A thickness calculation method for ceramic layer and fiber backboard composite anti-ballistic structure

Abstract

The application discloses a thickness calculation method for a ceramic layer and a fiber backboard composite anti-bullet structure, and the method comprises the following steps: determining the limit speed of a ceramic / fiber composite target based on the energy conservation and kinetic energy theorem; constructing a target function based on the condition of satisfying the minimum structure area density; constructing a thickness calculation equation of the fiber bottom plate and the ceramic plate in the composite target based on the target function and the limit speed; determining the bullet parameters and the mechanical parameters of the ceramic / fiber composite target material, solving the thickness calculation equation, and obtaining the thickness of the fiber bottom plate and the ceramic plate in the composite target. The method has the characteristics of universality and flexibility, is suitable for different bullet types and different material combinations in the design scene, and saves the time and cost in the design process of the anti-bullet structure.

Description

Technical Field

[0001] This invention relates to the field of ballistic structure design, and in particular to a method for calculating the thickness of a composite ballistic structure of ceramic layer and fiber backing plate. Background Technology

[0002] Ceramic / fiber composite targets represent the most advanced lightweight and efficient ballistic protection structure currently available, widely used worldwide as a protective structure for light armored vehicles, attack helicopters, and individual soldier protection. This structure fully leverages the performance characteristics of different materials to achieve highly efficient protection. First, a hard ceramic layer breaks down and abrades the projectile, reducing its kinetic energy. Then, a lightweight, high-strength fiber layer provides final interception, absorbing the remaining kinetic energy. Throughout the process, the fiber layer also provides effective support to the ceramic layer, preventing premature ceramic breakage. The ballistic protection mechanism of ceramic-fiber composite structures reveals that the thickness of the composite structure needs to be rationally designed for different damaging elements (bullet type, velocity) to fully utilize its energy absorption characteristics and achieve highly efficient protection.

[0003] Currently, the thickness of ceramic / fiber composite structures is typically determined based on experience, experimentation, and safety factors during the design process. Figure 1 As shown, for different bullet velocities, bullet types, and different ceramic and fiber materials, repeated experiments and verifications are required. This process is time-consuming, labor-intensive, and costly, and it is difficult to systematically cover all possible bullet types and velocity combinations. Furthermore, due to the lack of universal and systematic mathematical models and calculation methods, design efficiency is low, and it is difficult to finely optimize structural thickness, often resulting in serious redundancy or inadequacy in protective performance. Therefore, a systematic and universal method is needed—one that can calculate the optimal ceramic layer thickness and fiber backing plate thickness based on arbitrary bullet parameters and protective material properties, so that the structure has the lowest surface density while meeting protective requirements. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the thickness of a composite ballistic structure consisting of a ceramic layer and a fiber backing plate. This method automatically calculates the thickness of the ceramic layer and the fiber backing plate to meet protection requirements, minimizing the areal density of the composite ballistic structure while satisfying performance constraints. It combines versatility and flexibility, making it suitable for design scenarios involving different bullet types and material combinations, thus saving time and cost in the ballistic structure design process.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for calculating the thickness of a composite ballistic structure consisting of a ceramic layer and a fiber backing plate. This method can automatically calculate the optimal thickness of the ceramic layer and the fiber layer for any bullet type, bullet velocity, and ceramic and fiber types, including the following steps:

[0007] Based on the law of conservation of energy and the kinetic energy theorem, the limiting velocity of the ceramic / fiber composite target is determined;

[0008] Based on the condition of minimizing the surface density of the structure, an objective function is constructed;

[0009] Based on the objective function and the limiting velocity, the thickness calculation equations for the fiber base plate and ceramic plate in the composite target are constructed.

[0010] By determining the bullet parameters and the mechanical parameters of the ceramic / fiber composite target material, and solving the thickness calculation equation, the thickness of the fiber base plate and ceramic plate in the composite target is obtained.

[0011] Furthermore, the limiting velocity of the ceramic / fiber composite target was determined to be:

[0012] ;

[0013] ;

[0014] Among them, v 50 v0 represents the maximum velocity of impact when the probability of a bullet penetrating the target is 50%, v1 represents the maximum velocity of impact when the probability of a bullet penetrating the target is 0%, and k1 represents the velocity of impact when the probability of impact is 0%. 50 The conversion coefficient between v0 and d2, k1 is less than 1, d2 is the thickness of the fiber substrate, ε2 is the fracture strain of the substrate, σ2 is the ultimate tensile strength of the substrate, and m is the tensile strength of the substrate. p For the mass of the projectile core, and It is an intermediate variable.

[0015] Furthermore, the intermediate variable and for:

[0016] ;

[0017] ;

[0018] In the formula, ρ is the core radius, ρ1 is the density of the ceramic plate, ρ2 is the density of the fiber base plate, and d1 is the thickness of the ceramic plate.

[0019] Furthermore, the objective function is:

[0020] ;

[0021] The values ​​of d1 and d2 are to be found when f(d1, d2) reaches its minimum value.

[0022] Furthermore, the thickness calculation equations for the fiber substrate and ceramic plate in the composite target are constructed, specifically including:

[0023] Based on the limiting velocity equation, Equations, constructing constraint equations;

[0024] Construct the Lagrangian function based on the objective function and constraint equations;

[0025] By taking the partial derivative of the Lagrange function and rearranging it, the thickness calculation equation is obtained.

[0026] Furthermore, the constraint equations are rearranged as follows:

[0027] ;

[0028] Where: parameters , , .

[0029] Furthermore, the Lagrange function is:

[0030] ;

[0031] in, It is a Lagrange multiplier.

[0032] Furthermore, the thickness calculation equation is as follows:

[0033] ;

[0034] .

[0035] Furthermore, the thickness calculation equation is solved using the fsolve method to obtain d1 and d2.

[0036] A computer storage medium storing an executable program, the executable program being executed by a processor to implement the steps of the thickness calculation method.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] (1) High versatility: applicable to different bullet types, bullet velocities, and material combinations;

[0039] (2) High efficiency: Traditional design methods require experimentation to try different surface density and thickness matching conditions. Even experienced designers need 7 to 8 iterations to determine the best solution. This invention calculates the initial thickness of the structure through a mathematical model. Only a small number of experiments are needed for verification and optimization. Generally, the best solution can be obtained after 2 to 3 iterations.

[0040] (3) Standardizable: This method is easy to integrate into protective structure design software or automated design processes.

[0041] (4) The design process does not rely on the relevant experience of researchers: The traditional design process relies heavily on researchers’ accurate understanding of the bullet damage effect and the mechanical properties of protective materials. If there is no relevant design experience in the early stage, it is difficult to determine a suitable initial scheme. This invention provides a method for calculating the thickness of protective structure based on the mechanical parameters of bullets and protective materials. The calculation results are highly reliable and do not rely on the relevant design experience of researchers. Attached Figure Description

[0042] Figure 1 A flowchart for the design of traditional bulletproof structures.

[0043] Figure 2 This is a flowchart illustrating the bulletproof structure design of this invention. Detailed Implementation

[0044] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0045] Combination Figure 2 This invention proposes a method for calculating the thickness of a ceramic / fiber composite ballistic structure, including:

[0046] First, based on the law of conservation of energy and the kinetic energy theorem, the Florencen formula for the penetration of an armor-piercing incendiary projectile into a ceramic / fiber composite target is given, i.e., the limiting velocity v. 50 It can be represented as:

[0047] (1)

[0048] in and Calculate according to the following formula:

[0049] (2)

[0050] (3)

[0051] Where: m p For the mass of the projectile core, Let ρ be the core radius, ρ1 be the density of the ceramic plate, ρ2 be the density of the fiber base plate, d1 be the thickness of the ceramic plate, d2 be the thickness of the fiber base plate, ε2 be the fracture strain of the base plate, and σ2 be the ultimate tensile strength of the base plate.

[0052] Because of v 50 This indicates a 50% probability that the bullet will penetrate the target plate. This does not meet the requirement that a ballistic protective structure must effectively stop the bullet. Therefore, ballistic protective structure design needs to use the ballistic limit v0 for calculations. v0 represents the highest impact velocity at which the bullet has a 0% probability of penetrating the target plate. For the same structure, v 50 v0 has the following relationship:

[0053] (4)

[0054] In the formula, k1 represents v 50 The conversion coefficient between v0 and v0, due to the same structure of v 50 The value of k1 is greater than v0, so the value of k1 is less than 1. The value of k1 varies for different bullet types.

[0055] When designing bulletproof structures, it is also necessary to meet the condition of minimizing the surface density of the structure. Therefore, an equation for the surface density is constructed as the objective function.

[0056] (5)

[0057] Given the bullet type, bullet velocity, and protective material parameters during the design process, the thickness of the ceramic and fiber layers is calculated to minimize the surface density. Therefore, m p , ρ1, ρ2, ε2, σ2, ε2, v0, and k1 are known values. The value of d1 and d2 is to be found when f(d1, d2) reaches its minimum value. Therefore, the above formula needs to be derived.

[0058] Squaring both sides of equation (1) yields the constraint equation:

[0059] (6)

[0060] Substituting equations (2) and (4) into equation (1) and rearranging, we get:

[0061] (7)

[0062] Define constants:

[0063] (8)

[0064] Therefore, the constraint can be written as:

[0065] (9)

[0066] in:

[0067] (10)

[0068] (11)

[0069] Construct the Lagrangian function based on the optimal conditions:

[0070] (12)

[0071] in:

[0072] (13)

[0073] Take the partial derivative with respect to d1:

[0074] (14)

[0075] in:

[0076] (15)

[0077] Take the partial derivative with respect to d²:

[0078] (16)

[0079] in:

[0080] (17)

[0081] Combining equations (14) and (16) to eliminate λ, we get:

[0082] (18)

[0083] Simplifying equation (9) yields the following constraint equation:

[0084] (19)

[0085] Substituting equations (15) and (17) into equation (18) and simplifying, we obtain the following optimal conditions:

[0086] (20)

[0087] Equations (19) and (20) constitute a complete mathematical description of two unknowns (d1, d2). Since these two equations are a system of high-order mixed algebraic equations, an analytical solution cannot be obtained according to Abel's impossibility theorem. This invention employs a numerical iterative solution method, and d1 and d2 that satisfy the conditions can be solved using the fsolve method. To facilitate the use of this method for bulletproof structure design, this invention provides the following Python code to solve d1 and d2.

[0088] Determine the bullet parameters and the mechanical parameters of the protective materials. The model requires parameters including the bullet core mass m. p Core radius Bullet velocity upon impact v0, projectile velocity v 50The conversion coefficient k1 (0 < k1 < 1) between v and v0, the density ρ1 of the ceramic, the density ρ2 of the fiber, the fracture strain ε2 of the fiber, and the ultimate tensile strength σ2 of the fiber. Convert all the above parameters into international units and input them into the program to solve for the thickness d1 of the ceramic plate panel and the thickness d2 of the fiber bottom plate. Take the ceramic and fiber thickness values calculated by the program as the initial scheme and calculate the areal density of this structure.

[0089] Verify the protection effect of the initial scheme through experiments. Since the ballistic test has randomness, the test needs to be carried out on the target plate. Based on the ceramic layer and fiber thickness obtained in the previous step, in order to ensure that the structural protection performance meets the requirements, performance verification also needs to be carried out through the ballistic test. At the same time, due to the randomness of the ballistic test, 3 target plates of the same structure need to be subjected to the ballistic test.

[0090] If all 3 can prevent bullets, then this structure is considered the optimal structure or consider appropriately reducing the thickness of the ceramic and fiber and continue the experiment. If penetration occurs in 3 target plates, appropriately increase the areal density and continue the experiment.

[0091] Through the repeated experiments in the previous step, obtain the optimal scheme satisfactory to the designer. Generally, using this method, the optimal structure can be obtained after 2 - 3 rounds of iteration.

[0092] The present invention also provides a computer storage medium, which stores an executable program. The executable program is executed by a processor to implement the steps of the thickness calculation method described above.

[0093] Embodiment

[0094] Taking the damage element as the Type 53 7.62mm armor-piercing incendiary bullet (speed 878m / s) and the protective materials as boron carbide ceramic and aramid fiber as examples, the process of designing the thickness of the ceramic and aramid is described in detail.

[0095] First, determine the relevant parameters of the bullet and the protective material, the mass m of the bullet core p : 0.00525kg, the radius of the bullet core : 0.00318m, the bullet speed v0: 878m / s, the conversion coefficient k1 between the bullet v 50 and v0: 0.96, the density ρ1 of boron carbide ceramic: 2520kg / m 2 , the density ρ2 of aramid fiber: 1360kg / m 2 , the fracture strain ε2 of aramid: 0.03, the ultimate tensile strength σ2 of aramid: 1.57e9 pa.

[0096] Input the above parameters into the calculation program to obtain the ceramic thickness d1 = 0.008m and the aramid thickness d2 = 0.0089m.

[0097] Using this structure as the initial design, its areal density is calculated to be 32.3 kg / m³. 2 .

[0098] Further testing was conducted to verify the performance of this solution. A total of three target plates were subjected to impact tests, and the detailed test results are shown in Table 1. All three plates achieved effective protection.

[0099] Table 1. Impact Test Results of the Example

[0100]

[0101] Based on the initial design achieving effective protection, the areal density was reduced to 31.1 kg / m². 2 The ceramic thickness is 7.7mm and the aramid thickness is 8.6mm. The bullet impact test was carried out, and the test results are shown in Table 1. Two of them were penetrated from the back, so it can be considered that the density of this surface is too low to stop the bullet.

[0102] Therefore, based on the above analysis, the suitable bulletproof structure against the Type 53 7.62mm armor-piercing incendiary round (velocity 878m / s) is 8mm boron carbide ceramic + 8.9mm aramid fiber, with a structural surface density of 32.3kg / m³. 2 .

[0103] This invention utilizes mathematical models and optimization algorithms to: automatically calculate the ceramic layer thickness and fiber backing plate thickness that meet protection requirements, given any bullet velocity, bullet type, and material parameters; and minimize the areal density of the composite ballistic protection structure while satisfying performance constraints. This method is both versatile and flexible, applicable to design scenarios with different bullet types and material combinations, saving time and cost in the ballistic protection structure design process.

[0104] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0105] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for calculating the thickness of a composite ballistic structure consisting of a ceramic layer and a fiber backing plate, characterized in that, Including the following steps: Based on the law of conservation of energy and the kinetic energy theorem, the limiting velocity of the ceramic / fiber composite target is determined; Based on the condition of minimizing the surface density of the structure, an objective function is constructed; Based on the objective function and the limiting velocity, the thickness calculation equations for the fiber base plate and ceramic plate in the composite target are constructed. Determine the bullet parameters and the mechanical parameters of the ceramic / fiber composite target material, solve the thickness calculation equation, and obtain the thickness of the fiber base plate and ceramic plate in the composite target; The limiting velocity of the ceramic / fiber composite target is determined as follows: ； ； Among them, v 50 v0 represents the maximum velocity of impact when the probability of a bullet penetrating the target is 50%, v1 represents the maximum velocity of impact when the probability of a bullet penetrating the target is 0%, and k1 represents the velocity of impact when the probability of impact is 0%. 50 The conversion coefficient between v0 and d2, k1 is less than 1, d2 is the thickness of the fiber substrate, ε2 is the fracture strain of the substrate, σ2 is the ultimate tensile strength of the substrate, and m is the tensile strength of the substrate. p For the mass of the projectile core, and As an intermediate variable; The intermediate variable and for: ； ； In the formula, ρ1 is the radius of the core, ρ2 is the density of the ceramic plate, and d1 is the thickness of the ceramic plate. The objective function is: ； The values ​​of d1 and d2 are to be found when f(d1, d2) reaches its minimum value; The thickness calculation equations for the fiber substrate and ceramic plate in the composite target are constructed, specifically including: Based on the limiting velocity equation, Equations, constructing constraint equations; Construct the Lagrangian function based on the objective function and constraint equations; By taking the partial derivative of the Lagrange function and rearranging it, the thickness calculation equation is obtained.

2. The method for calculating the thickness of a composite ballistic structure of ceramic layer and fiber backing plate according to claim 1, characterized in that, The constraint equations are constructed as follows: ； Where: parameters , , .

3. The method for calculating the thickness of a composite ballistic structure of ceramic layer and fiber backing plate according to claim 2, characterized in that, The Lagrange function is: ； in, It is a Lagrange multiplier.

4. The method for calculating the thickness of a composite ballistic structure of ceramic layer and fiber backing plate according to claim 3, characterized in that, The thickness calculation equation is as follows: ； 。 5. The method for calculating the thickness of a composite ballistic structure of ceramic layer and fiber backing plate according to claim 4, characterized in that, The thickness calculation equation is solved using the fsolve method to obtain d1 and d2.

6. A computer storage medium, characterized in that, The computer storage medium stores an executable program, which is executed by a processor to implement the steps of the thickness calculation method according to any one of claims 1-5.

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