Research method for energy-gathered jet loss stability criterion and fracture time

Abstract

The invention provides a method for researching a shaped charge jet flow stability criterion and fracture time, which comprises the following steps of: 1) firstly, constructing a tensile model of shaped charge jet flow in a steady state based on strain hardening, a strain rate effect, a heat effect and a necking effect of a shaped charge liner material; 2) superposing disturbance on the basis of completion of the step 1) to construct a disturbance model; and 3) determining an instability criterion and fracture time by solving the disturbance model constructed in the step 2). The method is reasonable in conception, comprehensively considers various influence factors of strain hardening, strain rate effect, heat effect and necking effect of the material, deduces a corresponding instability criterion and fracture time determination method through deep analysis of the factors, can more comprehensively and accurately describe the instability behavior and fracture process of the energy-gathered jet flow, and has a good application prospect. Therefore, the jet flow performance can be predicted more effectively.

Description

Technical Field

[0001] The invention belongs to the technical field of equipment design, and in particular relates to a research method for an instability criterion and a fracture time of a shaped charge jet. Background Art

[0002] Shaped charge technology plays an important role in modern weapon systems, and the key lies in the design and optimization of the liner. The geometry and material properties of the liner determine its ability to effectively convert the explosion energy into a high-speed jet. However, the formation and stability of the jet are affected by many factors, including strain hardening, strain rate effect, thermal effect, and necking effect, and the jet may break. This will not only affect the shape and speed of the jet, but may also directly reduce its ability to strike the target.

[0003] Therefore, it is particularly important to conduct in-depth research on the stability of the jet. This is not only related to the effectiveness of the weapon system, but also to the improvement of the overall combat capability. In this context, it is urgent to establish a set of scientific and reasonable jet instability criteria. This criterion not only provides a theoretical basis for predicting the fracture of the jet, but also provides guidance for the structural optimization of the liner. Summary of the invention

[0004] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a research method for the instability criterion and fracture time of a focused energy jet. The method has a reasonable conception and comprehensively considers various influencing factors of the material's strain hardening, strain rate effect, thermal effect and necking effect. Through in-depth analysis of these factors, the corresponding instability criterion and fracture time determination method are derived, which can more comprehensively and accurately describe the instability behavior and fracture process of the focused energy jet, thereby more effectively predicting the jet performance.

[0005] In order to solve the above technical problems, the present invention provides a method for studying the instability criterion and fracture time of a shaped charge jet, which mainly includes the following steps: 1) Firstly, based on the strain hardening, strain rate effect, thermal effect and necking effect of the liner material, a tensile model of the shaped charge jet in steady state is constructed; 2) On the basis of the above step 1), a disturbance model is constructed by superimposing the disturbance; 3) Determine the instability criterion and fracture time by solving the disturbance model constructed in step 2) above.

[0006] The research method of the instability criterion and fracture time of the shaped charge jet, wherein the specific process of the step 1) is: 1.1) Simplified tensile model of focused jet First, the shaped jet formed by the detonation wave generated by the detonation of the explosive crushing the charge liner is simplified to a cylinder with a fixed support at the left end; the right end of the shaped jet is a free end, with a velocity of Moving to the right, the initial cross-sectional area of ​​the jet , the initial length is The initial strain rate is ; 1.2) Assumptions The speed of the free end of the jet moving to the right is The jet is incompressible; the jet stretching process is a small deformation and a small disturbance; assuming that the initial disturbance amplitude of the jet is , and the initial disturbance is stable, that is, ; 1.3) Setting the boundary conditions of the jet From the simplified model, we can see that in Lagrangian coordinates The velocity of the jet is ; In Lagrangian coordinates The velocity of the jet is ; 1.4) Setting the initial conditions of the jet From the simplified model, we can see that When the jet velocity is ;exist When the cross-sectional area of ​​the jet is ; 1.5) Convert the coordinates of the jet According to the mass conservation of the jet, the Lagrangian coordinates can be constructed and Euler coordinates Conversion: ; In the above formula (1), is the density of the jet at any time, is the cross-sectional area of ​​the jet at any position and at any time, is the density of the jet at the initial moment, is the cross-sectional area of ​​the jet at the initial moment, is the space coordinate of the Euler coordinate system; Assuming the jet is incompressible, we can obtain: ; 1.6) Constructing the equation of motion of the jet Assuming the axial stress of the jet is the only non-zero stress in the jet motion, and it is constant at any cross section of the jet. According to the law of conservation of momentum, we have: Micro-element force analysis of jet: ; Force analysis of any cross section of the jet: ; ; 1.7) Material constitutive structure of jet Since the jet stretching process involves strain hardening, strain rate effect and temperature effect; ; ; Mode ; ; ; ; ; ; In the above formulas (8)-(12), is the work-to-heat conversion coefficient, is the jet stress, is the density of the jet, is the specific heat capacity of the jet; 1.8) Necking effect When the jet surface is disturbed, the stress distribution of the jet cross section becomes three-dimensional, and the average axial stress is equivalent to: ; In the above formula (13), is the stress in ideal tension, is the radius of curvature at the neck, is the radius of the neck; Assuming the disturbance is small, , Then the above formula (13) can be equivalent to: ; In the above formula (14), represents the jet radius at any position; Simplifying the above formula (14) we can get The expression is: ; .

[0007] The research method of the instability criterion and break time of the shaped energy jet, wherein the specific process of building the perturbation model of the jet in step 2) is: Superimposing disturbances on the basis of the jet stretching model, consider the following initial surface disturbances of the jet: ; In the above formula (17), is the frequency, represents the wave number of the disturbance, is the wavelength of the disturbance, is the initial amplitude of the jet disturbance function; The surface function that satisfies the initial disturbance and control equations of the above jet is: ; In the above formula (18), is the amplitude function of the disturbance term, and ; ; ; Substituting equations (16), (18) and (20) into the jet motion equation (5), we obtain: ; The research method of the instability criterion and fracture time of the shaped charge jet, wherein the specific process of the step 3) is as follows: 3.1) Establishing the instability criterion of jet When the above formula (21) , then the jet is unstable, so we define: ; The instability criterion of the jet is: ; The constitutive equation of the jet can adopt the thermo-viscoplastic constitutive equation, such as the Johnson-Cook constitutive equation, which is expressed as follows: ; Formula (24) is the static yield strength, B is the hardening modulus, For strain, n is the hardening index, C is the strain rate constant, is the jet temperature, is room temperature, is the melting point of the jet, m is the thermal softening coefficient; The jet instability criterion can be expressed as: ; in, is the instability wave number and is related to the material. If the material is brittle, the necking phenomenon of the material does not need to be considered. , ; 3.2) Determination of jet break time Initial conditions of the jet disturbance: ; The equation of motion of the jet is: ; Since the motion equation of the jet is a nonlinear equation, the series solution of the equation at t=0 can be solved, that is, assuming: ; In the above formula (28): It can be obtained by the method of undetermined coefficients, ;when hour, , which means that the neck has broken, so the break time of the jet is: .

[0008] By adopting the above technical solution, the present invention has the following beneficial effects: The research method of the instability criterion and fracture time of the shaped charge jet of the present invention is reasonably conceived, and comprehensively considers various influencing factors of the material's strain hardening, strain rate effect, thermal effect and necking effect. Through in-depth analysis of these factors, the corresponding instability criterion and fracture time determination method are derived; the theoretical framework of the present invention lays a foundation for the performance optimization of shaped charges.

[0009] Traditional research on focused energy jets mostly focuses on a single factor, such as strain hardening, but the present invention can comprehensively consider multiple influencing factors such as material strain hardening, strain rate effect, thermal effect and necking effect. Through in-depth analysis of these factors, the present invention can more comprehensively and accurately describe the instability behavior and fracture process of the focused energy jet, thereby more effectively predicting the jet performance.

[0010] The present invention proposes a stretching model and a disturbance model for the jet, and obtains the instability criterion and fracture time of the jet. The model combines the response characteristics of the material under complex loads and can accurately describe the instability phenomenon of the focused jet in practical applications. Based on the instability criterion and fracture time of the jet, researchers can predict the stability of the focused jet in the design stage, providing more reliable theoretical support for engineering applications.

[0011] The stability of the shaped charge jet is determined to a certain extent by the damage effect of the liner. The present invention can provide a theoretical basis for the performance optimization of the shaped charge by quantitatively analyzing the instability and fracture process. In practical applications, the charge material, design parameters and manufacturing process can be adjusted according to the optimization results, thereby improving the effect and accuracy of the shaped charge jet. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0013] Figure 1 The figure is a flow chart of the research method of the instability criterion and fracture time of the shaped charge jet of the present invention. DETAILED DESCRIPTION

[0014] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0015] The present invention is further explained below in conjunction with specific implementation modes.

[0016] like Figure 1 As shown, this embodiment provides a method for studying the instability criterion and fracture time of a shaped charge jet. First, based on the strain hardening, strain rate effect, thermal effect and necking effect of the liner material, a tensile model of the shaped charge jet in the steady state is constructed. On this basis, a disturbance model is constructed by superimposing disturbances. The instability criterion and fracture time are determined by solving the constructed disturbance model.

[0017] The research method of the instability criterion and the break time of the shaped charge jet of the present invention specifically comprises the following steps: S001. Simplified concentrated jet model First, the shaped jet formed by the detonation wave generated by the detonation of the explosive crushing the charge liner is simplified to a cylinder with a fixed support at the left end; the right end of the shaped jet is a free end, with a velocity of Moving to the right, the initial cross-sectional area of ​​the jet , the initial length is The initial strain rate is .

[0018] S002. Assumptions setting The speed V0 of the free end of the jet moving to the right is a fixed value, and the jet is incompressible; the jet stretching process is a small deformation and small disturbance; assuming that the initial disturbance amplitude of the jet is , and the initial disturbance is stable, that is, .

[0019] S003. Set the boundary conditions of the jet From the simplified model, we can see that in Lagrangian coordinates The velocity of the jet is ; In Lagrangian coordinates The velocity of the jet is ; S004. Set the initial conditions of the jet From the simplified model, we can see that When the jet velocity is ;exist When the cross-sectional area of ​​the jet is ; S005. Convert the coordinates of the jet According to the mass conservation of the jet, the Lagrangian coordinates can be constructed and Euler coordinates Conversion: ; In the above formula (1), is the density of the jet at any time, is the cross-sectional area of ​​the jet at any position and at any time, is the density of the jet at the initial moment, is the cross-sectional area of ​​the jet at the initial moment, is the space coordinate of the Euler coordinate system; Assuming the jet is incompressible, we can obtain: ; .

[0020] S006. Construct the motion equation of the jet Assuming the axial stress of the jet is the only non-zero stress in the jet motion, and it is constant at any cross section of the jet. According to the law of conservation of momentum, we have: Micro-element force analysis of jet: ; Force analysis of any cross section of the jet: ; .

[0021] S007. Material Constitutive Model of Jet Since the jet stretching process involves strain hardening, strain rate effect and temperature effect; ; ; In formula (6)-(7), ; ; ; ; ; ; In the above formulas (8)-(12), is the work-to-heat conversion coefficient, is the jet stress, is the density of the jet, is the specific heat capacity of the jet.

[0022] S008, Necking effect When the jet surface is disturbed, the stress distribution of the jet cross section becomes three-dimensional, and the average axial stress is equivalent to: ; In the above formula (13), is the stress in ideal tension, is the radius of curvature at the neck, is the radius of the neck; Assuming the disturbance is small, Then the above formula (13) can be equivalent to: ; In the above formula (14), represents the jet radius at any position; Simplifying the above formula (14) we can get The expression is: ; ; S009. Construct a perturbation model of the jet Superimposing disturbances on the basis of the jet stretching model, consider the following initial surface disturbances of the jet: ; In the above formula (17), is the frequency, represents the wave number of the disturbance, is the wavelength of the disturbance, is the initial amplitude of the jet disturbance function; The surface function that satisfies the initial disturbance and control equations of the above jet is: ; In the above formula (18), is the amplitude function of the disturbance term, and ; ; ; Substituting equations (16), (18) and (20) into the jet motion equation (5), we obtain: .

[0023] S010. Establish the instability criterion of jet When the above formula (21) , then the jet is unstable, so we define:

[0024] The instability criterion of the jet is: ; The constitutive equation of the jet can adopt the thermo-viscoplastic constitutive equation, such as the Johnson-Cook constitutive equation, which is expressed as follows: ; In formula (24), is the static yield strength, B is the hardening modulus, is the strain, n is the hardening index, C is the strain rate constant, is the jet temperature, is room temperature, is the melting point of the jet, m is the thermal softening coefficient; The jet instability criterion can be expressed as: ; in, is the instability wave number and is related to the material. If the material is brittle, the necking phenomenon of the material does not need to be considered. , .

[0025] S011. Determination of jet break time Initial conditions of the jet disturbance: ; The equation of motion of the jet is: ; Since the motion equation of the jet is a nonlinear equation, the series solution of the equation at t=0 can be solved, that is, assuming: ; In the above formula (28): It can be obtained by the method of undetermined coefficients, ;when hour, , which means that the neck has broken, so the break time of the jet is: .

[0026] The present invention has a reasonable conception and comprehensively considers various influencing factors of material strain hardening, strain rate effect, thermal effect and necking effect. Through in-depth analysis of these factors, corresponding instability criterion and fracture time determination method are derived, which can more comprehensively and accurately describe the instability behavior and fracture process of the focused energy jet, thereby more effectively predicting the jet performance.

[0027] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for studying the instability criterion and fracture time of a shaped charge jet, characterized in that , including the following steps: 1) Firstly, based on the strain hardening, strain rate effect, thermal effect and necking effect of the liner material, a tensile model of the shaped charge jet in steady state is constructed; 2) On the basis of the above step 1), a disturbance model is constructed by superimposing the disturbance; 3) Determine the instability criterion and fracture time by solving the disturbance model constructed in step 2) above.

2. The method for studying the instability criterion and break time of a shaped charge jet as claimed in claim 1, characterized in that: The specific process of step 1) is: 1.1) Simplified tensile model of focused jet First, the shaped jet formed by the detonation wave generated by the detonation of the explosive crushing the charge liner is simplified to a cylinder with a fixed support at the left end; the right end of the shaped jet is a free end, with a velocity of Moving to the right, the initial cross-sectional area of ​​the jet , the initial length is The initial strain rate is ; 1.2) Assumptions The speed V0 of the free end of the jet moving to the right is a fixed value, and the jet is incompressible; the jet stretching process is a small deformation and small disturbance; assuming that the initial disturbance amplitude of the jet is , and the initial disturbance is stable, that is, ; 1.3) Setting the boundary conditions of the jet From the simplified model, we can see that in Lagrangian coordinates The velocity of the jet is ; In Lagrangian coordinates The velocity of the jet is ; 1.4) Setting the initial conditions of the jet From the simplified model, we can see that When the jet velocity is ;exist When the cross-sectional area of ​​the jet is ; 1.5) Convert the coordinates of the jet According to the mass conservation of the jet, the Lagrangian coordinates can be constructed and Euler coordinates Conversion: ； In the above formula (1), is the density of the jet at any time, is the cross-sectional area of ​​the jet at any position and at any time, is the density of the jet at the initial moment, is the cross-sectional area of ​​the jet at the initial moment, is the space coordinate of the Euler coordinate system; Assuming the jet is incompressible, we can obtain: ； ； 1.6) Constructing the equation of motion of the jet Assuming the axial stress of the jet is the only non-zero stress in the jet motion, and it is constant at any cross section of the jet. According to the law of conservation of momentum, we have: Micro-element force analysis of jet: ； Force analysis of any cross section of the jet: ； ； 1.7) Material constitutive structure of jet Since the jet stretching process involves strain hardening, strain rate effect and temperature effect; ； ； Mode ; ； ； ； ； ； In the above formulas (8)-(12), is the work-to-heat conversion coefficient, is the jet stress, is the density of the jet, is the specific heat capacity of the jet; 1.8) Necking effect When the jet surface is disturbed, the stress distribution of the jet cross section becomes three-dimensional, and the average axial stress is equivalent to: ； In the above formula (13), is the stress in ideal tension, is the radius of curvature at the neck, is the radius of the neck; Assuming that the disturbance is small, , Then the above formula (13) can be equivalent to: ； In the above formula (14), represents the jet radius at any position; Simplifying the above formula (14) we can get The expression is: ； 。 3. The method for studying the instability criterion and the break time of a shaped charge jet as claimed in claim 2, characterized in that: The specific process of building the disturbance model of the jet in step 2) is as follows: Superimposing disturbances on the basis of the jet stretching model, consider the following initial surface disturbances of the jet: ； In the above formula (17), is the frequency, represents the wave number of the disturbance, is the wavelength of the disturbance, is the initial amplitude of the jet disturbance function; The surface function that satisfies the initial disturbance and control equations of the above jet is: ； In the above formula (18), is the amplitude function of the disturbance term, and ; ； ； Substituting equations (16), (18) and (20) into the jet motion equation (5), we obtain: 。 4. The method for studying the instability criterion and the break time of a shaped charge jet as claimed in claim 3, characterized in that: The specific process of step 3) is as follows: 3.1) Establishing the instability criterion of jet When the above formula (21) , then the jet is unstable, so we define: ； The instability criterion of the jet is: ； The constitutive equation of the jet can adopt the thermo-viscoplastic constitutive equation, such as the Johnson-Cook constitutive equation, which is expressed as follows: ； Formula (24) is the static yield strength, B is the hardening modulus, For strain, n is the hardening index, C is the strain rate constant, is the jet temperature, is room temperature, is the melting point of the jet, m is the thermal softening coefficient; The jet instability criterion can be expressed as: ； in, is the instability wave number and is related to the material. If the material is brittle, the necking phenomenon of the material does not need to be considered. , ； 3.2) Determination of jet break time Initial conditions of the jet disturbance: ; The equation of motion of the jet is: ； Since the motion equation of the jet is a nonlinear equation, the series solution of the equation at t=0 can be solved, that is, assuming: ； In the above formula (28): It can be obtained by the method of undetermined coefficients, ;when hour, , which means that the neck has broken, so the break time of the jet is: 。

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