Modelling and Simulation of Compression Behaviour of 3D Woven Hollow Composite Structures Using FEM Analysis

Three-dimensional (3D) woven spacer composites have the advantage of being lightweight and strong for use in various segments of structural engineering and automobiles due to their superior mechanical properties than conventional counterparts. In this investigation, the influence of different cell geometries of 3D woven spacer fabrics, namely rectangular, triangular and trapezoidal with woven cross-links, upon their mechanical behaviours, especially compression energy, was studied through FEM (finite element method). Cell geometries were changed into different heights and widths and evaluated through simulation and experiments. Simulation of the structure was carried out by the Abaqus platform, and validation of the results was done for the rectangular structure. It was found that compression energy increases with an increment in width, while initially, it shows the tendency to increase and subsequently decrease with an increment in height for the rectangular structure. Compression energy increases with an increase in the angle of the triangular structure; however, it shows the opposite trend in the case of the trapezoidal structure. The outcome of the result shows good agreement between simulation and experimentation values of more than 94% accuracy.


INTRODUCTION
In the broad spectrum of novel engineering studies, researchers are using composites, which have become an inevitable alternative because of their favourable properties and superior integrity over their conventional counterparts. Excellent durability, high-bending stiffness, thermal insulation, the resistance of high skin-core debonding, acoustic damping, and secure processing make sandwich structures vastly accessible and preferable than isotropic components in varied and sophisticated industries like aerospace, locomotives, automobiles, structural engineering, windmills, and marine. In composite research, a distinct inclination towards low cost ''out-of-autoclave'' manufacturing methods has recently come into trend, especially in the aerospace and vehicle industry, for producing different components with superior structural integrity, high energy absorption and minimal delamination, as well as exploring the potentiality of the robotic manufacturing processes [1][2][3][4][5][6]. These structures are becoming popular as an integrated part of the automotive industry as it is shifting towards electric vehicle (EV) manufacturing to reduce carbon footprint from the www.textile-leather.com 7 environment by nulling fossil fuel consumption, where the reduction in weight of the vehicle compliments with low engine energy consumption, desired speed per hour, larger pay loads, and sustainable economy [7]. Typical sandwich structures are made of a variety of core materials like honeycomb core, expanded polymeric foams, and balsa wood, which have low density and face sheets of high modulus [8]. Although those core materials have the benefits of being lightweight and having superior damage resistance, the limited surface area of the poorly bonded face-core interface and physical dissimilarity cause delamination inexorably under external impacts [9,10]. Sandwich composites made of fibrous preforms have a few obstacles if they are manufactured by the stitching process. Stitching allows the sewing needle to pierce the preform and damages the fibres in the piled fabric layers, which entangle with stitched thread. Consequently, the resin gets drained from the rich resin areas at the resin infusion stage. However, weaving and knitting methods can be the alternative for producing consolidated sandwich structures without damaging fibres in stacking the fabric and compromising with a fibrous resin matrix, which may lead to delamination. These three-dimensional (3D) sandwich structures are also known as woven/knitted spacer or hollow fabrics [8,[11][12][13][14][15][16]. Through weaving technology, near net shape preforms can be made by eliminating any joining steps. 3D woven spacer fabrics are constructed with pile yarns or fabrics, which maintain hollow space between layers [17][18][19]. 3D woven spacer composites have better compression and shear features than conventional counterparts [20,21]. Furthermore, compression and low-velocity impact study were carried out by Vaidya et al., where it was found that with the increment of thickness and the presence of core piles in 3D woven spacer composites, the peak load and fracture under compression and low-velocity impact reduced respectively [22,23]. Belingardi et al. investigated that the sandwich structures which incorporate resin net walls in the foam core can be sustained in a remarkable increment of the dynamic impact response [24,25]. Furthermore, Torre et al. talked about ridged cores in their research, where cores are made of the same material as the face sheets. The channelled cores were filled with phenolic foams in the sandwich composites, which performed exponentially well than their conventional counterparts [26]. An extensive study was carried out by several researchers regarding the influence of the presence of corrugated cores in the sandwich structures. Jin et al. recorded very high delamination resistance of sandwich structures, which were incorporated with ridged cores along with face and bottom surfaces in his studies [27]. These corrugated cores enhance the mechanical performance of spacer structures such as high resistance to bending deformation, especially over the direction of corrugation. Therefore, woven cross-links in spacer woven composites can withstand better under bending loads than the structures connected with yarns [19,28,29]. Different geometrical shapes such as triangular [30,31], trapezoidal [19], and rectangular [32,33] can be found in the woven spacer composites which have core-face interfaces and are connected with woven cross-links. The structures may consist of a single layer of the same cell or multiple layers of cells vertically [19]. However, it is necessary to study the mechanical behaviour of different structures of the spacer composite through simulation [34]. In this research work, the compression energy of the sandwich structure with different cell geometrical shape was predicted through simulation by using the Abaqus platform. The dimensions of cell shapes were also varied within the shape, such as height, width, and angle, to find their effect on compression energy. The model is validated experimentally by analysing the rectangular spacer sample with different cell structural parameters.

Materials
A composite sandwich structure of the rectangular shape was manufactured from 3D woven spacer fabrics which have woven cross-links. Rectangular structures of different height and width were produced from E-glass tow of 600 Tex. A customized weaving machine was used to produce the fabric. Epoxy (LY556) resin and hardener Aradur HY951 were used to form the composite.

Production of spacer fabric and composite manufacturing
The primary requirement to produce the fabric is the weave design. The cross-sectional representation of the rectangular structure is shown in figure 1. The structure has a connecting fabric layer and two skin fabrics. The number of picks changed the cell dimensions of the fabric. EPI and PPI of the single-walled fabric was 10x10 and when the layers combined to form a double layer, then EPI becomes 20, and PPI remains the same. Vacuum-assisted resin infusion moulding technique (VARIM) was used to make the composite structure, in which resin impregnates the fabric. Customized wooden blocks were used to make the composites. They were inserted inside the cavities of the fabric according to the requirement of the shape of the structure. Teflon paper was wrapped around these wooden blocks so that during resin impregnation fabric would not stick to the blocks. Figure 2 shows the composite structure produced in the rectangular shape.

Lateral compression test
Lateral compression testing of rectangular composite samples was carried out on a universal testing machine (Instron 5982) shown in figure 3, according to the ASTM365 method. The speed of testing was 2 mm/min at the quasi-static loading rate. This test method covers the determination of compressive strength and modulus of sandwich cores. These properties are usually determined for design purposes in a direction normal to the plane of facings as the core would be placed in structural sandwich construction.
www.textile-leather.com 9 TRIPATHI L et al. Modelling and simualtion of compression bahaviour… TLR 3 (1) 2020 6-18.   The compression energy of the texti le preforms depends on various parameters which can be categorized as: 1. Mechanical properties of the composite (elastic modulus, shear modulus) 2. Structural properties 3. Geometry parameters 4. Structure surface condition. Three-dimensional models of diff erent structures were developed using Solid Works. Then this model was imported to the Abaqus platf orm for the simulati on of all the structures. The following physical properti es like density, elasti c moduli, Poisson's rati o, and bending properti es of the composite structure were entered as input parameters. Meshing tool was used to mesh the 3D model structures. It is the process of converti ng complex structures into thousands of fi nite elements. The boundary conditi on of fi xed support is to be imposed on the structure for fi nding out the soluti on of the structure, and compression energy was calculated using the Finite Element Method (FEM). Steps for the simulati on of the 3D hollow structure on the Abaqus platf orm is shown in fi gure 4. Figure 5 has shown the stepwise development of a 3D woven hollow composite structure and its behaviour under compression by using the Abaqus platf orm.

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equation 1 until the first peak, because after the first peak the material starts to yield or break both in the case of experiment (as shown in figure 6) and simulation. Compression Where σ =stress, Ɛ= strain

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equation 1 until the first peak, because after the first peak the material starts to yield or break both in the case of experiment (as shown in figure 6) and simulation. Compression Where σ =stress, Ɛ= strain

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equation 1 until the first peak, because after the first peak the material starts to yield or break both in the case of experiment (as shown in figure 6) and simulation. Compression Where σ =stress, Ɛ= strain

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equation 1 until the first peak, because after the first peak the material starts to yield or break both in the case of experiment (as shown in figure 6) and simulation. Compression Where σ =stress, Ɛ= strain

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equati on 1 unti l the fi rst peak, because aft er the fi rst peak the material starts to yield or break both in the case of experiment (as shown in fi gure 6) and simulati on.

Compressional behaviour of the rectangular structure
The compression energy was calculated from the area under the curve of stress-strain by using equation 1 until the first peak, because after the first peak the material starts to yield or break both in the case of experiment (as shown in figure 6) and simulation.

FEM Analysis
The 3D model developed in the Solidwork platform was imported to the Abaqus platform, as shown in figure 7. After that, a simulation was performed, and lateral compression was applied, as shown in figure 8, to get the desired results with proper constraints and settings for the structure. In this way, simulations of other structures, namely rectangular, trapezoidal, and triangular shape composites of different dimensions, were also carried out.

FEM Analysis
The 3D model developed in the Solidwork platf orm was imported to the Abaqus platf orm, as shown in fi gure 7. Aft er that, a simulati on was performed, and lateral compression was applied, as shown in fi gure 8, to get the desired results with proper constraints and setti ngs for the structure. In this way, simulati ons of other structures, namely rectangular, trapezoidal, and triangular shape composites of diff erent dimensions, were also carried out.

FEM Analysis
The 3D model developed in the Solidwork platform was imported to the Abaqus platform, as shown in figure 7. After that, a simulation was performed, and lateral compression was applied, as shown in

Rectangular structures
In rectangular structures, width and height of the structure are varied and fi nally the results obtained both from the experiment and the simulati on are given in table 1 and table 2. Table 1 gives the compression energy for diff erent widths of the composite cell at the constant height, whereas table 2 shows the energy values for diff erent cell heights at the constant width. Figure 12 (a) and (b) show that compression energy increases with increase in width, while, with increase in height, energy initi ally increases and then decreases. This behaviour reveals that the composite cell under compression load becomes unstable aft er a certain height and then starts buckling.

Rectangular structures
In rectangular structures, width and height of the structure are varied and finally the results obtained both from the experiment and the simulation are given in table 1 and table 2. Table 1  show that compression energy increases with increase in width, while, with increase in height, (a) (b) Figure 11. Trapezoidal structure (a) Schematic diagram (b) Stress-strain graph by simulation

Triangular structure
In the triangular structure, compression energy was found out by simulati on for various angles of the cell structure. The results obtained from the simulati on are given in table 3 for diff erent dimensions and fi gure 13 shows that with increase in angle, compression energy increases.

Triangular structure
In the triangular structure, compression energy was found out by simulation for various angles of the cell structure. The results obtained from the simulation are given in table 3 for different dimensions and figure 13 shows that with increase in angle, compression energy increases.   In the trapezoidal structure, compression energy was found out by simulation for different cell angles. The obtained results are given in table 4 for different dimensions. Figure 14 shows that with the increase in angle, compression energy decreases.

Trapezoidal structure
In the trapezoidal structure, compression energy was found out by simulati on for diff erent cell angles. The obtained results are given in table 4 for diff erent dimensions. Figure 14 shows that with the increase in angle, compression energy decreases.

Validation of the simulation results
In order to validate the simulation result, the experimentation and predicted values of compression energy of the rectangular shaped hollow composite structure were plotted in a bar chart. Figure 15 and figure 16 show the results for different widths and heights of the rectangular cell respectively. It may be observed from the figures that there is a good agreement between the simulation and experimentation results with prediction accuracy of more than 94%.

Valida� on of the simula� on results
In order to validate the simulati on result, the experimentati on and predicted values of compression energy of the rectangular shaped hollow composite structure were plott ed in a bar chart. Figure 15 and fi gure 16 show the results for diff erent widths and heights of the rectangular cell respecti vely. It may be observed from the fi gures that there is a good agreement between the simulati on and experimentati on results with predicti on accuracy of more than 94%.

Validation of the simulation results
In order to validate the simulation result, the experimentation and predicted values of compression energy of the rectangular shaped hollow composite structure were plotted in a bar chart. Figure 15 and figure 16 show the results for different widths and heights of the rectangular cell respectively. It may be observed from the figures that there is a good agreement between the simulation and experimentation results with prediction accuracy of more than 94%.

CONCLUSION
Compression energy for a sandwich structure is very crucial for the overall performance of the composite. Among various mechanical parameters, compression energy shows infl uence over the changes of cell geometries of the crosslinks in hollow structures. Therefore, for the numerical study of sandwich structures, diff erent geometrical cell shapes were developed on Solidworks and subsequently imported to the Abaqus platf orm to predict the compression energy by FEM. The compression behaviour of hollow structures of diff erent cell shapes and diff erent dimensions within the same shapes were studied, and compared with the experimentati on data of the rectangular shape for rati onalizing. The results show that the compression energy increases with an increment in the width of the rectangular cell, whereas it initi ally increases with the increment of the cell height and decreases aft er a specifi ed height while the cell becomes unstable as well. In the case of a triangular structure, compression energy increases with the increase of angle. However, in trapezoidal structures the energy decreases with the increase in angle. The consistency in trends in the simulati on and experimentati on data signifi es the reliability of the results obtained with a predicti on accuracy of more than 94%.