Effect of the core thickness on the flexural behaviour of polymer foam sandwich structures

Standard bending load equations were implemented for theoretical calculations. The load was applied at the mid-span and the sandwich composite was modelled as a beam under bending.

The stresses in the face sheets were given by:

$$\begin{eqnarray}&&{\sigma }_{f}=\displaystyle \frac{PL}{4btd}\end{eqnarray} \tag{ 1 }$$

Here, C is ¼ for a 3-point bending test.

For the core, shear stress was expressed as

$$\begin{eqnarray}&&{\tau }_{c\max }=\displaystyle \frac{{P}_{\max }}{2bd}\end{eqnarray} \tag{ 2 }$$

For the three-point bending test, the total elastic displacement of the load applicator was found by summing the flexural and shear deflections.

$$\begin{eqnarray}&&{w}_{t}={w}_{1}+{w}_{2}=\displaystyle \frac{P{L}^{3}}{48D}+\displaystyle \frac{PL}{4A{G}_{c}}\end{eqnarray} \tag{ 3 }$$

Here, P—bending load (N), L—span length (mm), b—composite breadth (mm), t—face skin thickness (mm), d—core thickness (mm), ${\sigma }_{f}$—face stress (MPa), w—total normal deflection (mm), w₁—flexural deflection (mm) and w₂—shear deflection (mm).

Numerical simulations were conducted to validate the theoretical results. The three-point bending test was replicated through ANSYS. Three different sandwich configurations were considered. The sandwich composite was modelled in the ACP module. Fabrics, orientation, layer thickness, and material properties were assigned suitably. The test loading rollers were designed and imported from Solidworks. A static structural analysis was performed. For meshing, SHELL181 and SOLID182 elements were used for the composite and loading rollers respectively (figure 2). Cohesive interaction between composite layers and bonded contact between the sandwich and the rollers was considered. The combined core and bilinear elastic glass fibre behaviour was accurately modelled for numerical simulation.

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The analysis was divided into sub-steps to obtain a list of response values. Outputs for face skin stresses, core shear stress, and deformation were extracted for each sandwich configuration and recorded. Individual ply wise data was obtained to give insights into the effect of distance from the neutral axis on the aforementioned parameters.

2.3.1. Material selection

2.3.2. Composite fabrication

The study of flexural properties is essential to designers and engineers for structure design. In this study, the flexural test was performed accurately to characterize the composite properties. The 3-point bending test (ASTM C393) was performed by using an Instron universal Testing Machine (UTM). The dimensions of the test specimens were in agreement with test standards. The samples were placed on two roller supports. The load was applied at the mid-span through a cylindrical applicator (figure 3).

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The composite may be compared to a beam with minor overhang. Stress varied along with its depth (figure 4). The stress was compressive at C, reduced to zero at N, and became tensile below to it (T). This was due to the simultaneous extension and compression of different layers. The top layers were compressed while lower layers were extended. The neutral axis AB experienced no change in length. In addition to the above, shear stresses were present in the sample as well. In bending, face skins carried the bending stresses while the core-skin interface and the core carried shear stresses.

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In this test, the specimens were subjected to shear, compressive, and tensile forces, as they would be under realistic loading conditions. The test parameters are mentioned in table 3. The test output data provided insights into the failure load, deflection properties, and face stresses. This data was then used in theoretical and FEA calculations.

The 3-point bending test was conducted as per the procedure outlined in the previous section. The material properties and sample dimensions were entered into the controlling programme before testing. Sensors on the UTM recorded forces acting on the test sample and its normal deflection at the mid-span. This data along with material and sample data was used to calculate parameters like maximum load and flexure stress, and generate the load versus deflection graph.

Figure 5 shows the bending test setup and the Load (N) versus Deflection (mm) test results for 5 mm core thickness sample. The result shows that, as the mid-span deflection increased, the load increased proportionally and reached a maximum point. This was the linear elastic region prior to cracking. Crack initiation caused a sudden drop in load, as this reduced the ability of the sample to bear additional load. This was followed by crack propagation, with a constant decrease in load which indicated the progressive failure of the specimen.

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Both the sandwich composite and its foam core were tested independently. Tests showed that the foam bore only 10% of the load (table 4). This indicated that the face skins were almost entirely responsible for the strength of the composite.

Standard bending load formulae and material properties were used to calculate various mechanical properties for the three composite configurations. For all calculations, the force applied was the same (235 N), which was obtained from experimental results (figure 5).

The parameters such as face stresses, mid-span deflection, and core shear stress were calculated (section 2.1) and plotted (figure 6).

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It was observed that as core thickness increased the face stress, deflection, and core shear stresses decreased. As thickness increased, the moment of inertia and stress distribution improved as well. This trend indicated that the composite's mechanical response improved with an increase in core thickness.

The simulation provided layer-wise properties of the sandwich composite (figures 7–8). Face skins bore the majority of the axial stress (tensile and compressive) and were responsible for composite strength. Here, core thicknesses of 5, 7, and 9 mm were modelled with 2 fabric layers on each face. Figure 6 displays the variation of the calculated mechanical properties on changing core thickness. As the core thickness increase, the properties of the sandwich composite improve. For the same load conditions, stresses and deflection are less. Because of the increase of in core thickness, the cross-sectional area and moment of inertia increased. This led to a decrease in stresses in the face skins, deflection, and core shear stress. The presence of more material distributed the forces thorough a larger region and improved the composite properties without significant weight increase. Thus, the mechanical strength increased with increased core thickness. The numerical model indicated that compressive and tensile stresses are present in the top and bottom face skins respectively. This was in agreement with the expected material behaviour. FEA of the samples for varying parameters provided results that were concurrent with theoretical calculations.

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Theoretical results were verified through FEA analysis. A good concurrence was obtained between the theoretical calculations and simulation results. Load increased linearly with deflection until the state of crack initiation, beyond which stiffness decreased (figure 6).

The general concurrency of the theoretical results and the simulation validated the theoretical results. It indicates that the assumptions made in the FEM model regarding contact types, geometry, interactions, and boundary conditions were valid.