Method for predicting the penetration depth of shaped charge

Abstract

This invention provides a method for predicting the penetration depth of shaped charge projectiles, comprising the following steps: dividing the projectile-target interaction into different penetration stages by sequentially simplifying the projectile model, analyzing the relative properties of the projectile-target materials, and analyzing the penetration mode and conversion velocity; determining the critical conversion velocity judgment criteria for each penetration stage; predicting the penetration depth of each stage according to the different penetration stages, combining the parameters obtained from the simplified projectile model formula and the relative property analysis of the projectile-target materials; conducting shaped charge penetration tests on the target, verifying the accuracy of the predicted penetration depth for each stage, and correcting the penetration mode, projectile-target strength factor, and correlation coefficient for each stage; and establishing a complete shaped charge penetration depth prediction model. This invention's method for predicting the penetration depth of shaped charge projectiles can systematically describe the entire process of projectile-target interaction and quickly and accurately predict the penetration depth of shaped charge projectiles.

Description

Technical Field

[0001] This invention relates to the field of engineering technology, and specifically to a method for predicting the penetration depth of shaped charge. Background Technology

[0002] Typical shaped charge projectiles can be classified into three types according to their shaped penetrators: shaped charge jets (JET), rod-shaped charge jets (JPC), and explosively formed projectiles (EFP). A significant common characteristic of all three is their high impact velocity. Generally, the head velocity of a traditional shaped charge jet can reach 8000–10000 m / s, a rod-shaped charge jet head velocity can reach 3000–6000 m / s, and an EFP velocity can reach 1500–3000 m / s. In the initial stage of the projectile-target interaction, the process of the shaped charge penetrator acting on the target can be approximated as a fluid penetration process, neglecting the strength effect of the target. Based on this, Brikhoff et al. established a hydrodynamic theoretical model for the high-speed penetration of a shaped charge jet into a metal target, in which both the metal jet and the metal target are considered ideal, incompressible fluids. However, as the penetration depth of the projectile increases, the projectile velocity continuously decreases, and the degree of deformation and erosion of the projectile during the penetration process becomes smaller and smaller. At this stage, the interaction mode between the projectile and the target will also change, and the relative strength between the projectile and the target can no longer be ignored.

[0003] Currently, the description of the penetration characteristics of shaped charge projectiles mainly draws on research findings on long-rod erosion penetration. Typical research results include: ① The Christman and Gehring semi-empirical penetration model; based on projectile-target penetration test observations and theoretical analysis, this model divides the high-speed penetration process of the projectile into four typical stages (initial transient stage, main penetration stage, secondary penetration stage, and target rebound stage). It studies and provides semi-empirical prediction formulas for the penetration depth of the projectile, including both the main and secondary penetration stages. However, the analytical description of the initial transient stage is complex and lacks accurate analysis of its impact on the total penetration depth; the target rebound stage contributes very little to the total penetration and is usually not considered. ② The Allen-Rogers theoretical model; based on fluid dynamics theory, Allen and Rogers added a strength term σ related to target drag to the Bernoulli equation, providing a theoretical prediction formula for the high-speed penetration depth of the projectile. This theoretical model has been verified through high-speed penetration tests of projectiles with various metallic materials, and the test results show a high degree of agreement with the model predictions. ③ Alekseevskii-Tate theoretical model. The Alekseevskii-Tate theoretical model is the most classic theoretical model for high-speed penetration of long-rod projectiles into targets. This model considers the projectile material strength (Yp) and target drag (Yt), and provides a set of nonlinear equations for predicting the projectile penetration depth. Numerical solutions are required to obtain relatively accurate analytical solutions. The values ​​of the projectile-target related terms Yp and Yt are key and challenging aspects of the Alekseevskii-Tate model's predictive accuracy during the solution process. The Alekseevskii-Tate theoretical model is applicable to various target materials, including typical / non-ideal long-rod projectiles penetrating semi-infinite / finite-thickness metal targets and ceramic targets.

[0004] Based on this, foreign scholars have proposed empirical or semi-empirical formulas for predicting the penetration capability of shaped charge (EFP). Typical models include: ① Liu Fei, using live-fire penetration tests and numerical simulations, focused on the calculation of EFP penetration against a semi-infinite thickness concrete target. He simplified the penetration process into a steady penetration stage and a rigid body penetration stage, and provided a criterion for the conversion between the two penetration modes. He derived the penetration depth calculation formula for each stage using the modified Bernoulli equation and proposed an engineering calculation method for EFP penetration depth; ② Xiao Qiangqiang applied the propagation of stress waves in solids... Based on the shaped charge jet penetration theory, combined with the AT equation and the Szendrei / Held equation, the axial penetration equation and radial aperture growth equation of the shaped charge jet against soil and concrete targets during supersonic penetration were derived, and a supersonic penetration model of the shaped charge jet against soil and concrete targets was established; ③ Hartmann et al. proposed an EFP high-speed penetration theoretical model for steel targets based on the Walker-Anderson high-speed penetration model, which considers the effect of the hollow structure of the projectile. The EFP penetration model prediction for solidity less than 80% is in very good agreement with numerical simulation and experimental results.

[0005] However, the aforementioned prediction methods largely draw on research findings on long-rod erosion penetration, focusing primarily on the main penetration stages of a type of shaped charge stable-formed projectile against a target of a specific characteristic. The models are relatively simplified and lack the ability to accurately describe the entire process of projectile-target interaction, resulting in significant discrepancies with macroscopic test results. Furthermore, considering that the projectile, after detonation of the shaped charge warhead, develops an irregularly shaped profile driven by the explosive detonation, it cannot be approximated as a symmetrical structure of revolution. It is necessary to consider the actual structural characteristics of the projectile (the discontinuity of the shaped charge jet, the hollow structure of the EFP, etc.) or to perform structural equivalence treatment on the projectile. Summary of the Invention

[0006] To address the problems of existing methods for predicting the penetration capability of shaped charge projectiles being relatively simplified, lacking the ability to accurately describe the entire process of projectile-target interaction, and having significant discrepancies with macroscopic test results of projectile-target interactions, this invention proposes a method for predicting the penetration depth of shaped charge projectiles.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the penetration depth of a shaped charge, comprising the following steps:

[0008] S1. By successively simplifying the projectile model, analyzing the relative properties of the projectile and target materials, and analyzing the penetration mode and conversion speed, the action of the projectile and target is divided into different penetration stages, and the critical conversion speed judgment criteria for each penetration stage are determined.

[0009] S2. Based on the parameters obtained from the simplified formula of the projectile model and the relative property analysis of the projectile and target materials, the penetration depth of each stage is estimated in turn according to the different penetration stages.

[0010] S3. Conduct penetration tests of shaped charge targets and verify the accuracy of the penetration depth estimates obtained in step S2 for each stage. Correct the penetration mode, target strength factor and correlation coefficient for each stage.

[0011] S4. Establish a complete model for predicting the depth of shaped charge.

[0012] Furthermore, in step S1, the projectile model is simplified to a solid cylindrical structure with a hemispherical head during shaped charge penetration. The effective diameter R of the projectile is calculated using the following formula:

[0013]

[0014] The effective length l of the projectile is calculated using the following formula:

[0015]

[0016] Where R1 is the head radius, R2 is the tail radius, M is the mass of the shaped charge liner, and ρ p The density of the projectile material.

[0017] Furthermore, the relative property analysis of the projectile target material described in step S1 is used to determine the projectile material strength Y. p and target resistance R t Projectile material strength Y p Solve using the following formula:

[0018]

[0019] Where, σ yp υ represents the dynamic yield strength of the projectile material, and υ represents the Poisson's ratio of the projectile material.

[0020] For metallic targets, the target resistance R t The empirical value is determined according to the following formula:

[0021]

[0022] Where σ yt E represents the dynamic yield strength of the target material. t The elastic modulus of the material;

[0023] For concrete targets, the target resistance R t According to the following formula:

[0024] R t =0.22ln(f c -0.285

[0025] Where R t For target drag, fc It represents the uniaxial compressive strength of concrete.

[0026] Furthermore, the analysis of penetration modes and conversion speeds is as follows: during the penetration of shaped charge, the projectile penetration modes are divided into three stages: steady penetration, quasi-steady penetration, and rigid projectile penetration. These different penetration stages are based on the basic properties of the projectile and target and according to the projectile velocity.

[0027] Furthermore, the critical velocity lower limit V of the steady penetration stage r Solve using the following formula:

[0028]

[0029] Where σ yt ρ represents the dynamic yield strength of the target material. p ρ is the density of the projectile material. t The density of the target material.

[0030] Furthermore, the critical velocity V of the quasi-steady penetration stage c In Y p ≤R t When the time comes, solve using the following formula:

[0031]

[0032] In Y p >R t When the time comes, solve using the following formula:

[0033]

[0034] Furthermore, the formula for calculating the penetration depth L1 in the steady-state penetration stage described in step S2 is as follows:

[0035]

[0036] Where ρ j The density of the penetrator.

[0037] Furthermore, the penetration depth L2 in the quasi-steady penetration stage described in step S2 satisfies the following formula:

[0038]

[0039] u is the instantaneous penetration velocity, calculated using the following formula:

[0040]

[0041] Furthermore, the formula for calculating the penetration depth L3 of the rigid penetration stage for the concrete target in step S2 is as follows:

[0042]

[0043] Furthermore, in step S3, the typical damage characteristics of the target are compared with the penetration depth and damage range of the three stages of the shaped charge. Based on the test results, the penetration mode and critical conversion velocity of the three-stage penetration model of the shaped charge are adjusted again, and the target strength factor and correlation coefficient of each stage in the target-projectile interaction are corrected.

[0044] The advantages of this invention are as follows: It proposes a systematic method for predicting the penetration depth of a shaped charge structure against a target. This method comprehensively considers the simplification of the projectile model, the relative properties of the projectile and target materials, the establishment of penetration modes, and the division of critical transition velocities. Furthermore, through a disassembly and analysis of the entire projectile-target interaction process, the penetration depth at different penetration stages is estimated. The model can be further refined using experimental data, increasing its accuracy. This method can accurately describe the entire projectile-target interaction process and quickly and accurately predict the penetration depth of shaped charges. Attached Figure Description

[0045] Figure 1 Flowchart of the method for predicting the penetration of shaped charge;

[0046] Figure 2 Simplified feature diagram of the shaped charge projectile model;

[0047] Figure 3 A schematic diagram of a shaped charge projectile penetrating a target at high speed. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0049] This invention addresses the prediction method for the penetration depth of shaped charge projectiles, proposing criteria and methods for a simplified projectile model, as well as calculation formulas for the penetration depth at different stages. This allows for the rapid and accurate prediction of the penetration depth of explosively formed projectiles (EFP) on different target bodies.

[0050] The method of the present invention includes:

[0051] S1. By successively simplifying the projectile model, analyzing the relative properties of the projectile and target materials, and analyzing the penetration mode and conversion speed, the action of the projectile and target is divided into different penetration stages, and the critical conversion speed judgment criteria for each penetration stage are determined.

[0052] S2. Based on the parameters obtained from the simplified formula of the projectile model and the relative property analysis of the projectile and target materials, the penetration depth of each stage is estimated in turn according to the different penetration stages.

[0053] S3. Conduct penetration tests of shaped charge targets and verify the accuracy of the penetration depth estimates obtained in step S2 for each stage. Correct the penetration mode, target strength factor and correlation coefficient for each stage.

[0054] S4. Establish a complete model for predicting the depth of shaped charge.

[0055] In step S3, the typical damage characteristics of the target are compared with the penetration depth and damage range of the three stages of the shaped charge. Based on the test results, the penetration mode and critical transition velocity of the three-stage penetration model of the shaped charge are adjusted again, and the target strength factor and coefficient of each stage in the target-projectile interaction are corrected.

[0056] like Figure 1 As shown, taking the penetration of an EFP warhead into a metal or concrete target as an example, the implementation of each step is as follows:

[0057] (1) Simplification of the projectile model

[0058] Considering that the EFP warhead, after detonation, undergoes explosive detonation to form a projectile with an irregular shape, such as Figure 2 As shown, the typical geometric features of the projectile can be summarized as follows: ① a symmetrical structure of revolution; ② a hollow tail structure; ③ the projectile can be considered as being composed of an infinite number of cylinders (rings) spliced ​​together. When simplifying the geometric model, it can be simplified to a solid part with a head radius of R1 and a hollow ring part with a tail radius of R2. When solving the EFP penetration of different targets, it can be simplified to a solid cylindrical structure with a hemispherical head. The effective diameter R of the projectile is approximately solved according to formula (1):

[0059]

[0060] The effective length l of the projectile can be approximately solved using formula (2):

[0061]

[0062] Where M is the mass of the propellant liner (assuming no mass loss occurs during the propellant liner forming process), ρ p The density of the projectile material, the mass of the projectile liner, the nose radius, and the tail radius among the projectile characteristic parameters can all be obtained directly through numerical calculation or experiment.

[0063] (2) Relative properties of projectile and target materials

[0064] From the current typical theories on long rod erosion penetration, the strength of the projectile material (Y) is considered. p ) and target drag (R t The description of the projectile's material properties is particularly important. Based on considerations of the projectile's material properties, Tate suggests that the projectile's material strength Y... pTake the Hugoniot elastic limit as the elastic material:

[0065]

[0066] Where, σ yp ν is the dynamic yield strength of the projectile material, and v is the Poisson's ratio of the projectile material.

[0067] For metallic targets, Tate derived the target drag R by fitting experimental data. t Empirical values:

[0068]

[0069] Where σ yt E represents the dynamic yield strength of the target material. t This is the elastic modulus of the material.

[0070] For concrete targets, Rosenberg and Dekel, based on extensive experimental data, proposed the target drag coefficient (R0). t ) and concrete compressive strength (f c Nonlinear descriptive relationship between them:

[0071]

[0072] Where R t For target drag, f c It represents the uniaxial compressive strength of concrete.

[0073] (3) Penetration mode and conversion speed analysis

[0074] When theoretically solving for the maximum penetration depth of a projectile, as the projectile's penetration velocity continuously decreases, the projectile's penetration mode successively transforms into three typical stages: steady penetration, quasi-steady penetration, and rigid projectile penetration. These three stages are mainly based on the basic properties of the projectile and target and are divided according to the projectile's penetration velocity.

[0075] ① The criterion for determining whether a steady penetration process can be transformed into a quasi-steady penetration process: In engineering approximate analysis, when the dynamic pressure at the collision point... Greater than the dynamic yield strength of the target material (σ yt When the strength of the target plate is 10 times that of the target, the strength effect can be ignored and the target plate can be treated as a fluid. Then, according to the Bernoulli equilibrium equation... Where the projectile velocity is v, the penetration velocity is u, and ρ p ρ is the density of the projectile material. t Let V be the density of the target material. Based on this, the lower critical velocity limit V for steady EFP penetration of the target can be calculated. r :

[0076]

[0077] ② The velocity judgment for the transformation of the quasi-steady penetration process into the rigid projectile penetration process needs to be determined based on the relative properties between the projectile and the target. When Y p ≤R t When the target has high relative hardness, penetration stops when u = 0. At this point, during projectile penetration, when the projectile velocity v decreases to... At that time, the remaining projectile will undergo plastic deformation similar to the Taylor rod penetration, but will no longer contribute to the penetration depth; when Y p >R t When the projectile has high relative hardness, penetration stops when v = u. At this point, during the projectile's penetration process, when the projectile velocity v decreases to... At that point, the velocity at the tail of the projectile is equal to the penetration velocity, and the projectile no longer erodes; the remaining projectile continues to penetrate like a rigid body.

[0078] After determining the simplified projectile model, the relative properties of the projectile and target materials, and the possible penetration modes and transition velocities, a three-stage penetration depth prediction model for EFP can be established. Depth predictions for the steady penetration stage, the quasi-steady penetration stage, and the rigid projectile penetration stage are then performed sequentially.

[0079] (4) EFP Three-Stage Penetration Depth Prediction Model

[0080] ① Penetration depth during steady penetration phase. Based on the hydrodynamic theory of high-speed jet penetration, both the projectile and the target are considered as ideal incompressible fluids. The state of the shaped charge projectile penetrating the target at high speed is as follows: Figure 3 As shown, establish coordinates at collision point A, and set the velocity of the shaped charge penetrator to v. j The penetration velocity is u, and the velocity of the target material on the moving coordinate is -u.

[0081] During the jet penetration of the target, the pressure balance relationship at the jet / target interface along the projectile-target centerline can be described by the Bernoulli equation:

[0082]

[0083] Where (p) j ) -∞ The pressure of the focused jet at an infinite distance from point A, (p t ) ∞ Let ρ be the pressure on the target at an infinite distance from A, and both can be ignored. j For the density of the penetrator, ρ t Given the density of the target, formula (7) becomes:

[0084]

[0085] Let the length of the uniformly oriented focused jet be l, and the total armor-piercing time be t, then:

[0086]

[0087] Penetration depth L1 is:

[0088] L1 = ut (10)

[0089] Formulas (8), (9), and (10) can be used to derive the formula for predicting the jet penetration depth based on fluid dynamics theory:

[0090]

[0091] The above formula shows that the penetration depth of a shaped charge is directly proportional to the projectile length *l* and the square root of the density ratio of the penetrator to the target. Furthermore, the formula also indicates that the maximum penetration depth of the projectile against the target during the steady-state penetration phase has a maximum value, meaning that the projectile velocity does not significantly contribute to the penetration depth.

[0092] This differs fundamentally from the traditional rigid projectile principle that penetration depth can be increased by increasing the projectile velocity under low and medium speed conditions. This is mainly because the strength effect of the projectile and the target can be ignored under high-speed penetration conditions, and thus fluid dynamics theory can be used in the theoretical analysis of high-speed penetration depth prediction of shaped charge. For the high-speed penetration effect of shaped charge, when the projectile's impact velocity satisfies the condition of formula (6), the penetration depth of the projectile in the steady penetration stage can be directly solved by formula (11).

[0093] ② Quasi-steady penetration stage. As the penetration depth increases, the projectile's penetration velocity continuously decreases. To ensure the accuracy of the projectile-target penetration depth prediction model during the process of the projectile penetrating from high speed to low speed, the projectile-target strength effect must be considered. Based on this, the penetration depth during this process is solved using the quasi-steady penetration equilibrium equation. Projectile-target interface axial stress equilibrium equation:

[0094]

[0095] Equation for the change in projectile length:

[0096]

[0097] Equation of projectile deceleration motion:

[0098]

[0099] Projectile penetration equation:

[0100]

[0101] In the formula, v represents the projectile velocity, l is the projectile length, u is the instantaneous penetration velocity, and L2 represents the penetration depth.

[0102] The penetration velocity of the projectile can be directly obtained from formula (12):

[0103]

[0104] ③ Rigid projectile penetration stage. After the steady penetration stage and quasi-steady penetration stage, the projectile head is severely abraded and gradually thickened. Generally speaking, the projectile can be approximated as a spherical projectile or a blunt-nosed projectile with a relatively small CRH. Especially for shaped charge warheads, the projectile is almost completely abraded when the shaped charge penetrator interacts with the target. Therefore, during the rigid projectile penetration stage, the remaining projectile can be approximated as a spherical blunt-nosed projectile. Entering the rigid penetration stage, the material effect of the target dominates the penetration depth. According to Rosenberg and Dekel's description of the rigid projectile's effect on concrete material, the projectile penetration depth L3 in this stage can be solved by referring to formula (17):

[0105]

[0106] Among them, the target resistance R t It can be obtained by formula (5), where v represents the velocity of the projectile.

[0107] After completing the above three-stage EFP penetration depth prediction, the shaped charge penetration test can be carried out to verify the accuracy of the penetration depth prediction at each stage and correct the penetration mode, target strength factor and coefficient at each stage.

[0108] (5) Accuracy verification of penetration depth

[0109] The accuracy of the penetration depth prediction method was verified and corrected by combining shaped charge penetration tests on targets. Typical target damage characteristics were compared with the penetration depth and damage range of the three stages of the shaped charge. Based on the test results, the penetration mode and critical transition velocity of the three-stage shaped charge penetration model were adjusted, and the target-projectile strength factor and correlation coefficient for each stage of the projectile-target interaction were corrected. Finally, a complete shaped charge depth prediction model was obtained.

[0110] The above description is merely the preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for predicting the penetration depth of a shaped charge, characterized in that, Includes the following steps: S1. By successively simplifying the projectile model, analyzing the relative properties of the projectile and target materials, and analyzing the penetration mode and conversion speed, the action of the projectile and target is divided into different penetration stages, and the critical conversion speed judgment criteria for each penetration stage are determined. S2. According to different penetration stages, the penetration depth of each stage is estimated by combining the simplified formula of the projectile model and the parameters obtained from the analysis of the relative properties of the projectile and target materials. S3. Conduct penetration tests of shaped charge targets and verify the accuracy of the penetration depth estimates obtained in step S2 for each stage. Correct the penetration mode, target strength factor and correlation coefficient for each stage. S4. Establish a complete model for predicting the depth of shaped charge; The analysis of penetration modes and conversion speeds described in step S1 is as follows: When a shaped charge penetrates, the projectile penetration modes are divided into steady penetration, quasi-steady penetration and rigid projectile penetration stages in sequence. The different penetration stages are based on the basic properties of the projectile and target and according to the projectile velocity. The relative property analysis of the projectile target material in step S1 is used to determine the strength of the projectile material. and target resistance Projectile material strength Solve using the following formula: in, The dynamic yield strength of the projectile material. The Poisson's ratio of the projectile material; For metallic targets, target resistance The empirical value is determined according to the following formula: in The dynamic yield strength of the target material. The elastic modulus of the material; For concrete targets, target resistance According to the following formula: in This refers to the uniaxial compressive strength of concrete. Lower critical velocity limit of steady penetration phase in projectile penetration mode Solve using the following formula: in The dynamic yield strength of the target material. Density of the projectile material Density of the target material; The penetration depth L2 in the quasi-steady penetration stage of step S2 satisfies the following formula: in The instantaneous penetration velocity is calculated using the following formula: in Density of the projectile material For the density of the target material, The critical velocity for the quasi-steady penetration stage. This represents the velocity of the projectile.

2. The method for predicting the penetration depth of a shaped charge according to claim 1, characterized in that, In step S1, the projectile model is simplified to a solid cylindrical structure with a hemispherical head during penetration by a shaped charge projectile. The effective diameter R of the projectile is calculated using the following formula: Effective length of the projectile Solve using the following formula: Where R1 is the head radius, R2 is the tail radius, and M is the mass of the shaped charge liner. The density of the projectile material.

3. The method for predicting the penetration depth of a shaped charge according to claim 1, characterized in that, The critical velocity of the quasi-steady penetration phase exist ≤ When the time comes, solve using the following formula: exist > When the time comes, solve using the following formula: 。 4. The method for predicting the penetration depth of a shaped charge according to claim 1, characterized in that, The formula for calculating the penetration depth L1 in the steady penetration stage of step S2 is: in The density of the penetrating projectile.

5. The method for predicting the penetration depth of a shaped charge according to claim 1, characterized in that, The formula for calculating the penetration depth L3 of the rigid projectile in step S2 for the concrete target penetration stage is as follows: in This represents the velocity of the projectile.

6. The method for predicting the penetration depth of a shaped charge according to claim 1, characterized in that, In step S3, the typical damage characteristics of the target are compared with the penetration depth and damage range of the three stages of the shaped charge. Based on the test results, the penetration mode and critical transition velocity of the three-stage penetration model of the shaped charge are adjusted again, and the target strength factor and correlation coefficient of each stage in the target-projectile interaction are corrected.

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