A method for calculating the coupling energy distribution and aftereffect damage of a metal reactive fragment target.

Abstract

This invention discloses a method for calculating the coupled energy distribution and aftereffect damage of metal reactive fragments after impact with a target. The invention considers fragment activation under load, energy release from secondary impact with the target, kinetic-chemical energy coupling, and the critical criterion for aftereffect target plate damage. By calculating the fragmentation and activation behavior after the reactive fragment collides with the protective target plate, and obtaining the remaining velocity of the reactive fragment after penetrating the target according to the law of conservation of energy, the fragmentation and scattering behavior behind the target are analyzed to establish a fragment scattering field behind the target. Considering the energy release efficiency of the secondary impact reaction, the kinetic-chemical energy density distribution acting on the aftereffect target plate is obtained. Finally, combined with the critical damage criterion for the aftereffect target plate, the damage area of ​​the coupled energy field on the aftereffect target plate is calculated, achieving a quantitative characterization of the destructive power of the metal reactive fragment on the aftereffect target plate.

Description

Technical Field

[0001] This invention relates to the field of reactive fragment damage assessment technology, specifically to a method for calculating the coupling energy distribution and aftereffect damage of a metal reactive fragment target. Background Technology

[0002] Reactive material fragments possess both the penetration capability of inert metal fragments and the energy release capability of energetic materials, causing coupled damage to targets through kinetic and chemical energy, significantly improving damage effectiveness. Missiles, aircraft, and radars are primary targets for fragment damage, and can typically be equivalent to a spaced target plate composed of a protective structural target plate and a follow-effect target plate. How to quickly and accurately assess the destructive power of reactive material fragments on follow-effect target plates is a key focus in the field of reactive fragment damage capability assessment.

[0003] Currently, the destructive capability of reactive material fragments is mainly assessed through three methods: First, experimental methods, which involve setting up instruments and devices such as pressure and temperature sensors, high-speed cameras, X-ray imaging, and equivalent target plates to conduct ballistic gun or static explosion experiments, obtaining damage effect parameters such as quasi-static pressure, temperature, spatiotemporal distribution of coupled energy fields, and target plate perforation area generated by the energy release of reactive material fragments; second, numerical simulation methods, which involve establishing a reaction state equation for explosive-like materials to calculate the interaction process between reactive material fragments and the target; and third, theoretical calculation methods, which involve establishing an impact response model for reactive materials to calculate the energy release of reactive materials.

[0004] However, existing methods for obtaining the destructive power of reactive material fragments on the aftereffect target plate in a spaced target plate have certain problems: In the actual application of reactive material fragments, parameters such as fragment density, strength, fracture toughness, energy content, reaction rate, and structure, as well as target plate material, thickness, spacing distance, and projectile-target collision velocity, all affect their destructive power; for experimental methods, the reactive material formulation system, preparation process, and equivalent target structure are diverse. To conduct destructive power verification experiments on reactive material fragments with vastly different properties and numerous equivalent target structures under different working conditions requires enormous human and material resources, and is also prone to... The methods are easily constrained by experimental conditions and site limitations. For numerical simulation methods, different reactive materials require corresponding material models and equations of state, necessitating extensive experimentation. Furthermore, there is a current lack of equations of state specifically for reactive materials, and the existing equations of state for explosives are not fully applicable to the impact response process of reactive materials. This leads to room for improvement in the accuracy and realism of numerical simulation results. For theoretical calculation methods, existing research focuses primarily on establishing models of the energy release behavior of reactive materials, lacking quantitative methods to characterize the impact of kinetic-chemical energy coupling on the destructive power of the resulting target plate. All these issues prevent experimental, numerical simulation, and theoretical calculation methods from meeting the need for rapid assessment of the destructive power of reactive fragments on spaced target plates. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the coupled energy distribution and aftereffect damage of metal reactive fragments on a target. It fully considers the parameters of the fragments and the target plate, as well as the projectile-target interaction conditions. All parameters can be obtained through simple performance characterization tests. By calculating the coupled energy distribution of the kinetic and chemical energy of the reactive fragments and combining it with the critical damage criterion of the aftereffect target plate, the destructive power on the aftereffect target plate can be obtained. This eliminates the need to conduct numerous experiments under various working conditions, thereby saving human and material resources and significantly improving the efficiency of assessing the damage of reactive fragments to spaced target plates. The present invention provides a method for calculating the coupling energy distribution and aftereffect damage of a metal reactive fragment target, comprising: Step 1: Based on the critical fragmentation pressure and critical reaction threshold of the metal reactive fragment, calculate the degree of fragmentation and activation of the metal reactive fragment when it collides with the target in front of the spaced target plate. Step 2: Calculate the remaining velocity of the metal reaction fragments before and after penetrating the target plate according to the law of conservation of energy. Step 3: Based on the dispersion behavior of metal reactive fragments after penetrating the target, establish the distribution of the debris cloud in the space behind the target. Step 4: Based on the spatial debris cloud distribution after the metal reactive fragments penetrate the front target and the activation degree of the reactive fragments after penetrating the front target, calculate the energy density distribution of the metal reactive fragment cloud acting on the rear target. Step 5: Calculate the damage area of ​​the metal reaction fragments to the aftereffect target plate based on the aftereffect target plate damage criterion and chemical energy coupling damage capability.

[0006] Preferably, in step one, the critical threshold for the reaction of the metal reaction fragment is the critical pressure threshold or the critical temperature threshold.

[0007] Preferably, in step one, The degree of fragmentation of metal reaction fragments L f for:

[0008] in, L f To account for the fracture size of sparse wave unloading; L s To disregard the fracture size due to sparse wave unloading; L 2 represents the sparse wave unloading size; , Y s The critical fragmentation pressure of reactive metal fragments under impact load; d The shock wave attenuation coefficient of the metal reactive fragment; , v0 represents the velocity of the metal reaction fragment hitting the target; r p and U p These are the density of the metal reactive fragments and the shock wave velocity within the metal reactive fragments, respectively. r t and U t These are the target density in front of the spaced target plate and the shock wave velocity in the target in front of the spaced target plate, respectively. , h The thickness of the target in front of the interval target plate; u p and u t These represent the particle velocities of the metal reaction fragments and the target in front of the spacer plate, respectively. C p and C t These are the rarefaction wave velocities in the metal reactive fragments and the front target of the spacer target plate, respectively. Based on the pressure criterion, the activation degree of the metal reactive fragments is as follows:

[0009] in, L r To account for the activation size of sparse wave unloading; L 1 represents the activation size without considering sparse wave unloading. , P c The critical threshold for the reaction of metal reactive fragment materials; Based on the temperature criterion, the activation degree of the metal reaction fragments is as follows:

[0010] in, L The length of the fragment; a These are constants related to the reactivity of metal reactive fragment materials; T r The critical temperature threshold for the reaction of metallic reactive fragment materials; T t The temperature at which the metal reactive fragment material reacts completely; T To determine the temperatures corresponding to different impact pressures on the Hugoniot curves. , , , ; T i The initial temperature of the metal reaction fragments; c G is the Grüneisen constant for metal reactive fragments;V fi and V f The specific volumes are, respectively, the metal reactive fragments in their initial state and the target volume before and after impacting the target plate at the impact interval; C Characteristic parameters of metal reaction fragments; r f The density of the metal reactive fragments impacting the target plate before and after the target plate.

[0011] Preferably, in step two, the residual velocity of the metal reaction fragments before and after penetrating the target plate is... v r for:

[0012] in, m p For the mass of metal reaction fragments; v 0 represents the velocity of the metal reaction fragment hitting the target; A and t The area and thickness of the stopper; G t The shear modulus of the target before the spacer plate; D The diameter of the metal reaction fragment. t ud The dynamic shear fracture strength of the target in front of the spaced target plate; m plug The mass of the stopper block.

[0013] Preferably, in step three, the metal reaction fragment target forms an approximately truncated cone-shaped empty fragment distribution with a scattering angle of […]. i , i + dth Number of fragments within ] N θi for:

[0014] in, i max The maximum scattering angle of the metal reaction fragments. , A , B These are material coefficients related to the properties of reactive metal fragments. v 0 represents the velocity of the metal reaction fragment hitting the target. U t The shock wave velocity in the target in front of the spaced target plate; N 0 represents the total number of fragments in the broken section. , L f The degree of fragmentation of the metal reaction fragments. L The length of the metal reaction fragment;m p For the mass of metal reaction fragments; r p Density of metal reaction fragments; s a This represents the average fragment size of the shattered portion of the metal reaction fragment. , Y The yield strength of the metal reactive fragment. v r The remaining velocity of the metal reactive fragment before and after penetrating the spaced target plate; Scattering Angle [ i , i + dth Fragment speed within the range v θi for

[0015] in, For the angle of dispersion [ i , i + dth Any angle within the range.

[0016] Preferably, in step four, the kinetic energy distribution per unit fragment of the fragment cloud... E ei for:

[0017] Chemical energy distribution per unit fragment of a fragment cloud E ai for:

[0018] Average kinetic energy density distribution of the target plate after the action of the debris cloud E kθ for:

[0019] Average chemical energy density distribution of the target plate after the action of the debris cloud E rθ for:

[0020] in, L f The degree of fragmentation of the metal reaction fragments; L r To account for the activation size of sparse wave unloading; m p For the mass of metal reaction fragments; v θi For the angle of dispersion [ i , i + dth Fragment velocity within the range; N 0 represents the total number of fragments in the broken section; N θi For the angle of dispersion [ i , i + dth The number of fragments within; i max The maximum scattering angle of the reaction fragments; The spacing between the target plates; Energy release efficiency of the secondary collision reaction after activation or for:

[0021] in, v mid and v s This is a constant related to the reaction characteristics of metal reactive fragment materials.

[0022] Preferably, in step five, the area of ​​damage to the target plate by the metal reaction fragments is... S e for: in, L f The degree of fragmentation of the metal reaction fragments; m p For the mass of metal reaction fragments; m l This refers to the mass loss due to fragmentation. v θi For the angle of dispersion [ i , i + dth Fragment velocity within the range; k A parameter characterizing the contribution of chemical energy to the damage process; L The length of the fragment; i max The maximum scattering angle of the metal reaction fragments; L r The activation size is taken into account for sparse wave unloading.

[0023] Preferably, the metal reaction fragments are prepared from intermetallic compounds, amorphous alloys, or high-entropy alloy metal reaction materials.

[0024] Beneficial effects: 1. This invention analyzes the reaction fragment collision process with the target plate in front of the target plate, and calculates the fragmentation, activation behavior and residual velocity of the reaction fragment after penetrating the target plate by combining the characteristic parameters of the reaction fragment itself. The complex process is simplified into a one-dimensional stress wave propagation process, and the residual velocity is calculated by energy conservation, without the need to carry out a large number of experiments to fit empirical formulas.

[0025] 2. This invention establishes a theoretical model for the dispersion of fragment clouds after reactive fragments penetrate the target. Combining the fragmentation and activation levels of the reactive fragments, it obtains the spatial evolution law of the fragment cloud and the coupled energy distribution of kinetic and chemical energy. Compared with traditional fragment spatial dispersion behavior, this model introduces the spatial distribution of chemical energy and considers the energy release efficiency of secondary impacts with the target, consistent with the actual process, making the calculation more comprehensive and reliable.

[0026] 3. This invention takes into account the mass loss during the penetration of the target by the reactive fragments, especially under high-speed collision conditions. By converting the contribution of chemical energy to the damage process into equivalent kinetic energy and combining it with the specific kinetic energy damage criterion of the target plate, the damage area of ​​the reactive fragments to the target plate after the damage is calculated. The calculation results are true and reliable.

[0027] 4. This invention supports the calculation of target parameters and projectile-target interaction conditions for various types of reaction fragments. It is more efficient than traditional numerical simulation methods and can be used as a basis for selecting fragments of high-explosive fragmentation warheads and evaluating the destructive power of high-explosive fragmentation warheads. It provides support for the design of high-explosive fragmentation warheads and optimizes the fragment design process.

[0028] 5. This invention is applicable to metal reaction fragments, such as intermetallic compounds, amorphous alloys, high-entropy alloy metal reaction materials, etc. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention.

[0030] Figure 2 This is a schematic diagram of the damage model of metal reactive fragments to the aftereffect target plate.

[0031] Figure 3 The curve shows the activation behavior of metal reactive fragments penetrating a 4mm steel target in Example 1 of this invention.

[0032] Figure 4 The curve shows the dispersion behavior of the metal reactive fragments after penetrating a 4mm steel target in Example 1 of this invention.

[0033] Figure 5 This is the energy distribution curve of the target plate after the metal reactive fragment penetrates the 4mm steel target and acts at a position of 300mm in Embodiment 1 of the present invention.

[0034] Figure 6 This is the damage area curve of a 1.5mm steel target damaged by metal reactive fragments according to the present invention. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0036] This invention provides a method for calculating the coupling energy distribution and aftereffect damage of metal reactive fragments to a target. The method considers fragment activation under load, secondary impact energy release, kinetic-chemical energy coupling, and the critical criterion for aftereffect target plate damage. It can achieve quantitative characterization of the damage effect of metal reactive fragments on aftereffect target plates, provide a theoretical method for predicting the damage effect of metal reactive fragments against target plates with different structural spacing, and provide strong support for the assessment of the damage effect of metal reactive fragment warheads.

[0037] The flowchart of this invention is as follows Figure 1 As shown, the specific steps include the following: Step 1: Calculate the degree of fragmentation and activation of the metal reactive fragments upon impact with the target plate in front of the spacer. The degree of fragmentation is calculated based on the material's critical fragmentation pressure; the degree of activation can be calculated using either the critical reaction pressure threshold or the critical reaction temperature threshold.

[0038] The degree of fragmentation of metal reaction fragments can be expressed as: (1) (2) (3) (4) (5) In the formula, P 0 represents the pressure when the metal reactive fragment collides with the front target of the spaced target plate; x This is the distance from the collision surface of the metal reactive fragment; P The distance from the metal reaction fragment collision surface x Pressure at a distance; v 0 represents the velocity of the metal reaction fragment hitting the target; r p and U p These are the density of the metal reactive fragments and the shock wave velocity within the metal reactive fragments, respectively. r t and U t These are the target density in front of the spaced target plate and the shock wave velocity inside the front target plate, respectively. L 2 represents the sparse wave unloading size; h The thickness of the target in front of the interval target plate; u p and ut These represent the particle velocities of the metal reaction fragments and the target in front of the spacer plate, respectively. C p and C t These are the rarefaction wave velocities in the metal reactive fragments and the front target of the spacer target plate, respectively. L s To disregard the fracture size due to sparse wave unloading; Y s This refers to the critical fragmentation pressure of metallic reactive materials under impact load. d The shock wave attenuation coefficient of the metallic reactive material. L f To account for the fracture size of sparse wave unloading.

[0039] When the pressure criterion is used, the degree of activation of the reaction fragments can be expressed as: (6) (7) In the formula, L 1 represents the activation size without considering sparse wave unloading; P c The critical threshold for the reaction of metallic reactive materials; Y s The critical fragmentation pressure of metallic reactive materials under impact load; L r The activation size is taken into account for sparse wave unloading.

[0040] Based on the temperature criterion, the impact temperature rise process of the metal reactive fragment can be expressed as: (8) (9) (10) In the formula, C and c Characteristic parameters of metal reaction fragments; r f The density of the metal reactive fragments before and after impacting the target plate in the spacer; V fi and V f The specific volumes are, respectively, the metal reactive fragments in their initial state and the target volume before and after impacting the target plate at the impact interval; T i The initial temperature of the metal reaction fragments; T The temperature corresponding to the Hugoniot curve under different impact pressures; T a , Tb , T c The three terms for solving the impact temperature rise can be summed; c G denoted as the Grüneisen constant for the reaction fragment.

[0041] Therefore, the activation degree of the metal reactive fragment can be expressed as: (11) In the formula, T r This refers to the critical temperature threshold for the reaction of metallic reactive materials. T t The temperature at which the metallic reactants react completely. L The length of the fragment; a This is a constant related to the reactivity of metallic reactive materials.

[0042] Step 2: Calculate the remaining velocity of the metal reaction fragment before and after penetrating the target plate. This can be obtained through experimental methods and theoretical calculations.

[0043] The experimental method involves testing the ballistic limits under different target back thicknesses. Based on the experimental results, the THOR equation is fitted to establish a semi-empirical predictive relationship for the ballistic limits of reactive metal fragments. (12) In the formula, v s This is the ballistic limit velocity; A The cross-sectional area of ​​the fragment; m For fragment quality; c , β The experimental coefficients are to be determined.

[0044] (13) In the formula, v r This represents the remaining velocity.

[0045] The theoretical calculation method uses the law of conservation of energy to calculate the residual velocity of the metal reactive fragment after penetrating the target plate before penetration, based on the process of the metal reactive fragment penetrating the target plate. Considering the influence of shear stress on the penetration of the metal reactive fragment, it is assumed that the metal reactive fragment does not deform during penetration, only causing a blocking effect on the target plate, and the plug is ejected along with the metal reactive fragment, maintaining the same residual velocity. Therefore, the energy of the metal reactive fragment during penetration can be divided into four parts: first, the work done by the metal reactive fragment during penetration due to the resistance of the target plate; second, the work done by the shear stress on the plug during its formation; third, the kinetic energy of the plug; and fourth, the residual kinetic energy of the metal reactive fragment.

[0046] (14) (15) (16) In the formula, m p For the mass of metal reaction fragments; t The thickness of the plug; G t The shear modulus of the target material in front of the spacer target plate; D The diameter of the metal reaction fragment. t ud The dynamic shear fracture strength of the target in front of the spaced target plate is typically expressed as twice the static shear fracture strength. A s The area of ​​the sheared region; m plug The mass of the stopper block.

[0047] Step 3: After the metal reactive fragment penetrates the target, it breaks apart, forming an approximately truncated cone of empty fragments. Assuming that the broken part of the metal reactive fragment is spherical, the fragment distribution within the truncated cone can be calculated using the following formula.

[0048] (17) (18) (19) (20) (twenty one) In the formula, s a The average fragment size of the shattered portion of the metal reaction fragment; Y The yield strength of the metal reaction fragment; L The length of the metal reaction fragment; N 0 represents the total number of fragments in the broken section; i max The maximum scattering angle of the metal reaction fragments. A , B Material coefficients related to the properties of metal reactive fragments; N θi For the angle of dispersion [ i , i + dth The number of fragments within; among which, v θi For the angle of dispersion [ i , i + dth Fragment speed within the range.

[0049] Step 4: Based on the spatial fragment distribution after the metal reactive fragments penetrate the front target and the activation degree of the metal reactive fragments after penetrating the front target, combined with the secondary collision reaction of the fragment cloud behind the target with the target plate, the energy density distribution of the metal reactive fragment cloud acting on the rear target is calculated.

[0050] (twenty two) (twenty three) (twenty four) (25) (26) In the formula, or The energy release efficiency of the secondary collision reaction after activation; v mid and v s These are constants related to the reactivity characteristics of metallic reactive materials; E ei This represents the kinetic energy distribution per unit fragment in a fragment cloud. E ai The unit fragment chemical energy distribution of the fragment cloud; E kθ The average kinetic energy density distribution of the target plate after the action of the debris cloud; E rθ This represents the average chemical energy density distribution of the target plate after the interaction of the debris cloud. The spacing between the target plates.

[0051] Step 5: Obtain the kinetic energy damage criterion for target plate damage based on the law of conservation of energy, consider the mass loss during the fragment penetration process, and calculate the damage area of ​​the reactive fragments on the aftereffect target plate by combining the contribution rate of chemical energy in the damage process.

[0052] The mass loss of the metal reactive fragment during the process of penetrating the target plate before the target plate is penetrated can be expressed as: (27) Considering the mass loss during the penetration of the pre-spaced target plate, the kinetic energy density of the metal reactive fragments acting on the post-spaced target plate region can be expressed as: (28) Considering the mass loss during the penetration of the pre-spacer target plate, the chemical energy density of the metal reaction fragments acting on the post-spacer target plate region can be expressed as: (29) The critical energy density at which fragments penetrate the target plate and cause damage to the affected area can be expressed as: (30) Therefore, the kinetic and chemical energies required for the target to destroy the spacer plate after the metal reaction fragments have a certain relationship: (31) When the damage area of ​​the metal reaction fragments to the target behind the spacer plate is smaller than the area affected by the fragment cloud, the total kinetic energy and chemical energy of the fragment cloud are expressed as follows: (32) Assuming the damaged area is S e We can obtain: (33) Substituting equations (32) and (33) into equation (31), we can obtain (34) When the damage area of ​​the metal reaction fragments on the target behind the spacer plate is greater than the area affected by the fragment cloud, there is no fragment action at the outer diameter of the damage area on the target behind the spacer plate, and damage is caused solely by chemical energy. Therefore, the following condition must be met: (35) Substituting equations (33) and (35) into equation (31), we get: (36) Therefore, the damage area of ​​the metal reactive fragments to the target behind the spacer plate can be expressed as: (37) In the formula, T The thickness of the target after the interval target plate. d y The yield strength of the target material behind the spacer target plate. S p The effective area of ​​the fragments on the target behind the spacer plate; m l This refers to the mass loss due to fragmentation. C The impact area of ​​the fragment; c 2, α 2, β 2, c 2, l 2 represents the parameters determined based on the target material; E klθ The average kinetic energy density distribution takes into account mass loss; E rlθ The average chemical energy density distribution taking mass loss into account; k A parameter characterizing the contribution of chemical energy to the damage process.

[0053] Example 1 The following description uses a specific example. The calculation example parameters are shown in Table 1.

[0054] Table 1 Calculation Example Parameters

[0055] Step 1: Calculate the impact pressure when the metal reactive fragment collides with the front target of the spacer plate, and calculate the degree of fragmentation and activation of the metal reactive fragment based on the critical fragmentation pressure and critical reaction threshold of the metal reactive fragment.

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] In the formula, v 0 represents the velocity of the metal reaction fragment hitting the target; r p and U p These are the density of the metal reactive fragments and the shock wave velocity within the metal reactive fragments, respectively. r t and U t These represent the target density in front of the spaced target plate and the shock wave velocity in the target plate, respectively. u p and u t These represent the particle velocities of the metal reaction fragments and the target plate, respectively. C p and C t These are the rarefaction wave velocities in the metal reaction fragments and the target plate, respectively. h The thickness of the target in front of the interval target plate; d The shock wave attenuation coefficient of the metallic reactive fragment material; P c The critical threshold for the reaction of metal reactive fragment materials; Y s The critical fragmentation pressure of the metallic reactive material under impact loading is given. The calculated fragmentation activation behavior curve of the metallic reactive fragment penetrating a 4mm steel target is shown below. Figure 3As shown.

[0064] Step 2: Using the law of conservation of energy, and considering the effect of shear stress on the penetration of the metal reactive fragments into the target plate before penetration, while ignoring the deformation of the metal reactive fragments during penetration, calculate the remaining velocity of the metal reactive fragments after penetration into the target plate.

[0065]

[0066] In the formula, m p For the mass of metal reaction fragments; A and t The area and thickness of the stopper; G t The shear modulus of the target material in front of the spacer target plate; D The diameter of the metal reaction fragment. t ud The dynamic shear fracture strength of the target in front of the spaced target plate is typically expressed as twice the static shear fracture strength. A s The area of ​​the sheared region; m plug The mass of the stopper block.

[0067] Step 3: After the metal reactive fragment penetrates the target, it breaks apart, forming an approximately truncated cone of empty fragments. Assuming that the broken part of the metal reactive fragment is spherical, the fragment distribution within the truncated cone can be calculated using the following formula.

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] In the formula, S a The average fragment size of the shattered portion of the metal reaction fragment; Y The yield strength of the metal reaction fragment; L The length of the metal reaction fragment; N 0 represents the total number of fragments in the broken section; i max The maximum scattering angle of the metal reaction fragments. A , B Material coefficients related to the properties of metal reactive fragments; Nθi For the angle of dispersion [ i , i + dth The number of fragments within; among which, v θi For the angle of dispersion [ i , i + dth The fragment velocity within the range is shown in the calculated curve of the dispersion behavior of the metal reactive fragments after penetrating a 4mm steel target. Figure 4 As shown.

[0074] Step 4: Based on the spatial fragment distribution after the metal reactive fragment penetrates the target and the activation degree of the metal reactive fragment after penetrating the target, combined with the spatial expansion of the fragment cloud behind the target colliding with the target, the energy density distribution of the metal reactive fragment fragment cloud acting on the target behind the target is calculated.

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] In the formula, or The energy release efficiency of the secondary collision reaction after activation; v mid and v r These are constants related to the reactivity characteristics of metallic reactive materials; E ei This represents the kinetic energy distribution per unit fragment in a fragment cloud. E ai This represents the energy distribution per unit fragment of a fragment cloud. E kθ The average kinetic energy density distribution of the target plate after the action of the debris cloud; E rθ The average chemical energy density distribution of the target plate after the impact of the fragment cloud is shown. The calculated energy distribution curve of the target plate after the metal reaction fragments penetrated the 4mm steel target and acted at a position of 300mm is shown in the figure. Figure 5 As shown.

[0081] Step 5: Obtain the kinetic energy damage criterion for target plate damage based on the law of conservation of energy, consider the mass loss during the fragment penetration process, and calculate the damage area of ​​the metal reaction fragment on the aftereffect target plate by combining the contribution rate of chemical energy in the damage process.

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] In the formula, T The thickness of the target behind the spacer plate. d y The yield strength of the target material behind the spacer target plate. S p This refers to the area of ​​the fragments acting on the target plate. m l This refers to the mass loss due to fragmentation. C The impact area of ​​the fragment; c 2, α 2, β 2, c 2, l 2 represents the parameters determined based on the target material; E klθ The average kinetic energy density distribution takes into account mass loss; E rlθ The average chemical energy density distribution taking mass loss into account; k This parameter characterizes the contribution of chemical energy to the damage process. The calculated damage area curve of a 1.5mm steel target damaged by metal reaction fragments is shown below. Figure 6 As shown.

[0089] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the coupled energy distribution and aftereffect damage of a metal reactive fragment target, characterized in that, include: Step 1: Based on the critical fragmentation pressure and critical reaction threshold of the metal reactive fragment, calculate the degree of fragmentation and activation of the metal reactive fragment when it collides with the target in front of the spaced target plate. Step 2: Calculate the remaining velocity of the metal reaction fragments before and after penetrating the target plate according to the law of conservation of energy. Step 3: Based on the dispersion behavior of metal reactive fragments after penetrating the target, establish the distribution of the debris cloud in the space behind the target. Step 4: Based on the spatial debris cloud distribution after the metal reactive fragments penetrate the front target and the activation degree of the reactive fragments after penetrating the front target, calculate the energy density distribution of the metal reactive fragment cloud acting on the rear target. Step 5: Calculate the damage area of ​​the metal reaction fragments to the aftereffect target plate based on the aftereffect target plate damage criterion and chemical energy coupling damage capability.

2. The method as described in claim 1, characterized in that, In step one, the critical threshold for the reaction of the metal reaction fragment is either the critical pressure threshold or the critical temperature threshold.

3. The method as described in claim 1 or 2, characterized in that, In step one, The degree of fragmentation of metal reaction fragments L f for: in, L f To account for the fracture size of sparse wave unloading; L s To disregard the fracture size due to sparse wave unloading; L 2 represents the sparse wave unloading size; , Y s The critical fragmentation pressure of reactive metal fragments under impact load; δ The shock wave attenuation coefficient of the metal reactive fragment; , v 0 represents the velocity of the metal reaction fragment hitting the target; ρ p and U p These are the density of the metal reactive fragments and the shock wave velocity within the metal reactive fragments, respectively. ρ t and U t These are the target density in front of the spaced target plate and the shock wave velocity in the target in front of the spaced target plate, respectively. , h The thickness of the target in front of the interval target plate; u p and u t These represent the particle velocities of the metal reaction fragments and the target in front of the spacer plate, respectively. C p and C t These are the rarefaction wave velocities in the metal reactive fragments and the front target of the spacer target plate, respectively. Based on the pressure criterion, the activation degree of the metal reactive fragments is as follows: in, L r To account for the activation size of sparse wave unloading; L 1 represents the activation size without considering sparse wave unloading. , P c The critical threshold for the reaction of metal reactive fragment materials; Based on the temperature criterion, the activation degree of the metal reaction fragments is as follows: in, L The length of the fragment; a These are constants related to the reactivity of metal reactive fragment materials; T r The critical temperature threshold for the reaction of metallic reactive fragment materials; T t The temperature at which the metal reactive fragment material reacts completely; T To determine the temperatures corresponding to different impact pressures on the Hugoniot curves. , , , ; T i The initial temperature of the metal reaction fragments; γ G is the Grüneisen constant for metal reactive fragments; V fi and V f The specific volumes are, respectively, the metal reactive fragments in their initial state and the target volume before and after impacting the target plate at the impact interval; C Characteristic parameters of metal reaction fragments; ρ f The density of the metal reactive fragments impacting the target plate before and after the target plate.

4. The method as described in claim 1, characterized in that, In step two, the remaining velocity of the metal reactive fragments after penetrating the target plate before and after the target plate is... v r for: in, m p For the mass of metal reaction fragments; v 0 represents the velocity of the metal reaction fragment hitting the target; A and t The area and thickness of the stopper; G t The shear modulus of the target before the spacer plate; D The diameter of the metal reaction fragment. τ ud The dynamic shear fracture strength of the target in front of the spaced target plate; m plug The mass of the stopper block.

5. The method as described in claim 1, characterized in that, In step three, the metal reaction fragment target forms an approximately truncated cone-shaped empty fragment distribution, with a scattering angle of […]. θ , θ + dθ Number of fragments within ] N θi for: in, θ max The maximum scattering angle of the metal reaction fragments. , A , B These are material coefficients related to the properties of reactive metal fragments. v 0 represents the velocity of the metal reaction fragment hitting the target. U t The shock wave velocity in the target in front of the spaced target plate; N 0 represents the total number of fragments in the broken section. , L f The degree of fragmentation of the metal reaction fragments. L The length of the metal reaction fragment; m p For the mass of metal reaction fragments; ρ p Density of metal reaction fragments; s a This represents the average fragment size of the shattered portion of the metal reaction fragment. , Y The yield strength of the metal reactive fragment. v r The remaining velocity of the metal reactive fragment before and after penetrating the spaced target plate; Scattering Angle [ θ , θ + dθ Fragment speed within the range v θi for in, For the angle of dispersion [ θ , θ + dθ Any angle within the range.

6. The method as described in claim 1, characterized in that, In step four, the distribution of unit fragment kinetic energy of the fragment cloud. E ei for: Chemical energy distribution per unit fragment of a fragment cloud E ai for: Average kinetic energy density distribution of the target plate after the action of the debris cloud E kθ for: Average chemical energy density distribution of the target plate after the action of the debris cloud E rθ for: in, L f The degree of fragmentation of the metal reaction fragments; L r To account for the activation size of sparse wave unloading; m p For the mass of metal reaction fragments; v θi For the angle of dispersion [ θ , θ + dθ Fragment velocity within the range; N 0 represents the total number of fragments in the broken section; N θi For the angle of dispersion [ θ , θ + dθ The number of fragments within; θ max The maximum scattering angle of the reaction fragments; The spacing between the target plates; Energy release efficiency of the secondary collision reaction after activation η for: in, v mid and v s This is a constant related to the reaction characteristics of metal reactive fragment materials.

7. The method as described in claim 1, characterized in that, In step five, the area of ​​damage to the target plate by the metal reaction fragments is... S e for: in, L f The degree of fragmentation of the metal reaction fragments; m p For the mass of metal reaction fragments; m l This refers to the mass loss due to fragmentation. v θi For the angle of dispersion [ θ , θ + dθ Fragment velocity within the range; k A parameter characterizing the contribution of chemical energy to the damage process; L The length of the fragment; θ max The maximum scattering angle of the metal reaction fragments; L r The activation size is taken into account for sparse wave unloading.

8. The method as described in claim 1, characterized in that, The metal reaction fragments are prepared from intermetallic compounds, amorphous alloys, or high-entropy alloy metal reaction materials.

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