CN114462146B - Method for constructing propellant creep constitutive model considering aging damage and finite element application - Google Patents
Method for constructing propellant creep constitutive model considering aging damage and finite element application Download PDFInfo
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Abstract
The invention discloses a propellant creep constitutive model construction and finite element application method considering aging damage, wherein the construction method comprises the following steps: acquiring creep parameters of the propellant; acquiring an aging parameter of the propellant; presetting relative variation of effective bearing area; determining an aging development equation according to the obtained aging parameters; constructing a creep constitutive model of the propellant according to the creep parameters; determining a damage variable according to the relative variation of the effective bearing area, and determining a damage development equation according to the damage variable; establishing a propellant creep constitutive model considering aging damage according to the determined aging development equation, the damage development equation and the constructed propellant creep constitutive model; the finite element application method comprises the following steps: and decomposing the propellant creep damage constitutive model which is constructed by the method and takes the aging effect into consideration, and deducing an aging increment form and a consistent tangential stiffness array. The method can calculate the creep damage mechanical behavior and the aging mechanical behavior of the propellant grain structure in the storage stage.
Description
Technical Field
The invention relates to a method for constructing a propellant creep constitutive model considering aging damage and a method for applying a finite element, belonging to the technical field of energetic material constitutive model research.
Background
The solid rocket engine is a power device of a remote rocket projectile, and the solid propellant is an important component of the solid rocket engine. During long-distance rocket projectile storage for a long time, the grain structure can generate an aging effect besides a creep and damage effect. In order to accurately simulate the structural response of an engine during long-term storage, it is first necessary to establish an accurate model of propellant creep damage that accounts for aging effects.
At present, the aging constitutive relation of the propellant is mostly established on the basis of the relaxed constitutive structure, and for the creep constitutive structure, the research on the aging effect of the propellant on the basis of the aging constitutive relation is not reported. In order to realize the refined modeling of the aging creep damage effect inside the grain structure during long-term storage, it is necessary to construct a propellant creep damage constitutive model considering the aging effect.
At present, the existing finite element simulation tool does not have the function of creep damage of the structure considering the aging effect, and is difficult to be directly utilized. Therefore, a secondary development interface of commercial software is needed to be adopted to realize development and application of the propellant creep damage organization considering the aging effect.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method for constructing a propellant creep constitutive model considering aging damage and applying a finite element, and can calculate the creep damage mechanical behavior and the aging mechanical behavior of a propellant grain structure in the storage stage.
In order to achieve the purpose, the invention adopts the following technical scheme:
in one aspect, the invention provides a method for constructing a propellant creep constitutive model considering aging damage, which comprises the following steps:
acquiring creep parameters of the propellant;
acquiring an aging parameter of the propellant;
presetting relative variation of effective bearing area;
determining an aging development equation according to the obtained aging parameters;
constructing a creep constitutive model of the propellant according to the creep parameters;
determining a damage variable according to the relative variation of the effective bearing area, and determining a damage development equation according to the damage variable;
and establishing a propellant creep constitutive model considering aging damage according to the determined aging development equation, the damage development equation and the constructed propellant creep constitutive model.
Further, the determining an aging development equation according to the obtained aging parameters includes the following steps:
the aging development parameters of the propellant are obtained through formulas (1) to (2), and are specifically as follows:
wherein, T 0 For storage temperature, k B Is a function of the Boltzmann constant,
aging reaction activation energy without stress strain field effect, t' aging time, h P Is a Planck constant, A is an aging reaction rate constant, upsilon m At maximum crosslink density, α c The undetermined coefficient of the chemical reaction equation,
beta is the initial ageing development parameter of the propellant c Aging hair for propellantUnfolding parameters;
the relative change in the degree of crosslinking of the propellant is obtained by the formulae (3) to (4), as follows:
wherein v () is a function of the degree of crosslinking of the propellant, T' is the aging temperature, B is a parameter of the aging development of the propellant, v 0 Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
wherein J () is a creep compliance function taking into account aging effects, J 0 () Is the creep modulus without aging, J 1 () Is the change in creep compliance caused by aging.
T is the loading time as a function of the relative change in the degree of crosslinking of the propellant.
Further, the injury development equation includes equations (6) - (9), which are as follows:
wherein D is a damage variable, D 0 For initial damage of the propellant, D △V To extend the new lesions formed, σ th The method comprises the following steps of setting a damage stress threshold value, wherein sigma is mechanical stress before propellant damage, gamma is a first parameter of propellant damage, K is a second parameter of propellant damage, beta is a third parameter of propellant damage, h () is a stress state function, and x is an input parameter of the stress state function.
Further, the propellant creep constitutive model comprises formulas (10) - (12), which are as follows:
wherein epsilon ij For mechanical strain, J ijkl () Is a creep tensor function, xi is the conversion time of time t, xi' is the conversion time of the first integrand tau, sigma kl τ is a first integrand function, T is a loading time, T () is a temperature, tt' is a second integrand function, a T Is a temperature shift factor, C 1 For the first parameter of the propellant WLF equation, C 2 For the second parameter of the WLF equation for the propellant, T is the current temperature, T r Is the reference temperature.
Further, the establishing of the propellant creep constitutive model considering the aging damage comprises updating the mechanical strain by the formula (13), which is specifically as follows:
wherein, the first and the second end of the pipe are connected with each other,
as a function of the effective stress tensor of the propellant after damage.
In another aspect, the present invention provides a finite element application method of a propellant creep damage constitutive model considering aging effect, comprising the following steps:
decomposing the propellant creep damage constitutive model which is constructed by the method and takes the aging effect into consideration, and obtaining a partial strain tensor and a spherical strain tensor;
dispersing the partial strain tensor and the spherical strain tensor, and deducing an aging increment form of the propellant creep damage constitutive model according to the dispersed partial strain tensor and the spherical strain tensor;
deriving a consistent tangential stiffness array according to the derived aging increment form;
programming the aging increment form and the consistent tangential stiffness array to obtain a subprogram, and calling the subprogram by adopting finite element software.
Further, decomposing the propellant creep damage constitutive model considering the aging effect to obtain the partial strain tensor and the spherical strain tensor including the formula (14) as follows:
wherein the content of the first and second substances,
as a function of the effective stress deflection tensor,
as a function of the effective stress sphere tensor, e ij () In order to be a function of the partial strain,
is the spherical strain tensor, J () is the propellant creep compliance function, and ν is the propellant Poisson ratio;
the creep compliance function of the propellant comprises the formula (15), which is as follows:
wherein N is J The term for the creep compliance level,
to balance the creep compliance without considering the aging effect,
to account for the initial creep compliance of the aging effect,
to account for the nth creep compliance coefficient of aging effects,
to account for the change in equilibrium creep compliance of the aging effect,
in order to consider the nth creep compliance coefficient of the aging effect, t is loading time;
the effective stress deflection tensor function includes the formula (16), which is specifically as follows:
wherein S is ij () Is a biased stress tensor function;
the effective stress sphere tensor function includes the following formula (17):
wherein σ kk () As a function of the ball stress tensor.
Further, the aging increment form of the propellant creep damage constitutive model comprises a formula (18), and the aging increment form comprises the following specific formula:
wherein < DELTA > ∈ ij (t m+1 ) Is t m+1 Increment of the strain tensor at time, Δ e ij (t m+1 ) Is t m+1 The increment of the moment strain offset is increased,
is t m+1 Increment of the global strain tensor of time, delta ij Is the fourth kronecker symbol.
Further, the consistent tangential stiffness array comprises formulas (19) - (20), which are as follows:
wherein, C ijkl () Is a tangential stiffness tensor function, delta sigma ij (t m+1 ) Is t m+1 Stress increment at time,. DELTA.. Epsilon kl (t m+1 ) Is t m+1 Increment of the moment strain tensor, C 2222 (t m+1 ) Is t m+1 First component of the tangential stiffness tensor at time, C 2233 (t m+1 ) Is t m+1 The second component of the tangential stiffness tensor at time, C 2323 (t m+1 ) Is t m+1 Third component of the tangential stiffness tensor at time, C 3333 (t m+1 ) Is t m+1 The fourth component of the tangential stiffness tensor at time, C 1133 (t m+1 ) Is t m+1 Time of dayThe fifth component of the tangential stiffness tensor, C 1313 (t m+1 ) Is t m+1 The sixth component of the tangential stiffness tensor at time, C 1111 (t m+1 ) Is t m+1 The seventh component of the tangential stiffness tensor at time, C 1122 (t m+1 ) Is t m+1 The eighth component of the tangential stiffness tensor at time, C 1212 (t m+1 ) Is t m+1 A ninth component of the tangential stiffness tensor at time;
the tangential stiffness tensor function t m+1 Of all components of the tangential stiffness tensor at the time, other components are zero except the first component to the ninth component.
Compared with the prior art, the invention has the following beneficial effects:
according to the invention, the development relation of aging and damage is respectively determined by considering aging and damage effects, so that the constructed propellant creep deformation constitutive model containing the aging damage not only can reflect the creep deformation rule of the propellant grain structure, but also can accurately calculate the damage mechanical behavior and the aging mechanical behavior of the propellant grain structure in the creep deformation stage.
According to the method, the aging increment form and the consistent tangential stiffness array are deduced by decomposing the propellant creep constitutive model containing the aging damage, the application program is obtained by programming the aging increment form and the consistent tangential stiffness array, and the application program is called by using finite element software, so that a theoretical basis and an implementation means can be provided for the fine structural integrity analysis of the remote rocket projectile charge column structure in the storage stage.
Drawings
FIG. 1 is a flow chart of a method for constructing a creep constitutive model of a propellant considering aging damage according to the present invention;
FIG. 2 is a flow chart of a finite element application method of the propellant creep constitutive model considering aging damage according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
The embodiment provides a method for constructing a creep constitutive model of a propellant considering aging damage, and with reference to fig. 1, the method comprises the following steps:
acquiring creep parameters of the propellant;
acquiring an aging parameter of the propellant;
presetting relative variation of effective bearing area;
determining an aging development equation according to the obtained aging parameters;
constructing a propellant creep constitutive model according to creep parameters;
determining a damage variable according to the relative variation of the effective bearing area, and determining a damage development equation according to the damage variable;
and establishing a propellant creep constitutive model considering aging damage according to the determined aging development equation, the damage development equation and the constructed propellant creep constitutive model.
According to the invention, the development relation of aging and damage is respectively determined by considering aging and damage effects, so that the constructed propellant creep deformation constitutive model containing the aging damage not only can reflect the creep deformation rule of the propellant grain structure, but also can accurately calculate the damage mechanical behavior and the aging mechanical behavior of the propellant grain structure in the creep deformation stage.
Example 2
On the basis of example 1, this example details the method of determining the aging development equation, the damage development equation, the propellant creep constitutive model, and the propellant creep constitutive model taking into account the aging damage.
Determining an aging development equation
Determining an aging development equation according to the obtained aging parameters, comprising the following steps:
the aging development parameter beta of the propellant is obtained by the formulas (1) to (2) c The method comprises the following steps:
wherein, T 0 For storage temperature, k B Is the Boltzmann constant and is,
aging reaction activation energy without stress strain field effect, t' aging time, h P Is the Planck constant, A is the aging reaction rate constant, upsilon m At maximum crosslink density, α c The undetermined coefficient of the chemical reaction equation,
is the initial aging development parameter of the propellant.
S12, obtaining the relative change of the crosslinking degree of the propellant through formulas (3) to (4), wherein the relative change is as follows:
wherein v () is a function of the degree of crosslinking of the propellant, T' is the aging temperature, B is a parameter of the aging development of the propellant, v 0 Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
wherein J () is a creep compliance function taking into account aging effects, J 0 () Is the creep modulus without aging, J 1 () Is the change in creep compliance caused by aging.
T is the loading time as a function of the relative change in the degree of crosslinking of the propellant.
Equation of development of lesions
The injury development equation includes equations (6) - (9), which are as follows:
wherein D is a damage variable, D 0 For initial damage of the propellant, D △V To spread the new lesions formed, sigma th The method comprises the following steps of setting a damage stress threshold value, wherein sigma is mechanical stress before propellant damage, gamma is a first parameter of propellant damage, K is a second parameter of propellant damage, beta is a third parameter of propellant damage, h () is a stress state function, and x is an input parameter of the stress state function.
(III) propellant creep constitutive model
The propellant creep deformation constitutive model comprises formulas (10) to (12), and specifically comprises the following formulas:
wherein epsilon ij For mechanical strain, J ijkl () Is a creep tensor function, xi is the conversion time of time t, xi' is the conversion time of the first integrand tau, sigma kl τ is a first integrand, T () is temperature, tt' is a second integrand, a T Is a temperature shift factor, C 1 For the first parameter of the propellant WLF equation, C 2 For the second parameter of the propellant WLF equation, T is the current temperature, T r Is the reference temperature.
(IV) propellant creep constitutive model considering aging damage
Establishing a propellant creep constitutive model considering aging damage comprises updating mechanical strain through a formula (13), which specifically comprises the following steps:
wherein the content of the first and second substances,
as a function of the effective stress tensor of the propellant after damage.
Example 3
The embodiment provides a finite element application method of a propellant creep damage constitutive model considering aging effect, and with reference to fig. 2, the method comprises the following steps:
decomposing the propellant creep damage constitutive model which is constructed in the embodiment 1 or 2 and takes the aging effect into consideration, and obtaining a partial strain tensor and a spherical strain tensor;
dispersing the partial strain tensor and the spherical strain tensor, and deducing an aging increment form of the propellant creep damage constitutive model according to the dispersed partial strain tensor and the spherical strain tensor;
deriving a consistent tangential stiffness array according to the derived aging increment form;
programming the aging increment form and the consistent tangential stiffness array to obtain a subprogram, and calling the subprogram by adopting finite element software.
According to the method, the aging increment form and the consistent tangential stiffness array are deduced by decomposing the propellant creep constitutive model containing the aging damage, the application program is obtained by programming the aging increment form and the consistent tangential stiffness array, and the application program is called by using finite element software, so that a theoretical basis and an implementation means can be provided for the fine structural integrity analysis of the remote rocket projectile charge column structure in the storage stage.
Example 4
On the basis of embodiment 3, this embodiment details a method for decomposing a propellant creep damage constitutive model considering an aging effect, a method for deriving an aging increment form of the propellant creep damage constitutive model, and a method for deriving a consistent tangential stiffness matrix.
Decomposition of propellant creep damage constitutive model considering aging effect
Decomposing a propellant creep damage constitutive model considering an aging effect to obtain a partial strain tensor and a spherical strain tensor, and comprising the following steps of:
s21 decomposes the strain tensor function into a partial strain tensor function and a spherical strain tensor function by the decomposition expression (21), which is specifically as follows:
wherein e is ij (t) is the partial strain tensor function, ε ij () As a function of the strain tensor, S ij () Is a biased stress tensor function, σ ij () As a function of the spherical stress tensor, Y 1 () As a function of the first creep of the propellant, Y 2 () As a function of the second creep of the propellant,
is a spherical strain tensor function;
in application, the spherical strain tensor is updated by the formula (211), which is specifically as follows:
wherein alpha is T Is the coefficient of thermal expansion, theta is the change in temperature, epsilon kk Is the mechanical sphere strain tensor;
when the temperature change is applied, the temperature change comprises a formula (212), which is specifically as follows:
Θ＝T-T 0 (212)
wherein T is the current temperature of the propellant, T 0 The initial temperature of the propellant.
S22, shearing the first creep function of the propellant and the second creep function of the propellant one by decomposing the formulas (22) to (24) to obtain a creep modulus function and a volume creep modulus function of the propellant creep constitutive model considering the aging damage, wherein the creep modulus function and the volume creep modulus function are as follows:
χ(t)＝2(1+ν)J(t,t′) (23)
B(t)＝3(1-2ν)J(t,t′) (24)
wherein x () is the creep modulus function of the damage-considered creep constitutive model of the propellant, and B () is the bulk creep modulus function.
S23 decomposes the polarization strain tensor function by expression (25), and decomposes the spherical strain tensor function by expression (26), as follows:
wherein, the first and the second end of the pipe are connected with each other,
as a function of the effective stress deflection tensor,
as a function of the effective stress sphere tensor.
S24, updating the bias strain tensor function and the spherical strain tensor function by the equation (14) according to the Stieltjes convolution integral definition, specifically as follows:
wherein the content of the first and second substances,
as a function of the effective stress deflection tensor,
as a function of the effective stress sphere tensor, e ij () In order to be a function of the partial strain,
is a spherical strain tensor function;
in application, the creep compliance function of the propellant comprises the formula (15), which is as follows:
wherein N is J The term for the creep compliance level,
to balance the creep compliance without considering the aging effect,
to account for the initial creep compliance of the aging effect,
to account for the nth creep compliance coefficient of aging effects,
to account for changes in equilibrium creep compliance due to aging effects,
the nth creep compliance coefficient for considering the aging effect, and t is loading time;
in application, the effective stress deflection tensor function includes the formula (16), which is as follows:
wherein S is ij () Is a biased stress tensor function;
in this embodiment, the effective stress sphere tensor function includes the following equation (17):
wherein σ kk () As a function of the spherical stress tensor.
(II) deducing aging increment form of propellant creep damage constitutive model
The aging increment form of the propellant creep damage constitutive model comprises a formula (18), and the aging increment form comprises the following specific formula:
wherein < DELTA > ∈ ij (t m+1 ) Is t m+1 Increment of the strain tensor at time, Δ e ij (t m+1 ) Is t m+1 The increment of the moment strain offset is increased,
is t m+1 Increment of the global strain tensor of time, delta ij Is a fourth kronecker symbol.
(III) deriving a consistent tangential stiffness matrix
Deriving a consistent tangential stiffness matrix from the derived incremental form of aging, comprising the steps of:
s31 simplifies the aging increment form by equations (28) to (29), specifically as follows:
wherein the content of the first and second substances,
is t m+1 The increase in time relative to the crosslink density,
is t m+1 The increment of the equivalent stress offset at that time,
is t m+1 Increment of the ball stress tensor at time, gamma 0,J () Is a function of a first intermediate variable, gamma 1,J () In order to construct the second intermediate variable function,
to construct the third intermediate variable function,
is the fourth intermediate variable function of the constitutive.
In application, the compound is obtained by the formula (30)
The method comprises the following specific steps:
wherein the content of the first and second substances,
in order to construct the fifth intermediate variable,
is the sixth intermediate variable of the structure.
Obtaining gamma by the formulae (31) to (32) 0,J The method comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,
is a seventh intermediate variable function of the constitutive model;
obtaining gamma by the formula (33) 1,J The method comprises the following steps:
obtained by the formula (34)
And
the method comprises the following specific steps:
s32, deducing a strain increment comprising the formulas (35) - (37) through a simplified aging increment form, wherein the specific expression is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is the eighth intermediate variable of the structure.
S33, deriving a consistent tangential stiffness array according to the strain increment, wherein the consistent tangential stiffness array comprises the following formulas (19) - (20):
wherein, C ijkl () Is a tangential stiffness tensor function, delta sigma ij (t m+1 ) Is t m+1 Stress increment at time,. DELTA.. Epsilon kl (t m+1 ) Is t m+1 Increment of strain tensor at time, C 2222 (t m+1 ) Is t m+1 First component of the tangential stiffness tensor at moment, C 2233 (t m+1 ) Is t m+1 The second component of the tangential stiffness tensor at time, C 2323 (t m+1 ) Is t m+1 Third component of the tangential stiffness tensor at time, C 3333 (t m+1 ) Is t m+1 The fourth component of the tangential stiffness tensor at time, C 1133 (t m+1 ) Is t m+1 The fifth component of the tangential stiffness tensor at time, C 1313 (t m+1 ) Is t m+1 The sixth component of the tangential stiffness tensor at time, C 1111 (t m+1 ) Is t m+1 The seventh component of the tangential stiffness tensor at time, C 1122 (t m+1 ) Is t m+1 The eighth component of the tangential stiffness tensor at time, C 1212 (t m+1 ) Is t m+1 A ninth component of the tangential stiffness tensor at time;
furthermore, the tangential stiffness tensor function t m+1 Of all components of the tangential stiffness tensor at the time, other components are zero except the first component to the ninth component.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the present invention has been described with reference to the particular illustrative embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but is intended to cover various modifications, equivalent arrangements, and equivalents thereof, which may be made by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A method for constructing a propellant creep constitutive model considering aging damage is characterized by comprising the following steps:
acquiring creep parameters of the propellant;
acquiring an aging parameter of the propellant;
presetting relative variation of effective bearing area;
determining an aging development equation according to the obtained aging parameters;
constructing a creep constitutive model of the propellant according to the creep parameters;
determining a damage variable according to the relative variation of the effective bearing area, and determining a damage development equation according to the damage variable;
establishing a propellant creep constitutive model considering aging damage according to the determined aging development equation, the damage development equation and the constructed propellant creep constitutive model;
the injury development equation comprises formulas (6) - (9), which are as follows:
wherein D is a damage variable, D 0 For initial damage of the propellant, D ΔV To extend the new lesions formed, σ th The method comprises the following steps of (1) setting a damage stress threshold value, wherein sigma is mechanical stress before propellant damage, gamma is a first parameter of propellant damage, K is a second parameter of propellant damage, beta is a third parameter of propellant damage, h () is a stress state function, and x is an input parameter of the stress state function;
the propellant creep deformation constitutive model comprises formulas (10) to (12), and specifically comprises the following steps:
wherein epsilon ij For mechanical strain, J ijkl () As a function of the creep tensor, ξ isThe reduced time, ξ' is the reduced time of the first integrand τ, σ kl τ is a first integrand, T () is temperature, tt' is a second integrand, a T Is a temperature shift factor, C 1 For the first parameter of the propellant WLF equation, C 2 For the second parameter of the WLF equation for the propellant, T is the current temperature, T r Is the reference temperature.
2. The method for constructing the propellant creep constitutive model considering the aging damage as claimed in claim 1, wherein the determining the aging development equation according to the obtained aging parameters comprises the following steps:
the aging development parameters of the propellant are obtained through formulas (1) to (2), and are specifically as follows:
wherein, T 0 For storage temperature, k B Is the Boltzmann constant and is,
aging reaction activation energy without stress strain field effect, t' aging time, h P Is the Planck constant, A is the aging reaction rate constant, upsilon m At maximum crosslink density, α c The undetermined coefficient of the chemical reaction equation,
for the initial ageing development parameter of the propellant, beta c Is a propellant aging development parameter;
the relative change in the degree of crosslinking of the propellant is obtained by the formulae (3) to (4), as follows:
wherein v () is a function of the degree of crosslinking of the propellant, T' is the aging temperature, B is a parameter of the aging development of the propellant, v 0 Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
wherein J () is a creep compliance function taking into account aging effects, J 0 () Is the creep modulus without aging, J 1 () For creep compliance changes due to aging,
t is the loading time as a function of the relative change in the degree of crosslinking of the propellant.
3. The method for constructing the aging damage-considered propellant creep constitutive model according to claim 2, wherein the establishing of the aging damage-considered propellant creep constitutive model comprises updating mechanical strain by a formula (13), and specifically comprises the following steps:
wherein, J ijkl () Is a function of the creep tensor, t' is the aging time, t is the loading time, tau is the first integrand,
for propellant damageThe latter effective stress tensor function.
4. A finite element application method of a propellant creep damage constitutive model considering an aging effect is characterized by comprising the following steps:
decomposing the aging effect-considered propellant creep damage constitutive model constructed according to any one of claims 1 to 3 to obtain a partial strain tensor and a spherical strain tensor;
dispersing the partial strain tensor and the spherical strain tensor, and deducing an aging increment form of the propellant creep damage constitutive model according to the dispersed partial strain tensor and the spherical strain tensor;
deriving a consistent tangential stiffness array according to the derived aging increment form;
programming the aging increment form and the consistent tangential stiffness array to obtain a subprogram, and calling the subprogram by adopting finite element software.
5. The finite element application method of the aging effect considered propellant creep damage constitutive model as claimed in claim 4, wherein the decomposing of the aging effect considered propellant creep damage constitutive model to obtain the partial strain tensor and the spherical strain tensor comprises the following formula (14):
wherein the content of the first and second substances,
as a function of the effective stress deflection tensor,
as a function of the effective stress sphere tensor, e ij () In order to be a function of the partial strain,
is the spherical strain tensor, and J () is the propellant creep complianceAs a function, ν is the propellant poisson's ratio;
the creep compliance function of the propellant comprises the formula (15), which is as follows:
wherein N is J The number of terms for the creep compliance level,
to balance the creep compliance without considering the aging effect,
to account for the initial creep compliance of the aging effect,
to account for the nth creep compliance coefficient of aging effects,
to account for the change in equilibrium creep compliance of the aging effect,
the nth creep compliance coefficient for considering aging effect; t is loading time;
the effective stress deflection tensor function comprises a formula (16), which is as follows:
wherein S is ij () Is a biased stress tensor function;
the effective stress sphere tensor function includes the following formula (17):
wherein σ kk () As a function of the ball stress tensor.
6. The finite element application method of the propellant creep damage constitutive model considering the aging effect as claimed in claim 4, wherein the aging increment form of the propellant creep damage constitutive model comprises an expression (18), and the aging increment form comprises the following specific expression:
wherein, delta epsilon ij (t m+1 ) Is t m+1 Increment of the time-of-day strain tensor, Δ e ij (t m+1 ) Is t m+1 The increment of the offset in strain at the moment,
is t m+1 Increment of the ball strain tensor at time, Δ e ij (t m ) Is t m The increment of the moment strain offset is increased,
is t m Increment of the strain tensor of the sphere at time, delta ij Is a fourth kronecker symbol.
7. The finite element application method of a propellant creep damage constitutive model considering the aging effect as claimed in claim 4, wherein the consistent tangential stiffness matrix comprises the following equations (19) - (20):
wherein, C ijkl () As a function of the tangential stiffness tensor, Δ σ ij (t m+1 ) Is t m+1 Stress increment of time, delta epsilon kl (t m+1 ) Is t m+1 Increment of the moment strain tensor, C 2222 (t m+1 ) Is t m+1 First component of the tangential stiffness tensor at moment, C 2233 (t m+1 ) Is t m+1 The second component of the tangential stiffness tensor at time, C 2323 (t m+1 ) Is t m+1 Third component of the tangential stiffness tensor at time, C 3333 (t m+1 ) Is t m+1 The fourth component of the tangential stiffness tensor at time, C 1133 (t m+1 ) Is t m+1 The fifth component of the tangential stiffness tensor at time, C 1313 (t m+1 ) Is t m+1 The sixth component of the tangential stiffness tensor at time, C 1111 (t m+1 ) Is t m+1 The seventh component of the tangential stiffness tensor at time, C 1122 (t m+1 ) Is t m+1 The eighth component of the tangential stiffness tensor at time, C 1212 (t m+1 ) Is t m+1 A ninth component of the moment tangent stiffness tensor;
the tangential stiffness tensor function t m+1 Of all components of the tangential stiffness tensor at the time, other components are zero except the first component to the ninth component.
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