A quantitative characterization method for reaction pressure based on shell expansion velocity
By dividing the shell into small deformation and large deformation stages, a model of the shell expansion speed and internal reaction pressure is established, which solves the problem of the inability to measure internal pressure in the constrained charging system, and improves the measurement accuracy of the reaction pressure. The assessment of the intensity of sensitive ammunition response provides a theoretical basis.
Patent Information
- Application Number
- CN202410501375.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-25
- Publication Date
- 2025-01-03
- Estimated Expiration
- 2044-04-25
AI Technical Summary
The existing technology cannot effectively measure the internal pressure of the restricted charging system, resulting in the lack of theoretical basis for quantitative evaluation of reaction intensity, and it is difficult to truly reflect the reaction evolution process after explosives ignition.
By dividing the shell into small deformation and large deformation stages, a function of the total surface area of the explosive combustion crack network and the pressure in the shell is established. Combined with the ideal gas state equation and Vielle's law, a model of the shell expansion speed and internal reaction pressure is obtained, and the precise characterization is performed. Constrain the reaction pressure of the charging system.
The accuracy of measuring internal reaction pressure during the evolution of the restricted charge reaction is improved, providing a theoretical basis for the evaluation of the reaction intensity of insensitive ammunition, and solving the problem of being unable to directly measure internal pressure of the system.
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Figure CN118484884B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of insensitive ammunition design and evaluation, and in particular to a reaction pressure quantitative characterization method based on shell expansion velocity. Background Art
[0002] During its entire life cycle, ammunition is often subjected to unexpected stimuli such as falling, impact, and friction, which can cause mechanical, chemical, and thermal responses in the ammunition structure, resulting in uncontrolled chemical reactions and energy release, and triggering typical accidents such as ignition, combustion, and even explosion of ammunition charges, or even detonation.
[0003] For the typical accidents mentioned above, the reaction evolution process of the constrained charge system after ignition is very complex, involving multiple physical change processes such as intrinsic combustion characteristics and crack evolution after ignition of explosives, mechanical deformation of the shell until failure and disintegration of the structural response. At present, there are few studies on the evolution of explosive ignition reaction. The mechanism model obtained by modeling the mechanism based on the reaction evolution mechanism is quite different from the actual evolution process of the explosive charge ignition reaction, and cannot truly reflect the internal reaction pressure of the system when solving constraints.
[0004] Therefore, how to establish a quantitative characterization method for the internal reaction pressure of the system based on the shell expansion velocity has become an urgent problem to be solved. Summary of the invention
[0005] In view of the above analysis, the present invention aims to provide a method for quantitative characterization of reaction pressure based on shell expansion velocity, so as to solve the problem that the internal pressure of the system cannot be directly measured during the evolution of existing constrained charge reactions, resulting in a lack of theoretical basis for quantitative evaluation methods of reaction intensity.
[0006] The present invention provides a method for quantitatively characterizing reaction pressure based on shell expansion velocity, the method comprising the following steps:
[0007] The shell of the constrained charge system is divided into small deformation and large deformation stages and thresholds of the small deformation and large deformation stages are set, and a function of the total surface area of the explosive combustion crack network in the system and the pressure inside the shell is constructed;
[0008] The volume of the system in the small deformation stage is obtained based on the initial volume and generalized equivalent stiffness of the system; the mass of the gas product of the explosion of the explosive is obtained based on the function of the total surface area of the combustion crack network and the pressure inside the shell and Vielle's law, and the volume of the system in the small deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain a model of the internal reaction pressure in the small deformation stage and the shell expansion speed with respect to time t;
[0009] The volume of the system in the large deformation stage is obtained based on the volume of the system in the small deformation stage and the generalized deformation equivalent stiffness; the volume of the system in the large deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain a model of the internal reaction pressure of the system in the large deformation stage and the shell expansion speed with respect to time t.
[0010] Furthermore, the generalized deformation equivalent stiffness of the system is:
[0011]
[0012] Among them, M′ is the generalized deformation equivalent stiffness of the system, I′ is the generalized deformation equivalent stiffness of the shell, B is the bulk modulus of the explosive, V eb is the volume of explosive at the end of the small deformation stage, V b is the system volume at the end of the small deformation stage.
[0013] Furthermore, the generalized deformation equivalent stiffness of the shell is:
[0014]
[0015] Where P is the pressure of the constrained charge system, ε v ′ is the volume strain of the constrained charge system in the large deformation stage.
[0016] Furthermore, the volume strain of the constrained charge system in the large deformation stage is obtained by the following method:
[0017]
[0018] Among them, v r is the radial motion speed of the shell, v z is the speed of the axial movement of the shell, R b L is the inner radius of the shell at the end of the small deformation stage. b is the shell height at the end of the small deformation stage, t b This is the end moment of the small deformation stage.
[0019] Furthermore, the volume growth of the system in the large deformation stage is obtained by the following method:
[0020]
[0021] Where ΔV′ is the volume of the system during the large deformation stage, P is the pressure of the constrained charge system, and V b is the system volume at the end of the small deformation stage, M′ is the generalized deformation equivalent stiffness of the system, P b is the pressure inside the shell at the end of the small deformation stage, P c is the pressure inside the shell at the end of the large deformation stage, P b≤P≤P c .
[0022] Further, the rate of increase in gas product mass is obtained by the following method:
[0023]
[0024]
[0025] Among them, α is the explosive combustion coefficient, β is the explosive combustion index, is the explosive burning rate, S i is the initial surface area of the combustion crack at the ignition moment, ρ e0 is the initial density of explosive, V e0 is the initial volume of explosive, S max is the saturated specific surface area of combustion cracks, P i is the initial pressure inside the shell at the time of ignition, P r is the reference pressure of combustion cracks, n is a positive integer, S[P] is the function of the total surface area of the explosive combustion crack network and the pressure inside the shell, m g is the mass of the gas product in the system, P is the pressure of the constrained charge system, and P c is the pressure inside the shell at the end of the large deformation stage, P≤P c .
[0026] Furthermore, the volume of the system in the large deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain the following formula:
[0027]
[0028] Among them, R p is the universal gas constant, T p is the gas product temperature, M g is the molar mass, V a is the initial volume of the void in the small deformation stage, P b is the pressure inside the shell at the end of the small deformation stage, V0 is the initial volume of the system in the small deformation stage, M is the generalized equivalent stiffness of the system, ΔV′ is the volume increase of the system in the large deformation stage, t b is the end time of the small deformation stage, t c is the end time of the large deformation stage, P b ≤P≤P c , t b ≤t≤t c ;
[0029] The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the large deformation stage with respect to time t:
[0030]
[0031]
[0032] in, V b is the system volume at the end of the small deformation stage, V eb is the volume of explosive at the end of the small deformation stage, ξ is the integral variable, B is the bulk modulus of explosive, V′ is the total volume of the system in the large deformation stage, v r is the radial motion speed of the shell, v z is the speed of the axial movement of the shell, R b L is the inner radius of the shell at the end of the small deformation stage. b is the shell height at the end of the small deformation stage.
[0033] Furthermore, the volume growth of the system in the small deformation stage is obtained by the following method:
[0034]
[0035] Among them, ΔV is the volume of the system increase in the small deformation stage, P is the pressure of the constrained charge system, V0 is the initial volume of the system in the small deformation stage, and M is the generalized equivalent stiffness of the system.
[0036] Furthermore, the volume of the system in the small deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain the following formula:
[0037]
[0038] Where P≤P b , 0≤t≤t b ;
[0039] The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the small deformation stage with respect to time t:
[0040]
[0041] Furthermore, the generalized equivalent stiffness of the system is:
[0042]
[0043] Among them, M is the generalized equivalent stiffness of the system, I is the generalized equivalent stiffness of the shell, B is the bulk modulus of the explosive, V0 is the initial volume of the system in the small deformation stage, V e0 is the initial volume of explosive at the small deformation stage.
[0044] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:
[0045] 1. The present invention obtains a model of the internal reaction pressure of the system and the expansion rate of the shell through the ideal gas state equation, the rate of increase of the mass of the gas product and the volume growth of the constrained charge system, thereby solving the problem that the internal pressure of the system cannot be directly measured during the evolution of the constrained charge reaction, resulting in the lack of a quantitative characterization method for the reaction intensity.
[0046] 2. In the process of constrained charge reaction evolution, the present invention divides the system shell into small deformation and large deformation stages, and obtains models of the internal reaction pressure and shell expansion rate of the constrained charge system corresponding to the two stages according to the different reaction evolution characteristics of the two stages, thereby improving the accuracy of obtaining the internal reaction pressure of the system according to the model.
[0047] 3. The present invention provides a theoretical basis for the evaluation of the reaction intensity of insensitive ammunition by realizing a quantitative characterization method of the shell expansion velocity and the internal reaction pressure of the constrained charge system.
[0048] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0049] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.
[0050] Figure 1 It is a flow chart of a method for quantitatively characterizing reaction pressure based on shell expansion velocity according to an embodiment of the present invention;
[0051] Figure 2 A schematic diagram of restricting charge combustion crack propagation according to an embodiment of the present invention;
[0052] Figure 3 This is a force analysis diagram of the cylindrical shell wall of an embodiment of the present invention. DETAILED DESCRIPTION
[0053] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.
[0054] A specific embodiment of the present invention discloses a method for quantitatively characterizing reaction pressure based on shell expansion velocity. Figure 1 As shown, the method comprises the following steps:
[0055] Step S1, dividing the shell of the constrained charge system into small deformation and large deformation stages and setting thresholds for the small deformation and large deformation stages, and constructing a function of the total surface area of the explosive combustion crack network in the system and the pressure inside the shell;
[0056] Step S2, based on the initial volume and generalized equivalent stiffness of the system, the volume of the system in the small deformation stage is obtained; based on the function of the total surface area of the combustion crack network and the pressure inside the shell and Vielle's law, the mass of the gas product of the explosion of the explosive is obtained, and the volume of the system in the small deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain a model of the internal reaction pressure in the small deformation stage and the shell expansion speed with respect to time t;
[0057] Step S3, obtaining the volume of the system in the large deformation stage based on the volume of the system in the small deformation stage and the generalized deformation equivalent stiffness; substituting the volume of the system in the large deformation stage and the mass of the gas product into the ideal gas state equation to obtain a model of the internal reaction pressure of the system in the large deformation stage and the shell expansion velocity with respect to time t.
[0058] Specifically, in step S1, the constrained charge system is composed of charges (explosives) and a shell, and the shell is spherical, cylindrical or other three-dimensional regular geometric bodies.
[0059] It is understandable that after the charge is ignited, local cracks are generated, and the combustion expands in the cracks and causes the pressure inside the system to continue to increase. Under the action of the continuous increase in internal pressure, that is, in the reaction evolution process of the constrained charge system, the deformation of the shell undergoes elastic, elastoplastic, plastic, and yield stages. When the shell reaches the full yield state, it loses its bearing capacity, but it will not break instantly. It usually breaks and forms fragments after continuing to expand to a certain extent. The continuous reaction of the internal constrained charge causes the system to be in a pressurized state and drives the expansion movement of the shell. The expansion movement of the shell causes the volume of the system to expand, causing the system to be in a depressurized state. Therefore, the energy release generated by the combustion and the external work generated by the gas products exist simultaneously. The coupling effect of the two is the core factor that determines the expansion speed of the shell and the change in the internal pressure of the system.
[0060] Specifically, the deformation of the shell is divided into a small deformation stage and a large deformation stage; the small deformation stage is from the ignition of the restrained charge system until the shell reaches a full yield state (i.e., the shell loses its bearing capacity) and the threshold of the small deformation stage. The shell deformation degree is small in this stage, so the shell expansion rate can be ignored; the large deformation stage is from the end of the small deformation stage until the threshold of the large deformation stage is reached. The shell deformation degree is large in this stage, so the shell expansion rate cannot be ignored. Preferably, the threshold of the small deformation stage is set to the shell failure strain reaching 3%, and the threshold of the large deformation stage is set to the shell inner radius reaching 1.3 times the initial inner radius. The shell failure strain refers to the process in which the shell material loses its original function or performance.
[0061] It can be understood that the gas products generated after the constrained charge system is ignited flow along the system gaps to drive the combustion cracks to expand into a network, resulting in an increase in the combustion specific surface area, thereby accelerating the reaction evolution. The combustion specific surface area refers to the combustion surface area per unit mass or unit volume during combustion. The larger the combustion specific surface area, the higher the fuel combustion efficiency and the more complete the combustion process. When the shell enters the large deformation stage, the growth rate of the internal pressure and the degree of deformation of the shell are significantly increased compared to the small deformation stage. The shell continues to expand under the action of internal pressure and tensile stress until it completely disintegrates. In the process of constrained charge reaction evolution, the present invention divides the shell of the system into small deformation and large deformation stages, and obtains the models of the internal reaction pressure and shell expansion rate of the corresponding constrained charge system in the two stages according to the different reaction evolution characteristics of the two stages, thereby improving the accuracy of obtaining the internal reaction pressure of the system according to the model.
[0062] Specifically, the function of the total surface area of the explosive combustion crack network and the pressure inside the shell in the system is:
[0063]
[0064] Among them, S i is the initial surface area of the combustion crack at the ignition moment, ρ e0 is the initial density of explosive, V e0 is the initial volume of explosive, S max is the saturated specific surface area of combustion cracks, P i is the initial pressure inside the shell at the time of ignition, P r is the combustion crack reference pressure, P is the pressure of the restraining charge system, and P c is the pressure inside the shell at the end of the large deformation stage, n is a positive integer, S[P] is the function of the total surface area of the explosive combustion crack network and the pressure inside the shell, P≤P c .
[0065] Understandable, S. iIt is related to the ignition intensity and can be calibrated through typical experiments. max , P r , e0 and n are determined by the properties of the charge itself and the combustion conditions, V e0 , P i Determined by the initial state of the system.
[0066] Specifically, in step S2, at the stage of small shell deformation, the total volume of the constrained charge system includes the charge volume, the initial void volume, and the volume of the system growth during the reaction evolution process. The volume of the system growth is the sum of the combustion crack extension volume and the shell expansion volume, that is, V = V e +V a +ΔV, where V is the total volume of the system at the small deformation stage, V e is the charge volume at this stage, V a is the initial void volume in this stage, and ΔV is the volume of the system growth in this stage.
[0067] In this stage, the initial volume of the charge system is constrained to satisfy V0 = V e0 +V a , where V0 is the initial volume of the system at the small deformation stage. Combining the above two formulas, we can get:
[0068]
[0069] It can be understood that the internal volume of the shell changes in the small deformation stage, that is, the volume strain of the system in this stage is The volume strain of the explosive at this stage is
[0070] Specifically, the generalized equivalent stiffness of the shell is:
[0071]
[0072] Where I is the generalized equivalent stiffness of the shell.
[0073] Assume that the bulk modulus of explosives at this stage satisfies:
[0074]
[0075] Where B is the bulk modulus of explosive.
[0076] Furthermore, the generalized equivalent stiffness of the system is:
[0077]
[0078] Where M is the generalized equivalent stiffness of the system.
[0079] Furthermore, the volume growth of the system in the small deformation stage is obtained by the following method:
[0080]
[0081] Among them, ΔV is the volume increase of the system in the small deformation stage.
[0082] For example, Figure 2 As shown, the shell is cylindrical, which constrains the ignition of a certain intensity in the center of the charging system. The high-temperature and high-pressure gas generated by the combustion triggers the combustion of the surface of the explosive matrix. The combustion causes the increase of gas products and promotes more local cracks in the explosive, providing more channels for combustion and gas products. The two promote each other and accelerate the reaction.
[0083] It can be understood that volume strain refers to the volume change of an object when it is subjected to an external force, which is the ratio of the volume change to the initial volume. When the external force is small or the object is relatively rigid, the volume strain is small. The bulk modulus of explosives refers to the degree of volume change of explosives when subjected to pressure. The larger the bulk modulus of explosives, the smaller the volume change when subjected to pressure, that is, the better the compression resistance. The present invention provides a theoretical basis for the evaluation of the reaction intensity of insensitive ammunition by realizing a quantitative characterization method of the shell expansion velocity and the internal reaction pressure of the constrained charge system.
[0084] Specifically, the explosive burning rate satisfies Vielle's law: Among them, α is the explosive combustion coefficient, β is the explosive combustion index, is the burning rate of explosive.
[0085] The rate of increase in the mass of the gas product during the small shell deformation stage is obtained by the following method:
[0086]
[0087] Among them, m g is the mass of the gas product in the system.
[0088] The ideal gas state equation is used to describe the gas product, and the ideal gas state equation is: Where ρ is the gas product density, R p is the universal gas constant, T p is the gas product temperature, M g is the molar mass.
[0089] Furthermore, the volume of the system in the small deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain the following formula:
[0090]
[0091] Among them, t b is the end time of the small deformation stage, P bis the pressure inside the shell at the end of the small deformation stage, P≤P b , 0≤t≤t b ;
[0092] The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the small deformation stage with respect to time t:
[0093]
[0094] in, ξ is the integration variable.
[0095] It can be understood that the present invention obtains a model of the internal reaction pressure of the system and the expansion rate of the shell through the ideal gas state equation, the rate of increase of the mass of the gas product and the volume growth of the constrained charge system, thereby solving the problem that the internal pressure of the system cannot be directly measured during the evolution of the constrained charge reaction, resulting in the lack of a quantitative characterization method for the reaction intensity.
[0096] Specifically, in step S3, during the large deformation stage of the shell, assuming that the gas pressure is dynamically uniformly distributed, the shell undergoes the same deformation behavior in the longitudinal and transverse directions, and the radial expansion of the cylinder is affected by the tensile "resistance". For example, according to Newton's second law, Figure 3 As shown in the figure, the radial and axial forces per unit area of the cylindrical shell at this stage are:
[0097]
[0098] Among them, m r is the radial unit area mass of the shell, m z H is the axial mass per unit area of the shell, r is the shell wall thickness, H z is the shell end cover thickness, v r is the radial motion speed of the shell, v z is the speed of the axial movement of the shell, R b L is the inner radius of the shell at the end of the small deformation stage. b is the shell height at the end of the small deformation stage, σ θ is the hoop stress on the shell that prevents the shell from expanding outward, τ is the axial shear force on the end cover, and ρ c is the shell material density, P b ≤P,t b ≤t.
[0099] The end time of the small shell deformation stage is taken as the start time of the large shell deformation stage. At this time, the total volume of the system is composed of the explosive volume and the void volume at this time: V b =V eb +V a′, where V b is the volume of the system at the end of the small deformation stage, V eb is the volume of explosive at the end of the small deformation stage, V a ′ is the void volume at that moment,
[0100] The motion process of the shell in the large deformation stage satisfies:
[0101] V′=V e ′+V a ′+ΔV′,
[0102] Where V′ is the total volume of the system in the large deformation stage, V e ′ is the volume of explosive in the large deformation stage, and ΔV′ is the volume increase of the system in the large deformation stage.
[0103] Combining the above formulas, we can get:
[0104]
[0105] It can be understood that the volume strain of the system in the large deformation stage of the shell is Among them, ε ve ′ is the volume strain of the explosive in the large deformation stage.
[0106] Furthermore, the volume strain of the constrained charge system in the large deformation stage is obtained by the following method:
[0107]
[0108] Furthermore, the generalized deformation equivalent stiffness of the shell is:
[0109]
[0110] Where I′ is the generalized deformation equivalent stiffness of the shell.
[0111] Assume that the bulk modulus of explosives at this stage satisfies:
[0112]
[0113] Furthermore, the generalized deformation equivalent stiffness of the system is:
[0114]
[0115] Where M′ is the generalized deformation equivalent stiffness of the system.
[0116] Furthermore, the volume growth of the system in the large deformation stage is obtained by the following method:
[0117]
[0118] Among them, P b ≤P≤P c .
[0119] Furthermore, the volume of the system in the large deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain the following formula:
[0120]
[0121] Among them, t c is the end time of the large deformation stage, P b ≤P≤P c , t b ≤t≤t c ;
[0122] The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the large deformation stage with respect to time t:
[0123]
[0124] It can be understood that the amount by which the volume of the system increases over time reflects the speed at which the shell expands. Therefore, the present application establishes a model of the internal reaction pressure of the system and the expansion speed of the shell with respect to time t.
[0125] Compared with the prior art, the method for quantitatively characterizing the reaction pressure based on the shell expansion velocity provided by the present invention has the following beneficial effects:
[0126] 1. The present invention obtains a model of the internal reaction pressure of the system and the expansion rate of the shell through the ideal gas state equation, the rate of increase of the mass of the gas product and the volume growth of the constrained charge system, thereby solving the problem that the internal pressure of the system cannot be directly measured during the evolution of the constrained charge reaction, resulting in the lack of a quantitative characterization method for the reaction intensity.
[0127] 2. In the process of constrained charge reaction evolution, the present invention divides the system shell into small deformation and large deformation stages, and obtains models of the internal reaction pressure and shell expansion rate of the constrained charge system corresponding to the two stages according to the different reaction evolution characteristics of the two stages, thereby improving the accuracy of obtaining the internal reaction pressure of the system according to the model.
[0128] 3. The present invention provides a theoretical basis for the evaluation of the reaction intensity of insensitive ammunition by realizing a quantitative characterization method of the shell expansion velocity and the internal reaction pressure of the constrained charge system.
[0129] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.
[0130] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.
Claims
1. A method for quantitatively characterizing reaction pressure based on shell expansion velocity, characterized in that: The method comprises the following steps: The shell of the constrained charge system is divided into small deformation and large deformation stages and thresholds of the small deformation and large deformation stages are set, and a function of the total surface area of the explosive combustion crack network in the system and the pressure inside the shell is constructed; The volume of the system in the small deformation stage is obtained based on the initial volume and generalized equivalent stiffness of the system; the mass of the gas product of the explosion of the explosive is obtained based on the function of the total surface area of the combustion crack network and the pressure inside the shell and Vielle's law, and the volume of the system in the small deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain a model of the internal reaction pressure in the small deformation stage and the shell expansion speed with respect to time t; The volume of the system in the large deformation stage is obtained based on the volume of the system in the small deformation stage and the generalized deformation equivalent stiffness; the volume of the system in the large deformation stage and the mass of the gas product are substituted into the ideal gas state equation to obtain a model of the internal reaction pressure of the system in the large deformation stage and the shell expansion velocity with respect to time t.
2. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 1, characterized in that: The generalized deformation equivalent stiffness of the system is: Among them, M′ is the generalized deformation equivalent stiffness of the system, I′ is the generalized deformation equivalent stiffness of the shell, B is the bulk modulus of the explosive, V eb is the volume of explosive at the end of the small deformation stage, V b is the system volume at the end of the small deformation stage.
3. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 2, characterized in that: The generalized deformation equivalent stiffness of the shell is: Where P is the pressure of the constrained charge system, ε v ′ is the volume strain of the constrained charge system in the large deformation stage.
4. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 3 is characterized in that: The volume strain of the constrained charge system in the large deformation stage is obtained by the following method: Among them, v r is the radial motion speed of the shell, v z is the speed of the axial movement of the shell, R b L is the inner radius of the shell at the end of the small deformation stage. b is the shell height at the end of the small deformation stage, t b This is the end moment of the small deformation stage.
5. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 1, characterized in that: The volume growth of the system in the large deformation stage is obtained by the following method: Where ΔV′ is the volume of the system during the large deformation stage, P is the pressure of the constrained charge system, and V b is the system volume at the end of the small deformation stage, M′ is the generalized deformation equivalent stiffness of the system, P b is the pressure inside the shell at the end of the small deformation stage, P c is the pressure inside the shell at the end of the large deformation stage, P b ≤P≤P c .
6. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 1, characterized in that: The rate of increase in gas product mass is obtained by the following method: Among them, α is the explosive combustion coefficient, β is the explosive combustion index, is the explosive burning rate, S i is the initial surface area of the combustion crack at the ignition moment, ρ e0 is the initial density of explosive, V e0 is the initial volume of explosive, S max is the saturated specific surface area of combustion cracks, P i is the initial pressure inside the shell at the time of ignition, P r is the reference pressure of combustion cracks, n is a positive integer, S[P] is the function of the total surface area of the explosive combustion crack network and the pressure inside the shell, m g is the mass of the gas product in the system, P is the pressure of the constrained charge system, and P c is the pressure inside the shell at the end of the large deformation stage, P≤P c .
7. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 6, characterized in that: Substituting the volume of the system and the mass of the gas product in the large deformation stage into the ideal gas state equation, the following formula is obtained: Among them, R p is the universal gas constant, T p is the gas product temperature, M g is the molar mass, V a is the initial volume of the void in the small deformation stage, P b is the pressure inside the shell at the end of the small deformation stage, V0 is the initial volume of the system in the small deformation stage, M is the generalized equivalent stiffness of the system, ΔV′ is the volume increase of the system in the large deformation stage, t b is the end time of the small deformation stage, t c is the end time of the large deformation stage, P b ≤P≤P c , t b ≤t≤t c ; The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the large deformation stage with respect to time t: in, V b is the system volume at the end of the small deformation stage, V eb is the volume of explosive at the end of the small deformation stage, ξ is the integral variable, B is the bulk modulus of explosive, V′ is the total volume of the system in the large deformation stage, v r is the radial motion speed of the shell, v z is the speed of the axial movement of the shell, R b L is the inner radius of the shell at the end of the small deformation stage. b is the shell height at the end of the small deformation stage.
8. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 1, characterized in that: The volume growth of the system in the small deformation stage is obtained by the following method: Among them, ΔV is the volume of the system increase in the small deformation stage, P is the pressure of the constrained charge system, V0 is the initial volume of the system in the small deformation stage, and M is the generalized equivalent stiffness of the system.
9. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 7, characterized in that: Substituting the volume of the system in the small deformation stage and the mass of the gas product into the ideal gas state equation, the following formula is obtained: Where P≤P b , 0≤t≤t b ; The above formula is derived and integrated to obtain the model of the internal reaction pressure and shell expansion speed in the small deformation stage with respect to time t:
10. The method for quantitatively characterizing reaction pressure based on shell expansion velocity according to claim 1, characterized in that: The generalized equivalent stiffness of the system is: Among them, M is the generalized equivalent stiffness of the system, I is the generalized equivalent stiffness of the shell, B is the bulk modulus of the explosive, V0 is the initial volume of the system in the small deformation stage, V e0 is the initial volume of explosive at the small deformation stage.