CN114462146A - 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 PDF

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CN114462146A
CN114462146A CN202210107098.5A CN202210107098A CN114462146A CN 114462146 A CN114462146 A CN 114462146A CN 202210107098 A CN202210107098 A CN 202210107098A CN 114462146 A CN114462146 A CN 114462146A
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崔辉如
程子健
张冬冬
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Army Engineering University of PLA
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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: 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

Method for constructing propellant creep constitutive model considering aging damage and finite element application
Technical Field
The invention relates to a propellant creep constitutive model construction and finite element application method considering aging damage, and belongs 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. In addition to the creep and damage effects that occur during long term storage of long range rocket projectiles, the charge structure can also experience aging effects. 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 takes into account 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 fine modeling of the aging creep damage effect inside the grain structure during long-term storage, a propellant creep damage constitutive model considering the aging effect needs to be constructed urgently.
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 is realized by adopting 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 the 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:
Figure BDA0003493766460000021
Figure BDA0003493766460000022
wherein, T0For storage temperature, kBIs the Boltzmann constant and is,
Figure BDA0003493766460000023
aging reaction activation energy without stress strain field effect, t' aging time, hPIs the Planck constant, A is the aging reaction rate constant, upsilonmAt maximum crosslink density, αcThe undetermined coefficient of the chemical reaction equation,
Figure BDA0003493766460000024
for the initial ageing development parameter of the propellant, betacIs 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:
Figure BDA0003493766460000025
Figure BDA0003493766460000026
wherein v () is the function of the variation of the crosslinking degree of the propellant, T' is the aging temperature, B is the aging development parameter of the propellant, v0Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
Figure BDA0003493766460000027
wherein J () is a creep compliance function taking into account aging effects, J0() Is the creep modulus without aging, J1() Is the creep compliance change caused by aging.
Figure BDA0003493766460000028
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:
Figure BDA0003493766460000029
Figure BDA00034937664600000210
Figure BDA00034937664600000211
Figure BDA0003493766460000031
wherein D is a damage variable, D0For initial damage of the propellant, D△VTo extend the new lesions formed, σthThe 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 deformation constitutive model comprises formulas (10) to (12), and specifically the following formulas:
Figure BDA0003493766460000032
Figure BDA0003493766460000033
Figure BDA0003493766460000034
wherein epsilonijFor mechanical strain, Jijkl() Is a creep tensor function, xi is the conversion time of time t, xi' is the conversion time of the first integrand tau, sigmaklτ is a first integrand function, T is a loading time, T () is a temperature, tt' is a second integrand function, aTIs a temperature shift factor, C1For the first parameter of the propellant WLF equation, C2For the second parameter of the WLF equation for the propellant, T is the current temperature, TrIs 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), specifically as follows:
Figure BDA0003493766460000035
wherein,
Figure BDA0003493766460000036
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:
Figure BDA0003493766460000041
wherein,
Figure BDA0003493766460000042
as a function of the effective stress deflection tensor,
Figure BDA0003493766460000043
as a function of the effective stress sphere tensor, eij() In order to be a function of the partial strain,
Figure BDA0003493766460000044
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:
Figure BDA0003493766460000045
wherein N isJThe number of terms for the creep compliance level,
Figure BDA0003493766460000046
to balance the creep compliance without considering the aging effect,
Figure BDA0003493766460000047
to account for the initial creep compliance of the aging effect,
Figure BDA0003493766460000048
to account for the nth creep compliance coefficient of aging effects,
Figure BDA0003493766460000049
to account for the change in equilibrium creep compliance of the aging effect,
Figure BDA00034937664600000410
in order to consider the nth creep compliance coefficient of the aging effect, t is loading time;
the effective stress deflection tensor function comprises a formula (16), which is as follows:
Figure BDA00034937664600000411
wherein S isij() Is a biased stress tensor function;
the effective stress sphere tensor function includes the following formula (17):
Figure BDA00034937664600000412
wherein σkk() As a function of the spherical 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:
Figure BDA00034937664600000413
wherein < DELTA > ∈ij(tm+1) Is tm+1Increment of the strain tensor at time, Δ eij(tm+1) Is tm+1The increment of the offset in strain at the moment,
Figure BDA00034937664600000414
is tm+1Increment of the global strain tensor of time, deltaijIs a fourth kronecker symbol.
Further, the consistent tangential stiffness array comprises formulas (19) - (20), which are as follows:
Figure BDA0003493766460000051
Figure BDA0003493766460000052
wherein, Cijkl() Is a tangential stiffness tensor function, Delta sigmaij(tm+1) Is tm+1Stress increment at time,. DELTA.. epsilonkl(tm+1) Is tm+1Increment of the moment strain tensor, C2222(tm+1) Is tm+1First component of the tangential stiffness tensor at time, C2233(tm+1) Is tm+1The second component of the tangential stiffness tensor at time, C2323(tm+1) Is tm+1Third component of the tangential stiffness tensor at time, C3333(tm+1) Is tm+1The fourth component of the tangential stiffness tensor at time, C1133(tm+1) Is tm+1The fifth component of the tangential stiffness tensor at time, C1313(tm+1) Is tm+1The sixth component of the tangential stiffness tensor at time, C1111(tm+1) Is tm+1The seventh component of the tangential stiffness tensor at time, C1122(tm+1) Is tm+1The eighth component of the tangential stiffness tensor at time, C1212(tm+1) Is tm+1A ninth component of the tangential stiffness tensor at time;
the tangential stiffness tensor function tm+1Of 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.
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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 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 the 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 evolution 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)cThe method comprises the following steps:
Figure BDA0003493766460000061
Figure BDA0003493766460000062
wherein, T0For storage temperature, kBIs the Boltzmann constant and is,
Figure BDA0003493766460000063
aging reaction activation energy without stress strain field effect, t' aging time, hPIs the Planck constant, A is the aging reaction rate constant, upsilonmAt maximum crosslink density, αcThe undetermined coefficient of the chemical reaction equation,
Figure BDA0003493766460000064
is the initial aging development parameter of the propellant.
S12 the relative change of the propellant crosslinking degree is obtained through formulas (3) to (4), and the relative change is as follows:
Figure BDA0003493766460000065
Figure BDA0003493766460000071
wherein v () is the function of the variation of the crosslinking degree of the propellant, T' is the aging temperature, B is the aging development parameter of the propellant, v0Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
Figure BDA0003493766460000072
wherein J () is a creep compliance function taking into account aging effects, J0() Is the creep modulus without aging, J1() Is the creep compliance change caused by aging.
Figure BDA0003493766460000073
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), as follows:
Figure BDA0003493766460000074
Figure BDA0003493766460000075
Figure BDA0003493766460000076
Figure BDA0003493766460000077
wherein D is a damage variable, D0For initial damage of the propellant, D△VTo extend the new lesions formed, σthThe 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:
Figure BDA0003493766460000078
Figure BDA0003493766460000079
Figure BDA00034937664600000710
wherein epsilonijIs a mechanical reactionChange, Jijkl() Is a creep tensor function, xi is the conversion time of time t, xi' is the conversion time of the first integrand tau, sigmaklτ is a first integrand, T () is temperature, tt' is a second integrand, aTIs a temperature shift factor, C1For the first parameter of the propellant WLF equation, C2For the second parameter of the WLF equation for the propellant, T is the current temperature, TrIs the reference temperature.
(IV) propellant creep constitutive model considering aging damage
Establishing a propellant creep constitutive model considering the aging damage comprises updating the mechanical strain by a formula (13), which is as follows:
Figure BDA0003493766460000081
wherein,
Figure BDA0003493766460000082
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, the present embodiment describes in detail 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, 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:
Figure BDA0003493766460000091
wherein e isij(t) is a function of the polarization strain tensor,. epsilonij() As a function of the strain tensor, Sij() Is a biased stress tensor function, σij() As a function of the spherical stress tensor, Y1() As a function of the first creep of the propellant, Y2() As a function of the second creep of the propellant,
Figure BDA0003493766460000092
is a spherical strain tensor function;
in application, the spherical strain tensor is updated by the formula (211), which is specifically as follows:
Figure BDA0003493766460000093
wherein alpha isTCoefficient of thermal expansionTheta is the change in temperature, epsilonkkIs the mechanical sphere strain tensor;
when the temperature-sensitive adhesive is applied, the temperature change comprises a formula (212), and the specific formula is as follows:
Θ＝T-T0 (212)
wherein T is the current temperature of the propellant, T0The 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:
Figure BDA0003493766460000094
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 is a method of decomposing the bias strain tensor function by equation (25) and the spherical strain tensor function by equation (26), as follows:
Figure BDA0003493766460000095
Figure BDA0003493766460000096
wherein,
Figure BDA0003493766460000097
as a function of the effective stress deflection tensor,
Figure BDA0003493766460000098
as a function of the effective stress sphere tensor.
S24 updates the bias strain tensor function and the spherical strain tensor function by the equation (14) according to the Stieltjes convolution integral definition, as follows:
Figure BDA0003493766460000101
wherein,
Figure BDA0003493766460000102
as a function of the effective stress deflection tensor,
Figure BDA0003493766460000103
as a function of the effective stress sphere tensor, eij() In order to be a function of the partial strain,
Figure BDA0003493766460000104
is a spherical strain tensor function;
in application, the creep compliance function of the propellant comprises the formula (15), which is as follows:
Figure BDA0003493766460000105
wherein N isJThe number of terms for the creep compliance level,
Figure BDA0003493766460000106
to balance the creep compliance without considering the aging effect,
Figure BDA0003493766460000107
to account for the initial creep compliance of the aging effect,
Figure BDA0003493766460000108
to account for the nth creep compliance coefficient of aging effects,
Figure BDA0003493766460000109
to account for the change in equilibrium creep compliance of the aging effect,
Figure BDA00034937664600001010
in order to consider the nth creep compliance coefficient of the aging effect, t is loading time;
in application, the effective stress deflection tensor function includes the formula (16), which is as follows:
Figure BDA00034937664600001011
wherein S isij() Is a biased stress tensor function;
in this embodiment, the effective stress sphere tensor function includes the following equation (17):
Figure BDA00034937664600001012
wherein σkk() 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:
Figure BDA00034937664600001013
wherein < DELTA > ∈ij(tm+1) Is tm+1Increment of the strain tensor at time, Δ eij(tm+1) Is tm+1The increment of the offset in strain at the moment,
Figure BDA00034937664600001014
is tm+1Increment of the global strain tensor of time, deltaijIs 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) - (29), as follows:
Figure BDA0003493766460000111
Figure BDA0003493766460000112
wherein,
Figure BDA0003493766460000113
is tm+1The increase in time relative to the crosslink density,
Figure BDA0003493766460000114
is tm+1The increment of the equivalent stress offset at that time,
Figure BDA0003493766460000115
is tm+1Increment of the ball stress tensor at time, gamma0,J() Is a function of a first intermediate variable, gamma1,J() In order to construct the second intermediate variable function,
Figure BDA0003493766460000116
to construct the third intermediate variable function,
Figure BDA0003493766460000117
is the fourth intermediate variable function of the constitutive.
In application, the compound is obtained by the formula (30)
Figure BDA0003493766460000118
The method comprises the following specific steps:
Figure BDA0003493766460000119
wherein,
Figure BDA00034937664600001110
in the fifth middle of the structureThe variables are the variables of the process,
Figure BDA00034937664600001111
is the sixth intermediate variable of the structure.
Obtaining gamma by the formulae (31) to (32)0,JThe method comprises the following steps:
Figure BDA00034937664600001112
Figure BDA00034937664600001113
wherein,
Figure BDA00034937664600001114
is a seventh intermediate variable function of the constitutive model;
obtaining gamma by the formula (33)1,JThe method comprises the following steps:
Figure BDA00034937664600001115
obtained by the formula (34)
Figure BDA00034937664600001116
And
Figure BDA00034937664600001117
the method comprises the following specific steps:
Figure BDA00034937664600001118
s32 deduces and knows the strain increment through a simplified aging increment form, wherein the strain increment comprises the following formulas (35) - (37):
Figure BDA0003493766460000121
Figure BDA0003493766460000122
Figure BDA0003493766460000123
wherein,
Figure BDA0003493766460000124
is the eighth intermediate variable of the structure.
S33, deriving a consistent tangential stiffness matrix according to the strain increment, wherein the consistent tangential stiffness matrix comprises the following formulas (19) - (20):
Figure BDA0003493766460000125
Figure BDA0003493766460000126
wherein, Cijkl() Is a tangential stiffness tensor function, Delta sigmaij(tm+1) Is tm+1Stress increment at time,. DELTA.. epsilonkl(tm+1) Is tm+1Increment of the moment strain tensor, C2222(tm+1) Is tm+1First component of the tangential stiffness tensor at time, C2233(tm+1) Is tm+1The second component of the tangential stiffness tensor at time, C2323(tm+1) Is tm+1Third component of the tangential stiffness tensor at moment, C3333(tm+1) Is tm+1The fourth component of the tangential stiffness tensor at time, C1133(tm+1) Is tm+1The fifth component of the tangential stiffness tensor at time, C1313(tm+1) Is tm+1The sixth component of the tangential stiffness tensor at time, C1111(tm+1) Is tm+1The seventh component of the tangential stiffness tensor at time, C1122(tm+1) Is tm+1Eighth of the moment tangential stiffness tensorComponent, C1212(tm+1) Is tm+1A ninth component of the tangential stiffness tensor at time;
furthermore, the tangential stiffness tensor function tm+1Of 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 the like) 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 embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (9)

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;
and establishing a propellant creep constitutive model considering the aging damage according to the determined aging development equation, the damage development equation and the constructed propellant creep constitutive model.
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:
Figure FDA0003493766450000011
Figure FDA0003493766450000012
wherein, T0For storage temperature, kBIs the Boltzmann constant and is,
Figure FDA0003493766450000013
aging reaction activation energy without stress strain field effect, t' aging time, hPIs a Planck constant, A is an aging reaction rate constant, upsilonmAt maximum crosslink density, αcThe undetermined coefficient of the chemical reaction equation,
Figure FDA0003493766450000014
for the initial ageing development parameter of the propellant, betacIs 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:
Figure FDA0003493766450000015
Figure FDA0003493766450000016
wherein v () is the function of the variation of the crosslinking degree of the propellant, T' is the aging temperature, B is the aging development parameter of the propellant, v0Is the initial crosslink density;
the aging development equation is determined by the formula (5), which is as follows:
Figure FDA0003493766450000017
wherein J () is a creep compliance function taking into account aging effects, J0() Is the creep modulus without aging, J1() For creep compliance changes due to aging,
Figure FDA0003493766450000018
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 propellant creep constitutive model considering the aging damage according to claim 2, wherein the damage development equation comprises the following equations (6) to (9):
Figure FDA0003493766450000021
Figure FDA0003493766450000022
Figure FDA0003493766450000023
Figure FDA0003493766450000024
wherein D is a damage variable, D0For initial damage of the propellant, D△VTo extend the new lesions formed, σthThe 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.
4. The method for constructing the propellant creep constitutive model considering the aging damage as claimed in claim 3, wherein the propellant creep constitutive model comprises formulas (10) to (12), and specifically comprises the following formulas:
Figure FDA0003493766450000025
Figure FDA0003493766450000026
Figure FDA0003493766450000027
wherein epsilonijFor mechanical strain, Jijkl() Is a creep tensor function, xi is the conversion time of time t, xi' is the conversion time of the first integrand tau, sigmaklτ is a first integrand, T () is temperature, tt' is a second integrand, aTIs a temperature shift factor, C1For the first parameter of the propellant WLF equation, C2For the second parameter of the WLF equation for the propellant, T is the current temperature, TrIs the reference temperature.
5. The method for constructing the aging damage-considered propellant creep constitutive model as claimed in claim 4, wherein the establishing the aging damage-considered propellant creep constitutive model comprises updating the mechanical strain by a formula (13), and specifically comprises the following steps:
Figure FDA0003493766450000031
wherein,
Figure FDA0003493766450000032
is effective stress after damage of propellantA tensor function.
6. 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 5 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.
7. The finite element application method of the aging effect considered propellant creep damage constitutive model as claimed in claim 6, 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):
Figure FDA0003493766450000033
wherein,
Figure FDA0003493766450000034
as a function of the effective stress deflection tensor,
Figure FDA0003493766450000035
as a function of the effective stress sphere tensor, eij() In order to be a function of the partial strain,
Figure FDA0003493766450000036
is the spherical strain tensor, J () is the propellant creep compliance function, v is the pushThe feed poisson ratio;
the creep compliance function of the propellant comprises the formula (15), which is as follows:
Figure FDA0003493766450000037
wherein N isJThe number of terms for the creep compliance level,
Figure FDA0003493766450000038
to balance the creep compliance without considering the aging effect,
Figure FDA0003493766450000039
to account for the initial creep compliance without considering aging effects,
Figure FDA00034937664500000310
to account for the nth creep compliance coefficient of aging effects,
Figure FDA00034937664500000311
to account for the change in equilibrium creep compliance of the aging effect,
Figure FDA00034937664500000312
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:
Figure FDA00034937664500000313
wherein S isij() Is a biased stress tensor function;
the effective stress sphere tensor function includes the following formula (17):
Figure FDA0003493766450000041
wherein σkk() As a function of the spherical stress tensor.
8. The finite element application method of the propellant creep damage constitutive model considering the aging effect as claimed in claim 6, wherein the aging increment form of the propellant creep damage constitutive model comprises an expression (18), and the following is concrete:
Figure FDA0003493766450000042
wherein < DELTA > ∈ij(tm+1) Is tm+1Increment of the strain tensor at time, Δ eij(tm+1) Is tm+1The increment of the offset in strain at the moment,
Figure FDA0003493766450000043
is tm+1Increment of the ball strain tensor at time, Δ eij(tm) Is tmThe increment of the offset in strain at the moment,
Figure FDA0003493766450000044
is tmIncrement of the global strain tensor of time, deltaijIs a fourth kronecker symbol.
9. The finite element application method of a propellant creep damage constitutive model considering the aging effect as claimed in claim 6, wherein the consistent tangential stiffness matrix comprises the following equations (19) - (20):
Figure FDA0003493766450000045
Figure FDA0003493766450000046
wherein, Cijkl() Is a tangential stiffness tensor function, Delta sigmaij(tm+1) Is tm+1Stress increment at time,. DELTA.. epsilonkl(tm+1) Is tm+1Increment of the moment strain tensor, C2222(tm+1) Is tm+1First component of the tangential stiffness tensor at moment, C2233(tm+1) Is tm+1The second component of the tangential stiffness tensor at time, C2323(tm+1) Is tm+1Third component of the tangential stiffness tensor at time, C3333(tm+1) Is tm+1The fourth component of the tangential stiffness tensor at time, C1133(tm+1) Is tm+1The fifth component of the tangential stiffness tensor at time, C1313(tm+1) Is tm+1The sixth component of the tangential stiffness tensor at time, C1111(tm+1) Is tm+1The seventh component of the tangential stiffness tensor at time, C1122(tm+1) Is tm+1The eighth component of the tangential stiffness tensor at time, C1212(tm+1) Is tm+1A ninth component of the moment tangent stiffness tensor;
the tangential stiffness tensor function tm+1Of 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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