Prediction method of explosive penetration damage behavior of active projectile

Abstract

The present invention discloses a method for predicting the damage behavior of explosive perforation of active projectiles. By constructing a temperature rise and energy conversion model of a quasi-closed container based on the first law of thermodynamics, and analyzing the energy release and global overpressure in the quasi-closed container of active materials based on this model, as well as the equivalent TNT equivalent relationship left by PTFE / AL for the deflagration products, a method for predicting the peak value of shock wave overpressure and the action time of the positive pressure zone in the air is further established. By modeling the specific kinetic energy of the penetrator projectile, the collision behavior of the projectile and the target is converted into the deformation work of the target plate. A prediction model for the deformation of the target plate is established by considering the factors of the shock wave overpressure and the action time of the positive pressure zone. At the same time, based on the analysis of fracture mechanics behavior, a prediction model for the ultimate deformation of the after-effect target is established by considering the ultimate crack strength factor. Based on this, this scheme provides a new solution for the damage behavior prediction method of active projectile energy release-temperature rise-overpressure-explosion perforation of PTFE / AL.

Description

Technical Field

[0001] The invention relates to the technical field of live ammunition penetration damage assessment, and in particular to a method for predicting explosive penetration damage behavior of active projectiles. Background Art

[0002] The process of active projectiles colliding with multi-layer spaced metal targets is complex, involving the stages of active core impact compression, fragmentation ignition, and fragment cloud deflagration. The damage includes temperature rise damage, overpressure damage, and burst perforation caused by overpressure. The existing prediction of active projectile burst perforation damage behavior is based on direct testing of sensors in the air, and overpressure and burst perforation damage models are constructed through test results. All of them are field test methods, which are costly and cumbersome. There is no burst perforation calculation method based on the theoretical calculation of the overpressure peak value of active projectiles hitting targets in the air. Therefore, it cannot be applied to large-scale damage behavior prediction, and there is no research on the burst perforation theoretical calculation method applicable to active projectiles hitting targets at home and abroad. On the other hand, the field test method has more influencing factors than the temperature and pressure test of quasi-closed containers, and the data acquisition error is large, which also limits the application of damage behavior prediction models for active projectiles and even related new warheads. Summary of the invention

[0003] In view of the problems existing in the prior art, the present invention provides a method for predicting the explosive perforation damage behavior of active projectiles, which provides a new solution for predicting the energy release-temperature rise-overpressure-explosive perforation damage behavior of PTFE / Al active projectiles.

[0004] To achieve the above-mentioned purpose, the present invention provides a method for predicting the explosive perforation damage behavior of active projectiles, which specifically includes the following steps:

[0005] Step S1: analyzing the blasting effect of PTFE / Al active projectiles;

[0006] Step S2: establishing a temperature rise and energy conversion model for PTFE / Al active projectiles;

[0007] Step S3: Establishing a calculation model for shock wave overpressure damage and positive pressure zone action time in the air;

[0008] Step S4: Establish a calculation model for the amount of deformation caused by the explosion and perforation of the aftereffect target by the PTFE / Al active projectile.

[0009] Furthermore, the step S2 is specifically as follows:

[0010] The energy release test of the active projectile in a quasi-closed container is carried out. The heat loss and pressure relief effect of the gas inside the test tank during the deflagration stage are ignored. The heat obtained by the gas inside the test tank can be considered as Equivalent to the heat released by the active material ,Right now ;

[0011] Introducing the standard energy function related to temperature and specific volume

[0012] ;

[0013] When the system mass and volume are constant, the energy increment of the gas in the container is

[0014] ;

[0015] The gas temperature increment is

[0016] ;

[0017] Therefore, the energy released by the active material into the target can be estimated by

[0018] ;

[0019] and are the final and initial thermodynamic temperatures of the gas in the container, respectively, in K; is the internal volume of the test tank, in m³; is the specific heat capacity at constant volume, the unit is kJ / (kg·K), and the corresponding value is taken at the final state.

[0020] Furthermore, the step S3 specifically includes the following steps:

[0021] Step S3-1: Establishing a PTFE / Al active projectile shock wave overpressure peak calculation model;

[0022] For PTFE / Al active materials, due to the different explosion heat, it is converted into TNT equivalent based on the energy similarity principle.

[0023] ;

[0024] is the static PTFE / Al active material equivalent TNT equivalent, unit: kg; is the mass of the active core participating in the reaction, in kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; is the explosion heat of TNT, in kJ / kg;

[0025] For active projectiles with a certain penetration speed, according to the energy similarity principle, the energy increase caused by the charge movement can be regarded as the increase in charge amount, so

[0026] ;

[0027] is the dynamic PTFE / Al active material equivalent TNT equivalent, unit: kg; It is the static PTFE / Al active material equivalent TNT equivalent, unit is kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; The residual speed of the active projectile after hitting the target, in m / s;

[0028] After the collision between the projectile and the target, part of the energy released by the active material will be converted into the shell deformation and destruction energy and the kinetic energy of the shell fragments, and the other part will be converted into the kinetic energy and internal energy of the deflagration products, forming an overpressure in the surrounding air. The activation rate and energy conversion of the active material can be expressed as

[0029] ;

[0030] Where n is the activation rate of the active material; is the mass of the active core participating in the reaction, in kg; is the total mass of the active core, in kg; is the activation length of the active core, in m; is the total length of the active core, in m;

[0031] is the total energy released by the active core; It is the reaction heat of the active core material; is the internal energy of the deflagration products; is the shell deformation failure energy; is the kinetic energy of the deflagration products; The added kinetic energy of all fragments; the unit is kJ;

[0032] Based on this, when the deflagration propagates after the target, the deflagration products expand according to the isentropic law, and the internal energy of the deflagration products can be obtained:

[0033] ;

[0034] In the formula, is the mass of the active core participating in the reaction, in kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; is the shell radius, in m; r is the distance from the test point to the center of the deflagration, in m;

[0035] Kinetic energy of deflagration products

[0036] ;

[0037] In the formula, is the mass of the active core participating in the reaction, in kg; vp is the fragment velocity, in m / s; is the acceleration due to gravity;

[0038] The added kinetic energy of all fragments

[0039] ;

[0040] In the formula, v p is the fragment velocity, in m / s; is the mass of all fragments, in kg; is the acceleration due to gravity;

[0041] For shell deformation and damage energy It accounts for about 3% of the total energy. Taking the head metal block and the shell as a whole, the chemical energy used to form the peak overpressure can be obtained from the equivalent relationship: Total energy released by the active core The ratio between

[0042] ;

[0043] In the formula, is the initial activation ratio; is the shell radius, in m; is the radius of the shell when it is deformed and broken, in m; is the dynamic PTFE / Al active material equivalent TNT equivalent, unit: kg; The equivalent TNT equivalent of PTFE / Al left for deflagration products, unit: kg;

[0044] By combining the above formulas, we can obtain the peak overpressure of the air shock wave: for

[0045] ;

[0046] in, is the equivalent TNT equivalent of PTFE / Al left for the deflagration products, in kg; r is the distance from the test point to the deflagration center, in m; and satisfies 1≤ ≤10;

[0047] Step S3-2: Establishing the positive pressure zone action time Computational models;

[0048] Positive pressure zone action time It is another characteristic parameter of the shock wave of the deflagration reaction of the active material and one of the important indicator parameters that affect the magnitude of the destructive effect on the target. Its calculation can be established through an empirical formula based on the explosion similarity rate through experiments. For the deflagration reaction of the PTFE / Al active core in the air, The calculation formula is:

[0049] ;

[0050] Where μ is the correction factor, and the value of PTFE / Al active material is 1.35×10 -3 ; r is the distance from the test point to the center of the deflagration, in meters; It is the equivalent TNT equivalent of PTFE / Al left as deflagration products, in kg.

[0051] Furthermore, the step S4 specifically includes the following steps:

[0052] Step S4-1: Establishing a calculation model for the specific kinetic energy of the aftereffect target plate of the active projectile;

[0053] Step S4-2: Establishing a calculation model for the aftereffect target plate deformation;

[0054] Step S4-3: Calculating the limit deformation of the aftereffect target plate;

[0055] Step S4-4: Calculate the aftereffect target plate deformation according to the test curve and compare it with the limit deformation.

[0056] Furthermore, the step S4-1 is specifically as follows:

[0057] The after-effect target plate penetration damage mainly comes from the specific kinetic energy of the penetrator being greater than the unit deformation work of the target plate. The dynamic deformation work of the target plate can be expressed as

[0058] ;

[0059] Where K1 is the proportionality coefficient, which mainly depends on the material properties. For Al2024, K1=3; A s is the penetration area of ​​the penetrator hitting the target plate, in cm 2 ;h * is the target plate thickness, in mm; σ b Expressed as the target plate's destructive strength limit, unit: kg / cm 2 ;

[0060] Therefore, the deformation work of the target plate per unit thickness and unit area can be expressed as

[0061] ;

[0062] When the projectile acts on the target plate, the specific kinetic energy per unit thickness per unit area is E b1 When the target plate is greater than the deformation work e, the target plate will be penetrated and damaged by the projectile; for the target plate made of Al2024, the penetration probability is P me The relationship between the kinetic energy of the penetrator and

[0063] ;

[0064] The specific kinetic energy of metal materials such as tungsten alloy / steel colliding with Al2024 target plate is expressed as

[0065] ;

[0066] In the formula, E ba is the specific kinetic energy per unit area of ​​Al2024 per unit thickness, in kg•m / (cm 2 •mm); w is the mass of the projectile, in g; v is the impact velocity, in m / s; S is the frontal area of ​​the projectile, in m 2 ;h * is the target plate thickness, in mm; g is the gravitational acceleration; Φ is the projectile shape coefficient, generally taken as 0.005;

[0067] For active materials, their mechanical strength and density are lower than those of metal materials, which results in a larger penetration area of ​​the target plate. Therefore, in the above formula, The specific kinetic energy of the active projectile acting on the Al2024 target plate is obtained by correction based on

[0068] ;

[0069] In the formula k is the correction factor, which is generally taken as 1.6 for PTFE / Al active materials; M is the total mass of the PTFE / Al active core, in g; is the mass of the punch block, in g; h * is the target plate thickness, in mm; It is the residual speed of the active projectile after hitting the target, in m / s.

[0070] Furthermore, the step S4-2 is specifically as follows:

[0071] After the target plate is penetrated and penetrated, the pressure released by the explosion of the debris cloud and its active materials on the target acts on the aftereffect target plate. The deformation of the aftereffect target plate is proportional to the impulse acting on the aftereffect target plate and inversely proportional to the density and thickness of the shell material. Therefore, the deformation of the aftereffect target plate can be expressed as

[0072] ;

[0073] In the formula K 2 is a constant, and the flat-head penetrator is generally taken as 2.212; ρ t is the target plate density, in g / cm³; is the shock wave load pressure at any time, in KPa; is the action time of the shock wave load, in ms; h * is the target plate thickness, in mm.

[0074] Furthermore, the step S4-3 is specifically as follows:

[0075] According to the stress intensity factor in fracture mechanics K I The physical meaning is that when the stress intensity factor at the edge of the through hole is greater than the ultimate strength factor of the material K IC When , the crack at the edge of the through hole will expand, otherwise it will not expand; the ultimate strength factor of the crack of the finite width and length strip can be expressed as

[0076] ;

[0077] In the formula G is a constant related to the crack geometry; E is the elastic modulus of the target material; a It is 1 / 2 of the crack length, in mm; L 0 is the side length of the aftereffect target plate, in mm; is the limit deformation of the aftereffect target plate, in mm;

[0078] For Al2024 target material K IC It can be obtained by looking up the table; so the limit deformation of the aftereffect target plate is

[0079] .

[0080] Furthermore, the step S4-4 is specifically as follows:

[0081] The pressure-time curve produced by the impact of the debris cloud and the explosion of the active material was measured by experiment. The deformation of the aftereffect target plate at the corresponding time can be calculated; the deformation of the aftereffect target plate obtained by the above calculation method is The value is less than the limit deformation of the aftereffect target plate value is a valid value.

[0082] The method for predicting the explosive perforation damage behavior of active projectiles provided by the present invention optimizes the accuracy of the method for predicting chain damage of active projectiles. According to the first law of thermodynamics in a quasi-closed container and the theory of shock loading and shock wave propagation, theoretical behavior analysis is carried out on the temperature and energy conversion method of PTFE / Al active projectiles, the equivalent TNT equivalent of PTFE / Al left for the deflagration products, the shock wave overpressure in the air and its target penetration characteristics, so as to realize the construction of a theoretical model for the explosive perforation damage behavior of the aftereffect aluminum target of the active projectile. Based on this, this scheme provides a new solution for the damage behavior prediction method of PTFE / Al active projectiles, which is energy release-temperature rise-overpressure-explosion perforation, and has been tested for its effectiveness. Based on the analysis of the energy release behavior of TNT explosives and the theoretical research on the target penetration of traditional kinetic projectiles, it is of great significance to expand the innovative theoretical prediction method of active projectiles. At the same time, it can also provide a reference for the damage efficiency prediction method of related new material warheads. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is a diagram of the process of active projectiles colliding with double-layer targets;

[0084] Figure 2 This is the propagation diagram of air shock wave of PTFE / Al deflagration;

[0085] Figure 3 This is the pressure attenuation diagram of the air shock wave front of PTFE / Al deflagration;

[0086] Figure 4 It is a schematic diagram of the deformation of the aftereffect target plate;

[0087] Figure 5 This is a comparison diagram of the experimental overpressure curve of PTFE / Al active projectile and the peak value calculated theoretically;

[0088] Figure 6 This is a comparison chart between the theoretical prediction and experimental values ​​of the aluminum target deformation after the PTFE / Al active projectile experiment. DETAILED DESCRIPTION

[0089] In order to clearly illustrate the technical features of this solution, this solution is described below through a specific implementation method.

[0090] The prediction method of explosive perforation damage behavior of active projectiles is a mathematical description of the damage behavior process of explosive perforation of active projectiles. By constructing a temperature rise and energy conversion model of a quasi-closed container based on the first law of thermodynamics, and analyzing the relationship between energy release and global overpressure in the closed container of active materials based on this model, the equivalent TNT equivalent of PTFE / Al left for the deflagration products can be obtained by introducing the energy release conversion relationship of TNT explosives, thereby obtaining the theoretical calculation model of the peak overpressure in infinite air of active projectiles and the calculation model of the action time of the positive pressure zone. Finally, by introducing the calculation formula of specific kinetic energy, the breakdown probability of the Al2024 after-effect target plate is obtained, and then the deformation and limit deformation of the target plate at any time can be calculated, and the calculation model of the explosive perforation damage behavior of active projectiles is obtained.

[0091] The prediction method of the explosive penetration damage behavior of active projectiles specifically includes the following steps:

[0092] Step S1: analyzing the blasting effect of PTFE / Al active projectiles;

[0093] The chain damage process of active projectiles is relatively complex, and the mechanism and mode of action are as follows: Figure 1 When this active projectile hits the target at high speed, it exhibits good kinetic penetration capability. At the same time, due to the strong impact, it is activated under the strong dynamic load during penetration and produces a chemical reaction. It further causes damage inside the target by relying on its own energy release effect, producing damage effects such as combustion and explosion-like damage, forming other types of damage effects and coupled damage effects in addition to mechanical damage such as strong flames, high temperature, high pressure, and burst perforation, which can greatly increase the damage power. This type of damage effect and coupled damage effect is called multi-effect coupled chain damage.

[0094] Step S2: establishing a temperature rise and energy conversion model for PTFE / Al active projectiles;

[0095] The energy release test of the active projectile in a quasi-closed container is carried out. The heat loss and pressure relief effect of the gas inside the test tank during the deflagration stage are ignored. The heat obtained by the gas inside the test tank can be considered as Equivalent to the heat released by the active material ,Right now ;

[0096] Introducing the standard energy function related to temperature and specific volume

[0097] ;

[0098] When the system mass and volume are constant, the energy increment of the gas in the container is

[0099] ;

[0100] The gas temperature increment is

[0101] ;

[0102] Therefore, the energy released by the active material into the target can be estimated by

[0103] ;

[0104] and are the final and initial thermodynamic temperatures of the gas in the container, respectively, in K; is the internal volume of the test tank, in m³; is the specific heat capacity at constant volume, the unit is kJ / (kg·K), and the corresponding value is taken at the final state.

[0105] Step S3: Establishing a calculation model for shock wave overpressure damage and positive pressure zone action time in the air;

[0106] Description of the overpressure generation process in different environments: To study the overpressure behavior of the shock wave of the core explosion of active materials in the air, we must first understand the basic principles of shock wave generation in the air, so as to find out the regularity and give a theoretical explanation. The active material explodes in the air and transforms into high-temperature and high-pressure gas-like products in a short period of time, which are higher than the initial pressure and density of the air. Therefore, the gas-like products expand rapidly, and the pressure and density decrease, forming a rarefaction wave in the explosion products. At the same time, the reaction products expand, strongly compressing the air, forming a short air shock wave in the air.

[0107] Expansion of reaction products: When the shock wave propagation distance r in infinite air is much larger than the radius of the cylindrical active charge, the expansion law of the reaction products can be approximately considered to conform to the polytropic exponential state equation , where are the pressure and specific volume (volume per unit mass) of the reaction products, respectively.

[0108] Propagation of air shock wave: After the air shock wave behind the target is formed, it separates from the reaction product and propagates independently in the air. During the propagation of the air shock wave, the front of the wave propagates at supersonic speed, while the tail of the positive pressure zone propagates at the speed of sound corresponding to the pressure, so the positive pressure zone is continuously widened. Figure 2 As shown in Figure 1. During the propagation of air shock waves, the wavefront pressure decays quickly in the initial stage and slows down in the later stage. After propagating to a certain distance, the shock wave decays into a sound wave. The change of shock wave front pressure over time is shown in Figure 1. Figure 3 As shown, is called peak overpressure, Indicates the positive pressure zone action time.

[0109] Step S3-1: Establishing a PTFE / Al active projectile shock wave overpressure peak calculation model;

[0110] From a quasi-closed container The relationship between the energy release of active materials and the global temperature rise is obtained. It can be seen that the energy released by the active materials in the quasi-closed container is proportional to the quasi-static temperature rise. Therefore, the temperature rise value of the quasi-closed container of the active materials can be measured experimentally to obtain the corresponding energy release for the peak overpressure formation stage. Through a certain conversion relationship, the energy release of the active material in the air can be obtained. Then, the equivalent TNT equivalent left by the active material for the deflagration product is obtained, and the theoretical peak value of the deflagration overpressure in the air of the active material and the action time of the positive pressure zone are obtained.

[0111] For PTFE / Al active materials, due to the different explosion heat, it is converted into TNT equivalent based on the energy similarity principle.

[0112] ;

[0113] is the static PTFE / Al active material equivalent TNT equivalent, unit: kg; is the mass of the active core participating in the reaction, in kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; is the explosion heat of TNT, in kJ / kg;

[0114] For active projectiles with a certain penetration speed, according to the energy similarity principle, the energy increase caused by the charge movement can be regarded as the increase in charge amount, so

[0115] ;

[0116] is the dynamic PTFE / Al active material equivalent TNT equivalent, unit: kg; is the static PTFE / Al active material equivalent TNT equivalent, unit: kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; The residual speed of the active projectile after hitting the target, in m / s;

[0117] In fact, the formula The calculated result is the chemical energy released by the active material used in the peak overpressure formation stage. For the calculation of peak overpressure, after the projectile-target collision, part of the energy released by the active material will be converted into the shell deformation and destruction energy and the shell fragment kinetic energy, and the other part will be converted into the kinetic energy and internal energy of the deflagration product scattering, forming overpressure in the surrounding air; the activation rate and energy conversion of the active material can be expressed as

[0118] ;

[0119] Where n is the activation rate of the active material; is the mass of the active core participating in the reaction, in kg; is the total mass of the active core, in kg; is the activation length of the active core, in m; is the total length of the active core, in m;

[0120] is the total energy released by the active core; It is the reaction heat of the active core material; is the internal energy of the deflagration products; is the shell deformation failure energy; is the kinetic energy of the deflagration products; The added kinetic energy of all fragments; the unit is kJ;

[0121] Based on this, when the deflagration propagates after the target, the deflagration products expand according to the isentropic law, and the internal energy of the deflagration products can be obtained:

[0122] ;

[0123] In the formula, is the mass of the active core participating in the reaction, in kg; It is the explosive heat of PTFE / Al active material, in kJ / kg; is the shell radius, in m; r is the distance from the test point to the center of the deflagration, in m;

[0124] Kinetic energy of deflagration products

[0125] ;

[0126] In the formula, is the mass of the active core participating in the reaction, in kg; v p is the fragment velocity, in m / s; is the acceleration due to gravity;

[0127] The added kinetic energy of all fragments

[0128] ;

[0129] In the formula, v p is the fragment velocity, in m / s; is the mass of all fragments, in kg; is the acceleration due to gravity;

[0130] For shell deformation and damage energy It accounts for about 3% of the total energy. Taking the head metal block and the shell as a whole, the chemical energy used to form the peak overpressure can be obtained from the equivalent relationship: Total energy released by the active core The ratio between

[0131] ;

[0132] In the formula, is the initial activation ratio; is the shell radius, in m; is the radius of the shell when it is deformed and broken, in m; is the dynamic PTFE / Al active material equivalent TNT equivalent, unit: kg; The equivalent TNT equivalent of PTFE / Al left for deflagration products, unit: kg;

[0133] By combining the above formulas, we can obtain the peak overpressure of the air shock wave: for

[0134] ;

[0135] in, is the equivalent TNT equivalent of PTFE / Al left for the deflagration products, in kg; r is the distance from the test point to the deflagration center, in m; and satisfies 1≤ ≤10;

[0136] Step S3-2: Establishing the positive pressure zone action time Computational models;

[0137] Positive pressure zone action time It is another characteristic parameter of the shock wave of the deflagration reaction of the active material and one of the important indicator parameters that affect the magnitude of the destructive effect on the target. Its calculation can be established through an empirical formula based on the explosion similarity rate through experiments. For the deflagration reaction of the PTFE / Al active core in the air, The calculation formula is:

[0138] ;

[0139] Where μ is the correction factor, and the value of PTFE / Al active material is 1.35×10 -3 ; r is the distance from the test point to the center of the deflagration, in meters; It is the equivalent TNT equivalent of PTFE / Al left as deflagration products, in kg.

[0140] Step S4: establishing a calculation model for the amount of deformation caused by the explosion and perforation of the aftereffect target by the PTFE / Al active projectile;

[0141] The media acting on the after-effect target plate mainly include the remaining penetrator, the plugging block, the debris cloud with uneven density, and the pressure released by the active material hitting the target and deflagration. In terms of the time domain of action, the remaining penetrator and the plugging block are located at the head of the secondary fragments and act on the after-effect target plate before the fragment particles, while the active materials in the fragments only undergo a relatively stable deflagration reaction during the target impact process. Therefore, it can be concluded that the remaining penetrator acts on the after-effect target plate first, mainly playing a role of penetration, and the load jointly generated by the debris cloud and its deflagration reaction mainly causes damage such as hole expansion, warping and crack extension to the after-effect target plate that has been penetrated.

[0142] Step S4-1: Establishing a calculation model for the specific kinetic energy of an active projectile acting on an Al2024 aftereffect target plate;

[0143] As for the penetration of the after-effect target plate, the penetration damage of the after-effect target plate mainly comes from the specific kinetic energy of the penetrator being greater than the unit deformation work of the target plate. The dynamic deformation work of the target plate can be expressed as

[0144] ;

[0145] Where K1 is the proportionality coefficient, which mainly depends on the material properties. For Al2024, K1=3; A s is the penetration area of ​​the penetrator hitting the target plate, in cm 2 ;h * is the target plate thickness, in mm; σ b Expressed as the target plate's destructive strength limit, unit: kg / cm 2 ;

[0146] Therefore, the deformation work of the target plate per unit thickness and unit area can be expressed as

[0147] ;

[0148] When the projectile acts on the target plate, the specific kinetic energy per unit thickness per unit area is E b1 When the target plate is greater than the deformation work e, the target plate will be penetrated and damaged by the projectile; for the target plate made of Al2024, the penetration probability is P me The relationship between the kinetic energy of the penetrator and

[0149] ;

[0150] The specific kinetic energy of metal materials such as tungsten alloy / steel colliding with Al2024 target plate is expressed as

[0151] ;

[0152] In the formula, E ba is the specific kinetic energy per unit area of ​​Al2024 per unit thickness, in kg•m / (cm 2•mm); w is the mass of the projectile, in g; v is the impact velocity, in m / s; S is the frontal area of ​​the projectile, in m 2 ;h * is the target plate thickness, in mm; g is the gravitational acceleration; Φ is the projectile shape coefficient, generally taken as 0.005;

[0153] For active materials, their mechanical strength and density are lower than those of metal materials, which results in a larger penetration area of ​​the target plate. Therefore, in the above formula, The specific kinetic energy of the active projectile acting on the Al2024 target plate is obtained by correction based on

[0154] ;

[0155] In the formula k is the correction factor, which is generally taken as 1.6 for PTFE / Al active materials; M is the total mass of the PTFE / Al active core, in g; is the mass of the punch block, in g; h * is the target plate thickness, in mm; It is the residual speed of the active projectile after hitting the target, in m / s.

[0156] Step S4-2: Establishing a calculation model for the aftereffect target plate deformation;

[0157] After the target plate is penetrated and penetrated, the pressure released by the explosion of the debris cloud and its active materials on the target acts on the aftereffect target plate. The deformation of the aftereffect target plate is proportional to the impulse acting on the aftereffect target plate and inversely proportional to the density and thickness of the shell material. The deformation of the aftereffect target plate is as follows: Figure 4 As shown. Therefore, the deformation of the aftereffect target plate can be expressed as

[0158] ;

[0159] In the formula K 2 is a constant, and the flat-head penetrator is generally taken as 2.212; ρ t is the target plate density, in g / cm³; is the shock wave load pressure at any time, in KPa; is the action time of the shock wave load, in ms; h * is the target plate thickness, in mm.

[0160] Step S4-3: Calculating the limit deformation of the aftereffect target plate;

[0161] According to the stress intensity factor in fracture mechanics K IThe physical meaning is that when the stress intensity factor at the edge of the through hole is greater than the ultimate strength factor of the material K IC When , the crack at the edge of the through hole will expand, otherwise it will not expand; the ultimate strength factor of the crack of the finite width and length strip can be expressed as

[0162] ;

[0163] In the formula G is a constant related to the crack geometry; E is the elastic modulus of the target material; a It is 1 / 2 of the crack length, in mm; L 0 is the side length of the aftereffect target plate, in mm; is the limit deformation of the aftereffect target plate, in mm;

[0164] For Al2024 target material K IC It can be obtained by looking up the table; so the limit deformation of the aftereffect target plate is

[0165] .

[0166] Step S4-4: Calculate the aftereffect target plate deformation according to the test curve and compare it with the limit deformation;

[0167] The pressure-time curve produced by the impact of the debris cloud and the explosion of the active material was measured by experiment. The deformation of the aftereffect target plate at the corresponding time can be calculated; the deformation of the aftereffect target plate obtained by the above calculation method is The value is less than the limit deformation of the aftereffect target plate value is a valid value.

[0168] The theoretical prediction model is compared with the experimental results to conduct validity analysis.

[0169] Based on the above analysis, the theoretical prediction model of shock wave overpressure and aftereffect aluminum target deformation is compared with the experimental results, such as Figure 5 , Figure 6 shown. Figure 5 The comparison results of the overpressure curve behind the target and the theoretically calculated peak value are shown when the initial velocity of the projectile is 1000m / s and the thickness of the homogeneous armor steel target is 10mm. The overpressure peak values ​​measured at 0.5m, 1m and 1.5m behind the target are all greater than the theoretically predicted peak values. Figure 6When the initial velocity of the projectile is 1000m / s and the spacing between the after-effect aluminum targets is 200mm, the comparison results of the theoretical prediction value and the experimental value of the deformation of the after-effect aluminum target show that with the increase of the thickness of the homogeneous armor steel target, the deformation of the Al2024 after-effect target increases first and then decreases, reaching the maximum deformation at 15mm, and the experimental results are slightly larger than the theoretical prediction model.

[0170] Analysis shows that this may be due to the coupling effect caused by the chain reaction in the process of the projectile-target interaction, and its damage mechanism is complex. The initial activation of the active material core deflagration reaction leads to further increase in pressure and temperature, which in turn causes a small amount of active material fragment cloud to be reactivated, making the experimental results slightly greater than the theoretical prediction. At the same time, due to the gradual increase in the thickness of the projectile homogeneous armor steel target, the activation rate of the active material projectile gradually increases, and the core has a significant radial effect on the shell, resulting in the gradual significant petal-shaped burst perforation of the after-effect aluminum target, and the deformation of the after-effect aluminum target increases. However, as the thickness of the projectile homogeneous armor steel target exceeds the critical target thickness for activation, more active materials act on the inside of the steel target, resulting in a gradual decrease in the deformation of the main burst perforation. In summary, the overall error is within 10%, and it is in good agreement with the experimental results, reflecting the actual law. Therefore, we believe that the theoretical prediction model is reasonable.

[0171] It should be noted that the above-described specific implementation methods can enable those skilled in the art to more fully understand the invention, but do not limit the invention in any way. Therefore, although the present specification and embodiments have described the invention in detail, those skilled in the art should understand that the invention can still be modified or replaced by equivalents; and all technical solutions and improvements that do not deviate from the spirit and scope of the invention are covered by the protection scope of the patent for the invention.

Claims

1. A method for predicting the explosive penetration damage behavior of active projectiles, characterized in that: The specific steps include: Step S1: analyzing the blasting effect of PTFE / Al active projectiles; Step S2: Establishing a temperature rise and energy conversion model for the PTFE / Al active projectile; the specific details of step S2 are as follows: The energy release test of the active projectile in a quasi-closed container is carried out. The heat loss and pressure relief effect of the gas inside the test tank during the deflagration stage are ignored. The heat obtained by the gas inside the test tank can be considered as Equivalent to the energy released by the active material into the target ,Right now ; Introducing the standard energy function related to temperature and specific volume ； When the system mass and volume are constant, the energy increment of the gas in the container is ； The gas temperature increment is ； Therefore, the energy released by the active material into the target can be calculated by the following formula: ； and are the final and initial thermodynamic temperatures of the gas in the container, respectively; is the internal volume of the test tank; is the specific heat at constant volume, taking the corresponding value of the final state; Step S3: Establishing a calculation model for the overpressure damage of shock waves in the air and the action time of the positive pressure zone; the step S3 specifically includes the following steps: Step S3-1: Establishing a PTFE / Al active projectile shock wave overpressure peak calculation model; For PTFE / Al active materials, due to the different explosion heat, it is converted into TNT equivalent based on the energy similarity principle. ； is the equivalent TNT weight of static PTFE / Al active material; is the mass of the active core participating in the reaction; Explosion heat of PTFE / Al active material; Hot for TNT; For active projectiles with a certain penetration speed, according to the energy similarity principle, the energy increase caused by the charge movement can be regarded as the increase in charge amount, so ； is the equivalent TNT weight of dynamic PTFE / Al active material; is the equivalent TNT weight of static PTFE / Al active material; Explosion heat of PTFE / Al active material; It is the residual speed of the active projectile after hitting the target; After the collision between the projectile and the target, part of the energy released by the active material will be converted into the shell deformation and destruction energy and the kinetic energy of the shell fragments, and the other part will be converted into the kinetic energy and internal energy of the deflagration products, forming an overpressure in the surrounding air. The activation rate and energy conversion of the active material can be expressed as ； Where n is the activation rate of the active material; is the mass of the active core participating in the reaction; is the total mass of the active core; is the activation length of the active core; is the full length of the active core; is the total energy released by the active core; It is the reaction heat of the active core material; is the internal energy of the deflagration products; is the shell deformation failure energy; is the kinetic energy of the deflagration products; Added kinetic energy to all fragments; Based on this, when the deflagration propagates after the target, the deflagration products expand according to the isentropic law, and the internal energy of the deflagration products can be obtained: ； In the formula, is the mass of the active core participating in the reaction; Explosion heat of PTFE / Al active material; is the shell radius; r is the distance from the test point to the center of the deflagration; Kinetic energy of deflagration products ； In the formula, is the mass of the active core participating in the reaction; v p is the fragment velocity; is the acceleration due to gravity; The added kinetic energy of all fragments ； In the formula, v p is the fragment velocity; is the mass of all fragments; is the acceleration due to gravity; For shell deformation and damage energy It accounts for about 3% of the total energy. Taking the head metal block and the shell as a whole, the energy released by the active material into the target can be obtained from the equivalent relationship. Total energy released by the active core The ratio between ； In the formula, is the initial activation ratio; is the shell radius; is the radius of the shell when it is deformed and broken; is the equivalent TNT weight of dynamic PTFE / Al active material; The equivalent TNT equivalent of PTFE / Al left for deflagration products; By combining the above formulas, we can obtain the peak overpressure of the air shock wave: for ； in, is the equivalent TNT equivalent of PTFE / Al left for the deflagration products; r is the distance from the test point to the deflagration center; and satisfies 1≤ ≤10; Step S3-2: Establishing the positive pressure zone action time Computational models; Positive pressure zone action time It is another characteristic parameter of the shock wave of the deflagration reaction of the active material and one of the important indicator parameters that affect the magnitude of the destructive effect on the target. Its calculation can be established through an empirical formula based on the explosion similarity rate through experiments. For the deflagration reaction of the PTFE / Al active core in the air, The calculation formula is: ； Where μ is the correction factor, and the value of PTFE / Al active material is 1.35×10 -3 ; r is the distance from the test point to the center of the deflagration; The equivalent TNT equivalent of PTFE / Al left for deflagration products; Step S4: Establishing a calculation model for the amount of deformation caused by the explosion and perforation of the aftereffect target by the PTFE / Al active projectile; the step S4 specifically comprises the following steps: Step S4-1: Establishing a calculation model for the specific kinetic energy of the aftereffect target plate of the active projectile; Step S4-2: Establishing a calculation model for the aftereffect target plate deformation; Step S4-3: Calculating the limit deformation of the aftereffect target plate; Step S4-4: Calculate the aftereffect target plate deformation based on the pressure-time curve generated by the debris cloud impact and the active material deflagration measured in the test, and compare it with the limit deformation. The value less than the limit deformation is considered to be effective.

2. The method for predicting the explosive penetration damage behavior of active projectiles according to claim 1 is characterized in that: The step S4-1 is specifically as follows: The after-effect target plate penetration damage mainly comes from the specific kinetic energy of the penetrator being greater than the unit deformation work of the target plate. The dynamic deformation work of the target plate can be expressed as ； Where K1 is the proportionality coefficient, which depends on the material properties. For Al2024, K1=3; A s is the penetration area of ​​the penetrator hitting the target plate; h * is the target plate thickness; σ b is the destructive strength limit of the target plate; Therefore, the deformation work of the target plate per unit thickness and unit area can be expressed as ； When the projectile acts on the target plate, the specific kinetic energy per unit thickness per unit area E b1 When the target plate is greater than the deformation work e, the target plate will be penetrated and damaged by the projectile; for the target plate made of Al2024, the penetration probability is P me The relationship between the kinetic energy of the penetrator and ； The specific kinetic energy of metal materials such as tungsten alloy / steel colliding with Al2024 target plate is expressed as ； In the formula, E ba is the specific kinetic energy per unit area of ​​Al2024 per unit thickness; w is the mass of the projectile; v is the impact velocity; S is the frontal area of ​​the projectile; h * is the target plate thickness; g is the gravitational acceleration; Φ is the projectile shape coefficient, which is taken as 0.005; For active materials, their mechanical strength and density are lower than those of metal materials, which results in a larger penetration area of ​​the target plate. Therefore, in the above formula, The specific kinetic energy of the active projectile acting on the Al2024 target plate is obtained by correction based on ； Where k is the correction factor, and the PTFE / Al active material is taken as 1.6; M is the total mass of the PTFE / Al active core; is the mass of the punch block; h * is the target plate thickness; It is the remaining speed of the active projectile after hitting the target.

3. The method for predicting the explosive perforation damage behavior of active projectiles according to claim 1, characterized in that: The step S4-2 is specifically as follows: After the target plate is penetrated and penetrated, the pressure released by the explosion of the debris cloud and its active materials on the target acts on the aftereffect target plate. The deformation of the aftereffect target plate is proportional to the impulse acting on the aftereffect target plate and inversely proportional to the density and thickness of the shell material. Therefore, the deformation of the aftereffect target plate can be expressed as ； Where K2 is a constant, and the flat-head penetrator is taken as 2.212; ρ t is the target plate density; is the shock wave load pressure at any time; h is the action time of the shock wave load; * is the target plate thickness.

4. The method for predicting the explosive perforation damage behavior of active projectiles according to claim 1, characterized in that: The step S4-3 is specifically as follows: According to the stress intensity factor in fracture mechanics K I The physical meaning is that when the stress intensity factor at the edge of the through hole is greater than the ultimate strength factor of the material K IC When , the crack at the edge of the through hole will expand, otherwise it will not expand; the ultimate strength factor of the crack of the finite width and length strip can be expressed as ； Where G is a constant related to the crack geometry; E is the elastic modulus of the target plate material; a is 1 / 2 of the crack length; L0 is the side length of the aftereffect target plate; is the limit deformation of the aftereffect target plate; For Al2024 target material K IC It can be obtained by looking up the table; so the limit deformation of the aftereffect target plate is 。 5. The method for predicting the explosive penetration damage behavior of active projectiles according to claim 3 is characterized in that: The step S4-4 is specifically as follows: The pressure-time curve produced by the impact of the debris cloud and the explosion of the active material was measured by experiment. The deformation of the after-effect target plate at the corresponding time is calculated; when the deformation value of the after-effect target plate obtained is less than the limit deformation value of the after-effect target plate, it is an effective value.

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