Mechanical property analysis and experimental validation of composite honeycomb sandwich radome considering perforation and impact damage

To carry out the experimental verification of the mechanical properties analysis of the radome considering the damage factors, the test matrix design is carried out according to the finite element analysis method of the equivalent elastic theory and the idea of building block test verification. Firstly, the necessity and basic principle of equivalent elasticity theory in the performance analysis of complex curvature products considering damage factors are explained. Then, combined with the theory, a modular test matrix design is carried out, which should be able to test the correctness of the equivalent elastic modulus. Finally, a case study is carried out, and the difference between the test results and the simulation results is analyzed with the damaged radome as the research object. The results show that the development of the equivalent elasticity theory and the design of the test matrix can make the analysis results meet the engineering requirements.


Introduction
Testing of composite materials usually requires a lot of time, cost, and resources.Through rational planning of the test matrix, the limited resources can be used to the maximum extent and rich information can be obtained.This helps to improve research efficiency and reduce costs.Complex curvature products typically involve multiple curvature, shape, and thickness variations.With trial matrix planning, trials can be designed to cover these ranges of variation and collect relevant data.This helps to quantitatively evaluate the performance of the composite under different curvature and shape conditions.To effectively realize its performance analysis, many finite element analysis methods have been proposed, such as multi-scale modelling, micromechanics, multi-modal, etc., to test the accuracy of these techniques.Trials should be conducted to match that.In recent years, many studies have been carried out in this regard.
Souza et al. [1] developed a finite element model mapping the natural frequency of laminates from the layup angle and verified it through a few experiments.The simulation analysis of composite corrugated plate crushing was carried out by Mou et al. [2], and the nonlinear mapping relationship between specific energy absorption and material parameters was obtained based on orthogonal test data fitting.Song et al. [3] used representative cells to characterize the multi-scale calculation process, simulated the modal behavior (natural frequency and modal shape) of composite materials by finite element method (FEM), and used a modal hammer with acceleration sensor to conduct experimental modal analysis of key vibration parameters.To evaluate the effective conductivity of graphite composites, Scocchi et al. [4] conducted a set of simulations through experimental design aimed at identifying the microstructure details that are most important for the effective properties of these materials; Zhang et al. [5] introduce a new virtual experimental method to estimate the effective transverse properties of fiber-reinforced composites (FRC) and analyze the effects of microscopic parameters (such as interphase strength and residual thermal stress) on the macroscopic properties of FRC.Wang et al. [6] prepared a modified 1-3 piezoelectric composite material based on the threecomponent phase and tested it by finite element simulation and experiment.In addition, there is also experimental verification on the consideration of natural defects, composite material performance verification considering splicing characteristics [7,8], rapid design [9,10], and test methods for honeycomb sandwich structures [11,12].In terms of finite element analysis and test verification considering damage factors, the study combined buckling [13], bending [14], axial compression [15], and other loads, The damage behaviors such as delamination [16,17], tear [18] or fracture [19,20], fatigue [21,22], etc. are simulated and verified by experiments.However, the above research has not yet combined with the block-type test verification idea to make a unified and complete test plan for materials, structural parts, and final products, considering the damage factors.In this paper, the design flow of the test matrix and the concrete test matrix planning are given according to the proposed equivalent elasticity theory.In the finite element simulation, the equivalent elastic theory is used to analyse the mechanical properties of the radome considering the damage factors.Combined with the building block test planning idea, the test planning idea from small to large is carried out, and finally, the test combination and the finite element analysis results are compared to meet the engineering needs.The remainder of this paper is organized as below.Section 2 introduces the methods of Equivalent elasticity theory and building block experimental design method.In Section 3, a radome with perforation, delamination, and debonding was used as a case study to introduce the damage information and modeling details of the radome.The accuracy requirements and the performance of the prediction model are described in Section 4, and some main conclusions are summarized in Section 5.

Equivalence performance theory
In the research status of mechanical property analysis of honeycomb sandwich structures and their products under the conditions of considering materials, loads, and repair parameters at home and abroad, multi-scale modeling and equivalence methods have been the focus of research in recent years, but the relevant research is mostly focused on structural components, or cylindrical honeycomb sandwich structures with simple structural features, which have not been implemented into the actual products, and the analysis is less considerate of the factors of damages and repairs, and it is not able to provide theoretical support for analyzing the conditions that may happen to the radome in actual operation.Derived from the theory of fine-scale mechanics, elastic parameters are artificially defined, two-or three-dimensional characterizations of the mechanical behavior of a material.In the case of composites, for example, the fibers and the matrix have their modulus to characterize their mechanical properties, and fiber-reinforced composites are made from a combination of these two types of materials, which creates a new modulus value.Therefore, the method of equivalent modulus of elasticity is a numerical analysis method similar to the agent model, in which the region with a certain characteristic and its neighborhood are regarded as a whole in a certain scale, and the modification of the mechanical property parameters is used to equate the effect brought by the internal or external structure, i.e., the equivalent modulus of elasticity.Consider a two-dimensional stress state and solve for the set of equivalent elastic parameters S={E1, E2, V12, G12, G13, G23} for damaged or repaired honeycomb sandwich structures.The dimensions of the equivalent elastic model are determined according to the dimensions of the damage and repair.In principle, the edges of the equivalent elastic model should not be causing stress concentrations and the equivalent elastic model should be much smaller than the product.Equivalent elastic parameters of anisotropically damaged or repaired honeycomb sandwich structures are solved Equivalent elastic parameters are calculated as shown below.
2.1.1Damage sandwich structure and radome.The radome is an important component of an aircraft that is used to protect the radar equipment from interference and damage from the external environment.However, because the radome is at the leading edge of the aircraft, it is often exposed to the threat of impact and damage from various objects in flight.The damage events were categorized into damage types according to perforation, debonding, delamination, collapse, etc., and their statistics are shown in Figure 1.Among these, perforation (ranked 3rd) and debonding or delamination (ranked 1st) were the most predominant modes of injury.

Figure. 1 Statistical damage type statistics with composite honeycomb sandwich structure
It is also clear to conclude from the graph that the frequency of perforation damage is high.Damage such as cracks and collapses are generally repaired by digging out the damaged area and utilizing patches.Tiny cracks and holes in the structure allow moisture to enter between the skin layers and inside the core section, which also aggravates the area of delamination and debonding.

Finite element analysis based on multi-scale modeling.
Radome are a class of equipment with complex curvature and thin-walled structures; therefore, modeling and analysis are often carried out in finite elements using two-dimensional cells.Not all damage factors need to be replaced by equivalent elastic modulus.The two types of damage forms chosen for this paper are the best examples.A simple damage pattern such as perforation can be modeled directly in the shell cell.The use of equivalent elasticity theory is redundant at this point.Unlike delamination and debonding, which cannot be modeled in shell elements without thickness, the equivalent elasticity theory needs to be used.The mechanical properties in a small area with damaged features are used to replace the geometrical features brought about by the damage.Therefore, the equivalent elastic modulus requires two parts of the work, one is to solve for the equivalent elastic modulus value in a tiny region; rather, it is to bring the equivalent elastic modulus value into a tiny region of the whole product model.As shown in Figure 2. The regions of the microstructure are not randomly generated.In the external dimensions of the microstructures, in the process of homogenization, most of the non-destructive units will dissipate the modulus change values of the damage units.Combined with the stress cloud diagram, it can also be observed that the amount of change in stress, strain, and displacement is still relatively obvious in the range of W=1.5D and L=1.5D.D is the size of the damaged area.

Experiment matrix design
The building block approach to test verification is a widely adopted idea in composite material test design and is widely recognized by authoritative standards.The "building block test" verification is a necessary way for composite material structure development and function verification, and is also an important part of airworthiness compliance verification, as well as an important aspect of airworthiness authority qualification.The purpose of the "building block test" program is to illustrate the high efficiency of investment that can be achieved by using a large number of low-cost small specimen tests and a small number of more expensive subcomponents and full-size test pieces.In addition, technology risks can be assessed more effectively early in the development and functional validation of composite structures.The "building block" validation system is used to gradually increase the size and complexity of the test pieces during the validation process and to gradually increase the scale of the test for test validation.Therefore, in combination with the planning idea of a "building block test", based on the principles that the size of the test object is from small to large; from material performance to structural function verification; and from standard test pieces to test pieces with structural characteristics, the composite honeycomb sandwich structure radome damage repair test validation framework is shown in Fig. 3.

Test grading considering damage factors.
The equivalent modulus of elasticity of microstructures, etc. can be verified experimentally or employing finite element analysis.The two models for comparison are the equivalent elastic modulus finite element analysis results of "modeling with damage characteristics ＆ conventional material properties" and the finite element analysis results of "modeling without damage characteristics ＆ equivalent elastic modulus properties" under the same tensile and shear loads.The delamination and debonding in this paper are the result of damage to the radome due to impact.The skin is a three-layer fabric, delamination was created between layers 1 and 2, and debonding was created between the skin and the core.As shown in Fig. 4 a).Then two mutually verified finite element models are shown in Fig. 4 b).

Damage information on the radome
Damage prefabrication was carried out on the radome, and there were 8 prefabrication locations.The damage locations were shown in Figure 5, and the coordinates of the damage locations were shown in Table 3.Among them, the first 4 open hole damage, and the last 4 places are delamination and debonding caused by impact.According to 637's opinion, the layering is set between Layer1 and Layer2 of the upper skin, and the debonding is set between the upper skin and the core.

Verification of equivalent elastic modulus of plate microstructure
The material parameters used in this paper are shown in Tables 4 to 5. To obtain a composite honeycomb sandwich structure plate with a total size of 2 types (layered/disbanded (25mm) sandwich structure plate 37.5mm×37.5mm,layered/disbanded (26mm) sandwich structure plate 39mm×39mm) under the delamination and delamination damage modes, 6 types of equivalent elastic parameters were obtained for each type of model, with a total of 24 types.The calculation process, simulation accuracy, and calculation results are as follows.
(1) Layered and deluged sandwich structure plate 37.5mm×37.5mmThe damage size of the laminated and deluged sandwich plate is 25mm in diameter.The simulation results of the model of "layered and deboned sandwich plate + lossless material properties" are shown in Figure 6.The simulation results of the model of "lossless plate + damaged material properties" are shown in Figure 7.When the damage size of the laminating and destocking sandwich plate is 26mm in diameter.Combined with Eq.1, the equivalent elastic parameters of 26mm delamination and debonding were obtained, and the mechanical performance of the equivalent elastic model was shown in Table 8-9.The analytical results clearly show that the strain field of the equivalent model tends to be homogeneous, and its size is close to the median or average in the original microstructure.From the perspective of the whole microstructure, the equivalent model can express E1, E2, and Poisson's ratio well, but its ability to express shear behavior, especially the interlayer shear behavior, is slightly weak, but still within the acceptable range.E1, E2, and G12 of the honeycomb sandwich structure are more affected by skin, while G13 and G23 are more affected by core material properties.

Damage radome experiment
The radome global coordinate system is adopted in this paper.The vertex coordinate of the radome is (0,0,0), which is the right-handed coordinate system.The test part is installed on the support fixture through the hinge, connecting lock, and 5 taper pins and the support fixture is fixed on the bearing floor.The experiment involved in this project adopts a fixed structure of radome static test loading wood block and uses the test symbol loading wood block and actuator to convert the concentrated force into the surface force.The loading method is shown in Figure 8. .Illustration of the damage test A total of 15 strain flares were pasted in this test.According to the local normal of the strain measuring point, the direction of strain flower 0° is the projection direction of the connection between the coordinate point and point (0,0,0) in Figure 7 on the radome, and the direction of 45° and 90° is determined according to the right-hand rule.At point (0,0,0), the normal line is inward, and the direction of strain flower 0° is the Z-axis direction in the section plane, and the directions of 45° and 90° are determined according to the right-hand rule.Three displacement measuring points are arranged in this experiment.The coordinates of strain and displacement measurement points are shown in Table 10.

Construction of finite element model of damage radome
The damage prefabrication was carried out on the radome.There were 8 prefabrication locations, among which the first 4 sites were open hole damage and the last 4 sites were delamination and debonding caused by impact.Among them, holes with a diameter of 25mm were prefabricated at places 1-4, equivalent elastic models corresponding to delamination and debunking with a diameter of 25mm were prefabricated at places 5 and 8, and equivalent elastic models corresponding to delamination and debunking with a diameter of 26mm were prefabricated at places 6 and 7. Draw four points 18.75mm or 19.5mm away from the center point with (x, z) on the Z-X plane, connecting (0,0) and the left and right two points; Make two parallel lines through the upper and lower two points, and both lines are perpendicular to the line between (0,0) and the damage center point.With (x, z) as the center, the Z-X plane is rotated to the direction of the tangent plane parallel to the surface, and the area surrounded by these four sides is projected onto the radome, that is, the area where the damage equivalent elastic model is located.The finite element model of the damaged radome is shown in Figure9.

Figure. 9. Damage radome and partition model
The test part is installed on the support fixture through the hinge, connecting a lock and 5 conical pins.The support fixture is fixed on the bearing floor according to the constraint conditions, the articulation constraint is set at the articulation and pin joint (U1=U2=U3=UR1=UR2=UR3=0), and the connection lock is set completely fixed (U1=U2=U3=UR1=UR2=UR3=0).The 17 partitions of the radome are respectively loaded with concentrated force, as shown in Figure 11.The experiment involved in this project adopted a fixed structure of radome static test loading wood block, which used the test symbol loading wood block and actuator cylinder to convert the concentrated force into the surface force, adopted the MPC constraint method, took the loading point of the concentrated force as the MPC constraint point, and mapped the concentrated force to a certain area of the partition.

Verification
The lay-up Angle of the radome is consistent with the actual one.The warp direction is along the radome bus, the weft direction is clockwise along the radome, and the sweep direction is along the radome thickness direction.The equivalent region brings in the equivalent elastic modulus in Table 6 and Table 8.The other areas bring in the material properties of Tables 4 and 5. Too small a strain value has no practical significance for analysis.Compare the precision of strain values and displacements greater than 2E-4, as shown in Figure 10

Conclusion
The multi-scale equivalent elasticity theory of composite honeycomb sandwich structure considering damage was introduced, and the damage was effectively introduced into the finite element analysis of complex curvature products through the design of a test matrix, the solution of damage equivalent elastic parameters, and the analysis of the mechanical properties of damage radome.The results show that this test plan can reduce the modeling burden caused by complex damage and repair mode, reduce the work burden, and improve the analysis accuracy.

Figure. 2
Figure. 2 Finite element analysis based on multi-scale modelling

Figure. 4
Figure. 4 Equivalence of delamination and debonding damage

Figure. 6 Figure. 7
Figure.6 Results of finite element analysis of laminated and unglued sandwich plate Figure 8. Illustration of the damage testA total of 15 strain flares were pasted in this test.According to the local normal of the strain measuring point, the direction of strain flower 0° is the projection direction of the connection between the coordinate point and point (0,0,0) in Figure7on the radome, and the direction of 45° and 90° is determined according to the right-hand rule.At point (0,0,0), the normal line is inward, and the direction of strain flower 0° is the Z-axis direction in the section plane, and the directions of 45° and 90° are determined according to the right-hand rule.Three displacement measuring points are arranged in this experiment.The coordinates of strain and displacement measurement points are shown in Table10.

4 Figure 10 .
Figure 10.Comparison between experiment and simulation

Core, rubber, prepreg static test Statistics analyze allowance Stress- strain curve Material properties payloads Plywood analysis Geometric dimensioning Experience and historical data references Typical tests on flat plates with structural features Damage Characteristics equivalent modulus of elasticity structural analysis structural design Conformity review preliminary design damage test Detailed design Product test validation Product Mechanical Properties Figure. 3
Composite honeycomb sandwich structure radome damage repair test validation process based on "building block test".2.2.1 Building block test matrix design.Combined with the influencing factors and is a "building block test" validation framework, the construction of the test matrix, the test planning covers six types of research objects such as cores, glues, panels, flat typical parts, curved plate typical parts, and products, and complete coverage of the repair material system and the repair of the size of the two types of influencing factors, according to the size of the test piece and the purpose of the test piece, which can be divided into three major categories, namely: material performance test, flat typical parts equivalent mechanical properties test, curved plate typical parts mechanical properties test and the mechanical properties of products test.Material performance tests have been based on the relevant standards and regulations and have very mature planning, this paper mainly gives structural details and product test planning.As shown in Table1 and Table 2.

Table 1 .
Matrix of equivalent modulus of elasticity tests for damaged plates in microregions

Table 2
Matrix of mechanical properties of damage radome tests

Table 3
List of damage coordinates

Table 4
Elastic constants of plain woven monolayer

Table 10
Coordinates of strain and displacement measurement points