A method for calculating rebound velocity of projectile penetrating ultra-high performance concrete

Abstract

The application relates to a method for calculating the rebound velocity of a projectile penetrating super high performance concrete, which comprises the following steps: obtaining the sectional area, length, mass, elastic modulus, density and parameters related to the shape of a bullet head and the friction coefficient of the projectile in the step of obtaining the parameters of the projectile; obtaining the yield strength and material coefficient of the target in the step of obtaining the parameters of the target; and finally, in the step of calculating the rebound velocity, the parameters of the projectile and the target are brought into a rebound effect model to calculate the rebound velocity of the projectile. The rebound velocity of the projectile penetrating the super high performance concrete can be accurately predicted, and the prediction result can provide a reference for the research and design of a bullet shielding structure, especially a super high performance concrete bullet shielding structure.

Description

Technical Field

[0001] This invention belongs to the field of impact dynamics technology or projectile penetration technology, specifically relating to a method for calculating the rebound velocity of a projectile penetrating ultra-high performance concrete. Background Technology

[0002] The rebound effect of projectiles is of great significance in engineering protection, weapon damage, and warhead design. Ultra-high performance concrete (UHVPC) possesses extremely high strength, good toughness, and superior durability. Projectile shielding structures built with UHVPC can significantly reduce the penetration depth of bunker-buster weapons and effectively resist the destructive effects of warhead explosions. Modern precision-guided bunker-buster weapons, such as the US GBU and JADM series missiles, have long, rod-shaped bodies and pointed, oval warheads. Preliminary research has found that long, rod-shaped, oval-headed penetrators, after penetrating UHVPC, especially at shallow penetration depths and before the tail of the projectile fully enters the target, are prone to rebound. This means that after penetration, the projectile generates a velocity opposite to the direction of penetration, ejecting it from the target. Compared to the penetration velocity, the rebound velocity is small but not negligible, as it can potentially cause the penetrator to bounce off the target crater. From an engineering protection perspective, the rebound effect during projectile penetration should be enhanced. This would allow the bunker-buster to rebound to a shallower depth or explode outside the shielding structure, even if the warhead's delayed fuse is not triggered, thus minimizing the destructive effect of the warhead explosion. From a weapon damage perspective, the rebound effect should be minimized to ensure the warhead explodes at a greater penetration depth, maximizing the destructive effect of the bunker-buster weapon. Therefore, both the projectile design and the shielding structure must consider the rebound effect after penetration. However, current technology lacks methods to predict the rebound effect after a projectile penetrates a target. Summary of the Invention

[0003] To address the above technical problems, this application proposes a method for calculating the rebound velocity of a projectile penetrating ultra-high performance concrete, comprising the following steps:

[0004] The steps for obtaining projectile parameters include: projectile cross-sectional area s, projectile length L, projectile mass M, elastic modulus E, projectile density ρ, and parameters N1 related to the projectile shape and friction coefficient. The steps for obtaining target parameters include: target yield strength σ. y The target parameters and the material coefficient A of the target;

[0005] The step of calculating the rebound velocity involves inputting both the projectile parameters and the target parameters into the rebound effect model to calculate the projectile's rebound velocity V. r The rebound effect model has the form of Equation 1:

[0006]

[0007] Among them, V r The projectile's rebound velocity is represented by E, the elastic modulus of the projectile is represented by ρ, and the density of the projectile is represented by σ. y The target's yield strength is represented by A, which is a dimensionless parameter. N1 represents a parameter related to the projectile shape and friction coefficient, which is also a dimensionless parameter. λ is a constant.

[0008] The technical solution proposed in this invention can accurately predict the rebound velocity of projectile penetration, providing valuable prediction results for the research and design of projectile shielding structures, especially ultra-high performance concrete projectile shielding structures. Attached Figure Description

[0009] Figure 1 A flowchart of one implementation method;

[0010] Figure 2 : Schematic diagram of the model in Example 1;

[0011] Figure 3 : Schematic diagram of the model in Example 2;

[0012] Figure 4 : Schematic diagram of penetration resistance time history curve, quasi-static resistance Fs (considering only the material dynamic strength term), and equivalent constant resistance Fc;

[0013] Figure 5 Model of the target;

[0014] Figure 6 Model of the projectile;

[0015] Figure 7 Numerical calculation results of the projectile velocity and acceleration time history curves under a certain initial velocity;

[0016] Figure 8 Projectile acceleration time history curve;

[0017] Figure 9-14 Stress contour map along the velocity direction during projectile penetration;

[0018] Figure 15 The axial stress time history is output during the numerical calculation process;

[0019] Figure 16 : Predicted values ​​and numerical simulation results of the axial stress time history curve of the measuring point unit;

[0020] Figure 17 Velocity-time history curves of a projectile under six different initial penetration velocities;

[0021] Figure 18 Velocity-time history curves of a projectile under six different initial penetration velocities. Detailed Implementation

[0022] First, a detailed explanation of the relevant technologies in this field is required.

[0023] Existing research shows that the projectile penetration velocity has a significant impact on the target damage effect. When the projectile penetrates at a low velocity, the target only produces small elastic deformation; when the impact velocity increases to a certain limit V... EA When the contact stress between the projectile and the target reaches the target's yield strength σ, yt The target will undergo plastic deformation. The elastic limit velocity V at the moment of plastic deformation can be determined using the impact compression relationship between the projectile and target materials. EA .

[0024]

[0025] Where ρ p and ρ t C represents the density of the projectile and the target, respectively. ep and C et The elastic wave velocities of the projectile material and the target material are σ and σ, respectively. yt The target material's yield strength. As the penetration velocity further increases, the plastic deformation rate limit V is reached. pA At this point, the target body begins to undergo plastic flow deformation, entering the plastic pore expansion stage. The plastic deformation rate limit V... pA The expression is as follows.

[0026]

[0027] Where, σ n F represents the axial compressive stress of the projectile, where x represents the coordinate system established with the penetration direction of the projectile as the positive direction and the free end of the projectile as the origin. n ρ is the inertial force opposite to the acceleration direction during the projectile's penetration process, s is the cross-sectional area of ​​the projectile, and ρ is the inertial force. t Let be the density of the projectile, and 'a' be the acceleration during the projectile's penetration.

[0028] When the penetration rate increases further, reaching the level of the material's compressive bulk modulus K... t The relevant propagation speed V HA At this point, the compressibility of the target body relatively decreases, and the deformation velocity exceeds the propagation velocity of compression waves in a solid, causing shock waves to begin to form within the target body. The velocity limit V for plastic flow deformation. HA The expression is as follows.

[0029]

[0030] Among them, K t V is the compressive bulk modulus of the material. HA ρ is the velocity limit for plastic flow deformation. t The density is the projectile density.

[0031] When a projectile penetrates a semi-infinite concrete medium, the stress state changes with the penetration velocity and penetration depth. The projectile penetration process can be divided into three stages:

[0032] Pit penetration phase: The projectile travels at an initial velocity V i Penetrating concrete medium, V i >V pA The target undergoes plastic flow deformation, and the warhead begins to create a plastic pore in the target. The penetration resistance increases with the increase of the pore depth in the warhead.

[0033] Tunnel Penetration Stage: After the initial cratering stage, the projectile continues to penetrate the target, forming a penetration tunnel with a diameter not less than the projectile's diameter. The projectile's velocity continuously decreases under the influence of the penetration resistance Fs, and the penetration resistance also decreases as the penetration velocity decreases. During the tunnel penetration stage, the penetration velocity is always greater than the velocity limit V for plastic deformation. pA (V i >V pA ), continuous plastic enlargement and penetration occur at the contact point between the projectile and the target;

[0034] Elastic deformation stage: The penetration velocity decreases to the elastic deformation velocity limit V of the target under the action of resistance. EA When the projectile's plastic penetration of the target stops, the target begins to undergo recoverable elastic deformation. When the penetration velocity drops to 0, the elastic deformation of the target reaches its maximum.

[0035] After the projectile penetration process is completed, the subsequent rebound process can be divided into two stages based on the changes in the force state.

[0036] The rebound acceleration phase: During penetration, both the projectile and the target undergo deformation. Therefore, at the moment penetration ends, the accumulated dynamic energy begins to be released. The energy release at the interface between the projectile and the bottom of the penetration crater is the primary cause of the projectile's rebound. The rebound force generated by both the projectile and the target at this point gives the projectile a certain reverse acceleration, under which its reverse velocity gradually increases. The rebound acceleration phase ends the instant the projectile detaches from the bottom of the penetration crater, at which point the rebound velocity reaches its maximum. From the above analysis, it can be seen that the direct cause of the projectile's rebound is the work done on the projectile by the rebound force at the projectile-target interface. The magnitude of the interface rebound force is determined by the accumulated dynamic energy of both the projectile and the target, and is related to factors such as the material properties and deformation state of both.

[0037] Rebound deceleration phase: After the projectile completely leaves the bottom of the penetration pit, it moves in the opposite direction along the penetration tunnel. During this process, it will be subjected to wall friction and other resistance f, and the speed of the reverse movement will continuously decrease until it becomes 0 or it will be ejected from the penetration pit.

[0038] The prior art presents a dynamic spherical cavity expansion model for strain-hardening elasto-plastic materials, which provides a dimensionless expression for radial stress in the incompressible case:

[0039]

[0040] Based on the dynamic spherical cavity expansion theory, existing technologies provide an expression for the penetration resistance during the penetration process of a rigid elastic beam.

[0041]

[0042] Where d is the diameter of the projectile, σ y Let ρ be the target material yield strength, ρ be the target material density, A and B be dimensionless parameters of the target material. If the target material is concrete, B is 1. V is the instantaneous velocity of the projectile during penetration. From the above formula, it can be seen that the penetration resistance consists of two parts. The first term is the quasi-static resistance part of the material (the material dynamic strength term), and the second term is the dynamic resistance part (the inertia term).

[0043] Material dynamic strength term Aσ y N1 primarily depends on the shear strength of the concrete material. N1 and N2 are dimensionless coefficients related to the projectile's head shape and friction coefficient. When surface friction of the target is neglected (μm = 0), N1 = 1, N2 = N*; where N1, N2, and N* are calculated using the following formula:

[0044]

[0045]

[0046] Where d is the diameter of the projectile, and A is the dimensionless parameter of the target material.

[0047] The dimensionless parameter B mainly depends on the compressibility of the target. For concrete targets, the value of B changes very little with strength, and is generally taken as B = 1.0.

[0048] Based on common knowledge in the field and the disclosed technology, projectile rebound is mainly caused by the combined release of the deformation energy of the projectile and the target. For target materials with good toughness, such as metals, the strain potential accumulated in the target during the plastic expansion penetration of the projectile cannot be ignored. However, for brittle materials such as ultra-high performance concrete, the target breaks into particles at the penetration interface, providing less strain energy for the projectile rebound. Therefore, the models of the above-mentioned existing technologies are not applicable.

[0049] This invention primarily addresses the prediction of projectile rebound velocity when the target material is ultra-high performance concrete (UHVPC). UHVPC typically achieves an extremely low cement ratio by incorporating highly efficient water-reducing agents, increases density by adding active minerals, and is cured at high temperatures. The uniaxial compressive strength of the cured UHVPC generally exceeds 120 MPa.

[0050] Some embodiments of the present invention include, for example: Figure 1 The steps in:

[0051] The steps to obtain projectile parameters include obtaining the projectile cross-sectional area s, projectile length L, projectile mass M, elastic modulus E, projectile density ρ, and parameters N1 related to the projectile shape and friction coefficient;

[0052] The steps for obtaining target parameters include obtaining the target's yield strength σ. y The target parameters and the material coefficient A of the target;

[0053] The step of calculating the rebound velocity involves inputting both the projectile parameters and the target parameters into the rebound effect model to calculate the projectile's rebound velocity Vr. The rebound effect model has the form of Equation 1:

[0054]

[0055] Where Vr represents the projectile's rebound velocity, E represents the projectile's elastic modulus, ρ represents the projectile's density, and σ y The target's yield strength is represented by A, which is a dimensionless parameter. N1 represents a parameter related to the projectile shape and friction coefficient, which is also a dimensionless parameter. λ is a constant.

[0056] In some implementations, λ takes the value from 1 to... Preferably, it is 1 or

[0057] The technical solution of the present invention will be further explained through specific examples.

[0058] Example 1

[0059] Values ​​of λ The rebound effect model at this point is constrained by the following conditions. A schematic diagram of the model is shown below. Figure 2 As shown.

[0060] 1. The target is a semi-infinite target; that is, during the penetration of the projectile, there is no influence from the back and side boundaries of the target.

[0061] 2. All the elastic potential energy accumulated by the projectile during penetration is converted into the projectile's rebound kinetic energy;

[0062] 3. Axial compressive stress distribution σ of the projectile bodyn (x) conforms to the axial compressive stress distribution equation of a one-dimensional elastic rod with constant penetration resistance at the head, as expressed in Equation 2:

[0063]

[0064] Where, σ n F represents the axial compressive stress of the projectile, where x represents the coordinate system established with the penetration direction of the projectile as the positive direction and the free end of the projectile as the origin. n ρ is the inertial force opposite to the direction of acceleration during the projectile penetration process, s is the cross-sectional area of ​​the projectile, ρ is the density of the projectile, and a is the acceleration during the projectile penetration process.

[0065] Among them, the rebound velocity V of the projectile r The relationship between the projectile's cross-sectional area s, length L, mass M, elastic modulus E, and density ρ is expressed by Equation 3, which converts all elastic potential energy into projectile rebound kinetic energy.

[0066]

[0067] Among them, V r The penetration resistance during the projectile's penetration process is M, the mass of the single unit is s, the cross-sectional area of ​​the projectile is E, the elastic modulus is ρ, the density of the projectile is a, the acceleration during the projectile's penetration process is a, and the length of the projectile is L.

[0068] Wherein, the acceleration a satisfies the constraint of Equation 4:

[0069]

[0070] Among them, the acceleration F during the penetration process of projectile a. c M represents the penetration resistance during the projectile's penetration process, and M represents the mass of the projectile.

[0071] Among them, the penetration resistance F during the projectile penetration process c The constant resistance form represented by Equation 5 is satisfied:

[0072]

[0073] Among them, F c σ represents the penetration resistance during projectile penetration; A is the material coefficient of the target; σ y d represents the yield strength of the target, N1 is a parameter related to the shape of the projectile and the coefficient of friction, and d is the diameter of the projectile.

[0074] The projectile's rebound velocity in this implementation depends primarily on two factors: the dynamic strength of the target material (characterizing the target's resistance to penetration) and the projectile's density and stiffness. The greater the target's yield strength and the lower the projectile's density and elastic modulus, the more pronounced the rebound effect.

[0075] Example 2

[0076] When λ is 1, the rebound effect model is constrained by the following conditions. A schematic diagram of the model is shown below. Figure 3 As shown.

[0077] 1. The projectile is a one-dimensional elastic rod;

[0078] 2. During the penetration process, the elastic wave C propagates as constrained by Equation 6-7:

[0079]

[0080] Where C represents the elastic wave, with right-traveling waves being positive and left-traveling waves being negative; X represents the coordinate system established with the penetration direction of the projectile as the positive direction and the free end of the projectile as the origin; t is the time variable.

[0081]

[0082] Where C represents the elastic wave, with left-traveling waves being positive and right-traveling waves being negative; ρ represents the target material density; σ represents the stress on the projectile; and v represents the projectile velocity.

[0083] 3. The penetration stress σc at the penetration end during the projectile penetration process is constrained by the following formula:

[0084]

[0085] Where, σ c σ1 represents the penetration stress at the penetration point, σ2 represents the material's dynamic strength term, and σ2 represents the inertial term.

[0086] The dynamic strength term σ1 of the material is calculated using the following formula:

[0087]

[0088] Where σ1 is the dynamic strength term of the material, σ y Let A be the target yield strength, A be the dimensionless parameter of the target material, and N1 be a parameter related to the shape of the projectile and the coefficient of friction.

[0089] The relationship between A and B and the penetration resistance F is shown in Equation 9:

[0090]

[0091] Where F is the penetration resistance, d is the projectile diameter, and σ yρ is the target material yield strength, ρ is the target material density, A and B are dimensionless parameters of the target material, V is the instantaneous velocity of the projectile during penetration, and B is 1 if the target is concrete material; N1 and N2 are dimensionless coefficients related to the shape of the projectile head and the coefficient of friction. When the friction of the projectile-target surface is ignored, N1 = 1.

[0092] The penetration resistance time history curve, the quasi-static resistance Fs (considering only the material dynamic strength term), and the equivalent constant resistance Fc are illustrated in the following diagram. Figure 4 .

[0093] The projectile's rebound velocity in this implementation depends on two factors: the dynamic strength of the target material (characterizing the target's resistance to penetration) and the projectile's density and stiffness. The greater the target's yield strength and the lower the projectile's density and elastic modulus, the more pronounced the projectile's rebound effect.

[0094] The technical effects of the present invention will be specifically illustrated below using numerical simulation as a test example.

[0095] Test Example 1

[0096] In this test, numerical simulations were conducted to investigate the rebound phenomenon of projectiles penetrating ultra-high performance concrete. The specific methods are as follows:

[0097] Finite element models of projectile penetration into ultra-high performance concrete are used, including, for example... Figure 5 The target and such Figure 6 The projectile body is designed using a 1 / 4 symmetric model to save computational costs. The projectile diameter is 40mm, the length is 260mm, and the radius-to-hedge (CRH) ratio of the projectile section is 3. The projectile penetration velocities are set to 300, 400, 500, 600, 700, and 800 m / s. The ultra-high performance concrete dimensions are 1000mm × 1000mm × 500mm. The projectile mesh size is 4mm, and the mesh size for the main contact area between the target and the projectile is also 4mm. The remaining areas use a gradient mesh with mesh sizes ranging from 4 to 12mm.

[0098] Theoretically, elastic materials are used to simulate projectiles, with elastic moduli set to 210 GPa and 105 GPa, and densities set to 7850 kg / m³. 3 and 3925kg / m 3 Specific parameters are shown in Table 1. The K&C model and Tabulated_Compaction equation of state were used to simulate ultra-high performance concrete, with a compressive strength of 150 MPa and ultimate tensile and shear strains at failure set to 0.2. Specific parameters are shown in Table 2. Normal displacement constraints were applied to the bottom of the target.

[0099] Table 1. Parameters of the Elastic Material Model for the Projectile

[0100]

[0101] Table 2 K&C Model Parameters for Ultra-High Performance Concrete

[0102]

[0103] Due to the large number of numerical calculation conditions, the calculation models are numbered for ease of analysis and comparison. For example, 7850-210-500 indicates that the projectile density, elastic modulus, and penetration velocity are 7850 kg / m3, 210 GPa, and 500 m / s, respectively; 3925-105-700 indicates that the projectile density, elastic modulus, and penetration velocity are 3925 kg / m3, 105 GPa, and 700 m / s, respectively, and so on.

[0104] Table 3 presents the numerical calculation results of the rebound velocity and the predicted values ​​obtained using the prediction method of this invention. When the penetration velocity is less than 500 m / s, the numerical calculation results are lower than the predicted values; when the penetration velocity is higher than 500 m / s, the numerical calculation results are closer to the predicted values. The reason for this is that when the impact velocity is low, the penetration process is mainly in the cratering stage, and the penetration resistance changes drastically, failing to form a stable penetration stress boundary, which differs significantly from the constant resistance assumption in the rebound effect model. When the penetration velocity is high, the projectile begins to enter the tunneling penetration stage, and the penetration resistance is relatively stable, matching the constant resistance assumption well and satisfying the resistance assumption in the rebound effect model.

[0105] Table 3 Numerical calculation results and predicted values ​​of rebound speed

[0106]

[0107] Figure 7 Numerical calculation results of the velocity and acceleration time history curves of the 3925-105-700 projectile are given. It can be seen from the velocity time history curves that after the penetration velocity decreases to 0, the projectile will have a continuous rebound acceleration and deceleration process, and finally the rebound velocity remains constant.

[0108] Figure 8 The numerical simulation and the projectile acceleration time history curves obtained by the prediction method of this invention are presented. The projectile acceleration rapidly jumps to its peak value after penetration begins, reaching 1.8 × 10⁶ m / s² at 0.1 ms, and then begins to oscillate downwards, dropping to near zero at 0.6 ms. The acceleration time history curve obtained from the numerical simulation generally exhibits a sudden pulse form, while the equivalent acceleration ac obtained by the prediction method of this invention is a single-step pulse. Although there is a certain error in the peak values ​​of the two curves, their impulses are approximately equal. Figure 4 The given curves are basically consistent, which proves that the assumptions of the elastic potential energy model are quite reasonable.

[0109] Figure 9-14The stress cloud diagram along the velocity direction during projectile penetration is presented, which shows the change of axial stress distribution with time and the stress wave propagation process during projectile penetration. Figure 9 This indicates that before penetration begins, the projectile is in a state of zero stress; once penetration begins, the penetration resistance at the projectile's head causes a compression wave to propagate axially from the projectile's interior towards the tail, as shown below. Figure 10 As shown; when the compression wave propagates to the free surface of the projectile's tail, the projectile's tail reflects a tensile wave, and the stress amplitude behind the wave decreases, as shown. Figure 11 As shown; during the continuous penetration of the projectile into the target, the stress waves inside the projectile are constantly reflected and propagated at the penetration end of the projectile's head and the free end of its tail, such as Figure 12 As shown; when the projectile's velocity drops to 0 and it begins to rebound, the tensile wave from the final reflection at the projectile's tail causes the axial stress within the entire projectile to be released, reducing the internal stress to 0, as... Figure 13 As shown; Figure 14 The state where the internal stress of the projectile is zero during the rebound process is given. The stress wave propagation process of the projectile obtained by numerical simulation is basically consistent with the stress wave propagation process obtained by the rebound effect model in Example 1.

[0110] Figure 15 The locations of the measuring points on the projectile body are given, and their axial stress time histories are output during the numerical calculation. According to the rebound effect model in Example 1, the stress wave propagates back and forth between the penetrating stress boundary and the tail free boundary. Theoretically, the stress time histories of the measuring points exhibit periodic pulses, and the pulse amplitude should be equal to the stress amplitude σc at the penetrating boundary. The magnitude of the amplitude can be determined by Equation 8. The elastic wave propagation period is from the middle of the projectile to the boundary and then reflects back to the middle of the projectile, with a propagation distance equal to the projectile length L. Therefore, the pulse period t... d =L / C.

[0111] Figure 16 The predicted values ​​and numerical simulation results of the axial stress time history curves of the measuring point element are presented. The predicted values ​​exhibit a regular periodic oscillation pattern with the same amplitude. Although the internal environment of the finite element model of the projectile is not an ideal one-dimensional elastic wave environment, the stress time history curves obtained by numerical simulation also have a similar periodic variation pattern. The period length and stress amplitude are basically consistent with the periodic pulses given by the theoretical solution, indicating that the one-dimensional elastic wave model also has good rationality.

[0112] Figure 17 and Figure 18The velocity-time history curves of two projectiles, 7850-210 and 3925-105, are presented under six different initial penetration velocities. The two figures show that the 7850-210 projectile decelerates to zero and rebounds within 0.7–1.2 ms, depending on the initial penetration velocity, while the 3925-105 projectile decelerates to zero and rebounds within 0.4–0.6 ms, depending on the initial penetration velocity. Overall, projectiles with lighter mass and lower elastic modulus exhibit shorter penetration duration and weaker penetration capability.

[0113] The magnified view within the red solid box in the figure provides a clearer view of the rebound velocity curve after the penetration velocity drops to zero. After penetration, the projectile undergoes a rebound acceleration phase before gradually approaching a constant rebound velocity. Overall, projectiles with lighter mass and lower elastic modulus exhibit a more pronounced rebound effect. The comparison with numerical calculation results shows that the method of this invention yields good results for both types of projectiles.

[0114] The embodiments and functional operations of the subject matter described in this specification can be implemented in the following ways: digital electronic circuits, tangibly implemented computer software or firmware, computer hardware, including the structures disclosed in this specification and their equivalents, or combinations thereof. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, that is, one or more modules of computer program instructions encoded on one or more tangible non-transitory program carriers, for execution by a data processing device or to control the operation of the data processing device.

[0115] The term "processor" encompasses all kinds of devices, apparatuses, and machines used for processing data, including, for example, programmable processors, computers, or multiprocessor systems or multiple computers. Devices may include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits). In addition to hardware, devices may include code that creates the execution environment for associated computer programs, such as processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0116] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather as descriptions of features that can embody specific embodiments of a particular invention. Specific features described in this specification within the context of an independent embodiment may also be implemented in combination with a single embodiment. Conversely, various features described within the context of a single embodiment may also be implemented independently in multiple embodiments, or in any suitable sub-combination. Furthermore, while features may be described for combination and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and the claimed combination may be redirected to a sub-combination or a variation thereof.

Claims

1. A method for calculating the rebound velocity of a projectile penetrating ultra-high performance concrete, characterized in that, Includes the following steps: The steps to obtain projectile parameters include obtaining the projectile cross-sectional area s, projectile length L, projectile mass M, elastic modulus E, projectile density ρ, and parameters N1 related to the projectile shape and friction coefficient; The steps for obtaining target parameters include obtaining the target's yield strength σ. y The target parameters and the material coefficient A of the target; The step of calculating the rebound velocity involves inputting both the projectile parameters and the target parameters into the rebound effect model to calculate the projectile's rebound velocity V. r The rebound effect model has the form of Equation 1: Formula 1 Among them, V r The projectile's rebound velocity is represented by E, the elastic modulus of the projectile is represented by ρ, and the density of the projectile is represented by σ. y The yield strength of the target is represented by A, which is a dimensionless parameter. N1 represents a parameter related to the shape of the projectile and the coefficient of friction, which is a dimensionless parameter. λ is a constant. When λ is a value When the constant is , the rebound effect model is constrained by the following conditions: The target is a semi-infinite target; The elastic potential energy accumulated by the projectile during the penetration process is entirely converted into the projectile's rebound kinetic energy; axial compressive stress distribution σ of the projectile n (x) conforms to the axial compressive stress distribution equation of a one-dimensional elastic rod with constant penetration resistance at the head, as expressed in Equation 2: Formula 2 Where, σ n F represents the axial compressive stress of the projectile, where x represents the coordinate system established with the penetration direction of the projectile as the positive direction and the free end of the projectile as the origin. n ρ is the inertial force opposite to the direction of acceleration during the projectile penetration process, s is the cross-sectional area of ​​the projectile, ρ is the density of the projectile, and a is the acceleration during the projectile penetration process. When λ is a constant taking the value 1, the rebound effect model is constrained by the following conditions: The projectile is a one-dimensional elastic rod; The elastic wave C propagating during the penetration process of the projectile is constrained by Equation 6-7: Formula 6 Where C represents the elastic wave, with right-traveling waves being positive and left-traveling waves being negative; X represents the coordinate system established with the penetration direction of the projectile as the positive direction and the free end of the projectile as the origin; t is the time variable. Formula 7 Where C represents the elastic wave, with left-traveling waves being positive and right-traveling waves being negative; ρ represents the target material density; σ represents the stress on the projectile; and v represents the projectile velocity.

2. The method as described in claim 1, characterized in that, The rebound velocity V of the projectile r The relationship between the projectile's cross-sectional area s, length L, mass M, elastic modulus E, and density ρ is expressed by Equation 3, which converts all elastic potential energy into projectile rebound kinetic energy. Formula 3 Among them, V r The penetration resistance during the projectile's penetration process is M, the projectile's mass is s, the projectile's cross-sectional area is E, the elastic modulus is ρ, the projectile's density is a, the projectile's acceleration during penetration is a, and the projectile's length is L.

3. The method as described in claim 2, characterized in that, The acceleration 'a' during the projectile penetration process satisfies the constraint of Equation 4: Formula 4 Among them, the acceleration F during the penetration process of projectile a. c The penetration resistance during the projectile's penetration process is M, and the projectile's mass is M.

4. The method as described in claim 3, characterized in that, The penetration resistance F during the projectile's penetration process c The constant resistance form represented by Equation 5 is satisfied: Formula 5 Among them, F c σ represents the penetration resistance during projectile penetration; A is the material coefficient of the target; σ y d represents the yield strength of the target, N1 is a parameter related to the shape of the projectile and the coefficient of friction, and d is the diameter of the projectile.

5. The method as described in claim 4, characterized in that, The penetration stress σ experienced by the penetrating end of the projectile during the penetration process c Constrained by the following formula: Formula 8 Where, σ c σ1 represents the penetration stress at the penetration point, σ2 represents the material's dynamic strength term, and σ2 represents the inertial term. The dynamic strength term σ1 of the material is calculated using the following formula: Formula 9 Where σ1 is the dynamic strength term of the material, σ y Let A be the target yield strength, A be the dimensionless parameter of the target material, and N1 be a parameter related to the shape of the projectile and the coefficient of friction.

6. The method as described in claim 5, characterized in that, The relationship between A and B and the penetration resistance F is shown in Equation 9: Formula 9 Where F is the penetration resistance, d is the projectile diameter, and σ y ρ is the target material yield strength, ρ is the target material density, A and B are dimensionless parameters of the target material, V is the instantaneous velocity of the projectile during penetration, and B is 1 if the target is concrete material; N1 and N2 are dimensionless coefficients related to the shape of the projectile head and the coefficient of friction, and N1=1 when the friction of the projectile-target surface is ignored.

7. The method according to any one of claims 1-6, characterized in that, The target is ultra-high strength concrete, and the inertial term σ2 in the rebound effect model is 0.

8. A projectile penetration and rebound velocity prediction system, characterized in that, The system includes a processor and a memory, the memory storing a program that, when executed by the processor, implements all the steps of the method as described in any one of claims 1-6.

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