribution across the width, confirming results obtained by Swanson. For both models, results compare well with Pagano analytical elasticity theory [6,7]. Having verified model load and constraint conditions as well as mesh size, 2D and 3D models of the sandwich structure under study were generated. A 3D model is necessary to correctly characterise the resin walls present within the foam. For the 3D models, 8-node-brick elements were used. Three elements across the thickness were used to model each face sheet, while 24 elements across the thickness were used to model the foam. Figure 3: An example of the stress distribution within the sandwich single components for the 3D model. Top row: von Mises stresses in the face sheets top and bottom view. Bottom row: shear stresses within the resin walls and in the foam.

6 8 High Performance Structures and Materials II FE model Figure 4: Distribution of axial strain along sandwich thickness as given by the FE model, Pagano elasticity theory and classical theory. The FE data basically overlap results by Pagano. Material input data were obtained through a calibration testing program which included tensile, compression and flexural tests run on the sandwich single elements and complete structure [9]. In analogy to Swanson numerical models, considering the similarity of the composite material, the face sheets were modelled as isotropic. FE models were run to simulate the flexural test run on face and core materials and the sandwich. Figure 3 shows representative stress distribution within the composite face sheets, resin walls and foam. For the sandwich model, numerical simulation was run up to formation of the first crack within the core. Comparison with experimental data was made on the value of specimen deflection at fracture and of the strain measured in some experimental tests by means of strain gauges. For all models, comparison between numerical and experimental results was good. For the sandwich, the model correctly predicted the area of crack formation within the core. Cracks were observed to form close to the resin wall nearest to the bottom bearing. Maximum shear stresses in the foam were about 0.73 MPa; significantly close to the foam nominal shear strength (0.7 MPa). Figure 4 shows distribution of axial strain along sandwich thickness for the median section of the sandwich as obtained by the FE model. For sake of comparison, results obtained with Pagano elasticity theory as well as the classical theory are also reported. As visible, results from the FE model basically overlap Pagano solution. 3.1 Alternative solutions for the foam core In a second part of the work, alternative solutions to the resin-foam core under study were examined. In particular, three types of foam were selected: the base foam of the resin-foam core sandwich under study (H60), a foam having mechanical properties closest to the resin-foam core sandwich (H100) and a

7 High Performance Structures and Materials II 9 foam having the same density of the resin-foam core sandwich (H130). Table 1 summarises a few mechanical and failure data for the four models. In the case of the resin-foam core sandwich, material properties are those of an equivalent homogenous material. For the three foams, values for mechanical properties are average properties for the nominal density as declared by the manufacturer. Load at failure is the load value which causes the maximum shear stress within the core to reach the foam shear strength. Table 1: Mechanical and failure data for the implemented core models. Resin-foam core H60 H100 H130 ρ (kg/m 3 ) E (MPa) Shear strength (MPa) Load at failure (N) Deflection at failure (mm) Some of the data shown in Table 1 are worthwhile a few comments. With respect to the base foam (H60), the introduction of the resin walls has increased the load to failure of about 46% with an increase in weight of 113%. The H100 foam allows mechanical properties similar to the resin wall-foam core with a weight reduction of around 20%. On the contrary, the H130 foam has the same density of the resin wall-foam core yet allowing for an increase in the load at failure of around 70% and in specimen deflection of around 24%. In the above discussion cost of foams is not taken into account; while as obvious as it is costs do play an important role in material selection. In any case, the insertion of resin walls within the sandwich foam core appears to increase the sandwich stiffness and strength quite significantly. A similar result was obtained by Corigliano et al. [12] considering a syntactic foam made by hollow glass microspheres embedded in a epoxy matrix. Contrary to the resin-foam core for which the area of maximum shear stresses was located near the resin wall closest to the bottom bearing, for the three models with a homogenous foam core the area of maximum shear stresses is located at the interface with the top face sheet. Cracks nucleate at the face sheet/core interface and propagate inwards. In general, shear distribution is found to be similar for the three foam core sandwich models. Obviously the magnitude of the shear stresses is different. Figure 5 reports shear stress values along foam thickness in the most highly stressed section for the four models. The comparison is made at the same load level. Shear values are maximum for the resin-foam core sandwich. Among the foam core sandwich models, the H60 is obviously the most highly stressed. Nevertheless, with reference to this last point, some comments are worthwhile considering, in particular with respect to stress distribution within the composite face sheets. By increasing foam density, the maximum compression stresses in the top face sheet close to the point of loading and maximum tensile stresses at the

8 10 High Performance Structures and Materials II interface between the core and the bottom face sheet increase considerably. Stresses within the face sheets increase as well. As shown by Swanson and Kim [13], indentation of the face sheet becomes possible when around half of the core area below the loading point reaches the material elastic limit. Comparing the model of maximum and minimum foam density (i.e. the H130 and H60 foam), it can be noted that while for the H60 model only few points at the top face sheet/core interface below the loading point exceed the material elastic limit, in the case of the H130 a much larger area is subjected to stresses above the elastic limit. By increasing the core density, failure modes other than core shear cracking become possible. For the H130 foam, face indentation may indeed occur at force values below those that determine core shear cracking. H60 H100 H130 Resin-foam core Figure 5: Shear stress distribution along foam thickness in the most highly stressed foam section for the four models. 3.2 On the scattering of experimental data To investigate the scattering of experimental data [9], models were created where mechanical properties and geometrical quantities represent actual values for the specimens tested rather than average data. In particular, for the composite face sheets, variation in thickness and elastic modulus was considered, while for the core, the variable taken into account was the position of the resin walls with respect to the load bearings. Results show that, as for the face sheets, the parameter that mostly affects the sandwich behaviour is the thickness of the top lamina. In the experimental

9 High Performance Structures and Materials II 11 program [9], the thickness of the face sheet could vary of around 10%. On the contrary, the scattering of the elastic modulus value, even if greater and around 30%, did not have a significant effect on results. As for the resin wall position, a configuration of higher stiffness was found which corresponds to having the longitudinal walls at equal distances from the specimen sides and the central vertical walls on the specimen axis of symmetry. A reduction in stiffness (i.e. in the equivalent elastic modulus) was obtained when moving the resin walls in the direction perpendicular to the specimen longitudinal axes, while by moving the resin walls along the specimen longitudinal axes no reduction of stiffness was observed. In this latter case, however, the resin walls are not symmetric with respect to the load bearings and cracks are to form near the resin wall closest to the bottom bearing. Both effects were obviously observed in models where the resin walls were moved in a mixed direction. By considering variation in the above described parameters, most of the experimentally observed load-deflection failure points could be correctly predicted by the FE simulation. 4 Conclusions The paper summarises results of an experimental characterisation and FE modelling of a polymeric foam/glass-fibre composite sandwich subjected to bending loads. A 3D model was created which could correctly characterise the resin walls present within the foam. Literature and experimental data were used to validate the model. The models run for the single sandwich components and complete sandwich structure showed a good agreement with the experimental data in terms of load and deflection at failure as well as mode of failure. When considering variation in sandwich geometry, the FE models were also capable of predicting the experimentally observed scattering. Numerical simulation was also used to compare the bending behaviour of the resin-wall foam core sandwich with homogeneous foam core sandwiches. The insertion of the resin walls allowed a significant increase in the load at failure with respect to the base foam. By increasing the foam density, greater mechanical properties were obviously obtained. However, modelling showed that by increasing the foam density failure modes other than core shear cracking become possible, like face indentation. Acknowledgements The research work was partially supported through financial funds by TESCO TS S.p.A. The authors acknowledge contribution of former student Ivan Rocci. References [1] Meyer-Piening HR, Remarks on higher order sandwich stress and deflection analysis. In: Olsson K-A, Reichard RP, editors. Proc of the

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