A macro-micro analysis method for the failure process of solid propellants

Abstract

The present invention provides a macro- and micro-analysis method for solid propellant failure processes, comprising the following steps: 1) hierarchically dividing a particle-filled composite material from a macroscopic model to a microscopic model, and then superimposing the constitutive response from the microscopic model onto the macroscopic model, thereby achieving cross-scale constitutive modeling of the particle-filled composite material from the microscopic to the macroscopic scale; and 2) mapping the mesoscopic model structure to constitutive parameters, and from sub-model constitutive parameters to intermediate sub-model constitutive parameters, using an artificial neural network model. This method is well-conceived and can describe the influence of the local microstructure of the particle-filled composite material on its macroscopic mechanical properties, achieving a unified macroscopic and microscopic analysis, significantly improving the efficiency of macro- and micro-analysis of solid propellant failure processes.

Description

Technical Field

[0001] The present 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 are composite materials formed by using a polymer as a binder resin and spheres, cylinders, or small platelets as fillers. Particle fillers can modify the material's dielectric properties, heat resistance, and hardness, and are commonly used in thermal insulation and solid propellants. Solid propellants are a typical example of particle-filled composites. Due to the uneven distribution of particles, current constitutive behavior modeling of particle-filled composites is unable to describe the influence of local microstructure on macroscopic mechanical properties, making it difficult to achieve a unified macroscopic and microscopic understanding and characterize the failure behavior of solid propellants across scales. Summary of the Invention

[0003] In response to 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 propellants. 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 macroscopic and microscopic aspects and greatly improving the efficiency of macro-micro analysis of the failure process of solid propellants.

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

[0005] 1) Split the particle-filled composite material from the macroscopic model level to the mesoscopic model level, 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 microscopic 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 a macroscopic region Ω. Assume that the interior of Ω is filled with circular particles of varying sizes. The set of all particles is V. The difference between Ω and V is called the matrix. Draw a particle image and calculate the distribution of particle radius within 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 split 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 recorded as Repeat the above operation to obtain the k-level bottom segmentation area where 1≤i k ≤n k , 1≤j k ≤n k ;

[0010] 1.3) Then the macro region Ω was segmented step by step. The bottom segmentation 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 respectively. 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 also included the parameters E1, E2, E3, E4 of the matrix viscoelastic constitutive model. ∞ , 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; uniaxial tensile simulation was performed on the microscopic model using finite element simulation to obtain the 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 segmentation area The unit material obeys the matrix viscoelastic constitutive model and the matrix phase field fracture model, which can be obtained from the parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameters 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 is performed can obtain the stress-strain curve S after the homogenization assumption ISO ; Using the least squares method, select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameters G of the matrix phase field fracture model c , l value, so that S RVE With S ISO The error is minimal.

[0012] The macro-micro 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 the solid propellant material. Its one-dimensional function form is as follows:

[0014]

[0015] in:

[0016] In the above equations (1) and (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 is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; h i (t n ) is the Maxwell element at t n Relaxation effect accumulates stress within the

[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, which is expressed as follows (4); t n is the time it takes to iterate to step n; t n+1 is the time it takes 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 The geometric features to parameter sets The mapping relationship;

[0028] Any middle area of ​​the k-1th layer By n k ×n k k-th bottom-level segmentation region Composed of, each Equivalent to an isotropic unit, the middle area of ​​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 k-1th layer region n of the region 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. It can be compared with the macro-scale 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 microscopic analysis method of the solid propellant failure process of the present invention is rationally conceived and can describe the influence of local microstructure on macroscopic mechanical properties, thereby achieving the unification of macroscopic and microscopic aspects. In particular, by layer-by-layer segmentation of the macroscopic region and bottom-up constitutive response superposition, the constitutive modeling of particle-filled composite materials from microscopic to macroscopic scales can be achieved, and the cross-level constitutive mapping between multiple models at the same level to a higher-level model also takes into account the heterogeneous behavior of the particle-filled composite materials. An artificial neural network model is used to construct a mapping from the microscopic model structure to the corresponding isotropic unit constitutive parameters, as well as a mapping from the isotropic unit constitutive parameters corresponding to the mesoscopic model to the sub-model constitutive parameters. This can greatly improve the efficiency of the macro- and microscopic 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 embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any 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-microscopic 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-microscopic 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 microscopic scale sub-model diagram and particle radius statistical diagram involved in the macroscopic and microscopic analysis method of the solid propellant failure process of the present invention (wherein, Figure 3 middle Figure 3 (a) is the microscopic scale sub-model, Figure 3 (b) is the statistical distribution diagram of particle radius);

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

[0037] Figure 5 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 showing the mapping process from the underlying region to the model parameters involved in the macro-micro analysis method of the solid propellant failure process of the present invention;

[0039] Figure 7 This 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 clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0041] The present invention will be further explained below with reference to specific embodiments.

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

[0043] S100, step-by-step segmentation of macro to micro structures

[0044] Define a two-dimensional square macroscopic 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, for example Figure 1 As shown in (a), the internal particle radius distribution is statistically analyzed, for example Figure 1 (b) shown.

[0045] The macro region Ω is divided 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 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 recorded 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 as follows 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 as follows 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 bottom level division adopted the microscopic 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 microscopic 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 ∞ ,τ1,τ2,τ3), two parameters of the particle elastic constitutive model (Young's modulus and Poisson's ratio), 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); uniaxial tensile simulation of the microscopic model using finite element simulation can obtain each bottom segmentation area The stress-strain curve S RVE .

[0048] Then, for each bottom layer, 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 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 ; Using the least squares method, select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameters 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 from 10 0 ~10 -6 The same constitutive equations are applicable to the scale of meters, but the 10 0 ~10 -6 The particle-filled composite material parameters required at the meter scale need to be calibrated individually for each cutting level.

[0051] The classical viscoelastic constitutive model consisting of a spring component and a generalized Maxwell model in parallel is used as the constitutive model of the solid propellant material. 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 is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; h i (t n ) is the Maxwell element at t n Relaxation effect accumulates stress within the

[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 it takes to iterate to step n; t n+1 is the time it takes 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 composite materials is:

[0061]

[0062]

[0063] Wherein, d in the above formulas (5)-(6) 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, 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 The geometric features to parameter sets The mapping relationship 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, each Equivalent to an isotropic unit, the k-1 layer area It can be expressed as n k ×n k The grid form. Similarly, the nth k-1 ×n k-1 k-1th layer region n of the region 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. It can be compared with the macro-scale experiment to analyze the feasibility and accuracy of the model.

[0069] The present invention has a reasonable concept and 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 efficiency of macroscopic and microscopic analysis of the failure process of solid propellant.

[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 above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above 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) Split the particle-filled composite material from the macroscopic model level to the microscopic model level, and superimpose the constitutive response from the microscopic model level to the macroscopic model level to achieve cross-scale constitutive modeling of the particle-filled composite material from the microscopic to the macroscopic level. The specific process is as follows: 1.1) First, define a macroscopic region Ω. Assume that the interior of Ω is filled with circular particles of varying sizes. The set of all particles is V. The difference between Ω and V is called the matrix. Draw a particle image and calculate the distribution of particle radius within 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 split 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 recorded as Repeat the above operation to obtain the k-level bottom segmentation area where 1≤i k ≤n k , 1≤j k ≤n k ; 1.3) Then the macro region Ω was segmented step by step. The bottom segmentation 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 respectively. 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 also included the parameters E1, E2, E3, E4 of the matrix viscoelastic constitutive model. ∞ , 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; uniaxial tensile simulation was performed on the microscopic model using finite element simulation to obtain the 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 segmentation area The unit material obeys the matrix viscoelastic constitutive model and the matrix phase field fracture model, which can be obtained from the parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameters 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 is performed can obtain the stress-strain curve S after the homogenization assumption ISO ; Using the least squares method, select the optimal set of parameters E1, E2, E3, E ∞ , τ1, τ2, τ3 and the parameters G of the matrix phase field fracture model c , l value, so that S RVE With S ISO The error is minimal; 2) An artificial neural network model is used to map the microscopic 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 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 the solid propellant material. Its one-dimensional function form is as follows: in: In the above equations (1) and (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 is the ratio of the elastic modulus of the Maxwell spring element to the stable spring component; h i (t n ) is the Maxwell element at t n Relaxation effect accumulates stress within the Its three-dimensional discrete form is shown in the following formula (3): In the above formula (3), [C e ] is the elasticity matrix, which is expressed as follows (4); t n is the time it takes to iterate to step n; t n+1 is the time it takes 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 The geometric features to parameter sets The mapping relationship; Any middle area of ​​the k-1th layer By n k ×n k k-th bottom-level segmentation region Composed of, each Equivalent to an isotropic unit, the middle area of ​​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 k-1th layer area n of the region 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. It can be compared with the macro-scale experiment to analyze the feasibility and accuracy of the model.

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