CRS prediction method for solid propellant grain based on multi-field coupling constitutive model

Abstract

The present invention discloses a CRS prediction method for solid propellant grains based on a multi-field coupling constitutive model, including: obtaining viscoelastic test data of the entire solid propellant curing process, characterizing the solid propellant curing degree based on the equilibrium modulus, and fitting a curing reaction kinetic model; obtaining the curing reaction heat release of the solid propellant, and establishing a solid propellant heat flow equation containing an internal heat source; obtaining a viscoelastic evolution model of the entire solid propellant curing process based on the viscoelastic test data; establishing a three-dimensional viscoelastic constitutive model and its incremental equation related to time-temperature-curing degree; establishing a multi-field coupling finite element analysis model of solid propellant grains to obtain CRS results. The present invention is applied to the field of solid propellant curing simulation technology, and comprehensively considers the thermal-chemical-force multi-field coupling characteristics such as curing reaction heat release, curing volume shrinkage, and viscoelastic evolution, and can quickly and accurately predict the CRS of solid propellant grains.

Description

Technical Field

[0001] The invention relates to the technical field of solid propellant curing simulation, and in particular to a solid propellant grain CRS (Cure Residual Stress) prediction method based on a multi-field coupling constitutive model. Background Art

[0002] Solid rocket engines have the advantages of fast response, long storage durability and reliable structure. They are widely used in propulsion devices in the aerospace field. Their service capability depends largely on the solidification quality of solid propellant grains. With the development of technology, the solidification process of solid propellant grains has changed. Traditional curing, pressurized curing and temperature-pressure synergistic curing have emerged. Regardless of the curing process, when solid propellant grains are cured and formed, there are thermal-chemical-mechanical multi-field coupling effects such as heat release of curing reaction, curing volume shrinkage and viscoelastic evolution; when cooling, the inconsistency of thermal expansion coefficients between solid propellant grains and engine casings, as well as the interaction between solid propellant grains and core molds and engine casings, will produce CRS during the solidification process. The CRS of solid propellants has an important influence on the storage life and ignition and launch of solid rocket engines. Accurately predicting the CRS of solid propellant grains and revealing the mechanism of curing residual stress are the basis for reducing CRS, which is of great significance for changing the curing process, improving the curing quality and improving the curing efficiency.

[0003] In the development process of traditional solid propellant grains, due to the lack of precise theoretical model guidance, repeated trial and error and correction are mainly based on engineering experience. However, solid propellant grains have pain points such as long curing cycle, high manufacturing cost, great safety hazards, and difficult stress testing. The traditional passive design method will greatly increase its development cycle, which is not conducive to product updates and iterations. Establishing a theoretical model that can accurately predict the CRS of solid propellant grains and guiding the development of solid propellant grains through numerical analysis will greatly save the development cycle, save manpower and material resources, and reduce development costs. In addition, the development of solid propellant grains can also be transformed from passive design to active regulation, using technology to empower the development and production of solid propellant grains.

[0004] Among the existing constitutive models used for structural CRS prediction, the linear elastic constitutive model only has ideal results for thin-walled / thin-shell structures, the path-dependent constitutive model has poor prediction results for structural CRS, and the viscoelastic constitutive model has good prediction results for both structural CRS and deformation. In addition, in the numerical implementation of the constitutive model, most of them ignore the influence of viscoelasticity on the thermal-chemical field to simplify the calculation, and use the multi-field sequential coupling method to simulate and analyze the structure, which leads to distortion of the CRS prediction results.

[0005] To this end, combined with the complex multi-field coupling effects in the solidification process of solid propellant grains, a multi-field coupling viscoelastic constitutive model is constructed to accurately predict the CRS of solid propellant grains. It is used for the design, calculation and analysis of solid propellant grain curing processes such as traditional curing, pressurized curing and temperature-pressure coordinated curing, which has great engineering value. Summary of the invention

[0006] In view of the problem that the CRS of solid propellant grains cannot be accurately predicted in the above-mentioned prior art, the present invention provides a solid propellant grain CRS prediction method based on a multi-field coupling constitutive model, which comprehensively considers the thermal-chemical-mechanical multi-field coupling characteristics of the solid propellant grains, such as the exothermic reaction of the curing reaction, the shrinkage of the curing volume and the viscoelastic evolution, and constructs a multi-field coupling viscoelastic constitutive model based on the experimental test results, thereby realizing the characterization of the mechanical behavior of the solid propellant grain curing process, and can quickly and accurately predict the CRS of the solid propellant grains.

[0007] To achieve the above object, the present invention provides a solid propellant grain CRS prediction method based on a multi-field coupling constitutive model, comprising the following steps:

[0008] Step 1, obtaining viscoelastic test data of the whole solid propellant curing process, and characterizing the curing degree of the solid propellant based on the equilibrium modulus in the viscoelastic test data, and obtaining a curing reaction kinetic model of the solid propellant by nonlinear fitting;

[0009] Step 2, obtaining the heat released by the solid propellant curing reaction, and establishing a heat flow equation for the solid propellant containing an internal heat source in combination with the curing reaction kinetic model;

[0010] Step 3, based on the viscoelastic test data and the generalized Maxwell model, a viscoelastic evolution model of the whole solidification process of the solid propellant is obtained;

[0011] Step 4, based on the viscoelastic evolution model, a three-dimensional viscoelastic constitutive model and its incremental equation related to time-temperature-curing degree are established;

[0012] Step 5: Develop a user material subroutine based on the heat flow equation of solid propellant with internal heat source, the three-dimensional viscoelastic constitutive model related to time-temperature-curing degree and its incremental equation, and establish a multi-field coupled finite element analysis model of solid propellant grains to obtain the CRS results of solid propellant grains.

[0013] In one embodiment, in step 1, the viscoelastic test data includes the dynamic viscoelasticity of the viscous fluid solid propellant and the quasi-static viscoelasticity of the solid propellant after gelation.

[0014] In one embodiment, in step 1, the degree of solidification is specifically:

[0015] ;

[0016] in, β is the solidification degree of the solid propellant, E ( t ) is the solid propellant at different curing times t The equilibrium modulus under E 0 is the equilibrium modulus of the solid propellant in the initial state of solidification, E c is the equilibrium modulus of the solid propellant in the final state of solidification;

[0017] The curing reaction kinetic model is:

[0018] ;

[0019] in, A is the pre-exponential factor, E a is the activation energy of the curing reaction, R is the gas constant, m , n is the reaction order, T is the temperature, A.E a , m , n are the parameters to be fitted.

[0020] In one embodiment, in step 2, the heat flow equation of the solid propellant containing an internal heat source is specifically:

[0021] ;

[0022] in, , are the mass density of the solid propellant and the mass density of the matrix, , are the specific heat capacity and thermal conductivity components of the solid propellant, is the volume fraction of the solid propellant matrix, is the Hamilton operator, H t The curing reaction generates heat.

[0023] In one embodiment, in step 3, the viscoelastic evolution model of the whole solidification process of the solid propellant is specifically:

[0024] ;

[0025] in, is the viscoelastic response of solid propellant during curing, E∞ , E i They are the equilibrium modulus and non-equilibrium modulus related to the solidification degree of solid propellant, is the relaxation time related to the solidification degree of the solid propellant, is the displacement factor of the solid propellant.

[0026] In one embodiment, in step 4, the three-dimensional viscoelastic constitutive model related to time-temperature-curing degree is:

[0027] ;

[0028] in, is the stress component, is the stiffness component, is the effective strain component, is the current conversion time, is the historical conversion time, is the accumulated time;

[0029] Specifically:

[0030] ;

[0031] ;

[0032] ;

[0033] in, is the total strain, , are the thermal expansion coefficient and curing volume shrinkage coefficient of the solid propellant, , are the temperature change and the curing degree change, t′ is the accumulated time, t c and t h They are the current time and the historical time respectively.

[0034] In one embodiment, in step 4, the process of obtaining the incremental equation of the three-dimensional viscoelastic constitutive model is:

[0035] In a discrete time interval , and the corresponding time increment is , the initial state of solid propellant curing is zero stress state, and the stress increment in the discrete time interval is for:

[0036] ;

[0037] Among them,t n and t n+1 The physical quantity with a superscript indicates its value at the corresponding moment;

[0038] Based on time increment The inner logarithmic shift factor is linearly related to time, and the reduced time increment is obtained ,for:

[0039] ;

[0040] In addition, the partial differential of strain is:

[0041] ;

[0042] in, is the effective strain increment in the discrete time interval.

[0043] In one embodiment, step 5 specifically includes:

[0044] Develop UMAT user material subroutine based on the incremental equation of 3D viscoelastic constitutive model;

[0045] Develop UMATHT user material subroutine based on the solid propellant heat flow equation with internal heat source;

[0046] Develop the UEXPAN user material subroutine based on the effective strain equation of the three-dimensional viscoelastic constitutive model;

[0047] Develop FILM user material subroutines based on thermal boundary conditions in the process;

[0048] The finite element model of solid propellant grain was established using Abaqus software;

[0049] Based on the finite element model of solid propellant grains and all user material subroutines, a multi-field coupled finite element analysis model is established through the temperature-displacement coupling analysis step, and the CRS results of solid propellant grains are predicted.

[0050] Compared with the prior art, the present invention has the following beneficial technical effects:

[0051] The present invention considers the heat-chemical-mechanical multi-field coupling effects such as the heat release of the solid propellant curing reaction, the shrinkage of the curing volume, and the evolution of viscoelasticity, and combines experimental tests to construct a multi-field coupling viscoelastic constitutive model for predicting the CRS of solid propellant grains, thereby achieving the technical problem of characterizing the mechanical behavior of the solid propellant grain curing process; subsequently, the finite element incremental equation of the constitutive model is derived, and the multi-field coupling simulation analysis of the solid propellant grain is performed using the temperature-displacement coupling analysis step of the finite element software Abaqus to accurately predict the CRS of the solid propellant grain. Compared with traditional experimental methods and traditional solid propellant grain CRS prediction theories and simulation models, the method provided by the present invention can quickly and accurately predict the CRS of the solid propellant grain, and can also simultaneously obtain key characteristic parameters such as the temperature and curing degree of the solid propellant grain, and the results are all visualized, which can effectively improve the research and development efficiency, reduce the research and development cost, and shorten the research and development cycle, provide guidance and suggestions for the innovation of the curing process, and promote the high-quality, efficient and intelligent manufacturing of solid propellant grains. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in the drawings of the embodiments of the present invention without paying any creative work.

[0053] Figure 1 Flow chart of a solid propellant grain CRS prediction method based on a multi-field coupling constitutive model in an embodiment of the present invention;

[0054] Figure 2 Schematic diagram of the viscoelasticity test results of the solid propellant in the embodiment of the present invention, wherein: Figure 2 (a) is a schematic diagram of the HTPB viscoelastic test results at a certain degree of curing. Figure 2 (b) Schematic diagram of the fitting curve of the viscoelastic evolution model of the entire curing process of HTPB propellant;

[0055] Figure 3 This is a schematic diagram of the solidification degree field distribution of the HTPB drug column at a certain moment in an embodiment of the present invention;

[0056] Figure 4 Schematic diagram of the temperature field distribution of the HTPB propellant grain at a certain moment in an embodiment of the present invention;

[0057] Figure 5 Schematic diagram of CRS distribution of HTPB propellant grains in an embodiment of the present invention.

[0058] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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.

[0060] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0061] This embodiment discloses a solid propellant grain CRS prediction method based on a multi-field coupling constitutive model, which can quickly and accurately predict the CRS of the solid propellant grain. Figure 1 In this embodiment, the solid propellant grain CRS prediction method based on the multi-field coupling constitutive model specifically includes the following steps:

[0062] Step 1, obtaining viscoelastic test data of the whole solidification process of the solid propellant, and characterizing the solidification degree of the solid propellant based on the equilibrium modulus in the viscoelastic test data, and then obtaining the solidification reaction kinetic model of the solid propellant by nonlinear fitting, wherein the viscoelastic test data includes the dynamic viscoelasticity of the viscous fluid solid propellant and the quasi-static viscoelasticity of the solid propellant after gelation;

[0063] Step 2, obtaining the heat release of the solid propellant curing reaction, and establishing a heat flow equation of the solid propellant containing an internal heat source in combination with a curing reaction kinetic model;

[0064] Step 3, based on the viscoelastic test data and the generalized Maxwell model, a viscoelastic evolution model of the whole solidification process of the solid propellant is obtained;

[0065] Step 4, based on the viscoelastic evolution model, a three-dimensional viscoelastic constitutive model and its incremental equation related to time-temperature-curing degree are established;

[0066] Step 5: Develop a user material subroutine based on the heat flow equation of solid propellant with internal heat source, the three-dimensional viscoelastic constitutive model related to time-temperature-curing degree and its incremental equation, and establish a multi-field coupled finite element analysis model of solid propellant grains to obtain the CRS results of solid propellant grains.

[0067] The following takes the CRS prediction of HTPB (Hydroxyl-terminated polybutadiene) propellant grains as an example to further illustrate the CRS of the HTPB propellant grains in this embodiment.

[0068] In the specific implementation process of step 1, the viscoelastic test data of the solid propellant is first measured, including the dynamic viscoelasticity of the viscous fluid solid propellant and the quasi-static viscoelasticity of the solid propellant after gelation, specifically:

[0069] The oscillation mode of the rotational rheometer was used, the strain was set to 0.5%, the frequency range was 0.1Hz~10Hz, and the test temperatures were selected to be 40℃, 20℃, 0℃, −20℃ and −40℃, respectively, to test the dynamic viscoelasticity of the viscous HTPB propellant;

[0070] The quasi-static viscoelasticity of the gelled HTPB propellant was tested using an electronic universal testing machine with the strain set to 5%, the loading rate set to 500 mm / min, and the test temperatures selected to be 40°C, 20°C, 0°C, −20°C, and −40°C.

[0071] Combining the dynamic viscoelasticity and quasi-static viscoelasticity of HTPB propellant, the viscoelastic data of the whole curing process of HTPB propellant are obtained, such as Figure 2 (a) is the viscoelastic test result of HTPB propellant at a certain degree of curing.

[0072] After obtaining the viscoelastic data of the HTPB propellant, the equilibrium modulus in the viscoelastic data can be used to characterize the curing degree of the HTPB propellant, specifically:

[0073] (1)

[0074] in, β is the curing degree of HTPB propellant, E ( t ) is the HTPB propellant at different curing times t The equilibrium modulus under E 0 is the equilibrium modulus of the HTPB propellant in the initial state of curing, E c is the equilibrium modulus of the final cured state of HTPB propellant;

[0075] Then, the viscoelastic data measured at a certain temperature (for example, 40°C) are selected, and the curing reaction kinetic model of HTPB propellant is obtained by nonlinear fitting, which is:

[0076] (2)

[0077] in, Ais the pre-exponential factor, E a is the activation energy of the curing reaction, R is the gas constant, m , n is the reaction order, T is the temperature, A.E a , m , n are the parameters to be fitted.

[0078] In the specific implementation process of step 2, it is first necessary to obtain the heat released by the curing reaction of the HTPB propellant, which can be obtained by the following exemplary implementation method:

[0079] The heating rates were selected as 5mm / min, 10mm / min, 15mm / min and 20mm / min, and the starting and ending temperatures were set at 20℃~180℃. The heat flow curves of HTPB propellant at different heating rates were tested by differential scanning calorimetry.

[0080] The thermal data obtained by differential scanning calorimetry were processed to obtain the heat release of HTPB propellant at different curing rates and the average value was taken to obtain the heat release of the curing reaction of HTPB propellant. H t .

[0081] The heat released by the curing reaction of HTPB propellant H t Then, combined with the curing reaction kinetic model of formula (2), the heat flow equation of the solid propellant containing internal heat source can be obtained:

[0082] (3)

[0083] in, , are the mass density of HTPB propellant and the mass density of matrix, , are the specific heat capacity and thermal conductivity components of HTPB propellant, is the volume fraction of HTPB propellant matrix, is the Hamilton operator.

[0084] In the specific implementation process of step 3, based on the viscoelastic test data measured in step 1, the generalized Maxwell model is used for nonlinear fitting to obtain the viscoelastic evolution model of the entire curing process of HTPB propellant, which is:

[0085] (4)

[0086] in, is the viscoelastic response of solid propellant during curing, E ∞ , E i They are the equilibrium modulus and non-equilibrium modulus related to the solidification degree of solid propellant, is the relaxation time related to the solidification degree of the solid propellant, is the displacement factor of the solid propellant.

[0087] For example Figure 2 (b) is the fitting curve of the viscoelastic evolution model of the whole curing process of HTPB propellant, where:

[0088] (5)

[0089] In the specific implementation process of step 4, the thermal expansion coefficient and solid volume shrinkage coefficient of HTPB propellant during the curing process are considered to be constants, so the three-dimensional viscoelastic constitutive model related to time-temperature-curing degree is established as follows:

[0090] (6)

[0091] in, is the stress component, is the stiffness component, is the effective strain component, is the current conversion time, is the historical conversion time, is the accumulated time;

[0092] Specifically:

[0093] (7)

[0094] (8)

[0095] (9)

[0096] in, is the total strain, , are the thermal expansion coefficient and curing volume shrinkage coefficient of HTPB propellant, , are the temperature change and the curing degree change, t′ is the accumulated time, t c and t h They are the current time and the historical time respectively.

[0097] In a discrete time interval , and the corresponding time increment is , the initial state of HTPB propellant curing is zero stress state, and the stress increment in the discrete time interval is for:

[0098] (10)

[0099] Among them, t n and t n+1 The physical quantity with a superscript indicates its value at the corresponding moment;

[0100] Rearranging formula (10) yields:

[0101] (11)

[0102] Intermediate Parameters , , for:

[0103] (12)

[0104] (13)

[0105] (14)

[0106] Based on time increment The inner logarithmic shift factor is linearly related to time, and the reduced time increment can be obtained ,for:

[0107] (15)

[0108] In addition, the partial differential of strain is:

[0109] (16)

[0110] in, is the effective strain increment in the discrete time interval.

[0111] Substituting equations (15) and (16) into the integral equation of equation (10), we can obtain:

[0112] (17)

[0113] (18)

[0114] (19)

[0115] After completing the construction of the heat flow equation of solid propellant with internal heat source, the multi-field coupled viscoelastic constitutive model and its incremental equation, the multi-field coupled finite element analysis model of solid propellant grain can be established to predict the CRS of HTPB propellant. The specific implementation process includes the following steps:

[0116] Step 501, based on the multi-field coupled viscoelastic constitutive model and its incremental equation, the UMAT user material subroutine is developed by combining equations (11), (17) to (19);

[0117] Step 502, measuring the mass density of the HTPB matrix, the mass density, specific heat capacity, thermal conductivity, and volume fraction of the HTPB propellant in the heat flow equation of the solid propellant containing an internal heat source through experiments, and developing a UMATHT user material subroutine based on formula (3);

[0118] Step 503, measuring the thermal expansion coefficient and chemical contraction coefficient of the HTPB propellant in the effective strain equation (6) through experiments, and developing a UEXPAN user material subroutine based on equation (6);

[0119] Step 504, developing a FILM user material subroutine based on the thermal boundary conditions in the specific process;

[0120] Step 505, using Abaqus software to establish a finite element model of the HTPB propellant grain;

[0121] Step 506, based on the finite element model of the HTPB propellant grain and all the user material subroutines of steps 501 to 504, a multi-field coupling finite element analysis model is established through a temperature-displacement coupling analysis step to obtain the CRS result of the HTPB propellant grain.

[0122] Taking a certain type of HTPB propellant grain as an example, the established multi-field coupling simulation analysis model is used to simulate and analyze its curing process. The field distribution of the curing degree of the HTPB grain at a certain moment is as follows: Figure 3 As shown in the figure, different colors represent the field distribution of the solidification degree of the HTPB propellant grain; the temperature field distribution of the HTPB propellant grain at a certain moment is shown in the figure. Figure 4 As shown in Figure 2, different colors represent the temperature field distribution of HTPB propellant grains; the CRS distribution of HTPB propellant grains is shown in Figure 2. Figure 5 As shown in the figure, different colors represent the CRS distribution of HTPB propellant grains. It can be seen that the CRS prediction method of solid propellant grains based on the multi-field coupling constitutive model in this embodiment can provide theoretical guidance for improving the solidification process of solid propellant grains, so as to improve the quality, efficiency and intelligent level of solid propellant grain molding.

[0123] The above description is only a preferred embodiment of the present invention, and does not limit the protection scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the protection scope of the present invention.

Claims

1. A solid propellant grain CRS prediction method based on a multi-field coupling constitutive model, characterized in that: The steps include: Step 1, obtaining viscoelastic test data of the whole solid propellant curing process, and characterizing the curing degree of the solid propellant based on the equilibrium modulus in the viscoelastic test data, and obtaining a curing reaction kinetic model of the solid propellant by nonlinear fitting; Step 2, obtaining the heat released by the solid propellant curing reaction, and establishing a heat flow equation for the solid propellant containing an internal heat source in combination with the curing reaction kinetic model; Step 3, based on the viscoelastic test data and the generalized Maxwell model, a viscoelastic evolution model of the whole solidification process of the solid propellant is obtained; Step 4, based on the viscoelastic evolution model, a three-dimensional viscoelastic constitutive model and its incremental equation related to time-temperature-curing degree are established; The three-dimensional viscoelastic constitutive model related to time-temperature-curing degree is: ； in, is the stress component, t For time, β is the solidification degree of the solid propellant, T is the temperature, is the stiffness component, is the effective strain component, is the current conversion time, is the historical conversion time, is the accumulated time; Specifically: ； ； ； in, is the total strain, , are the thermal expansion coefficient and curing volume shrinkage coefficient of the solid propellant, , are the temperature change and the curing degree change, t′ is the accumulated time, t c and t h The current time and historical time respectively; The process of obtaining the incremental equation of the three-dimensional viscoelastic constitutive model is as follows: In a discrete time interval , and the corresponding time increment is , the initial state of solid propellant curing is zero stress state, and the stress increment in the discrete time interval is for: ； Among them, t n and t n+1 The physical quantity with a superscript indicates its value at the corresponding moment; Based on time increment The inner logarithmic shift factor is linearly related to time, and the reduced time increment is obtained ,for: ； In addition, the partial differential of strain is: ； in, is the effective strain increment in the discrete time interval Step 5: Develop a user material subroutine based on the heat flow equation of solid propellant with internal heat source, the three-dimensional viscoelastic constitutive model related to time-temperature-curing degree and its incremental equation, and establish a multi-field coupled finite element analysis model of solid propellant grains to obtain the CRS results of solid propellant grains.

2. The solid propellant grain CRS prediction method based on the multi-field coupling constitutive model according to claim 1 is characterized in that: In step 1, the viscoelastic test data includes the dynamic viscoelasticity of the viscous fluid solid propellant and the quasi-static viscoelasticity of the solid propellant after gelation.

3. The solid propellant grain CRS prediction method based on the multi-field coupling constitutive model according to claim 2 is characterized in that: In step 1, the degree of solidification is specifically: ； in, E ( t ) is the solid propellant at different curing times t The equilibrium modulus under E 0 is the equilibrium modulus of the solid propellant in the initial state of solidification, E c is the equilibrium modulus of the solid propellant in the final state of solidification; The curing reaction kinetic model is: ； in, A is the pre-exponential factor, E a is the activation energy of the curing reaction, R is the gas constant, m , n is the reaction order, A.E a , m , n are the parameters to be fitted.

4. The solid propellant grain CRS prediction method based on the multi-field coupling constitutive model according to claim 3 is characterized in that: In step 2, the heat flow equation of the solid propellant with internal heat source is: ； in, , are the mass density of the solid propellant and the mass density of the matrix, , are the specific heat capacity and thermal conductivity components of the solid propellant, is the volume fraction of the solid propellant matrix, is the Hamilton operator, H t The curing reaction generates heat.

5. The solid propellant grain CRS prediction method based on the multi-field coupling constitutive model according to claim 3 or 4, characterized in that: In step 3, the viscoelastic evolution model of the whole solidification process of solid propellant is as follows: ； in, is the viscoelastic response of solid propellant during curing, E ∞ , E i They are the equilibrium modulus and non-equilibrium modulus related to the solidification degree of solid propellant, is the relaxation time related to the solidification degree of the solid propellant, is the displacement factor of the solid propellant.

6. The solid propellant grain CRS prediction method based on the multi-field coupling constitutive model according to claim 1 is characterized in that: Step 5 specifically includes: Develop UMAT user material subroutine based on the incremental equation of 3D viscoelastic constitutive model; Develop UMATHT user material subroutine based on the solid propellant heat flow equation with internal heat source; Develop the UEXPAN user material subroutine based on the effective strain equation of the three-dimensional viscoelastic constitutive model; Develop FILM user material subroutines based on thermal boundary conditions in the process; The finite element model of solid propellant grain was established using Abaqus software; Based on the finite element model of solid propellant grains and all user material subroutines, a multi-field coupled finite element analysis model is established through the temperature-displacement coupling analysis step, and the CRS results of solid propellant grains are predicted.

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