Combined impulse characterization method of prefabricated fragment warhead fragment and shock wave combined load

Abstract

The invention discloses a combined impulse characterization method of a prefabricated fragment warhead fragment and shock wave combined load, and the method comprises the steps: building a combined impulse calculation model through researching the motion law of fragments and shock waves after explosion, and the impact load characteristics of the fragments and shock waves on a target when the fragments and shock waves act on the target; a correction coefficient is obtained through an impulse test in combination with an impulse calculation model, the calculation model can basically represent the change rule of the combined impulse, and a reference is provided for coupling damage research.

Description

Technical Field

[0001] The present invention belongs to the field of ammunition damage, and particularly relates to a method for characterizing the combined impulse of fragments and shock waves of a prefabricated fragment warhead Background Technique

[0002] The main damage elements of the high-explosive fragmentation bombs used in modern battlefields are fragments and shock waves. Due to the energy dissipation of the fragments in such shell-loaded charges, the overpressure generated will be lower than that generated by a bare charge structure of the same mass and type. However, the high-speed fragments generated by such warheads will make the overall response of the structure subjected to the combined load of explosion and fragments very complex. Researchers are used to calling this damage effect the coupling effect. Compared with the action of a single load, under the coupling effect, the target can be more easily deflected and the deflection can be increased, the penetration time can be prolonged, and more energy can be transmitted to the target. Therefore, the relevant analysis of the coupling effect of the two damage elements after the explosion of the fragment warhead has been a research hotspot in recent years.

[0003] The current research focuses on the damage effect of the fragment warhead on the target and the mechanism and process of the coupling effect, lacking a description of the complete damage area of such charge structures. After the warhead explodes, for the change law of the detonation wave impulse, there are already mature calculation methods; for the fragments generated after the explosion, it has been found that the fragments also have impulse, which is easily affected by the charge amount and the spacing distance. However, there is no relevant report on the change law before and after the two impulses are superimposed and analyzed on the target. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for characterizing the combined impulse of fragments and shock waves of a prefabricated fragment warhead, so as to realize the description of the damage area of high-explosive fragmentation warheads in the form of impulse.

[0005] The technical solution for realizing the purpose of the present invention is as follows:

[0006] A method for characterizing the combined impulse of fragments and shock waves of a prefabricated fragment warhead, using the following formula to obtain the combined impulse:

[0007]

[0008] where M1 is the mass of the target square plate, V1 is the velocity obtained by the target square plate, λ′ is the dimension coefficient; H is the thickness of the target square plate, L is the width of the target square plate, ρ t is the density of the square plate material, σ′ is the static yield limit of the square plate material; α1 is the correction coefficient, obtained according to the following formula and the test of the damage degree of the target square plate:

[0009]

[0010] where Nfrag The number of fragments hitting the target square plate, m frag The mass of the fragments hitting the square plate, V avg The expected value of the fragment velocity, L is the width of the target square plate, R b The distance between the warhead and the target square plate, A is the fitting coefficient, ω e2 The equivalent TNT explosive of the detonation products.

[0011] Compared with the prior art, the remarkable advantages of the present invention are as follows:

[0012] (1) By studying the motion laws of fragments and shock waves after explosion, and the impact load characteristics of fragments and shock waves on the target when they act on the target, a combined impulse calculation model is established.

[0013] (2) Through impulse witnessing tests, the rationality of the combined impulse related calculation model is verified, and the variation laws of the combined impulse at different distances and different charge structures are obtained. Description of the Drawings

[0014] Figure 1 It is a derivation process of the combined impulse of the fragment and shock wave composite load of a prefabricated fragment warhead.

[0015] Figure 2 It is a schematic diagram of the ideal distribution of the combined impulse.

[0016] Figure 3 It is the test arrangement.

[0017] Figure 4 It is a diagram of the test results of the combined impulse of the fragment and shock wave composite load of a prefabricated fragment warhead. (a) is the analysis of the actual impulse of the target, and (b) is the combined impulse and solution combined analysis after explosion. Specific Embodiments

[0018] The following further introduces the present invention in conjunction with the drawings and specific embodiments.

[0019] A method for characterizing the combined impulse of the fragment and shock wave composite load of a prefabricated fragment warhead of the present invention, according to the motion laws of fragments and shock waves after explosion, establishes a combined impulse calculation model for the fragment and shock wave composite load, which specifically includes the following steps:

[0020] According to Figure 1 , first output the axial velocity distribution V of a one-end initiated prefabricated fragment cylindrical warhead 0x , take the average value of the output axial velocity and output V avg . Assume that there is a square plate with a length and width of L at a distance R b from the warhead, as Figure 2, the number of fragments hitting the target plate can be determined by the number probability density function of fragments in space and the dispersion angle of the warhead. By determining the number of fragments hitting the target plate, the impulse of the fragments on the target plate can be determined, and then the impulse value generated by the warhead at the target plate can be calculated. The sum of the two is the combined impulse generated by the warhead at the target plate.

[0021] Step 1: Establish the impulse model of the fragments

[0022] 1.1. Calculate the velocity of the preformed fragment cylindrical warhead with one-end initiation:

[0023]

[0024] In the formula, β is the ratio of the charge mass to the shell mass, V 0x is the velocity distributed along the axis of the warhead, D e is the detonation wave velocity, l and d are the length-diameter ratio and inner diameter of the warhead respectively, x is the relative initiation position of the fragment on the warhead from the initiation point, and E is the Gurney energy constant of the explosive.

[0025] 1.2. Establish the number probability density function curve of the fragments in space:

[0026] Obtain the distribution density of the fragments at different positions. According to the azimuth angle between the target plate and the warhead, after integration, N(θ i ~θ j ) can be obtained. N(θ i ~θ j ) is the number of fragments in the dispersion area within the space angle range of (θ i ~θ j ).

[0027]

[0028] ρ N (θ) is the distribution of the fragments in a certain angle interval, θ is the space angle of the fragments at the explosion radius R, is the mathematical expectation of the space angle θ, and its value is usually close to π / 20; σ is the mean square deviation of the space angle θ.

[0029] 1.3. Calculate the number of fragments hitting the target:

[0030]

[0031] L is the width of the target plate, R b is the distance between the warhead and the target plate.

[0032] 1.4. Take the average value of V 0x to obtain the expected value V avg of the fragment velocity, and calculate the average impulse of the fragments hitting the target plate as:

[0033]

[0034] N frag The number of fragments hitting the target square plate, m frag is the mass of the fragments hitting the square plate.

[0035] Step 2: Establish the impulse model of the shock wave

[0036] Calculate the average impulse of the preformed fragment warhead on the shock wave of the target:

[0037]

[0038] In the formula, ω e2 is the equivalent TNT explosive (kg) of the detonation products, A is the fitting coefficient, which is taken as 200 - 250 in the air and 300 - 370 on the ground.

[0039] Step 3: Establish the combined impulse calculation model of the fragment and shock wave composite load

[0040] 3.1 Calculate the combined impulse of the fragment and shock wave composite load:

[0041]

[0042] The combined impulse calculation model established above is the magnitude of the impulse at a certain position after the superposition of the fragment and the shock wave. After the combined impulse acts on the target, the magnitude of the impulse that produces the damage effect will be reduced due to the inertia of the target. To explore this attenuation, Figure 3 an impulse witness device is used for relevant research. This device consists of a slide rail, a low-friction slide rail vehicle, and a target square plate. The overpressure is measured by an overpressure sensor, the fragment velocity is measured by a velocity measurement target paper, and the motion velocity of the target square plate is measured by high-speed photography and a displacement sensor. Ideally, according to Figure 2 the explosion shock form, the impulse obtained by the target and the deflection of the square plate are what we want. In the actual situation (that is, Figure 3 the test layout form), after the combined impulse of the composite load acts on the square plate, it does work on the square plate in the form of penetration and deflection. The combined impulse of the composite load can be characterized by the impulse of the square plate and the degree of deflection of the square plate, but it cannot be a simple addition. This is because the test system has inertia and friction is inevitable, and the combined impulse of the composite load will be greater than the sum of the impulse of the square plate and the deflection deformation of the square plate.

[0043] Step 4: Establish the deflection impulse calculation model of the target square plate

[0044] 4.1 Calculate the deflection impulse of the target square plate

[0045]

[0046] In the formula, δ′ is the central deflection of the target square plate; λ′ is the dimensional coefficient; H is the thickness of the target square plate; I deb is the specific impulse of the shock wave; L is the width of the square plate; ρ t is the density of the square plate material; σ′ is the static yield limit of the square plate material.

[0047] The relationship between the combined impulse generated by the prefabricated fragment warhead and the impulse obtained by the target square plate is as follows:

[0048] 4.2. For the impulse witness device, the transformation relationship of the combined impulse is as follows:

[0049]

[0050] M1 is the mass of the target square plate, V1 is the velocity obtained by the target square plate, and α1 is the correction coefficient.

[0051] Step 4. Determine the correction coefficient

[0052] Without determining the magnitude of the correction coefficient, design an impulse witness test (such as Figure 3 ). After the explosion, the fragments and the shock wave do work on the target respectively. The load generated by the explosion wave and the impact of the fragments reaches the target. The initial velocity V1 of the square plate moving above the slide rail vehicle and the deformation degree δ′ of the target square plate are measured.

[0053] Table 1 Test condition settings

[0054]

[0055] First, conduct 1 group of 56×112mm bare charge impact tests for the impulse witness test. Calibrate the impulse witness test measurement system according to the movement of the square plate under the bare charge. Conduct several groups of 56×112mm prefabricated fragment warhead impact tests, with the prefabricated fragment warhead and the square plate at distances of 1m, 1.5m, 2m, and 2.5m respectively. Collect the velocities and overpressure values of the fragments at several locations. Collect the velocity of the square plate through high-speed photography and displacement sensors, and obtain the deformation of the square plate before the test through a 3D scanner.

[0056] Table 2 Test data on the damage degree of the target square plate

[0057]

[0058] Table 3 Calculation results and test data of each impulse at different explosion distances

[0059]

[0060]

[0061] Obtained from Table 2 and Table 3Figure 4 The impulse analysis curve, from Figure 4 (a) Within the explosion distance of 0 - 4m, I sum , I blast varies significantly with the distance, and the value is higher the closer it is to the explosion center. As the explosion distance increases, the combined impulse shows an exponential decline trend. The impulse value in the near - field region is relatively large, and it is considered that coupled damage can only occur in the near - field region. After exceeding 5m, the number of fragments hitting the square plate is small and the peak overpressure drops rapidly. I sum , I blast shows a slow decline trend and the value is close to 0. From Figure (b), it can be seen that in the near - field region, after the action of the composite load, due to inertia, the target plate will absorb part of the energy, making the impulse value of the rail vehicle in the ideal state higher than the actual value, and the difference between the calculated value and the test value is 20.2%. When the test distance is greater than 3.5m, the difference between the test value and the theoretical value is close to 50%. Most of the impulse acting on the square plate makes the square plate vibrate by itself or is converted into the internal energy of the square plate, and a small part of the energy is used to do work on the square plate. An explosion at close range can increase the acting load on the target structure, thereby improving the damage effect on the target.

[0062] If there is no influence of friction and inertia, it can be considered that the combined impulse of the composite load is equal to the sum of the impulse of the rail vehicle and the flexural deformation of the square plate. Comparing the impulse value of the rail vehicle under ideal near - field conditions with the actual impulse value of the rail vehicle, the actual value is about 15.6% lower than the ideal value. The correction coefficient α1 is taken as 1.156.

Claims

1. A combined impulse characterization method for composite loads of prefabricated fragment warhead fragments and shock waves, characterized in that: The combined impulse is obtained using the following formula: Where M1 is the mass of the target square plate, V1 is the velocity obtained by the target square plate, λ′ is the dimension coefficient; H is the thickness of the target square plate, L is the width of the target square plate, ρ t is the density of the square plate material, σ′ is the static yield limit of the square plate material; α1 is the correction coefficient, which is obtained according to the following formula and the target square plate damage degree test: Where N frag is the number of fragments hitting the target square plate, m frag is the mass of the fragments of the square plate, V avg is the expected value of fragment velocity, L is the width of the target square plate, R b is the distance between the warhead and the target square plate, A is the fitting coefficient, ω e2 The equivalent of TNT explosives for the detonation products.

2. The combined impulse characterization method of prefabricated fragment warhead fragments and shock wave composite load according to claim 1 is characterized in that: The number of fragments hitting the target square plate is: N(θ i ~θ j ) is (θ i ~θ j ) The number of fragments in the scattered area within the spatial angle range.

3. The combined impulse characterization method of prefabricated fragment warhead fragments and shock wave composite load according to claim 1 is characterized in that: The dimension coefficient λ′ is:

4. The combined impulse characterization method of prefabricated fragment warhead fragment and shock wave composite load according to claim 1, characterized in that: Expected value of fragment velocity V avg Obtained by taking the average of the output warhead axial velocity.

5. The combined impulse characterization method of prefabricated fragment warhead fragments and shock wave composite load according to claim 4 is characterized in that: The warhead axial velocity is: Where β is the ratio of charge mass to shell mass, D e is the detonation wave velocity, l and d are the warhead aspect ratio and inner diameter respectively, x is the relative detonation position of the fragment on the warhead from the detonation point, and E is the Gurney energy constant of the explosive.

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