Method for calculating impact compression reaction characteristics of energetic structural material

Abstract

A method for calculating the impact compression reaction characteristics of energetic structural materials (ESMs) is proposed. The method combines impact dynamics and chemical reaction kinetics, and takes into account the static pressure parameters of products and the microstructure of materials. A theoretical model of impact reaction is established, and the wave specific volume, impact temperature, and reaction temperature of materials are calculated and corrected. The correlation mechanism between the microstructure and macroscopic reaction behavior of ESMs under impact compression is established, which effectively improves the calculation accuracy of the impact compression reaction characteristics of ESMs.

Description

Technical Field

[0001] This invention relates to the field of energetic structural materials technology, and in particular to a method for calculating the impact compression response characteristics of energetic structural materials. Background Technology

[0002] Compared to high-energy explosives, energetic structural materials (ESMs) possess higher mechanical strength and better energy release characteristics, attracting increasing attention and being widely used in the fabrication of energetic fragments and reactive metal shaped charges. For ESMs, maintaining a certain energy release capacity while preserving high mechanical strength is a key objective in engineering applications. Therefore, understanding the reaction process of ESMs under impact loads is crucial for advancing efficient damage and protection technologies.

[0003] Theoretical studies on the impact compression reaction behavior of ESMs mainly include impact compression equations of state and impact reaction thermochemical models. The Mie-Gruneisen equation of state is often used to describe the impact compression characteristics of dense metallic materials and some specific non-metallic materials. Based on the idea of ​​treating porous materials as dense materials with different initial densities, Mcqueen RG et al. proposed an avalanche model along the isochoric path. Herrmann W. analyzed the compression process of material pores based on the avalanche model and established the "P-α" model. Subsequently, Carroll MM and Holt AC extended and simplified the "P-α" model, proposing the Carroll-Holt's model. Zhang Xianfeng, based on the principle of cold energy superposition and combining the Wu-Jing model and the pore collapse model proposed by Carroll MM, obtained a calculation method for the equation of state of porous mixed materials. For the mechanical effects and reaction behavior of ESMs under high pressure, Graham RA proposed the CONMAH model, namely the flow forming-mixing-reaction-thermal model. Based on Batsanov's research, Yu LH and Song I proposed a thermodynamic calculation model for calculating the equations of state of ESMs chemical reaction products. Boslough MB proposed a "thermal detonation" type thermochemical reaction model based on his research on the impact-induced chemical reactions of aluminothermic ESMs.

[0004] Studies on the thermochemical models of impact reactions include Zhang Xianfeng's model considering the degree of reaction, developed by combining the equation of state of loose mixtures and the Arrhenius reaction rate equation; and Jiang Jianwei's computational model of Al / PTFE materials, including both reacted and unreacted states, based on the principle of mixture superposition and condensed explosive processing methods. However, these methods do not consider the influence of the actual specific volume and isostatic pressure parameters of the products on the post-shock state of ESMs, nor the correlation between the material's microstructure and the impact compression and reaction state of ESMs, leading to inaccurate calculations of the impact compression reaction characteristics of ESMs. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this disclosure provides a calculation method for the impact compression reaction characteristics of energetic structural materials. It combines impact dynamics and chemical reaction kinetics methods, and comprehensively considers the static pressure parameters of the products and the microstructure of the materials to establish a theoretical model of impact reaction. The material's post-wave volume, impact temperature, and reaction temperature are corrected and calculated, and a correlation mechanism between the microstructure and macroscopic reaction behavior under ESMs impact compression is established.

[0006] The computational model for the impact compression response characteristics of ESMs constructed in this disclosure mainly consists of two parts:

[0007] I. Macroscopic Model of Impact Response

[0008] Mainly includes:

[0009] (1) Calculation of ESMs equation of state under impact compression: Based on Grünesen's dense state equation of state, the mass averaging principle of mixtures, the Wu-Jing model, the Carroll-Holt's model and thermodynamic relations, a calculation model for the ESMs loose state mixture equation of state was derived.

[0010] (2) Calculation of impact temperature: Using the impact adiabatic line and thermodynamic relationship, starting from the isobaric path, the impact temperature of ESMs is calculated by using the ESMs impact compression equation of state model and combining thermodynamic relationship.

[0011] (3) Impact-induced chemical reaction: Combining impact kinetics and chemical reaction kinetics, an ESMs impact-induced chemical reaction model considering the degree of reaction was established.

[0012] II. Microscopic Model of Impact Response

[0013] Based on the expansion process of the "hot spot" reaction zone, the entire reaction is divided into two parts: the independent reaction stage and the interpenetrating reaction stage, to study the material impact reaction process at the microscale.

[0014] The relationship between the degree of impact reaction and the distance of reaction zone expansion was established, and material particle size and combustion rate parameters were introduced to represent the reaction duration of the material under different particle sizes and different combustion rates;

[0015] Finally, by combining the reaction degree-reaction duration relationship with the Arrhenius reaction rate theory, a calculation model for the impact reaction degree at the mesoscale was obtained. Substituting this mesoscale impact reaction degree calculation model into the macroscale impact reaction model yields the relationship between impact temperature T and reaction degree y in the mesoscale model of ESMs impact reaction.

[0016] Based on the above model, the calculation method for the impact compression response characteristics of energetic structural materials provided in this disclosure mainly includes the following steps:

[0017] S1, Establish a physical state calculation model for the impact compression dense mixture to obtain the reactant PV s -U s Calculation of relationships and products Calculation of relationships; establishment of a physical state calculation model for impact compression loose mixtures to obtain the PV of reactants. p -U pore Calculate relations and products Calculate the relationship;

[0018] S2, Establish an ESMs shock temperature calculation model, including: shock pressure P and shock temperature T of the dense reactant. s Calculate the relationship between the impact pressure P and impact temperature T of the loose-state reactants. p Calculation of relationships and dense-state products Calculation of relationships and loose-state products Calculate the relationship;

[0019] S3, based on the Arrhenius reaction rate theory, establishes a model that combines macroscopic and microscopic perspectives to establish the relationship between the impact temperature T and the degree of reaction y, according to the expansion process of the "hot spot" reaction zone;

[0020] S4, based on McQueen's mixing principle, yields the specific volume V of ESMs that undergo partial chemical reactions. real Impact temperature T real and shock wave velocity U real And the reaction temperature T, which contains the reaction energy. reaction The computational model;

[0021] S5. Based on the combined static pressure parameters of reactants and products, respectively, substitute them into the models obtained in steps S1 and S2 to obtain the relationship between the PVUTs of reactants or products.

[0022] Substituting the reactant shock temperature into the model of step S3, the degree of reaction y is obtained;

[0023] Substituting the impact temperatures of the reactants and products, and y, into the model of step S4, we obtain T. real Based on T real Correct y; then recalculate T. real Then, y is adjusted again; this process is repeated until y converges to a certain value.

[0024] The preferred construction methods for the various computational models used in this disclosure are further detailed below:

[0025] 1. The equation of state for impact compression in step S1

[0026] (1) For a compressed, dense mixture, the reactant specific volume (V s ) and the specific volume of the product (V s * ) and shock wave velocity (U s The equation of state for a mixed dense matter was calculated based on the Rankine-Hugoniot energy equation and the Grüneisen equation of state.

[0027] The calculation model for the equation of state of a material under impact compression in its dense state is as follows:

[0028]

[0029] Where V0 is the initial specific volume of the material; V s E represents the specific volume of the material after the shock wave. c For cold energy, P c For cold compression, γ is the Grünesen coefficient, and E0 is the initial specific internal energy;

[0030] Considering the isobaric specific heat capacity C at room temperature p Compared with the specific heat capacity at constant volume C v Approximately equal, the Debye model is applied to estimate the initial specific internal energy E0 of the material:

[0031]

[0032] Where R is the molar mass of the material; g The universal gas constant is taken as 8.31 J / (mol·K); T0 is room temperature, taken as 300 K; Θ D Let be the Debye characteristic temperature of the material. In the Debye model, the influence of electronic terms is neglected.

[0033] The cold energy (E) obtained from the Born-Mayer potential c ) and cold pressing (P cSubstituting expressions (3-4) into the Dugdale-MacDonald expression (5), the Grünesen coefficients are simplified to expression (6):

[0034]

[0035]

[0036]

[0037]

[0038] Where δ is the compressibility of the material at 0K, and V 0k Let be the initial specific volume of the material at 0 K, and Q and q be material constants.

[0039] The analytical solutions for the material constants Q and q were calculated using the Hu Jinbiao-Jing Fuqian method and corrected for temperature.

[0040]

[0041]

[0042] I shock =C0+SU particle (9)

[0043] Where, α v γ is the volume expansion coefficient, T0 is room temperature, γ0 is the Grüneisen coefficient at zero temperature, and C0 and S are the experimentally measured shock wave velocities U of the elemental material. shock With the velocity U of the wave-after particles particle The Hugoniot parameters obtained by linear fitting.

[0044] Therefore, a calculation model for the equation of state of impact-compressed dense mixtures was established. By substituting the hydrostatic parameters of each component of the reactant material into the model, the PV can be obtained. s -U s Calculation of relationships. Substituting the known hydrostatic parameters of each component of the product into the model yields the results. Calculate the relationship.

[0045] (2) For a compressible loose mixture, the reactant specific volume (V p ) and product specific volume (V p * ) and shock wave velocity (U p Based on the compressed and dense state equation of state described in (1) above, the loose state material equation of state (Equation 12) further established using the Wu-Jing model and the P-α model is calculated as follows:

[0046]

[0047] Among them, V0, V s V c E0 and E c V represents the initial specific volume, post-shock wave specific volume, zero-temperature specific volume, initial specific internal energy, and cold energy of a dense material. 00 V p V c '、E 00 E c 'The initial specific volume, post-shock wave specific volume, zero-temperature specific volume, initial specific internal energy, and cold energy of the porous material;

[0048] Similarly, the Born-Meyer potential is used to describe the zero-temperature cold-pressing line of dense materials to calculate the zero-temperature specific volume V of dense materials. c :

[0049]

[0050] Zero-temperature porosity α of porous materials c It can be represented as:

[0051]

[0052] The Carroll-Holt model is used to describe the porosity of loose materials under strong impact loads:

[0053]

[0054] Where α0 is the porosity of the material in its initial state. Y represents the elastic limit of the dense material. P crit The elastic limit of a porous material is expressed as follows:

[0055]

[0056] Based on the three conservation equations, the expression for the shock wave velocity of porous materials under impact load is derived:

[0057]

[0058] Among them, U pore The shock wave velocity of a porous material.

[0059] Therefore, based on the calculation model of the equation of state of impact-compressed dense mixtures, a calculation model of the equation of state of impact-compressed loose mixtures was established.

[0060] By substituting the hydrostatic parameters of each component of the reactant material into the model, the PV can be calculated. p -U poreThe relationship between the components is determined by substituting the known hydrostatic parameters of the products into the model. The relationship.

[0061] 2. The method for calculating the impact temperature of reactants and products in step S2.

[0062] Considering the influence of the free electron term, the first-order differential equation (18) for calculating the impact temperature is obtained according to the "isobar method" in the thermodynamic relation:

[0063]

[0064]

[0065] Where V′ is the specific volume of the material after the shock wave considering the influence of free electrons, and β0 is the initial electronic specific heat coefficient.

[0066] R s The Wu-Jing parameter is calculated as shown in expressions (20) to (21):

[0067]

[0068]

[0069] Among them, K T For the isothermal bulk modulus (approximated by 0 K), R can be obtained by substituting equation (20) into equation (21). s .

[0070] Therefore, a theoretical calculation model for impact temperature was established. Based on equations (18) and (19), the impact temperature of the material can be obtained using the numerical differential equation solution method, and the impact insulation line can completely determine the numerical value of the impact temperature of the material. This method can well describe the impact temperature of both dense and porous materials under impact pressure.

[0071] From equations (18) and (19), we can obtain the formula for calculating the impact temperature of dense materials:

[0072]

[0073]

[0074] Among them, T s V represents the impact temperature of a dense material under impact pressure. s ′ is the shock wave back volume of a dense material considering the influence of free electrons.

[0075] Similarly, from equations (18) and (19), we can obtain the formula for calculating the impact temperature of porous materials:

[0076]

[0077]

[0078] Among them, T p V represents the impact temperature of a porous material under impact pressure. p ′ is the shock wave back volume of a loose material considering the influence of free electrons.

[0079] For ESMs that generate new products, the impact of the generated products on the material's impact temperature must be considered.

[0080] For dense ESMs, substituting the hydrostatic parameters of the products into the model yields the following results. Relationship; for loose ESMs, substituting the hydrostatic parameters of the products into the model yields... relation.

[0081] 3. The macroscopic impact-induced thermochemical model of the chemical reaction in step S3.

[0082] Based on the Arrhenius reaction rate theory, the chemical reaction rate can be expressed as:

[0083]

[0084] Where y is the degree of chemical reaction, t is the reaction duration, k is the chemical reaction rate constant, and f(y) is the kinetic model function.

[0085] Substituting the shock temperature and kinetic parameters of the reactants into the Arrhenius rate theory, a first-order differential equation for the degree of reaction as a function of temperature is obtained, and the first derivative of the shock temperature T with respect to the degree of reaction y is calculated:

[0086]

[0087] Where T is the shock temperature of the reactants, and R g E is the gas constant. a is the apparent activation energy, and n is the reaction mechanism function factor; the degree of chemical reaction that ESMs can achieve at different shock temperatures can be obtained by solving equation (27) using the numerical differential equation method.

[0088] 4. The microscopic impact-induced chemical reaction thermochemical model in step S3.

[0089] During the compression process of a material under shock wave, the particles accelerate, compress, and rub against each other, depositing impact energy at the spatial boundaries between particles and forming "hot spot" reaction zones. The basic geometric space containing these "hot spot" reaction zones is called a unit cell. Assuming these reaction zones are spherically distributed, these regions are the centers of the unit cells (whose spatial configuration is tetrahedral) in a three-dimensional view. A top view is shown in the attached figure. Figure 1 As shown.

[0090] Assume each material particle has N reaction initiation zones, all equidistant from each other by a distance d. After the material undergoes impact pressure compression and consolidation, the unit cell size is compressed to 2R (where R is the particle radius). Therefore:

[0091] Nd 3 =a 3 =2 3 R 3 (38)

[0092] The expansion process of the "hotspot" reaction area is shown in the attached figure. Figure 2 As shown. If all reaction initiation regions are simultaneously activated at time t0, the reaction transformation process over time can be divided into two stages: (1) Independent reaction stage (t0 <t≤t mid (2) Interpenetration reaction stage (t) mid <t≤t max The degree of reaction, y, is estimated as a function of the reaction zone expansion distance, r. If N1 is the number of reaction initiation zones per unit volume, then at r0... <r≤r mid (r mid When = d / 2):

[0093] dy=N1dV=N14πr 2 dr (39)

[0094] In equation (39), it is assumed that the reaction occurs on the surface of the spherical reaction region. Integrating from r0 to r, we can obtain the relationship between the degree of reaction y and the distance r of the reaction region expansion:

[0095]

[0096] For r>r mid The overlapping volume of the spherical reaction region, Vol0, needs to be subtracted (see attached figure). Figure 2 As shown in IV and V), if each reaction initiation region has N2 adjacent reaction regions, we can obtain:

[0097]

[0098] The overlapping volume portion Vol0 is:

[0099]

[0100] Combining equations (41) and (42), we can obtain the relationship between the degree of reaction y and the distance r of the reaction zone expansion:

[0101]

[0102] The reaction rate ξ is defined as the mass of reactants reacting per unit area at the reaction interface per unit time, and its calculation expression is:

[0103]

[0104] In equation (44), A r Let be the interface area between reactants and products, and m, V, and ρ0 be the mass, volume, and initial density of the reactants, respectively. Additionally, The distance the reaction zone expands per unit time, i.e., the combustion rate V. burn Assuming the reaction rate ξ is constant, integrating equation (44) yields:

[0105]

[0106] For the initial moment of the reaction, r0 = t0 = 0, therefore we can obtain:

[0107]

[0108] When r = 0.61d (r max When the distance from the center of the tetrahedron to its vertex is 0.61d, t reaches its maximum value, which is:

[0109]

[0110] Substituting equation (46) into equations (40) and (43), we can obtain the relationship between the degree of reaction y and the reaction duration t:

[0111]

[0112] Wherein, the reaction region extends by a distance of r. mid When, the required time is t mid .

[0113] For the number of initial reaction zones per unit volume, N1 = d -3 =(1.1R) -3 For mixtures, R is calculated by averaging the particle sizes of each component according to the proportion of particle number, and its expression is:

[0114]

[0115] Where, m i R represents the mass percentage of the i-th component.i Let ρ be the particle size of the i-th component. i Let be the initial density of the i-th component.

[0116] Considering that each reaction initiation region has 6 adjacent reaction regions, N2 = 6. Therefore, when t = t mid When, y = y mid =π / 6; when t=t max When, y = y max ≈1. Appendix Figure 3 The relationship between the degree of chemical reaction (y) and the reaction duration (t) is shown under different combustion rates and particle sizes. Calculations indicate that the chemical reaction is completed within microseconds for all combustion rates and particle sizes. The faster the material combustion rate and the smaller the particle size, the shorter the time required for the reaction to complete.

[0117] To calculate the expression for the chemical reaction rate, let When 0 <t<t mid hour, Differentiating equation (48) yields:

[0118]

[0119] When t mid ≤t <t max When the reaction degree is related to time, the formula is y = a1t 3 +a2t 2 -a3, considering that the impact reaction is completed within a few microseconds, the higher-order terms of t are omitted, and the relational form can be written as y≈a2t. 2 -a3, then Similarly, differentiating equation (48) yields:

[0120]

[0121] Combining equations (50) and (51), we can obtain the chemical reaction rate expression based on the microscopic model:

[0122]

[0123] The thermochemical model of macroscopic impact-induced chemical reactions has been elaborated in detail above. Based on equation (26) and the Arrhenius rate theory, combined with equation (52), g(T,y)=0, a microscopic relationship model between the impact temperature T and the degree of reaction y based on the macroscopic model can be obtained:

[0124]

[0125] Among them, T0, T mid and T max Represented by room temperature and degree of reaction ymid The impact temperature and degree of reaction at that time are y max Impact temperature at that time.

[0126] Equation (27) represents the relationship between the impact temperature and the degree of response in the macroscopic model, and Equation (53) represents the relationship between the impact temperature and the degree of response in the microscopic model, respectively describing the macroscopic and microscopic performance of ESMs under impact load.

[0127] 5. Calculation model for the impact reaction characteristics of ESMs in step S4 where partial chemical reactions occur.

[0128] Based on McQueen's mixing principle, the specific volume V of ESMs that undergo partial chemical reactions can be determined. real Impact temperature T real and shock wave velocity U teal Represented as:

[0129] V real (P)=(1-y)V(P)+yV * (P) (28)

[0130] T real (P)=(1-y)T(P)+yT * (P) (29)

[0131] U real (P)=(1-y)U(P)+yU * (P) (30)

[0132] The reaction temperature T, which contains the reaction energy reaction It can be viewed as the superposition of the impact temperature and the energy released by the chemical reaction:

[0133]

[0134] Where ΔH is the chemical energy released by the complete reaction of a unit mass of reactants.

[0135] Based on equations (28)-(30), the specific volume V of dense ESMs after partial chemical reaction can be obtained. real Impact temperature T real and shock wave velocity U real :

[0136]

[0137]

[0138]

[0139] Similarly, based on equations (28)-(30), the specific volume V of loosely packed ESMs after partial chemical reaction can be obtained. real Impact temperature T real and shock wave velocity U real :

[0140]

[0141]

[0142]

[0143] Preferably, the mass averaging method is used as the mixing rule for solving the equation of state of the mixture in step S5. The combined static pressure parameters of the ESMs are calculated from the static pressure parameters of each component of the ESMs:

[0144]

[0145]

[0146] Where i represents each component in ESMs, F i For the static pressure parameters of a single component, m i denoted as the mass percentage of the i-th component.

[0147] Compared with the prior art, the beneficial effects of this disclosure are: (1) a calculation path for the impact compression equation of state in the macroscopic model of impact reaction is established. In order to verify the effectiveness of the equation of state calculation model, typical metallic elements and multi-component mixed metallic materials are used as examples to calculate their impact compression Hugoniot curves and compare them with experimental results. The results show that the model is suitable for describing the impact compression degree of inert materials and ESMs in the unreacted stage. For ESMs in the reaction stage, the influence of the appearance of products on their impact compression Hugoniot state needs to be considered.

[0148] (2) A calculation method for impact temperature and impact-induced chemical reaction applied to a macroscopic model of impact reaction was constructed. Based on the equation of state calculation model and combined with the principles of impact kinetics and thermodynamics, a first-order differential expression for calculating the impact temperature of materials was derived from the isobaric path, and the impact temperature was calculated using the numerical differential equation solution method. Then, based on the chemical reaction kinetic model, Arrhenius reaction rate theory, and the n-dimensional core / growth control reaction function proposed by Avrami-Erofeev, a calculation model for the degree of impact reaction of ESMs controlled by the impact temperature was established. Finally, the post-wave reaction state of ESMs was obtained by the McQueen mixing rule and the principle of linear superposition.

[0149] (3) Based on the macroscopic model of the impact reaction, a microscopic model of the ESMs impact reaction was established based on the "hot spot" reaction theory. This model, from a microscopic perspective, quantifies and calculates the entire impact reaction process in stages, exploring the influence of material particle size and combustion rate on the reaction duration. Then, based on the Arrhenius reaction rate theory, the microscopic reaction process model was transformed into a microscopic reaction state model, thus obtaining the microscopic impact reaction degree calculation model. Combining this microscopic impact reaction degree calculation model with the macroscopic impact compression equation of state, impact temperature calculation model, and post-wave reaction state calculation theory yields the ESMs impact reaction microscopic model. Attached Figure Description

[0150] The above and other objects, features and advantages of this disclosure will become more apparent from the more detailed description of exemplary embodiments of this disclosure taken in conjunction with the accompanying drawings, in which the same reference numerals generally represent the same components.

[0151] Figure 1 A top view of the "hot spot" reaction zone at the particle interface;

[0152] Figure 2 This is a schematic diagram of the expansion process of the reaction zone over time; where: (Ⅰ) initial state; (Ⅱ) independent expansion stage; (Ⅲ) tangent state of the reaction surface; (Ⅳ) interpenetration stage of the reaction zone; (Ⅴ) complete reaction state;

[0153] Figure 3 The relationship between the degree of reaction and the duration of reaction; where: (a) different combustion rates (particle size constant at 50 μm); (b) different particle sizes (combustion rate constant at 25 m / s);

[0154] Figure 4 The calculation results of the impact compression characteristics of Ni / Al ESMs with different stoichiometric ratios are shown; among them: (a) the relationship curve between impact pressure and relative specific volume; (b) the relationship curve between impact pressure and impact temperature;

[0155] Figure 5 The results of the impact reaction characteristics of Ni / Al ESMs with different stoichiometric ratios are shown in the figures: (a) the relationship between impact pressure and reaction degree; and (b) the relationship between impact pressure and reaction temperature.

[0156] Figure 6 Fitting curves for the impact reaction pressure threshold and Ni content of Ni / Al ESMs with different stoichiometric ratios; where (a) y = 0; (b) y = 1;

[0157] Figure 7The calculation results of impact compression characteristics of Ni / Al ESMs with different initial densities are shown, including: (a) the relationship curve between impact pressure and relative specific volume; and (b) the relationship curve between impact pressure and impact temperature.

[0158] Figure 8 The calculation results of the impact reaction characteristics of Ni / Al ESMs with different initial densities are shown, including: (a) the relationship between impact pressure and reaction degree; (b) the relationship between impact pressure and reaction temperature.

[0159] Figure 9 Fitting curves for the impact response pressure threshold and initial density of Ni / Al ESMs with different initial densities, where: (a) y = 0; (b) y = 1;

[0160] Figure 10 The calculation results of the impact compression characteristics of Ni / Al ESMs with different raw material particle size ratios are shown, including: (a) the relationship curve between impact pressure and relative specific volume; (b) the relationship curve between impact pressure and impact temperature; and (c) the relationship curve between impact pressure and impact temperature difference.

[0161] Figure 11 The calculation results of the impact reaction characteristics of Ni / Al ESMs with different raw material particle size ratios are shown, including: (a) the relationship curve between impact pressure and reaction degree; (b) the relationship curve between impact pressure and reaction temperature;

[0162] Figure 12 Fitting curves for the relationship between impact reaction pressure threshold and initial density of Ni / Al ESMs with different raw material particle size ratios, where: (a) y = 0; (b) y = 1;

[0163] Figure 13 The calculation results of the impact compression characteristics of Ni / Al ESMs with different combustion rates are shown, including: (a) the relationship curve between impact pressure and relative specific volume; (b) the relationship curve between impact pressure and impact temperature; and (c) the relationship curve between impact pressure and impact temperature difference.

[0164] Figure 14 The calculation results of the impact reaction characteristics of Ni / Al ESMs with different combustion rates are shown, including: (a) the relationship curve between impact pressure and reaction degree; (b) the relationship curve between impact pressure and reaction temperature;

[0165] Figure 15 Fitting curves for the relationship between the impact reaction pressure threshold and initial density of Ni / Al ESMs with different combustion rates, where: (a) y = 0; (b) y = 1;

[0166] Figure 16 This is a flowchart illustrating an exemplary embodiment of the present disclosure. Detailed Implementation

[0167] Preferred embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0168] This disclosure provides a method for calculating the impact compression response characteristics of energetic structural materials. A flowchart illustrating an exemplary embodiment of this disclosure is attached. Figure 1 As shown, the calculation process mainly includes:

[0169] For dense ESMs, the PV can be calculated by substituting the hydrostatic parameters of each reactant component into the model. s -U s -T s The relationship, in which the impact temperature T s Substituting into equation (53), the degree of reaction y can be obtained. Substituting the known hydrostatic parameters of the products into the model, the following can be calculated: Relationship. Then... Substituting y into equation (33) yields the first corrected impact temperature T. real Then T real Substituting into equation (53), we can obtain the reaction degree y after the first update, and then... T s Substituting the reaction degree y after the first update into equation (33) yields the second corrected shock temperature T. real Repeat the cycle until the degree of reaction y converges to a certain value. Finally, based on equations (32)-(34) and combined with equation (31), the specific volume V can be obtained. real Impact temperature T real Shock wave velocity U real and reaction temperature T reaction .

[0170] For loosely packed ESMs, the PV can be calculated by substituting the hydrostatic parameters of each reactant component into the model. p -U pore -T p The relationship, in which the impact temperature T p Substituting into equation (53), the degree of reaction y can be obtained. Substituting the known hydrostatic parameters of the products into the model, the following can be calculated: Relationship. Then... T p Substituting y into equation (36) yields the first corrected impact temperature T. real Then T real Substituting into equation (53), we can obtain the reaction degree y after the first update, and then... Tp Substituting the reaction degree y after the first update into equation (36) yields the second corrected shock temperature T. real Repeat the cycle until the degree of reaction y converges to a certain value. Finally, based on equations (35)-(37) and combined with equation (31), the specific volume V can be obtained. real Impact temperature T real Shock wave velocity U real and reaction temperature T reaction .

[0171] Application Examples

[0172] Example 1

[0173] The impact compression and reaction characteristics of Ni / Al ESMs with three different stoichiometric ratios were calculated using the following method:

[0174] For these three typical Ni / Al ESMs, the initial density is set to 60%, the raw material particle size ratio is Ni:Al = 20μm:25μm, and the combustion rate is assumed to be V. burn =25m / s. The static pressure calculation parameters of the reactants, the static pressure parameters of the products, and the reaction parameters are shown in Tables 1, 2, and 3, respectively.

[0175] Table 1. Calculation parameters of reactant static pressure for Ni / Al ESMs with different stoichiometric ratios

[0176]

[0177] Table 2. Calculation parameters for hydrostatic pressure of Ni / Al ESMs products with different stoichiometric ratios.

[0178]

[0179] Table 3 Reaction parameters of Ni / Al ESMs with different stoichiometric ratios

[0180]

[0181]

[0182] The impact compression characteristics of Ni / Al ESMs calculated based on the relevant parameters in Tables 1-3 are shown in the appendix. Figure 4 As shown in the attached figure, the impact response characteristics are as follows. Figure 5 and attached Figure 6 As shown, it was found that the higher the Al content, the better the compressibility of Ni / Al ESMs, the higher the impact temperature and reaction temperature under the same impact load, and the lower the metallogenic reaction pressure threshold.

[0183] Example 2

[0184] The impact compression and reaction characteristics of Ni / Al ESMs with four different initial densities were calculated using the following method:

[0185] Taking Ni / Al ESMs with a stoichiometric ratio of Ni:Al = 1:1, a raw material particle size distribution of Ni:Al = 20μm:25μm, and a combustion rate V_burn = 25m / s as representatives, the impact compression reaction characteristics were calculated using four initial densities: 45%, 60%, 80%, and 90%. The relevant static pressure calculation parameters of the reactants and products from Tables 1, 2, and 3 were input. The calculated impact compression characteristics of Ni / Al ESMs are shown in the attached figure. Figure 7 As shown in the attached figure, the impact response characteristics are as follows. Figure 8 and attached Figure 9 As shown in the figure. The results indicate that the lower the initial density, the better the compressibility of Ni / Al ESMs, the higher the impact temperature and reaction temperature under the same impact load, and the lower the metallogenic reaction pressure threshold.

[0186] Example 3

[0187] The impact compression characteristics and reaction characteristics of Ni / Al ESMs with four different raw material particle size ratios were calculated using the following method:

[0188] With a stoichiometric ratio of Ni:Al = 1:1, an initial density of 60%, and a combustion rate V... burn Taking Ni / Al ESMs with a particle size distribution of 25 m / s as a representative, four raw material particle size ratios of Ni:Al = 1 μm:25 μm, 1 μm:40 μm, 1 μm:100 μm, and 20 μm:25 μm were selected for impact compression reaction characteristic calculations. The relevant static pressure calculation parameters of the reactants and the static pressure parameters of the products in Tables 1 and 2, and the relevant reaction parameters are shown in Table 4.

[0189] Table 4 Reaction parameters of Ni / Al ESMs with different raw material particle size ratios

[0190]

[0191]

[0192] The calculated impact compression characteristics of Ni / Al ESMs are shown in the attached figure. Figure 10 As shown in the attached figure, the impact response characteristics are as follows. Figure 11 and attached Figure 12 As shown in the figure. The results indicate that the smaller the particle size of each component, the better the compressibility of Ni / Al ESMs, the higher the impact temperature and reaction temperature under the same impact load, and the lower the metallogenic reaction pressure threshold.

[0193] Example 4

[0194] The impact compression characteristics and reaction characteristics of Ni / Al ESMs with four different raw material particle size ratios were calculated using the following method:

[0195] Taking Ni / Al ESMs with a stoichiometric ratio of Ni:Al = 1:1, an initial density of 60%, and a raw material particle size distribution of Ni:Al = 20μm:25μm as a representative, V was selected. burn Impact compression characteristics were calculated using four combustion rates: 25 m / s, 50 m / s, 75 m / s, and 100 m / s. The relevant static pressure calculation parameters for reactants and products were input from Tables 1, 2, and 3. The calculated impact compression characteristics of Ni / Al ESMs are shown in the attached figure. Figure 13 As shown in the attached figure, the impact response characteristics are as follows. Figure 14 and attached Figure 15 As shown in the figure. The results indicate that when the internal and external conditions are controlled to increase the reaction combustion rate, the compressibility of Ni / Al ESMs is better, the impact temperature and reaction temperature generated under the same impact load are higher, and the metal combination reaction pressure threshold is lower.

[0196] The above technical solutions are merely exemplary embodiments of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the specific embodiments of the present invention. Therefore, the methods described above are merely preferred and not restrictive.

Claims

1. A method for calculating the impact compression response characteristics of energetic structural materials, comprising the following steps: S1, Establish the equation of state model for the impact compression mixture to obtain the impact pressure. P Specific volume of reactants or products V and shock wave velocity U The calculation relationship between them; S2, Establishing ESMs shock temperature T Computational model; S3, based on the Arrhenius reaction rate theory, establishes the impact temperature based on a macroscopic model of the impact reaction according to the expansion process of the reaction zone. With degree of reaction A detailed relational model; S4, based on McQueen's mixing principle, yields a calculation model for the specific volume, shock temperature, shock wave velocity, and reaction temperature of ESMs undergoing partial chemical reactions. S5, based on the combined hydrostatic parameters of the reactants and products, respectively, substitute them into the models obtained in steps S1 and S2 to obtain the reactants or products. P - V - U - The relationship between them; Substituting the reactant shock temperature into the model of step S3, the degree of reaction is obtained. ; In an iterative manner, using the model from step S4, the material's back-wave volume, impact temperature, reaction temperature, and reaction degree are iteratively corrected until the reaction degree converges to a certain value. Step S3 specifically includes: S31, Constructing a macroscopic model: Based on Arrhenius reaction rate theory: in, To the degree of chemical reaction, For the duration of the reaction, For chemical reaction rate, This is a kinetic model function; considering the chemical reaction type is solid-state thermally activated, the reaction rate... The reciprocal of absolute temperature expressed in exponential form is: In the formula, For impact temperature, and These are the pre-exponential factor and the apparent activation energy, respectively, which are calculated from DSC test data; Substituting the shock temperature and kinetic parameters of the reactants into the equation, we obtain the first-order differential equation for the degree of reaction as a function of temperature: Where T is the shock temperature of the reactants, and R g E is the gas constant. a It is the apparent activation energy, and n is the reaction mechanism function factor; The degree of chemical reaction that ESMs can achieve at different shock temperatures is obtained by solving equation (27) using the numerical differential equation method; S32, Detailed Model Construction: Assume each material particle has There are 1 reaction initiation zone, and the distance between these reaction initiation zones is 1. After the material is compressed and consolidated under impact pressure, the unit size is compressed to... , Where the particle radius is; Assume all reaction initiation zones are at time... When both are activated simultaneously, the expansion of the reaction region is divided into two stages: the independent reaction stage and the independent reaction stage. Interpenetration reaction stage ; Among them, the reaction zone expansion distance for = The required time is ;when =0.61 At that time, that is The distance from the center of the tetrahedron to its vertices is 0.

61. d hour, Get the maximum value : The chemical reaction rate expression based on the mesoscopic model is: In the formula: when hour, ;when hour, ; , ； The number of initial reaction zones per unit volume. Each reaction initiation zone has Adjacent reaction regions; For the reaction rate, The initial density of the reactants, = ; For mixtures, The value is calculated by averaging the particle sizes of each component according to the proportion of particle number: in, For the first Component mass percentage For the first Particle size of the component For the first The initial density of the component; S33, an expression for the chemical reaction rate based on the Arrhenius and Arrhenius rate theories combined with a mesoscopic model. The impact temperature was obtained based on a macroscopic model. With degree of reaction Micro-relationship model: in, and Respectively, room temperature and degree of reaction are 100%. The impact temperature and degree of reaction at that time were Impact temperature at that time.

2. The method according to claim 1, characterized in that, The equation of state in step S1 specifically includes: (1) Equation for calculating the state of a mixture under impact compression: In the formula, V0 is the initial specific volume of the material; V s E represents the specific volume of the material after the shock wave. c For cold energy, P c For cold compression, γ is the Grünesen coefficient, E0 is the initial specific internal energy, and P is the impact pressure. Among them, internal energy The calculation is shown in the following formula: In the formula, M The molar mass of the material; It is the universal gas constant; Room temperature; The Debye characteristic temperature of the material; Cold energy E c and cold-pressed P c expression: The Gruneisen coefficient γ is simplified to: In the formula, The compressibility of the material at 0K. The initial specific volume of the material at 0K. and These are material constants; Among them, material constants and The analytical solution is calculated as follows: in, The coefficient of volume expansion is 1. At room temperature The Grünesen coefficient at zero temperature. and These are the shock wave velocities of the elemental materials measured experimentally. With the velocity of the wave-back particles The Hugoniot parameters obtained by linear fitting; (2) Equation of state for compressible loose mixtures: In the formula, V0 and V s V c E0 and E c These are the initial specific volume, post-shock wave specific volume, zero-temperature specific volume, initial specific internal energy, and cold energy of the dense material, respectively; V 00 V p V c '、E 00 E c ' represents the initial specific volume, post-shock volume, zero-temperature specific volume, initial specific internal energy, and cold energy of the porous material, respectively; P represents the impact pressure.

3. The method according to claim 2, characterized in that, The impact temperature T calculation model in step S2 includes: Formula for calculating the impact temperature of dense materials: In the formula, The impact temperature of a dense material under impact pressure. Shock wave back specific volume for dense materials and considering the influence of free electrons; This is the initial electronic specific heat coefficient; C p The specific heat capacity at constant pressure of the material; R s The Wu-Jing parameter is calculated as follows: in, Formula for calculating the impact temperature of porous materials: in, This refers to the impact temperature of a porous material under impact pressure. The shock wave back-capacitance is considered for a loose material and taking into account the influence of free electrons.

4. The method according to claim 1, characterized in that, The model in step S4 includes: The specific volume of ESMs that undergo partial chemical reactions Impact temperature and shock wave speed They are represented as follows: Where P is the impact pressure, and V, T, and U are the specific volume of the reactants, impact temperature, and impact wave velocity, respectively. , , These are the specific volume of the product, the shock temperature, and the shock wave velocity, respectively. Reaction temperature containing reaction energy Viewed as the superposition of impact temperature and energy released by the chemical reaction: in, Chemical energy released per unit mass of reactants upon complete reaction.

5. The method according to any one of claims 1-4, characterized in that, In step S5, the calculation method for the combined static pressure parameters includes: The combined static pressure parameter F of ESMs is calculated from the static pressure parameters of each component of ESMs: in, i For each component in ESMs, These are the static pressure parameters for a single component. For the first i Mass percentage of the component.

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