Research method for instability criterion and fracture time of shaped charge jet

Abstract

The present invention provides a research method for the instability criterion and fracture time of a shaped charge jet, which includes: 1) 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; 2) On the basis of the completion of the above step 1), a perturbation model is constructed by superimposing perturbations; 3) The instability criterion and fracture time are determined by solving the perturbation model constructed in the above step 2). The concept of the present invention is reasonable, comprehensively considering various influencing factors such as the strain hardening, strain rate effect, thermal effect, and necking effect of the material. Through in-depth analysis of these factors, the corresponding methods for determining the instability criterion and fracture time are derived, which can more comprehensively and accurately describe the instability behavior and fracture process of the shaped charge jet, thereby more effectively predicting the jet performance.

Description

Technical Field

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

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

[0003] Therefore, it is particularly important to deeply study the stability problem of the jet. This is not only related to the effectiveness of the weapon system, but also related to the improvement of the overall combat ability. In this context, it is urgent to establish a scientific and reasonable jet instability criterion. 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] Aiming at the technical problems existing in the above background art, the present invention proposes a research method for the instability criterion and fracture time of a shaped charge jet. Its concept is reasonable, comprehensively considering various influencing factors such as the strain hardening, strain rate effect, thermal effect, and necking effect of the material. 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 shaped charge jet, thereby more effectively predicting the jet performance.

[0005] To solve the above technical problems, a research method for the instability criterion and fracture time of a shaped charge jet provided by the present invention mainly includes the following steps:

[0006] 1) 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;

[0007] 2) On the basis of completing the above step 1), a perturbation model is constructed by superimposing perturbations;

[0008] 3) The instability criterion and fracture time are determined by solving the perturbation model constructed in the above step 2).

[0009] For the research method of the instability criterion and fracture time of the shaped charge jet, wherein the specific process of the above step 1) is:

[0010] 1.1) Simplification of the tensile model of the shaped charge jet

[0011] First, the shaped charge jet formed by the detonation wave generated by the initiation of explosives is simplified to a cylinder with a fixed left end; the right end of the shaped charge jet is a free end, moving to the right at a speed The initial cross-sectional area of the jet , the initial length is , and the initial strain rate is ;

[0012] 1.2) Setting of assumptions

[0013] The moving speed of the free end of the jet to the right is a fixed value, and the jet is incompressible; the stretching process of the jet is small deformation and small disturbance; it is assumed that the initial disturbance amplitude of the jet is , and the initial disturbance is stable, that is ;

[0014] 1.3) Setting the boundary conditions of the jet

[0015] From the model simplification, at the Lagrangian coordinate , the velocity of the jet is ; at the Lagrangian coordinate , the velocity of the jet is ;

[0016] 1.4) Setting the initial conditions of the jet

[0017] From the model simplification, at , the velocity of the jet is ; at , the cross-sectional area of the jet is ;

[0018] 1.5) Converting the coordinates of the jet

[0019] According to the mass conservation of the jet, the conversion between the Lagrangian coordinate and the Eulerian coordinate can be constructed as follows:

[0020] ;

[0021] 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 any time, is the density of the jet at the initial time, is the cross-sectional area of the jet at the initial time, is the spatial coordinate of the Eulerian coordinate system;

[0022] Assuming the jet is incompressible, we can obtain:

[0023] ;

[0024] 1.6) Construct the motion equation of the jet

[0025] Assume that the axial stress of the jet is the only non - zero stress in the jet motion and remains unchanged on any cross - section of the jet. Then, according to the conservation of momentum, we have:

[0026] Analysis of the force on an infinitesimal element of the jet:

[0027] ;

[0028] Analysis of the force on any cross - section of the jet:

[0029] ;

[0030] ;

[0031] 1.7) Material constitutive of the jet

[0032] Since strain hardening, strain rate effect, and temperature effect are involved in the jet stretching process;

[0033] ;

[0034] ;

[0035] Equation ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] In the above equations (8) - (12), is the work - heat conversion coefficient, is the stress of the jet, is the density of the jet, is the specific heat capacity of the jet;

[0042] 1.8) Necking effect

[0043] When the surface of the jet is disturbed, the stress distribution on the jet cross - section becomes three - dimensional, and the average axial stress is equivalent to:

[0044] ;

[0045] In the above formula (13), is the stress during ideal stretching, is the radius of curvature at the necking, is the radius at the necking;

[0046] Assuming that the perturbation is small, , then the above formula (13) can be made equivalent:

[0047] ;

[0048] In the above formula (14), represents the jet radius at any position;

[0049] Simplifying the above formula (14) gives The expression of is:

[0050] ;

[0051] .

[0052] The research method of the instability criterion and fracture time of the shaped charge jet, wherein the specific process of establishing the perturbation model of the jet in step 2) is as follows:

[0053] Based on the jet stretching model, a perturbation is superimposed, and the following initial surface perturbation of the jet is considered:

[0054] ;

[0055] In the above formula (17), is the frequency, represents the wave number of the perturbation, is the wavelength of the perturbation, is the initial amplitude of the jet perturbation function;

[0056] The surface function that satisfies the above initial perturbation and control equation of the jet is:

[0057] ;

[0058] In the above formula (18), is the amplitude function of the perturbation term, and ;

[0059] ;

[0060] ;

[0061] Substituting the above formulas (16), (18) and (20) into the motion equation (5) of the jet gives:

[0062] ;

[0063] The research method of the instability criterion and fracture time of the shaped charge jet, wherein the specific process of step 3) is as follows:

[0064] 3.1) Establish the instability criterion of the jet

[0065] When in the above formula (21) , the jet becomes unstable, so it is defined that:

[0066] ;

[0067] The instability criterion of the jet is:

[0068] ;

[0069] The constitutive equation of the jet can adopt the thermo-viscoplastic constitutive equation, such as the Johnson-Cook constitutive equation, and the expression is as follows:

[0070] ;

[0071] In formula (24) is the static yield strength, B is the hardening modulus, is the strain, n is the hardening exponent, C is the strain rate constant, is the jet temperature, is the room temperature, is the melting point of the jet, m is the thermal softening coefficient;

[0072] Then the instability criterion of the jet can be expressed as:

[0073] ;

[0074] Among them, is the instability wave number and is related to the material. If the material is brittle and the necking phenomenon of the material does not need to be considered, then ,

[0075] ;

[0076] 3.2) Determine the fracture time of the jet

[0077] Initial conditions of jet perturbation: ;

[0078] Equation of motion of the jet:

[0079] ;

[0080] Since the motion equation of the jet is a non - linear equation, the series solution of the equation at t = 0 can be solved, that is, assume:

[0081] ;

[0082] In the above formula (28) can be obtained by the method of undetermined coefficients, ; when at this time, , which means that the necking has broken, so the fracture time of the jet is:

[0083] .

[0084] Adopting the above technical solution, the present invention has the following beneficial effects:

[0085] The research method of the instability criterion and fracture time of the shaped charge jet of the present invention is reasonably conceived, comprehensively considering various influencing factors such as the strain hardening, strain rate effect, thermal effect and necking effect of the material. 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.

[0086] Traditional research on shaped charge jets mostly focuses on a single factor, such as strain hardening, etc. However, the present invention can comprehensively consider various influencing factors such as the strain hardening, strain rate effect, thermal effect and necking effect of the material. Through in - depth analysis of these factors, the present invention can more comprehensively and accurately describe the instability behavior and fracture process of the shaped charge jet, so as to more effectively predict the jet performance.

[0087] The present invention proposes a tensile model and a perturbation model of the jet, obtains the instability criterion and fracture time of the jet. This model combines the response characteristics of the material under complex loads and can accurately describe the instability phenomenon of the shaped charge jet in practical applications. Based on the instability criterion and fracture time of the jet, researchers can predict the stability of the shaped charge jet at the design stage, providing more reliable theoretical support for engineering applications.

[0088] The stability of the shaped charge jet to a certain extent determines the damage effect of the liner. The present invention can provide a theoretical basis for the performance optimization of shaped charges by quantitatively analyzing the instability and fracture processes. 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

[0089] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0090] Figure 1 It is a flowchart of the research method for the instability criterion and fracture time of the shaped charge jet of the present invention. Specific embodiments

[0091] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0092] The following further explains the present invention in conjunction with specific embodiments.

[0093] As Figure 1 shown, a research method for the instability criterion and fracture time of the shaped charge jet provided in this embodiment first constructs a tensile model of the shaped charge jet at steady state based on the strain hardening, strain rate effect, thermal effect, and necking effect of the liner material. On this basis, a perturbation model is constructed by superimposing perturbations, and the instability criterion and fracture time are determined by solving the constructed perturbation model.

[0094] The research method for the instability criterion and fracture time of the shaped charge jet of the present invention specifically includes the following steps:

[0095] S001. Simplification of the shaped charge jet model

[0096] First, the shaped charge jet formed by the detonation wave generated by the explosive initiation crushing the liner is simplified into a cylinder with a fixed left end; the right end of the shaped charge jet is a free end, moving to the right at a speed , the initial cross-sectional area of the jet , the initial length is , and the initial strain rate is .

[0097] S002. Setting of assumptions

[0098] The moving speed V 0 of the free end of the jet to the right is a fixed value, and the jet is incompressible; the stretching process of the jet is small deformation and small perturbation; it is assumed that the initial perturbation amplitude of the jet is , and the initial perturbation is stable, that is, .

[0099] S003. Set the boundary conditions of the jet

[0100] From the model simplification, in the Lagrangian coordinate the velocity of the jet is ; in the Lagrangian coordinate the velocity of the jet is ;

[0101] S004. Set the initial conditions of the jet

[0102] From the model simplification, at the velocity of the jet is ; at the cross-sectional area of the jet is ;

[0103] S005. Transform the coordinates of the jet

[0104] According to the mass conservation of the jet, the transformation between the Lagrangian coordinate and the Eulerian coordinate can be constructed as follows:

[0105] ;

[0106] 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 any time, is the density of the jet at the initial time, is the cross-sectional area of the jet at the initial time, is the spatial coordinate in the Eulerian coordinate system;

[0107] Assuming the jet is incompressible, we can get:

[0108] ;

[0109] .

[0110] S006. Construct the motion equation of the jet

[0111] Assume that the axial stress of the jet is the only non-zero stress in the Jet motion and is invariant on any cross-section of the jet. Then, according to the momentum conservation, we have:

[0112] Force analysis of the infinitesimal element of the jet:

[0113] ;

[0114] Force analysis of any cross-section of the jet:

[0115] ;

[0116] 。

[0117] S007, Material Constitutive of Jet

[0118] Since the jet stretching process involves strain hardening, strain rate effect and temperature effect;

[0119] ;

[0120] ;

[0121] In Equations (6)-(7), ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] In the above Equations (8)-(12), is the work-heat conversion coefficient, is the stress of the jet, is the density of the jet, is the specific heat capacity of the jet.

[0128] S008, Necking Effect

[0129] When the surface of the jet is disturbed, the stress distribution of the jet cross-section becomes three-dimensional, and the average axial stress is equivalent to:

[0130] ;

[0131] In the above Equation (13), is the stress during ideal stretching, is the radius of curvature at the necking, is the radius at the necking;

[0132] Assuming that the disturbance is small, then the above Equation (13) can be equivalent:

[0133] ;

[0134] In the above Equation (14), represents the radius of the jet at any position;

[0135] Simplifying the above equation (14) gives The expression of is:

[0136] ;

[0137] ;

[0138] S009. Construct a perturbation model of the jet

[0139] Based on the jet stretching model, superimpose perturbations and consider the following initial surface perturbations of the jet:

[0140] ;

[0141] In the above equation (17), is the frequency, represents the wave number of the perturbation, is the wavelength of the perturbation, is the initial amplitude of the jet perturbation function;

[0142] The surface function that satisfies the above initial perturbation and control equation of the jet is:

[0143] ;

[0144] In the above equation (18), is the amplitude function of the perturbation term, and ;

[0145] ;

[0146] ;

[0147] Substitute the above equations (16), (18) and (20) into the motion equation (5) of the jet to get:

[0148] .

[0149] S010. Establish an instability criterion for the jet

[0150] When in the above equation (21), , the jet becomes unstable. Therefore, define:

[0151]

[0152] The instability criterion of the jet is:

[0153] ;

[0154] The constitutive equation of the jet can adopt the thermo-viscoplastic constitutive equation, such as the Johnson-Cook constitutive equation, and the expression is as follows:

[0155] ;

[0156] In Equation (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 the room temperature, is the melting point of the jet, m is the thermal softening coefficient;

[0157] Then the instability criterion of the jet can be expressed as:

[0158] ;

[0159] Among them, is the instability wave number and is related to the material. If the material is brittle and the necking phenomenon of the material does not need to be considered, then ,

[0160] .

[0161] S011, Determination of the fracture time of the jet

[0162] Initial conditions of jet perturbation: ;

[0163] Equation of motion of the jet:

[0164] ;

[0165] Since the equation of motion of the jet is a non-linear equation, the series solution of the equation at t = 0 can be solved, that is, assume:

[0166] ;

[0167] In the above formula (28) can be obtained by the method of undetermined coefficients, ; when When,[[]]END]] , which means that the necking part has broken, so the fracture time of the jet is:

[0168] .

[0169] The inventive concept is reasonable, comprehensively considering various influencing factors such as the strain hardening, strain rate effect, thermal effect, and necking effect of the material. 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 shaped charge jet, thereby more effectively predicting the jet performance.

[0170] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and 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 by comprising 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 the fracture time by solving the disturbance model constructed in the above step 2); 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 of the free end of the jet moving to the right is is a fixed value, 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 in 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; ； ； In formulas (5)-(6), ; ； 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 (8), 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 (8) can be equivalent to: ； In the above formula (9), represents the jet radius at any position; Simplifying the above formula (9) we can get The expression is: ； 。 2. The method for studying the instability criterion and the break time of a shaped charge jet as claimed in claim 1, 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 (12), 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 (13), is the amplitude function of the disturbance term, and ; ； ； Substituting equations (11), (13) and (15) into the jet motion equation (4), we obtain: 。 3. The method for studying the instability criterion and break time of a shaped charge jet as claimed in claim 2, characterized in that: The specific process of step 3) is as follows: 3.1) Establishing the instability criterion of jet When the above formula (16) , 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: ； In formula (19), is the static yield strength, is the hardening modulus, For strain, is the hardening index, 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; ； ； ； ； In the above formulas (20)-(23), 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; The jet instability criterion can be expressed as: ； in, is the instability frequency 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 equation of motion of the jet is a nonlinear equation, the equation can be solved in The series solution of , that is, assume that: ； In the above formula (27): 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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