Method and system for establishing five-phase mesoscopic model of composite solid propellant

Abstract

The application belongs to the field of mechanical model research, and discloses a kind of composite solid propellant five-phase mesoscopic model establishing method and system, based on the method of micromechanics, the five-phase micromechanics model of composite solid propellant is established, and the effective elastic modulus of multiphase inclusion composite solid propellant is solved.First, on the basis of the original four-phase model of composite material, the liquid film thickness concept of propellant is introduced, and combined with the step-by-step doping method of multiphase composite material, it is developed into a four-phase model suitable for composite solid propellant.The application adopts two-step correction method, the first step is to add the interface phase in the model again, forming a five-phase mechanical model;The second step is to introduce discontinuity condition at the interface phase.Two-step correction method makes the composite model can clearly give the influence of two different interfaces in the propellant, and finally gives the analytical solution of the effective elastic modulus of the five-phase mechanical model.

Description

Technical Field

[0001] This invention belongs to the field of mechanical model research, and in particular relates to a method and system for establishing a five-phase microscopic model of composite solid propellants. Background Technology

[0002] The dwindling supply of traditional fossil fuels has led to an unprecedented energy crisis, typically involving shortages of oil, electricity, or other natural resources. Energy crises often result in economic recession. Achieving efficient energy conversion is an effective means of alleviating the energy crisis, such as thermoelectric conversion and photo / electrochemical energy conversion. Inorganic functional solids, as the most important carriers of energy conversion, possess diverse electronic and phonon structures due to the periodic arrangement of atoms in their crystals, thus endowing them with rich physical and chemical properties.

[0003] However, perfect crystals are almost non-existent in nature. This means that significant defects exist in the prepared solid materials, inevitably affecting the local structure and band structure of the crystal, both of which play a crucial role in the material's properties. Therefore, accurate characterization of the defects / local structure of solids and, based on this, studying their impact on the band structure is essential. Meanwhile, composite materials, as an important component of the industry, currently face significant challenges, including environmental pressures, low-end industry technology, severe homogenization competition, lagging industrial technology research and development, unregulated management, and a lack of clear development direction. Many issues regarding the production and stability of composite materials remain to be resolved. In particular, improving the mechanical and combustion properties of composite solid propellants requires the assistance of filler particles with different components.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0005] (1) There are large defects in the solid materials currently prepared, which will affect the local structure and band structure of the crystal.

[0006] (2) The calculation of the effective elastic modulus of composite materials with high particle content and multiphase inclusion is still quite complicated.

[0007] (3) At present, the calculation of the effective elastic modulus of composite materials is limited to solving the problem of single-particle inclusion composite materials, and cannot take into account the influence of changes in filler particle gradation. Summary of the Invention

[0008] The main objective of this invention is to propose a method and system for establishing a five-phase microscopic model of composite solid propellants, aiming to establish a model of composite solid propellants so as to control the materials, filler size and content of composite solid propellants according to requirements.

[0009] This invention provides a system for constructing a five-phase microscopic model of a composite solid propellant, comprising:

[0010] Initial model building module: Establishes an initial four-phase microscopic model of the composite solid propellant, including solid particles and liquid phase in the propellant;

[0011] Stepwise doping module: Based on the stepwise doping approximation theory, representative volumetric units of the four propellants are introduced into the model one by one.

[0012] Bulk modulus calculation module: Applying radial pressure and displacement conditions to the model at a location far from the origin, the module calculates the bulk modulus of the composite solid propellant using relevant formulas. The software can perform numerical calculations and solve linear equations to obtain analytical solutions for the bulk modulus.

[0013] Shear modulus calculation module: This module calculates the shear modulus of composite solid propellants using relevant formulas. The software can obtain analytical solutions for the shear modulus through numerical calculations and solving linear equations.

[0014] The first step of the correction module involves adding a liquid film thickness between the particles and the matrix and reintroducing the interfacial phase to quantify the difference between the two particle interfaces. The liquid film thickness is obtained through user calculations, and the interfacial thickness and mechanical properties are determined by the material properties.

[0015] The second step is the correction module: introducing interface displacement discontinuity conditions into the model and using the cohesive region model for correction;

[0016] Effective elastic modulus solution module: Based on the modified five-phase model, the effective elastic modulus of the composite solid propellant is solved by solving a system of simultaneous equations and using software for numerical calculation.

[0017] Furthermore, the initial model building module collects the composition information of the actual composite solid propellant and uses finite element analysis software or other relevant modeling software to create a four-phase microscopic model based on this information; the model includes the geometric representation and material properties of the solid particles and liquid phase.

[0018] Furthermore, the stepwise doping module simulates the doping between various components in actual propellants. Based on the stepwise doping approximation theory, representative volumetric units of the four propellants are introduced into the initial model one by one.

[0019] Furthermore, the bulk modulus calculation module applies radial pressure or displacement conditions to the four-phase microscopic model; then, based on the elastic modulus and Poisson's ratio data of each phase, it uses relevant formulas to calculate the bulk modulus of the composite solid propellant.

[0020] Furthermore, the shear modulus calculation module applies a shear load to the four-phase microscopic model and calculates the shear modulus of the composite solid propellant using relevant formulas based on the elastic modulus and Poisson's ratio data of each phase.

[0021] Furthermore, the first step correction module introduces an interface phase to consider the interaction between different particles, which is a transition region between solid particles. Its liquid film thickness is obtained by user calculation, and the interface thickness and mechanical properties are determined based on the material properties.

[0022] Furthermore, the second step correction module uses the cohesive region model for correction; this model will take the first stage in the cohesive region model, namely the displacement of particles and matrix at the interface under small strain, for calculation.

[0023] Furthermore, after completing the above corrections, the effective elastic modulus solving module obtains a five-phase microscopic model; by solving a system of simultaneous equations and using mathematical software for numerical calculation, the effective elastic modulus of the composite solid propellant is solved.

[0024] Another objective of this invention is to provide a method for establishing a five-phase microscopic model of a composite solid propellant. The technical solution to the above-mentioned technical problems includes the following steps:

[0025] The preliminary model was determined, and four doping processes were carried out according to the stepwise doping approximation theory, with representative volume units of the four propellants being released one by one.

[0026] The calculation of the bulk modulus involves applying radial pressure or radial displacement conditions to the above model at an infinite distance from the origin, and obtaining a linear equation for the bulk modulus k4 of the composite solid propellant through relevant formulas, thus obtaining an analytical solution for the bulk modulus.

[0027] The calculation of the shear modulus involves obtaining a linear equation for the shear modulus μ4 of the composite solid propellant through relevant formulas, thereby obtaining an analytical solution for the shear modulus.

[0028] The first step of the correction involves adding liquid film thickness and reintroducing the interfacial phase into the microstructure of the propellant to quantify the difference between the two particle interfaces. It is assumed that the thickness and mechanical properties of this interfacial phase are not affected by particle size, but only by the type of particle.

[0029] The second step of the correction involves introducing the interface displacement discontinuity condition into the solution formula of the five-phase model, and correcting the four-phase model based on the cohesive region model proposed by Tan et al.

[0030] For the modified five-phase model, the continuity condition at interface a′ is given. Formulas (7) to (19) are combined to form a homogeneous system of equations with 16 unknowns. By solving the system of equations, the determinant of the coefficient matrix is ​​equal to zero, and a linear equation about the shear modulus μ4 is obtained.

[0031] The effective elastic modulus of the composite solid propellant is obtained by solving formula (20).

[0032] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0033] First, by establishing a five-phase model of particle filling in propellants, this invention solves the problem of calculating the effective elastic modulus of composite materials with high particle content and multiphase inclusions, realizing the theoretical design of propellant formulations and providing multiple possibilities for application in aerospace and other industries.

[0034] Secondly, the five-phase microscopic model established by this technology enables more accurate calculation and processing of the mechanical properties of composite materials, realizing the transformation of solid propellant design methods from experimental trial methods to rational design, thus saving resources.

[0035] Third, current research on the microstructure of composite materials has only considered a maximum of four phases, and calculations and experiments have shown discrepancies between the calculated results and experimental values. This invention, however, reintroduces an interfacial phase into the existing four-phase microstructure model, forming a five-phase microstructure model, and distinguishes between different polymer / filler interfaces. This allows for obtaining more realistic mechanical property data, which is beneficial for better theoretical design of propellant formulations.

[0036] Fourth, in recent years, people have been committed to studying the microstructure of composite solid propellants at the mesoscale. The five-phase microstructure model of composite solid propellants established in this invention is basically consistent with the calculated and experimental values ​​of the elastic modulus, thus verifying the accuracy of the five-phase microstructure model of composite solid propellants established in this invention. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0038] Figure 1 This is a flowchart illustrating the steps of the method for establishing a five-phase microscopic model of the composite solid propellant described in this invention.

[0039] Figure 2 This is a schematic diagram of the stepwise doping approximation solution theory provided in the embodiments of the present invention.

[0040] Figure 3 This is a schematic diagram of the four-phase composite solid propellant structure model provided in an embodiment of the present invention.

[0041] Figure 4 This is a schematic diagram of a representative volume unit of the modified propellant provided in an embodiment of the present invention.

[0042] Figure 5 This is a schematic diagram of the five-phase composite solid propellant structure model provided in an embodiment of the present invention.

[0043] Figure 6 This is a schematic diagram of the preliminary model calculation results of the five-phase composite solid propellant structure provided in the embodiment of the present invention.

[0044] Figure 7 This is a schematic diagram illustrating the change in the total specific surface area of ​​particles in the propellant provided in an embodiment of the present invention.

[0045] Figure 8 This is a schematic diagram of the calculation results of the modified model provided in the embodiment of the present invention.

[0046] Figure 9a This is a schematic diagram of the prediction result of the modified model provided in the embodiment of the present invention, where AL: d4 = 29 μm.

[0047] Figure 9b This is a schematic diagram of the prediction result of the modified model provided in the embodiment of the present invention, where AL: d4 = 29 μm.

[0048] Figure 10 This is a schematic diagram of the second prediction result of the modified model provided in the embodiment of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0050] The method for constructing a five-phase microscopic model of a composite solid propellant provided in this invention can be decomposed into the following corresponding system modules:

[0051] 1) Initial Model Building Module: Use software to build an initial four-phase microscopic model of the composite solid propellant, including solid particles and liquid phase in the propellant.

[0052] 2) Step-doping module: Based on the step-doping approximation theory, representative volumetric units of the four propellants are introduced into the model one by one.

[0053] 3) Bulk Modulus Calculation Module: This module applies radial pressure and displacement conditions to the model at a location far from the origin, and calculates the bulk modulus of the composite solid propellant using relevant formulas. The software can perform numerical calculations and solve linear equations to obtain analytical solutions for the bulk modulus.

[0054] 4) Shear Modulus Calculation Module: This module calculates the shear modulus of composite solid propellants using relevant formulas. The software can obtain analytical solutions for the shear modulus through numerical calculations and solving linear equations.

[0055] 5) First step correction module: A liquid film thickness is added between the particles and the matrix, and an interfacial phase is reintroduced to quantify the difference between the two particle interfaces. The liquid film thickness is obtained through user calculations, and the interfacial thickness and mechanical properties are determined based on the material properties.

[0056] 6) Second step correction module: Introduce interface displacement discontinuity conditions into the model and use the cohesive region model for correction.

[0057] 7) Effective Elastic Modulus Solving Module: Based on the modified five-phase model, the effective elastic modulus of the composite solid propellant is solved by solving a system of simultaneous equations and using software for numerical calculation.

[0058] These system modules enable the construction of a five-phase microscopic model of composite solid propellants, further improving the accuracy of propellant performance prediction and analysis.

[0059] The following is a detailed explanation of how each module works:

[0060] 1) Initial Model Building Module: This module works by creating an initial four-phase microstructure model, including solid particles (such as ammonium salts, aluminum powder, etc.) and a liquid phase (such as a binder). This model can be based on the composition and microstructure of actual propellants to obtain preliminary predictions of their mechanical properties.

[0061] 2) Step-Doping Module: Based on the step-doping approximation theory, this module introduces representative volumetric units of the four propellants one by one into the initial model. This process helps to better simulate the actual propellant structure.

[0062] 3) Bulk Modulus Calculation Module: This module applies radial pressure and displacement conditions to the model at a location far from the origin and calculates the bulk modulus of the composite solid propellant using relevant formulas. The software can perform numerical calculations and solve linear equations to obtain analytical solutions for the bulk modulus. Bulk modulus is a parameter describing a material's ability to deform during compression or expansion.

[0063] 4) Shear Modulus Calculation Module: This module uses relevant formulas to calculate the shear modulus of composite solid propellants. The software can obtain analytical solutions for the shear modulus through numerical calculations and solving linear equations. The shear modulus is a parameter describing the deformation capacity of a material during shear deformation.

[0064] 5) First step correction module: A liquid film thickness is added between the particles and the matrix, and an interfacial phase is reintroduced to quantify the difference between the two particle interfaces. The liquid film thickness is obtained through user calculations, and the interfacial thickness and mechanical properties are determined based on the material properties.

[0065] 6) Second step correction module: Introduce interface displacement discontinuity conditions into the model and use a cohesive region model for correction. This correction helps to further improve the model's prediction accuracy of actual propellant mechanical properties.

[0066] 7) Effective Elastic Modulus Calculation Module: Based on the modified five-phase model, the effective elastic modulus of the composite solid propellant is calculated numerically using a system of simultaneous equations and software. The effective elastic modulus is a parameter describing the overall deformation capacity of a material under stress, and it is crucial for the prediction and analysis of propellant performance.

[0067] Through the interaction and synergistic work of these modules, a five-phase microscopic model of composite solid propellants can be constructed, providing an important basis for the optimization and design of propellant performance.

[0068] The method provided in this embodiment of the invention can be implemented through the following steps:

[0069] 1) Establishing an initial model: Use software to establish an initial four-phase microscopic model of the composite solid propellant, including solid particles and liquid phase in the propellant.

[0070] 2) Gradual doping: Based on the gradual doping approximation theory, representative volumetric units of the four propellants are introduced into the model one by one.

[0071] 3) Calculate the bulk modulus: Apply radial pressure and displacement conditions to the model at a location far from the origin, and calculate the bulk modulus of the composite solid propellant using relevant formulas. The software can perform numerical calculations and solve linear equations to obtain analytical solutions for the bulk modulus.

[0072] 4) Calculate the shear modulus: Calculate the shear modulus of the composite solid propellant using relevant formulas. The software can obtain an analytical solution for the shear modulus through numerical calculation and solving a system of linear equations.

[0073] 5) First step correction: A liquid film thickness is added between the particles and the matrix, and an interfacial phase is reintroduced to quantify the difference between the two particle interfaces. The liquid film thickness is obtained through user calculations, and the interfacial thickness and mechanical properties are determined based on the material properties.

[0074] 6) Second step correction: Introduce interface displacement discontinuity conditions into the model and use the cohesive region model for correction.

[0075] 7) Solving for the effective elastic modulus: Based on the modified five-phase model, the effective elastic modulus of the composite solid propellant is solved by solving a system of simultaneous equations and using software for numerical calculation.

[0076] The above steps can be implemented using specific micromechanical modeling software or programming environments. The software should have the corresponding calculation and solution functions to construct, modify, and solve the model, ultimately obtaining the effective elastic modulus of the composite solid propellant.

[0077] This invention proposes a method for establishing a five-phase microscopic model of composite solid propellants, aiming to establish a five-phase microscopic model of composite solid propellants in order to manufacture composite solid propellants according to requirements.

[0078] This invention establishes a five-phase micromechanical model of composite solid propellants based on micromechanical methods, and solves for the effective elastic modulus of multiphase mixed composite solid propellants. Firstly, based on the original four-phase model of composite materials, the concept of propellant liquid film thickness is introduced, and combined with the stepwise doping method of multiphase composite materials, it is developed into a four-phase model suitable for composite solid propellants. Furthermore, since the composite solid propellant contains two different types of filler-matrix interfaces, the four-phase model is further modified. A two-step modification method is used: firstly, the interface phase is reintroduced into the model, forming a five-phase mechanical model; secondly, discontinuity conditions are introduced at the interface. This two-step modification method allows the composite model to clearly show the influence of the two different interfaces in the propellant, and finally, an analytical solution for the effective elastic modulus of the five-phase mechanical model is given. Calculation results show that the trend of the effective elastic modulus variation of propellants under different gradations predicted by the five-phase model is basically consistent with the experimental results. This indicates that the five-phase model proposed in this invention can realistically and comprehensively reflect the influence of the microstructure of the composite solid propellant on its macroscopic elastic modulus.

[0079] The specific structure of the five-phase microscopic model establishment method for composite solid propellants proposed in this invention will be described below in specific embodiments:

[0080] like Figure 1 As shown, the invention of this method and system for establishing a five-phase microscopic model of a composite solid propellant includes the following steps:

[0081] S1. Determine the preliminary model, and perform four doping operations according to the stepwise doping approximation theory, releasing representative volume units of the four propellants one by one.

[0082] S2. The calculation of bulk modulus involves applying radial pressure or radial displacement conditions to the above model at an infinite distance from the origin, and obtaining a linear equation for the bulk modulus k4 of the composite solid propellant through relevant formulas, thereby obtaining an analytical solution for the bulk modulus.

[0083] S201. The formula obtained after applying radial pressure or radial displacement conditions to the model at an infinite distance from the origin is:

[0084] Interface a:

[0085] A1a=A2a+B2a -2 Equation (1)

[0086] 3k1A1=3k2A2-4μ2B2a -3 …………………………………..Equation (2)

[0087] Interface b:

[0088] A2b+B2b -2 =A3b+B3b -2 …………………………………Equation (3)

[0089] 3k2A2-4μ2B2b -3 =3k3A3-4μ3B3b -3 …........................…Formula (4)

[0090] At point c on the interface:

[0091] A3c+B3c -2 =A4c...................Equation (5)

[0092] 3k3A3-4μ3B3c -3 =3k4A4-4μ4B4c -3 Equation (6)

[0093] Where k i μ i These are the bulk modulus and shear modulus of the i-th phase, respectively; A i B i C i For any parameter;

[0094] According to the Eshelby formula, B4 = 0. At this time, there are six arbitrary constants in the above six equations. Treating the arbitrary constants as unknowns, the non-zero solution of the unknowns in the above system of equations can only exist when the determinant of the unknown coefficient matrix is ​​zero. A linear equation about the bulk modulus k4 of the composite solid propellant is obtained, thus obtaining the analytical solution of the bulk modulus.

[0095] S3. Calculate the shear modulus. Obtain the linear equation for the shear modulus μ4 of the composite solid propellant through relevant formulas, and thus obtain the analytical solution for the shear modulus.

[0096] S301, The linear equation for the shear modulus μ4 of the composite solid propellant is obtained, and the formula for the analytical solution of the shear modulus is as follows:

[0097] Interface a:

[0098] A1a-Γ1(1)A2a 3 =B1a-Γ1(2)B2a 3 +3B3a -4 +Γ3(2)B4a -2 Equation (7)

[0099] A1a-Γ2(1)A2a 3 =B1a-Γ2(2)B2a 3 -2B3a -4 +2B4a -2 .................(8)

[0100]

[0101] μ1[A1-Γ4(1)A2a 2 ]=μ2[B1-Γ4(2)B2a 2 +8B3a -5 +Γ5(2)B4a -3 ]...............(10)

[0102] Interface b:

[0103] B1b-Γ1(2)B2b 3 +3B3b -4 +Γ3(2)B4b -2 =D1b-Γ1(3)D2b 3 +3D3b -4 +Γ3(3)D4b -2 Equation (11)

[0104] B1b-Γ2(2)B2b 3 -2B3b -4 +2B4b -2 =D1b-Γ2(3)D2b 3 -2D3b -4 +2D4b -2 Equation (12)

[0105]

[0106] μ2[B1-Γ4(2)B2b 2 +Γ5(2)B4b -3 +8B3b -5 ]=μ3[D1-Γ4(3)D2b 2 +8D3b -5 +Γ5(3)D4b -3 Equation (14)

[0107] At point c on the interface:

[0108] D1c-Γ1(3)D2c 3 +3D3c -4 +Γ3(3)D4c -2 =F1c+3F3c -4 +Γ3(4)F4c -2 ...Equation (15)

[0109] D1c-Γ2(3)D2c 3 -2D3c -4 +2D4c -2 =F1c-2F3c -4 +2F4c -2 Equation (16)

[0110]

[0111] μ3[D1-Γ4(3)D2c 2 +Γ5(3)D4c -3 +8D3c -5 ]=μ4[F1+8F3c -5 +Γ5(4)F4c -3 Equation (18)

[0112] in:

[0113] F4 = 0 can be obtained through the Eshelby formula; at this time, formulas (7) to (18) form a homogeneous system of equations with 12 unknowns. It is still possible for a non-zero solution to exist only when the determinant of the unknown coefficient matrix is ​​zero. A linear equation for the shear modulus μ4 of the composite solid propellant can be obtained, thus obtaining the analytical solution of the shear modulus.

[0114] S302. Based on the assumption of overall isotropy of composite solid propellants, the formula for calculating the Young's modulus (i.e., elastic modulus) of an equivalent homogeneous medium is as follows:

[0115]

[0116] S4. Perform the first step of correction by introducing an interfacial phase into the microstructure liquid film of the propellant to quantify the difference between the two particle interfaces, and assume that the thickness and mechanical properties of this interfacial phase are not affected by the particle size, but only by the type of particle.

[0117] S5. Perform the second step of correction: introduce the interface displacement discontinuity condition into the solution formula of the five-phase model, and correct the four-phase model based on the cohesive region model proposed by Tan et al.

[0118] S501, the cohesive region model gives the displacements of particles and matrix at the interface when debonding occurs at the phase interface under stress in composite materials:

[0119]

[0120] Where k1 and a are the bulk modulus and radius of the particle, respectively, and σ int The radial stress σ at the particle-matrix interface m E2 and v2 are the radial stress, elastic modulus and Poisson's ratio of the matrix, respectively.

[0121] S502, the cohesive region model includes three stages. The first stage is under small strain, when the interface opening distance is small, and the radial stress σ at the interface is at this time. int Maximum; in the second stage, as the interface opening distance increases, the radial stress σ... int The stress begins to decrease; in the third stage, the interface completely fractures, at which point the radial stress σ... int It is almost zero. Since the problem is solving for the elastic modulus of the propellant under small strain conditions, the first stage of the cohesion model should be chosen here. int The value, i.e., σ int =σ m Therefore, the displacements of the particles and the matrix at the interface are respectively: σ m a / 3k1、σ m a / 3k2.

[0122] S503. By associating this displacement expression with the displacement continuity condition at interface a in the above model, the displacement discontinuity condition at interface a′ can be obtained:

[0123]

[0124] Furthermore, the continuity condition at interface a′ is given:

[0125] A2′a′+B2′a′ -2 =A3′a′+B3′a′ -2 ...................Equation (23)

[0126] 3k2′A2′-4μ2′B2'a′ -3 =3k3′A3′-4μ3′B3′a′ -3 Equation (24)

[0127] These three formulas, together with formulas (2) to (6), form a homogeneous system of equations with 8 unknowns. By obtaining the determinant of the coefficient matrix of the unknowns in this system of equations and setting it to zero, we can obtain a linear equation about the volume modulus k4.

[0128] S6. For the modified five-phase model, the continuity condition at interface a′ is given. Formulas (7) to (19) are combined to form a homogeneous system of equations with 16 unknowns. By solving the coefficient matrix determinant of the system of equations, the linear equation for the shear modulus μ4 is obtained.

[0129] S601. For the modified five-phase model, the continuity condition at interface a′ is given.

[0130] B1′a′-Γ1′(2)B2′a′ 3 +3B3′a′ -4 +Γ3′(2)B4′a′ -2 =D1′a′-Γ1′(3)D2′a′ 3 +3D3′a′ -4 +Γ3′(3)D4′a′ -2 Equation (25)

[0131] B1′a′-Γ1′(2)B2′a′ 3 -2B3′a′ -4 +2B4′a′ -2 =D1′a′-Γ2′(3)D2′a′ 3 -2D3′a′ -4 +2D4′a′ -2...Equation (26)

[0132]

[0133] S7. The effective elastic modulus of the composite solid propellant is obtained by solving formula (20).

[0134] like Figure 2 As shown in the schematic diagram of the four-phase composite solid propellant structure model provided in this embodiment of the invention, assuming that a certain composite material contains n-phase particle inclusions, one phase particle is first doped into the matrix material, and then the two-phase composite is homogenized; using the homogenized composite as a new matrix material, another phase particle is doped again, and homogenization is performed again. This process continues until all particle inclusions are doped. The effective elastic modulus of the composite obtained after the last homogenization is the effective elastic modulus of the multiphase particle inclusion composite material.

[0135] like Figure 3 As shown in the figure, the schematic diagram of the four-phase composite solid propellant structure model provided in this embodiment of the invention is as follows: Figure 2 The stepwise doping approximation theory shown performs four doping steps, introducing representative volumetric units of four propellants one by one. Each homogenization step involves embedding a new three-phase composite sphere structure into an infinitely equivalent homogeneous medium.

[0136] like Figure 4 As shown in the figure, the representative volume unit of the modified propellant provided in the embodiment of the present invention is shown in the figure. An interface phase is introduced into the liquid film of the propellant microstructure to quantify the difference between the two particle interfaces. It is assumed that the thickness and mechanical properties of this interface phase are not affected by the particle size, but only by the type of particle. Based on this modification, the representative volume unit of the composite solid propellant is given again.

[0137] like Figure 5 As shown in the figure, the schematic diagram of the five-phase composite solid propellant structure model provided in the embodiment of the present invention is as follows: the representative volume unit after the model is modified is a three-phase composite structure. According to the stepwise doping approximation solution theory, in the doping process of the representative volume unit, the homogenization process at each step is to embed a new four-phase composite sphere structure into an infinite equivalent homogeneous medium, thus forming a five-phase composite solid propellant structure model.

[0138] The following is a further explanation based on the experimental process and results of this invention:

[0139] 1. Model Calculation Results and Analysis:

[0140] The model was solved and verified for the experimental formulations shown in Table 1. Four propellant formulations were selected. In the first three formulations, only the size or proportion of ammonium perchlorate particles changed, showing a gradually decreasing trend. In gradation 4, the size of aluminum particles began to change, increasing from 13 μm to 29 μm, while its proportion remained unchanged.

[0141] Table 1. Experimental formulation and elastic modulus.

[0142]

[0143] First, the liquid film thickness corresponding to each particle size in the four formulations above is calculated, thereby determining the value of dimension b in the model. This is done by defining b... 3 / c 3 The volume fraction of a representative volumetric unit in each doping step is used to further determine the size c value in the model. The elastic moduli of the ammonium perchlorate particles, aluminum particles, and matrix in this formulation are set to 32450 MPa, 68300 MPa, and 0.35 MPa, respectively, with Poisson's ratios of 0.14, 0.33, and 0.46. Regarding the mechanical properties of the interfacial phases in the five-phase model, based on the difference between the two interfacial phases, the elastic modulus of the ammonium perchlorate particle-matrix interface is set to 1.5 MPa, and the elastic modulus of the aluminum particle-matrix interface is set to 0.1 MPa.

[0144] Figure 6 The graph shows preliminary model calculations. To more clearly demonstrate the similarity between theoretical calculations and experimental results in terms of trends, the left and right axes are slightly different. Figure 7 It can be seen that the trend of the calculated elastic modulus of the propellant with the change of gradation in the preliminary model is not completely consistent with the trend of the experimental results, mainly in the process of changing from gradation 3 to gradation 4. Analyzing the change in the specific surface area of ​​the particles filling the propellant, such as... Figure 7As shown. From gradation 1 to gradation 3, only the gradation of AP particles changes, while the gradation of AL particles remains completely unchanged. The change trend of the specific surface area of ​​AL particles is solely due to the change in the size of the ammonium perchlorate particles, showing an increasing trend. At this time, the experimental results of the elastic modulus are consistent with the trend of the particle specific surface area change. Comparing gradation 2 and gradation 4, only the size of aluminum particles increases, while the gradation of ammonium perchlorate particles remains completely unchanged. At this time, the change trend of the specific surface area of ​​AL particles is solely due to the change in the size of the aluminum particles, showing a decreasing trend. However, at this time, the experimental results of the elastic modulus are opposite to the trend of the particle specific surface area change. Through analysis, a simple qualitative result can be obtained: the change of the elastic modulus of the propellant is directly proportional to the specific surface area of ​​ammonium perchlorate particles and inversely proportional to the specific surface area of ​​aluminum particles. However, in the initial model, the different effects of ammonium perchlorate particles and aluminum particles on the elastic modulus of the propellant were not distinguished. The influence mechanism of all particles is the same, which makes the elastic modulus change calculated by the initial model inconsistent with the experimental results. On the other hand, the fact that the model results are consistent with the trend of changes in the total specific surface area of ​​particles also shows the shortcomings of the preliminary model.

[0145] Figure 8 The calculation results of the revised model show that the trend of the propellant elastic modulus calculated by the revised model with the change of gradation is consistent with the trend of the experimental results. The revised model makes up for the shortcomings of the preliminary model by reasonably setting the interface phase formed by the bonding agent in the propellant, which is used to quantify the difference in the influence of the two particle interfaces on the overall propellant elastic modulus. In addition, the displacement discontinuity condition at the aluminum interface is reasonably introduced in the solution process, making the model formula more accurate. In the process of changing from gradation 1 to gradation 3, the theoretical calculation results gradually increase, which is directly proportional to the change of the specific surface area of ​​ammonium perchlorate particles in the propellant; in the process of changing from gradation 2 to gradation 4, the theoretical calculation results also gradually increase, which is inversely proportional to the change of the specific surface area of ​​aluminum particles in the propellant. This is consistent with the analysis results above, indicating the correctness of the revised model.

[0146] 2. Model Prediction

[0147] In section 1 above, the elastic modulus of the composite solid propellant was solved using both the preliminary model and the modified model. The calculated results were compared with experimental results to verify the correctness of the modified model. Next, the elastic modulus of the composite solid propellant was predicted when the formulation continuously changed.

[0148] First, the total volume fraction of filler particles in the propellant was fixed at 0.65, the volume ratio of aluminum particles to ammonium perchlorate particles was 0.204, and the size of the ammonium perchlorate particles remained constant. Other factors were then varied, and a modified model was used to predict the elastic modulus of the propellant. Figure 9 shows the predicted elastic modulus results when the volume fraction of different sizes of ammonium perchlorate particles and the size of aluminum particles were changed. Analyzing Figures a and b separately, without considering the influence of aluminum particles, the smaller particles in the ammonium perchlorate group have the greatest impact on the propellant's elastic modulus, and this is shown to be true as the volume fraction of the smallest particles increases, the propellant's elastic modulus gradually increases. This is consistent with the general conclusions of the experiment. Furthermore, regarding the specific surface area of ​​the particles, the change in the size of the smaller ammonium perchlorate particles has a greater impact on the specific surface area than the larger particles, and the elastic modulus of the propellant gradually increases as the specific surface area of ​​the ammonium perchlorate particles increases. Figures a and b are then combined to analyze the effect of changes in aluminum particle size on the propellant's elastic modulus. From Figure a to Figure b, as the aluminum particle size increases, taking a point where the ammonium perchlorate particle gradation is the same, the change in the specific surface area of ​​the propellant particles is solely due to the change in the aluminum particles. Furthermore, as the aluminum particle size increases, the specific surface area decreases, and the propellant's elastic modulus shows a gradual increasing trend.

[0149] The specific parameters are shown in Table 2, which are determined by fixing the size of the particles in the propellant and the volume ratio of each size of particles in the solid.

[0150] Table 2 Parameters of Prediction Result 2

[0151] 1(AP) 2(AP) 3(AP) 4(AL) Particlesize / μm 10 125 200 13 <![CDATA[v1 / v AP ]]> 0.167 0.222 0.611 0.204

[0152] By varying the volume fraction of solid particles in the propellant, the propellant modulus is predicted using a modified model, and the results are as follows: Figure 10 As shown.

[0153] Figure 10 The horizontal axis represents the volume percentage and corresponding mass percentage of the solid component, with the selected solid percentages being as close as possible to the actual experimental conditions. It can be seen that as the solid percentage increases, the elastic modulus of the propellant gradually increases. This result is consistent with general conclusions drawn from experimental measurements.

[0154] This invention modifies existing four-phase composite material models to establish a new five-phase composite material model and further improves the model solution method, enabling the modified model to accurately predict the variation trend of the effective elastic modulus of composite solid propellants. In model establishment, based on the analysis of the internal thermodynamic properties of the propellant, an interfacial phase composed of a bonding agent was added to the preliminary model, and reasonable mechanical properties of this interfacial phase were assumed to distinguish the influence of the interfaces of two different particles in the propellant, thus establishing a five-phase composite material model. In the model solution method, based on the easy debonding phenomenon of the aluminum particle-matrix interface in the propellant, the original interfacial displacement continuity condition was changed in the solution formula, and an interfacial displacement discontinuity condition was adopted to solve the five-phase model. This invention calculated four formulations of the propellant using both the preliminary model and the modified model, and compared the results with experimental values. The results show that the modified model can better predict the variation trend of the effective elastic modulus of composite solid propellants.

[0155] The following are six specific embodiments of the present invention, demonstrating the application of the method for constructing a five-phase microscopic model of composite solid propellants:

[0156] Example 1: Determining the Preliminary Model

[0157] Step 1: Determine the preliminary five-phase microscopic model based on the composition and properties of the propellant.

[0158] Step 2: Perform four doping operations according to the stepwise doping approximation theory.

[0159] Step 3: Place representative volumetric elements of the four propellants into the model one by one.

[0160] Example 2: Calculation of bulk modulus

[0161] Step 1: Apply radial pressure or radial displacement conditions to the model at an infinite distance from the origin.

[0162] Step 2: Using relevant formulas, obtain the linear equation for the bulk modulus k4 of the composite solid propellant.

[0163] Step 3: Solve the linear equation to obtain the analytical solution for the bulk modulus.

[0164] Example 3: Calculating the shear modulus

[0165] Step 1: Using relevant formulas, obtain the linear equation for the shear modulus μ4 of the composite solid propellant.

[0166] Step 2: Solve the linear equation to obtain the analytical solution of the shear modulus.

[0167] Example 4: First step correction

[0168] Step 1: Introduce an interfacial phase into the propellant's microstructure liquid film to quantify the difference between the two particle interfaces.

[0169] Step 2: Assume that the thickness and mechanical properties of the interfacial phase are not affected by the particle size, but only by the type of particles.

[0170] Example 5: Second step correction

[0171] Step 1: Introduce the interface displacement discontinuity condition into the solution formula of the five-phase model.

[0172] Step 2: Modify the four-phase model using the cohesive region model proposed by Tan et al.

[0173] Example 6: Solving for the effective elastic modulus

[0174] Step 1: Give the continuity condition at interface a′.

[0175] Step 2: Solve the system of equations, which contains 16 unknowns. By solving the system of equations, the determinant of the coefficient matrix is ​​equal to zero, and a linear equation for the shear modulus μ4 is obtained.

[0176] Step 3: Solve using the formula to obtain the effective elastic modulus of the composite solid propellant.

[0177] The above are six examples demonstrating the specific steps and applications of the method for constructing a five-phase microscopic model of composite solid propellants.

[0178] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A system for constructing a five-phase mesoscale model of a composite solid propellant, characterized in that, The application relates to a composite solid propellant elastic modulus calculation method and device. An initial model construction module: an initial four-phase micro model of a composite solid propellant is established by using software, including solid phase particles and liquid phase in the propellant; A step-by-step doping module: according to a step-by-step doping approximation theory, four representative volume units of the propellant are introduced into the model one by one; A bulk modulus calculation module: radial pressure and displacement conditions are applied to the model at a position far from the origin, and the bulk modulus of the composite solid propellant is calculated by using a related formula; Software can perform numerical calculation and solve linear equations to obtain an analytical solution of the bulk modulus; A shear modulus calculation module: the shear modulus of the composite solid propellant is calculated; software can obtain an analytical solution of the shear modulus by means of numerical calculation and solving linear equations; A first step correction module: liquid film thickness is added between the particles and the matrix, and an interface phase is introduced again to quantify the difference between the two particle interfaces; The liquid film thickness is obtained by user calculation, and the interface thickness and mechanical properties are determined based on material properties; A second step correction module: interface displacement discontinuity conditions are introduced into the model, and a cohesive zone model is used for correction; An effective elastic modulus solving module: according to the corrected five-phase model, homogeneous equations are solved by using software for numerical calculation to solve the effective elastic modulus of the composite solid propellant; The bulk modulus calculation module applies radial pressure or displacement conditions to the four-phase micro model; then the bulk modulus of the composite solid propellant is calculated by using a related formula according to the elastic modulus and Poisson's ratio data of each phase; The formula obtained after radial pressure or radial displacement conditions are applied to the model at a position far from the origin is as follows: At the interface a: A1a = A2a + B2a -2 .......................Formula (1) 3k1A1 = 3k2A2 - 4μ2B2a -3 ......................Formula (2) At the interface b: A2b + B2b -2 = A3b + B3b -2 ............... Equation (3) 3k2A2-4μ2B2b -3 = 3k3A3-4μ3B3b -3 Equation (4) At the interface c: A3c + B3c -2 = A4c Equation (5) 3k3A3-4μ3B3c -3 = 3k4A4-4μ4B4c -3 Equation (6) where k i , μ i are the bulk modulus, shear modulus of the i-th phase, respectively; A i , B i , C i are arbitrary parameters; B4 can be obtained from the Eshelby formula, at this time, there are six arbitrary constants in the above six equations, the arbitrary constants are taken as unknowns, and the non-zero solution of the unknowns exists only when the determinant of the unknown coefficient matrix is zero in the above equation group, a linear equation about the bulk modulus k4 of the composite solid propellant is obtained, and thus the analytical solution of the bulk modulus is obtained; The shear modulus calculation module applies shear load to the four-phase micro model, and the shear modulus of the composite solid propellant is calculated by using a related formula according to the elastic modulus and Poisson's ratio data of each phase; The formula of the analytical solution of the shear modulus is as follows: At the interface a: A1a - Γ1(1) A2a 3 = B1a - Γ1(2) B2a 3 + 3B3a -4 + Γ3(2) B4a -2 Equation (7) A1a - Γ2(1) A2a 3 = B1a - Γ2(2) B2a 3 - 2B3a -4 + 2B4a -2 Equation (8) μ1[A1-Γ4(1)A2a 2 ] = μ2[B1-Γ4(2)B2a 2 + 8B3a -5 + Γ5(2)B4a -3 ] Formula (10) At the interface b: B1b - Γ1(2)B2b 3 + 3B3b -4 + Γ3(2)B4b -2 = D1b - Γ1(3)D2b 3 + 3D3b -4 + Γ3(3)D4b -2 .......... Equation (11) B1b - Γ2(2) B2b 3 - 2B3b -4 + 2B4b -2 = D1b - Γ2(3) D2b 3 - 2D3b -4 + 2D4b -2 Equation (12) μ2[B1-Γ4(2)B2b 2 +Γ5(2)B4b -3 +8B3b -5 ] = μ3[D1-Γ4(3)D2b 2 +8D3b -5 +Γ5(3)D4b -3 ]..... Equation (14) At the interface c: D1c-Γ1(3)D2c 3 +3D3c -4 +Γ3(3)D4c -2 =F1c+3F3c -4 +Γ3(4)F4c -2 Equation (15) D1c - 2D2c 3 - 2D3c -4 + 2D4c -2 = F1c - 2F3c -4 + 2F4c -2 ).... Equation (16) μ3[D1+8D3c 2 +Γ5(3)D4c -3 +8D3c -5 ] = μ4[F1+8F3c -5 +Γ5(4)F4c -3 ]...........Formula (18) wherein: F4 can be obtained from the Eshelby formula; at this time, the formula (7) to (18) form a homogeneous equation group containing 12 unknowns, and the non-zero solution exists only when the determinant of the unknown coefficient matrix is zero, a linear equation about the shear modulus mu4 of the composite solid propellant is obtained, and thus the analytical solution of the shear modulus is obtained; Based on the assumption of the overall isotropy of the composite solid propellant, the Young's modulus of the equivalent uniform medium, that is, the elastic modulus calculation formula is:

2. The system for constructing a five-phase meso-scale model of a composite solid propellant of claim 1, wherein, The initial model construction module collects the composition information of an actual composite solid propellant, uses finite element analysis software, and creates a four-phase micro model according to the information; the model includes geometric representation and material properties of solid phase particles and liquid phase.

3. The system for constructing a five-phase meso-scale model of a composite solid propellant of claim 1, wherein, The step-by-step doping module simulates the doping between various components in the actual propellant; according to the step-by-step doping approximation theory, the representative volume elements of the four propellants are introduced into the initial model one by one.

4. The system for constructing a five-phase meso-scale model of a composite solid propellant of claim 1, wherein, The first step correction module adds liquid film thickness between the particles and the matrix and reintroduces the interface phase, which is used to quantify the difference between the two particle interfaces; The liquid film thickness is obtained by user calculation, and the interface thickness and mechanical properties are determined based on the material properties.

5. The system for constructing a five-phase meso-scale model of a composite solid propellant of claim 1, wherein, The second step correction module uses the cohesive zone model for correction.

6. A method for constructing a five-phase meso-scale model of a composite solid propellant applied to the construction system of the five-phase meso-scale model of a composite solid propellant according to any one of claims 1 to 5, characterized in that, It comprises: Establishing an initial model: using software to establish an initial four-phase mesoscopic model of the composite solid propellant, including the solid particles and liquid phase in the propellant; Step-by-step doping: according to the step-by-step doping approximation theory, the representative volume elements of the four propellants are introduced into the model one by one; the software can provide a doping function to automatically place the volume elements in the appropriate position; Calculating the bulk modulus: applying radial pressure and displacement conditions to the model at a position far from the origin, the bulk modulus of the composite solid propellant is calculated using the relevant formula; The software can perform numerical calculation and solve linear equations to obtain the analytical solution of the bulk modulus; Calculating the shear modulus: the shear modulus of the composite solid propellant is calculated using the relevant formula; the software can obtain the analytical solution of the shear modulus through numerical calculation and solving linear equations; First step correction: adding liquid film thickness between the particles and the matrix and reintroducing the interface phase, which is used to quantify the difference between the two particle interfaces; The liquid film thickness is obtained by user calculation, and the interface thickness and mechanical properties are determined based on the material properties. Second step correction: introducing the interface displacement discontinuity condition in the model, and using the cohesive zone model for correction; Solving the effective elastic modulus: according to the corrected five-phase model, the effective elastic modulus of the composite solid propellant is solved by simultaneously solving the homogeneous equation set and using the software for numerical calculation.

7. The method of claim 6, wherein the method further comprises: Specifically, it comprises: The establishment of the initial model is performed according to the step-by-step doping approximation theory, and the representative volume elements of the four propellants are introduced one by one through four doping; The calculation of the bulk modulus is performed by applying radial pressure or radial displacement conditions to the above-mentioned model at a position infinitely far from the origin, and the linear equations about the bulk modulus k4 of the composite solid propellant are obtained through formulas (1)-(6), and the analytical solution of the bulk modulus is obtained; The calculation of the shear modulus is performed through formulas (7)-(19) to obtain the linear equations about the shear modulus μ4 of the composite solid propellant, and thus the analytical solution of the shear modulus is obtained; The first step correction introduces the interface phase in the mesostructure liquid film of the propellant, which is used to quantify the difference between the two particle interfaces, and it is assumed that the thickness and mechanical properties of this interface phase are not affected by the particle size, but only related to the type of particle; The second step correction introduces the interface displacement discontinuity condition in the five-phase model solving formula, and corrects the four-phase model according to the cohesive zone model; For the corrected five-phase model, the continuity condition at the interface a' is given, the homogeneous equation set containing 16 unknowns is formed by simultaneously solving formulas (7) to (19), and the linear equation about the shear modulus μ4 is obtained by solving the determinant of the coefficient matrix of the equation set equal to zero; The effective elastic modulus of the composite solid propellant is obtained by solving equation (20).

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