Macro-micro analysis method for failure process of solid propellant

Abstract

The invention provides a macro-micro analysis method for a failure process of a solid propellant, which mainly comprises the following steps of: 1) hierarchically slitting a particle filling composite material from a macro model to a micro model, hierarchically superposing constitutive response from the micro model to the macro model, and realizing cross-scale local modeling of the particle filling composite material from micro to macro; and 2) mapping from a mesoscopic model structure to constitutive parameters and from submodel constitutive parameters to intermediate submodel constitutive parameters by using an artificial neural network model. The method is reasonable in conception, can describe the influence of the local microstructure of the particle-filled composite material on the macroscopic mechanical property, realizes unification of macroscopic and mesoscopic properties, and greatly improves the macroscopic and mesoscopic analysis efficiency of the failure process of the solid propellant.

Description

Technical Field

[0001] The invention relates to the technical field of composite materials, and in particular to a macroscopic and microscopic analysis method for a solid propellant failure process. Background Art

[0002] Particle-filled composites refer to composite materials that use polymer components as bonding resins and spheres, cylinders or small flakes as fillers. Particle fillers can change the dielectric properties, heat resistance, hardness, etc. of the material and are often used in thermal insulation materials and solid propellants. Solid propellants are a type of particle-filled composite material and a typical particle-filled composite material. Due to the uneven distribution of its particles, the current modeling of the constitutive behavior of particle-filled composites cannot describe the influence of local microstructures on macroscopic mechanical properties, and it is difficult to achieve the unity of macro and micro structures, and it is difficult to characterize the failure behavior of solid propellants across scales. Summary of the invention

[0003] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a macro-micro analysis method for the failure process of solid propellant. The method has a reasonable concept and can describe the influence of the local microstructure of particle-filled composite materials on the macroscopic mechanical properties, thereby achieving the unification of macro and micro, and greatly improving the efficiency of macro-micro analysis of the failure process of solid propellant.

[0004] In order to solve the above technical problems, the present invention provides a macro-micro analysis method of the failure process of solid propellant, which mainly includes the following steps:

[0005] 1) Divide the particle-filled composite material from the macroscopic model level to the mesoscopic model, and superimpose the constitutive response from the mesoscopic model level to the macroscopic model to achieve cross-scale constitutive modeling of particle-filled composite materials from the mesoscopic to the macroscopic level;

[0006] 2) An artificial neural network model is used to map the mesoscopic model structure to the constitutive parameters and the sub-model constitutive parameters to the intermediate sub-model constitutive parameters.

[0007] The macro-micro analysis method of the solid propellant failure process, wherein the specific process of step 1) is as follows:

[0008] 1.1) First define the macro region Ω. Assume that the interior of Ω is filled with circular particles of different sizes. The set of all particles is V. The difference set Ω-V between Ω and V is called the matrix. Draw the particle image and count the distribution of the particle radius inside it.

[0009] 1.2) Then divide the macro region Ω into n1×n1 level 1 sub-regions, where the level 1 sub-region in the i-th row and j-th column is denoted as Continue to divide each level 1 sub-region into n2×n2 level 2 sub-regions, where The second-level sub-region of the i-th row and j-th column is denoted as Repeat the above operation to obtain the k-level bottom-level segmentation area. Where 1≤i k ≤n k , 1≤j k ≤n k ;

[0010] 1.3) Then the macro region Ω was divided step by step. The bottom layer of the division used the microscopic mechanical modeling method to perform finite element modeling on the particle elastic mechanical constitutive model, matrix viscoelastic constitutive model, matrix phase field fracture model and interface phase field fracture model. During the modeling, the model parameters only considered the elastic mechanical constitutive parameters of the particles, the viscoelastic constitutive parameters of the matrix, the phase field fracture parameters of the matrix and the phase field fracture parameters of the interface. The model parameters included the parameters E1, E2, E3, E4 of the matrix viscoelastic constitutive model and the phase field fracture parameters of the interface. ∞ , τ1, τ2, τ3, Young's modulus and Poisson's ratio of the particle elastic constitutive model, and the parameter G of the matrix phase field fracture model c , l, parameter G of the interface phase field fracture model c2 , l2; finite element simulation is used to perform uniaxial tensile simulation on the microscopic model to obtain each bottom-level segmentation area The stress-strain curve S RVE ;

[0011] 1.4) Then divide each bottom layer into regions Make a homogenization assumption and no longer consider the internal particles, matrix and interface characteristics. Replace them with an isotropic unit of the same size. Each bottom-level segmentation area The unit material obeys the matrix viscoelastic constitutive model and the matrix phase field fracture model, which can be obtained by the parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameter G of the matrix phase field fracture model c , l are described, and the uniaxial tensile simulation of the isotropic unit after the homogenization assumption can obtain the stress-strain curve S after the homogenization assumption ISO ; Use the least squares method to select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameter G of the matrix phase field fracture model c , l value, so that S RVE With S ISO The error is minimal.

[0012] The macroscopic and microscopic analysis method of the solid propellant failure process, wherein the specific process of step 2) is as follows:

[0013] The classic viscoelastic constitutive model consisting of a spring component and a generalized Maxwell model in parallel is used as the constitutive model of solid propellant materials. Its one-dimensional function form is as follows:

[0014]

[0015] in:

[0016] In the above equations (1)-(2), the elastic coefficient of the spring element of the i-th Maxwell unit is E i , the viscosity coefficient of the viscosity pot element is η i , the elastic constant of the independent spring component is E ∞ ; t is time; ε0 is the strain at the initial moment; ε t is the strain at time t; σ(t) is the stress at time t; s is the frequency parameter after Laplace transformation; τ i is the relaxation time; γ i h is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; i (t n ) is the Maxwell element at t n The relaxation effect accumulates stress inside;

[0017] Its three-dimensional discrete form is shown in the following formula (3):

[0018]

[0019] In the above formula (3), [C e ] is the elasticity matrix, expressed as follows (4); t n is the time to iterate to step n; t n+1 is the time to iterate to step n+1; Δt n+1 is the time increment of the n+1th step; N is the total number of viscous elements; e is the natural logarithm;

[0020]

[0021] In the above formula (4), K is the bulk modulus; λ0 and μ0 are the Lame constants;

[0022] The phase field fracture method is used to describe the failure process of particle-filled composites. The governing equation for the damage evolution of particle-filled composites is:

[0023]

[0024]

[0025] In the above formulas (5)-(6), d is the variable in the fracture phase field; G cis the fracture toughness; l is the characteristic length; σ0 is the stress when there is no damage; ε is the strain; u is the displacement; ψ0 is the strain energy density and is expressed as follows (7), where C0 is the elastic matrix when there is no damage; is the gradient operator;

[0026]

[0027] For each bottom layer segmentation area Do the same equivalent processing, the nth k ×n k The optimal parameter set corresponding to the underlying partition area is recorded as Train a suitable neural network model and establish segmentation areas From geometric features to parameter sets The mapping relationship of

[0028] Any middle area of ​​the k-1th layer By n k ×n k kth bottom-level segmentation region Composed of Equivalent to an isotropic unit, the middle area of ​​the k-1 layer It can be expressed as n k ×n k The grid form; similarly, it will form the nth k-1 ×n k-1 The k-1th layer region Region n k ×n k The stress-strain response of the grid is mapped to a unit, and the corresponding optimal parameter set is obtained Train a suitable neural network model and establish a mapping relationship between the model parameters of the k-layer segmentation area and the k-1-layer segmentation area;

[0029] Repeat the above operations until mapping to the global region Ω. From the sub-model to the macro-scale model, use isotropic units to replace the corresponding sub-model, and simulate and calculate the mechanical response of the macro-model, which can be compared with the macro-experiment to analyze the feasibility and accuracy of the model.

[0030] By adopting the above technical solution, the present invention has the following beneficial effects:

[0031] The macro- and micro-analysis method of the solid propellant failure process of the present invention is reasonably conceived, can describe the influence of local microstructure on macroscopic mechanical properties, and realize the unification of macro and micro. In particular, by layer-by-layer segmentation of the macro region and bottom-up constitutive response superposition, the constitutive modeling of particle-filled composite materials from micro to macro scales can be realized, and the cross-level constitutive mapping between multiple models at the same level to a higher-level model also considers the heterogeneous behavior of particle-filled composite materials. The use of an artificial neural network model to construct a mapping of the mesoscopic model structure to the corresponding isotropic unit constitutive parameters, as well as a mapping of the isotropic unit constitutive parameters corresponding to the mesoscopic model to the sub-model constitutive parameters, can greatly improve the efficiency of the macro- and micro-analysis of the solid propellant failure process, and lay a foundation for its subsequent performance analysis and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 The macro-scale model diagram and particle radius statistical diagram of the particle-filled composite material involved in the macro-micro analysis method of the solid propellant failure process of the present invention (wherein, Figure 1 middle Figure 1 (a) Macroscale model of particle-filled composite materials. Figure 1 (b) is the statistical distribution diagram of particle radius);

[0034] Figure 2 The block sub-model diagram and particle radius statistical diagram divided from the macro-scale model involved in the macro-micro analysis method of the solid propellant failure process of the present invention (wherein, Figure 2 middle Figure 2 (a) is a block sub-model diagram divided from the macro-scale model. Figure 2 (b) is the statistical distribution diagram of particle radius);

[0035] Figure 3 The micro-scale sub-model diagram and particle radius statistical diagram involved in the macro-micro analysis method of the solid propellant failure process of the present invention (wherein, Figure 3 middle Figure 3 (a) is the micro-scale sub-model, Figure 3 (b) is the statistical distribution diagram of particle radius);

[0036] Figure 4 A hierarchical cutting process diagram of the area involved in the macro-micro analysis method of the solid propellant failure process of the present invention;

[0037] Figure 5 It is a schematic diagram of the classical viscoelastic constitutive model elements involved in the macro-micro analysis method of the solid propellant failure process of the present invention;

[0038] Figure 6 A diagram of the mapping process from the bottom layer area to the model parameters involved in the macro-micro analysis method of the solid propellant failure process of the present invention;

[0039] Figure 7 It is a diagram of the intermediate region interlayer mapping process involved in the macro-micro analysis method of the solid propellant failure process of the present invention. DETAILED DESCRIPTION

[0040] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] The present invention is further explained below in conjunction with specific implementation modes.

[0042] like Figure 1 As shown, the macro-micro analysis method of the solid propellant failure process provided in this embodiment mainly includes the following steps:

[0043] S100, step-by-step segmentation of macroscopic to microscopic microstructures

[0044] Define a two-dimensional square macro region Ω, assume that the interior of Ω is filled with circular particles of different sizes, and the set of all particles is V. The difference set Ω-V between Ω and V is called the matrix. Draw the particle image, for example Figure 1 As shown in (a), the internal particle radius distribution is statistically analyzed, for example Figure 1 (b) as shown.

[0045] The macro region Ω is divided into n1×n1 level 1 sub-regions, where the level 1 sub-region of the i-th row and j-th column is denoted as Similarly, each level 1 sub-region can be divided into n2×n2 level 2 sub-regions, where The second-level sub-region of the i-th row and j-th column is denoted as Repeat the above operation to get k-level sub-regions Where 1≤i k ≤n k , 1≤j k ≤n k .

[0046] Assume k = 3, the segmentation process is as follows Figure 4 As shown in the figure, the mapping process from macroscopic to microscopic structure is established by step-by-step segmentation. The particle filling structure of a level 1 sub-region is shown in the figure. Figure 2 (a), the internal particle radius distribution is as follows Figure 2 (b) The particle filling structure of a level 2 sub-region is shown in Figure 3 (a), the internal particle radius distribution is as follows Figure 3 (b).

[0047] The macro region Ω was divided step by step, and the lowest level division adopted the mesoscopic mechanical modeling method to model the particle elastic mechanical constitutive model, matrix viscoelastic constitutive model, matrix phase field fracture model and interface phase field fracture model respectively (particle-filled composite materials include particles and matrix. Tensile tests have found that the material will not crack from the particles, but from the inside of the matrix or the interface between the particles and the matrix; therefore, only the elastic mechanical constitutive parameters of the particles, the viscoelastic constitutive parameters and phase field fracture parameters of the matrix, and the phase field fracture parameters of the interface are considered during modeling; the specific simulation process is to perform uniaxial tensile simulation through finite element modeling to obtain the tensile stress-strain response of the mesoscopic model). Its model parameters include 7 parameters of the matrix viscoelastic constitutive model (E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E111, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E30, E41, E52, E63, E74, E85, E96, E106, E111, E20 ∞ ,τ1,τ2,τ3), two parameters of the particle elastic constitutive model (Young's modulus and Poisson's ratio), and two parameters of the matrix phase field fracture model (G c , l) and two parameters of the interface phase field fracture model (G c2 , l2); finite element simulation is used to simulate the uniaxial tension of the microscopic model to obtain each bottom-level segmentation area The stress-strain curve S RVE .

[0048] Then for each bottom layer segmentation area Make a homogenization assumption and no longer consider the internal particles, matrix and interface characteristics. Replace them with an isotropic unit of the same size. Each bottom-level segmentation area The unit material obeys the matrix viscoelastic constitutive model and the matrix phase field fracture model, which can be represented by 9 parameters (E1, E2, E3, E ∞ ,τ1,τ2,τ3,G c ,l) is described, and the uniaxial tensile simulation of the isotropic unit after the homogenization assumption can obtain the stress-strain curve S after the homogenization assumption ISO ; Use the least squares method to select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameter G of the matrix phase field fracture model c , l value, so that S RVE With S ISOThe error is minimal.

[0049] S200, step-by-step mapping of constitutive model parameters

[0050] The microscopic model scale applicable to the present invention is 10 -6 m, at this time, the definition domain of particle-filled composite materials still applies the continuum assumption; in the framework of continuum mechanics, particle-filled composite materials are 0 ~10 -6 The same constitutive equations are applicable to the scale of meters, but the 0 ~10 -6 The particle-filled composite material parameters required at the meter scale need to be calibrated individually for each cut level.

[0051] The classic viscoelastic constitutive model consisting of a spring component and a generalized Maxwell model in parallel is used as the constitutive model of solid propellant materials. The component relationship is as follows: Figure 5 As shown, its one-dimensional function form is as follows:

[0052]

[0053] in:

[0054] In the above formula, the elastic coefficient of the spring element of the i-th Maxwell unit is E i , the viscosity coefficient of the viscosity pot element is η i , the elastic constant of the independent spring component is E ∞ ; t is time; ε0 is the strain at the initial moment; ε t is the strain at time t; σ(t) is the stress at time t; s is the frequency parameter after Laplace transformation; τ i is the relaxation time; γ i h is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; i (t n ) is the Maxwell element at t n The relaxation effect accumulates stress inside;

[0055] Its three-dimensional discrete form is shown in formula (3):

[0056]

[0057] In the above formula (3), [C e ] is the elasticity matrix, which is expressed as follows (4); t n is the time to iterate to step n; t n+1 is the time to iterate to step n+1; Δt n+1is the time increment of the n+1th step; N is the total number of viscous elements; e is the natural logarithm;

[0058]

[0059] In the above formula (4), K is the bulk modulus; λ0 and μ0 are the Lame constants;

[0060] The phase field fracture method is used to describe the failure process of the material. The governing equation for the damage evolution of particle-filled composites is:

[0061]

[0062]

[0063] Wherein, d in the above equations (5)-(6) is a variable in the fracture phase field; G c is the fracture toughness; l is the characteristic length; σ0 is the stress when there is no damage; ε is the strain; u is the displacement; ψ0 is the strain energy density, which is expressed as follows (7), where C0 is the elastic matrix when there is no damage; is the gradient operator:

[0064]

[0065] For each bottom layer segmentation area Do the same equivalent processing, the nth k ×n k The optimal parameter set corresponding to the underlying partition area is recorded as

[0066] Train a suitable neural network model and establish segmentation areas From geometric features to parameter sets The process is as follows Figure 6 As shown;

[0067] Similarly, any k-1th layer region By n k ×n k k-th layer (bottom layer) segmentation area Composed of is equivalent to an isotropic unit, then the k-1 layer area It can be expressed as n k ×n k The grid form of . Similarly, the nth k-1 ×n k-1 The k-1th layer region Region n k ×n k The stress-strain response of the grid is mapped to a unit, and the corresponding optimal parameter set is obtained Train a suitable neural network model and establish a mapping relationship between the model parameters of the k-layer segmentation area and the k-1-layer segmentation area, such as Figure 7 As shown;

[0068] Repeat the above operations until mapping to the global region Ω. From the sub-model to the macro-scale model, use isotropic units to replace the corresponding sub-model, and simulate and calculate the mechanical response of the macro-model, which can be compared with the macro-experiment to analyze the feasibility and accuracy of the model.

[0069] The invention has a reasonable conception, can describe the influence of the local microstructure of the particle-filled composite material on the macroscopic mechanical properties, realize the unification of macroscopic and microscopic, and greatly improve the macroscopic and microscopic analysis efficiency of the solid propellant failure process.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A macroscopic and microscopic analysis method for the failure process of solid propellant, characterized in that: The main steps include: 1) Divide the particle-filled composite material from the macroscopic model level to the mesoscopic model, and superimpose the constitutive response from the mesoscopic model level to the macroscopic model to achieve cross-scale constitutive modeling of particle-filled composite materials from the mesoscopic to the macroscopic level; 2) An artificial neural network model is used to map the mesoscopic model structure to the constitutive parameters and the sub-model constitutive parameters to the intermediate sub-model constitutive parameters.

2. The macroscopic and microscopic analysis method of the solid propellant failure process according to claim 1, characterized in that: The specific process of step 1) is as follows: 1.1) First define the macro region Ω. Assume that the interior of Ω is filled with circular particles of different sizes. The set of all particles is V. The difference set Ω-V between Ω and V is called the matrix. Draw the particle image and count the distribution of the particle radius inside it. 1.2) Then divide the macro region Ω into n1×n1 level 1 sub-regions, where the level 1 sub-region in the i-th row and j-th column is denoted as Continue to divide each level 1 sub-region into n2×n2 level 2 sub-regions, where The second-level sub-region of the i-th row and j-th column is denoted as Repeat the above operation to obtain the k-level bottom-level segmentation area. Where 1≤i k ≤n k , 1≤j k ≤n k ; 1.3) Then the macro region Ω was divided step by step. The bottom layer of the division used the microscopic mechanical modeling method to perform finite element modeling on the particle elastic mechanical constitutive model, matrix viscoelastic constitutive model, matrix phase field fracture model and interface phase field fracture model. During the modeling, the model parameters only considered the elastic mechanical constitutive parameters of the particles, the viscoelastic constitutive parameters of the matrix, the phase field fracture parameters of the matrix and the phase field fracture parameters of the interface. The model parameters included the parameters E1, E2, E3, E4 of the matrix viscoelastic constitutive model and the phase field fracture parameters of the interface. ∞ , τ1, τ2, τ3, Young's modulus and Poisson's ratio of the particle elastic constitutive model, and the parameter G of the matrix phase field fracture model c , l, parameter G of the interface phase field fracture model c2 , l2; finite element simulation is used to perform uniaxial tensile simulation on the microscopic model to obtain each bottom-level segmentation area The stress-strain curve S RVE ; 1.4) Then divide each bottom layer into regions Make a homogenization assumption and no longer consider the internal particles, matrix and interface characteristics. Replace them with an isotropic unit of the same size. Each bottom-level segmentation area The unit material obeys the matrix viscoelastic constitutive model and the matrix phase field fracture model, which can be obtained by the parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameter G of the matrix phase field fracture model c , l are described, and the uniaxial tensile simulation of the isotropic unit after the homogenization assumption can obtain the stress-strain curve S after the homogenization assumption ISO ; Use the least squares method to select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameter G of the matrix phase field fracture model c , l value, so that S RVE With S ISO The error is minimal.

3. The macroscopic and microscopic analysis method of the solid propellant failure process according to claim 1, characterized in that: The specific process of step 2) is as follows: The classic viscoelastic constitutive model consisting of a spring component and a generalized Maxwell model in parallel is used as the constitutive model of solid propellant materials. Its one-dimensional function form is as follows: in: In the above equations (1)-(2), the elastic coefficient of the spring element of the i-th Maxwell unit is E i , the viscosity coefficient of the viscosity pot element is η i , the elastic constant of the independent spring component is E ∞ ; t is time; ε0 is the strain at the initial moment; ε t is the strain at time t; σ(t) is the stress at time t; s is the frequency parameter after Laplace transformation; τ i is the relaxation time; γ i h is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; i (t n ) is the Maxwell element at t n The relaxation effect accumulates stress inside; Its three-dimensional discrete form is shown in the following formula (3): In the above formula (3), [C e ] is the elasticity matrix, expressed as follows (4); t n is the time to iterate to step n; t n+1 is the time to iterate to step n+1; Δt n+1 is the time increment of the n+1th step; N is the total number of viscous elements; e is the natural logarithm; In the above formula (4), K is the bulk modulus; λ0 and μ0 are the Lame constants; The phase field fracture method is used to describe the failure process of particle-filled composites. The governing equation for the damage evolution of particle-filled composites is: In the above formulas (5)-(6), d is the variable in the fracture phase field; G c is the fracture toughness; l is the characteristic length; σ0 is the stress when there is no damage; ε is the strain; u is the displacement; ψ0 is the strain energy density and is expressed as follows (7), where C0 is the elastic matrix when there is no damage; is the gradient operator; For each bottom layer segmentation area Do the same equivalent processing, the nth k ×n k The optimal parameter set corresponding to the underlying partition area is recorded as Train a suitable neural network model and establish segmentation areas From geometric features to parameter sets The mapping relationship; Any middle area of ​​the k-1th layer By n k ×n k kth bottom-level segmentation region Composed of Equivalent to an isotropic unit, the middle area of ​​the k-1 layer It can be expressed as n k ×n k The grid form; similarly, it will form the nth k-1 ×n k-1 The k-1th layer region Region n k ×n k The stress-strain response of the grid is mapped to a unit, and the corresponding optimal parameter set is obtained Train a suitable neural network model and establish a mapping relationship between the model parameters of the k-layer segmentation area and the k-1-layer segmentation area; Repeat the above operations until mapping to the global region Ω. From the sub-model to the macro-scale model, use isotropic units to replace the corresponding sub-model, and simulate and calculate the mechanical response of the macro-model, which can be compared with the macro-experiment to analyze the feasibility and accuracy of the model.

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