Experimental and numerical study on flexural properties of glass fiber reinforced plastic sandwich plates

Due to their high specific strength and stiffness, glass fiber reinforced plastic (GFRP) sandwich plates are widely used in various fields such as construction, aerospace, shipbuilding, and military. This paper studies the bending performance of FRP sandwich plates with reinforcement through experimental and numerical simulation methods. The study shows that the bending performance of unidirectional and bidirectional reinforced plates under the same concentrated load is similar, and bidirectional reinforcement cannot significantly reduce the bending deformation of the sandwich plate. Under uniform load, the four-sided supported bidirectional reinforced sandwich plate can significantly reduce the deformation of the plate, and the deformation can be reduced by 40% compared to the unidirectional reinforced plate.


Introduction
The glass fiber reinforced plastic (GFRP) sandwich structure has high specific stiffness, high specific strength, and good heat and sound insulation capabilities, widely used in construction, aerospace, marine, military, and other fields.Typical sandwich structures mainly include honeycomb, foam, and other structures.The traditional honeycomb sandwich structure has high strength, but it is difficult to manufacture and maintain and high cost [1][2] ; the production of foam sandwich plates is relatively simple, but the bending stiffness is relatively low.Research has shown that adding stiffeners to composite sandwich structures could effectively improve the structural performance of the sandwich plates [3][4][5] .Theoretical, experimental, and numerical methods are widely used in the research of the mechanical properties of composite sandwich plates [6][7][8][9][10][11] .With the development of numerical simulation technology, the numerical method could reduce the experimental work and improve the research efficiency of composite sandwich structure study [12][13][14][15] .To reveal the effects of reinforced forms and boundary conditions on the bending performance of GFRP sandwich plates, two kinds of reinforced forms of GFRP sandwich plates were designed, and through bending tests and numerical simulation research, the deformation laws of GFRP sandwich plates under different boundary conditions were studied.

Specimen preparation
The GFRP reinforced sandwich plate proposed in this paper uses GFRP as the skin, filled with phenolic foam as the interlayer, and a GFRP square tube as the stiffener.Phenolic foam and GFRP square tube are bonded by vinyl room temperature curing resin.Figure 1 is the structural diagram of the GFRP reinforced sandwich plate.The basic mechanical parameters of each part of the GFRP reinforced sandwich plate are: The elastic modulus of GFRP skin is 29.6 GPa, tensile strength is 483 MPa; the elastic modulus of the stiffener is 46 GPa, and the tensile strength is 670 MPa; the compressive strength of foam is 0.19 MPa, and the elastic modulus is about 16 MPa.The length, width, and height of the GFRP reinforced sandwich plate specimens are 2000 mm, 1000 mm, and 50 mm, respectively.The skin thickness is 10 mm; the thickness of the phenolic foam filling layer is 30 mm.The side length of the stiffener cross section is 30 mm, and the wall thickness is 4 mm. Figure 2(a) shows the unidirectional stiffened model.

Flexural properties test
The three-point flexural test is carried out on the specimens of unidirectional stiffened sandwich plates.The loading device of the flexural test adopts the gradual loading mode of heavy objects, and the loading diagram of the three-point flexural test is shown in Figure 3.The concentrated load was gradually applied during the test, and the midspan displacement of the sandwich plate specimen was recorded.Figure 4. Deflection curve of a specimen.Figure 4 shows the variation of mid-span displacement of unidirectional reinforced specimens with load.It shows that the displacement gradually increases with the increase of load.When the load is less than 13.8 kN, the mid-span displacement increases linearly with the load; when the load exceeds 13.8 kN, the slope of the load displacement curve reduces.

Numerical simulation of flexural test
This paper uses the finite element software COMSOL to simulate the bending of a reinforced sandwich plate.Firstly, the bending test and numerical simulation results of the unidirectional stiffened sandwich structure are compared.Based on verifying the reliability of the numerical method, the bending performance of a bidirectional stiffened sandwich structure is numerically simulated.

Numerical model and parameters
According to the symmetry principle, a quarter of the stiffened sandwich plate model is constructed to improve the calculation efficiency.A uniformly distributed surface load is applied within 125 mm from the symmetrical boundary on the upper surface of the right end of the model to replace the concentrated load in the test, as shown in Figure 5.The plate and support adopt the contact boundary.
Model parameters are as follows: The length is 1000 mm, the width is 500 mm, and the height is 50 mm.To improve computational efficiency, hexahedral structured grids are used for skin and foam, and triangular prism grids are used for stiffeners.Figure 5 shows the meshing results of the model.

Numerical simulation results of the unidirectional stiffened model
In this paper, the flexural properties test of unidirectional stiffened sandwich plate under different loads were simulated respectively.The mid span displacement of the sandwich plate is listed in Table 1.The numerical simulation results are close to the experimental values, and the error is within 9%.Therefore, the numerical simulation method can effectively simulate the bending deformation behavior of the sandwich structure.6.It shows that the high stress is mainly distributed in the mid span of the skin and the upper and lower sides of the stiffener, and the maximum value is about 28.77 MPa, which is far less than the tensile strength.The stress of the foam filling layer is very small, and the maximum value is about 31.75KPa.

Numerical simulation results of the bidirectional stiffened model
Aiming to reveal the influence of different reinforcement forms on the bending performance of sandwich plates, a numerical simulation method was used to simulate the bending deformation of bidirectional reinforced sandwich plates under different loads.Table 2 lists the displacement at the middle of the sandwich plate under different loads.It shows that under the same load, the displacement at the middle of the plate span is close, and the difference is less than 4%.The bidirectional stiffened reinforcement mode in this paper cannot significantly improve the bending performance compared to the unidirectional stiffened mode.7. It shows that the stress of the middle part of the skin and the upper and lower sides of the stiffener of the sandwich plate is large, and the maximum value is about 29.86 MPa, which is far less than the tensile strength.The stress of the foam filling layer is very small, and the maximum value is about 34.47 KPa.The stress distribution is more uniform in the bidirectional stiffened model than in the unidirectional stiffened model.

Simulation of four sides supported stiffened sandwich plate
To study the influence of boundary conditions on plate deformation, two kinds of stiffened sandwich plates under the same uniform load in the state of four sides supported were studied by numerical simulation.Figure 8 shows the deformation of the stiffened model.The results show that for the four side supported model, the deformation of the center of the plate is the largest under the uniformly distributed load.The deformation of the bidirectional stiffened model is significantly less than that of the unidirectional stiffened model, and the deformation is reduced by about 40% under the same load conditions.Figure 9 shows that under the same load, the internal stress of the bidirectional stiffened reinforced model is much smaller than that of the unidirectional stiffened reinforced model, and the maximum stress is reduced by about 50%; the high stress area of the unidirectional reinforced model is mainly distributed around the stiffener, and the internal stress distribution of sandwich structure is quite nonuniform; the stress distribution of the bidirectional stiffened model is relatively uniform, and the high stress is mainly distributed on the skin surface and the side of the short stiffener.The above results show that under the condition of being supported on four sides, the mechanical properties of different parts of the sandwich plate can be effectively played by bidirectional reinforcement.

Conclusions
In this paper, two types of GFRP reinforced sandwich plates were constructed, and the flexural properties of the plate were studied through points test and numerical simulation.A numerical model was developed for a four side simple supported reinforced sandwich plate to investigate the effect of reinforcement type on deformation.The conclusions are as follows: (1) With the three-point bending condition, the bidirectional stiffened reinforcement paper could not significantly improve the bending performance of the unidirectional stiffened.
(2) Under four sides simple supported boundary condition, the deformation of the bidirectional stiffened model is significantly less than that of the unidirectional stiffened model, and the deformation is reduced by about 40%.
(3) The stress distribution inside the two types of reinforced model is similar under a three-point bending condition; the internal stress of the bidirectional stiffened plate is about 50% of that of the unidirectional stiffened model under four side simple supported boundary condition.

Figure 2 (
b) shows the bidirectional stiffened model.

Figure 3 .
Figure 3. Sketch map of flexural test set-up.Figure4.Deflection curve of a specimen.Figure4shows the variation of mid-span displacement of unidirectional reinforced specimens with load.It shows that the displacement gradually increases with the increase of load.When the load is less than 13.8 kN, the mid-span displacement increases linearly with the load; when the load exceeds 13.8 kN, the slope of the load displacement curve reduces.

Figure 8 .
Figure 8. Deformation of the stiffened model with four sides supported.

Figure 9 .
Figure 9.The stress of the stiffened model with four sides supported.

Table 1 .
The mid span displacement of the unidirectional stiffened sandwich plate.the stress of different parts of the unidirectional reinforced sandwich structure under 18.3 kN is shown in Figure

Table 2 .
The mid span displacement of the stiffened sandwich plate.the stresses of the bidirectional stiffened reinforced sandwich structure under 18.3 kN are shown in Figure