CN115270479A - Theoretical calculation method for tensile property of composite propellant - Google Patents
Theoretical calculation method for tensile property of composite propellant Download PDFInfo
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Abstract
The invention discloses a theoretical calculation method for tensile property of a composite propellant, which comprises the following steps: s1: measuring the specific surface area S and the surface area average particle size D of the filling particles by using a particle size spectrometer; s2: inquiring the empirical binding coefficient B and the particle density of the particles on the surface of the matrix, and performing a tensile experiment on the matrix according to an experimental formula to obtain the maximum tensile strength of the matrix; s3: substituting the formula of the established empirical composite material, and calculating the maximum tensile strength of the composite material containing the particles. The invention adopts a theoretical calculation method, thereby shortening the total test time, reducing the test amount, reducing the cost of manpower and material resources, solving the problems of long test time consumption, large test amount and large consumption of manpower and material resources in the prior art, and guiding the prediction test by comparing the maximum tensile strength and the maximum elongation calculated by theory with the test.
Description
Technical Field
The invention relates to the technical field of composite solid propellants, in particular to a theoretical calculation method for the maximum tensile strength of a composite solid propellant.
Background
The composite solid propellant is a composite material which takes a binder as a matrix and is filled with an energetic solid filler, and the mechanical property of the solid propellant is one of the most important physical properties of the propellant, which means that the propellant is subjected to various exotic response characteristics. Similar to other materials, these response characteristics are typically described in terms of modulus, strength, deformation, poisson's ratio, etc. parameters that occur when a load is applied. In the design of the charge, parameters related to the failure process, such as yield stress and elongation, breaking strength and elongation, are also used for description.
The application of the breaking strength of the composite material is successfully the theoretical prediction of the tensile strength and the maximum tensile rate of the fiber-filled composite material and the short fiber rubber composite material, and indicates that the strength of the composite material depends on the strength of a matrix, the volume of a filler, the particle size, the bonding strength of an adhesive and particles and the like.
As mentioned above, the factors influencing the mechanical properties of the composite energy-containing solid propellant are very complex, the tensile strength of the composite propellant is mainly determined by tests at present, few reports about the theoretical calculation method of the tensile strength and the maximum elongation of the composite solid propellant at home and abroad are reported at present, generally, after the formula is determined, a large number of repeated tests are needed to stretch the composite material, a large amount of manpower and material resources are needed, in addition, the test period is long, a large amount of 6-8 days are needed for one round of test, the test result can have certain fluctuation, and the test accuracy is influenced by a plurality of factors such as the test times, the charge process and the like.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a theoretical calculation method for tensile property of a composite propellant.
In order to achieve the purpose, the invention adopts the following technical scheme:
a theoretical calculation method for tensile property of a composite propellant comprises the following steps:
s1: determining the specific surface area S, the surface area average particle diameter D and the volume fraction phi f of the filling particles by using a particle size spectrometer;
s2: inquiring the empirical binding coefficient B of the particles on the surface of the substrate and the particle density phi ρ Carrying out a tensile test on the substrate according to the test formula to obtain the maximum tensile strength of the substrate;
s3: substituting the established empirical formula of the composite material, and calculating the maximum tensile strength of the composite material containing the particles;
s4: introducing the related viscoelastic performance of each phase in three-phase viscoelasticity, establishing a three-phase viscoelasticity model, and performing stress-strain analysis on the model;
s5: the maximum tensile strength is obtained by calculation through the correlation of the time of the maximum tensile strength and the time of the maximum elongation, and the maximum elongation epsilon is obtained by solving the maximum tensile strength yc And finishing the calculation.
Further, for the step S3, the specific calculation method is as follows:
further, the specific manner of stress-strain analysis used in step S4 is as follows: sigma 1 ＝E 3 ε 2 ；
σ＝σ 1 +σ 2 ＝ε 1 E 1 ；
ε＝ε 1 +ε 2 +ε 3 ；
Wherein E is 1 : particle phase elastic modulus;
E 3 : adhesive matrix elastic modulus;
η 2 : middle sticky tapeThe viscosity coefficient of the mixture;
η 3 : adhesive matrix adhesive viscosity coefficient;
ε 1 : the phase change experienced by the particle phase;
ε 2 : the phase change experienced by the mesophase;
ε 3 : the phase change suffered by the matrix phase;
σ 1 : the base spring portion is strained;
σ 2 : stress on the pot-sticking part of the substrate;
σ＝σ 1 +σ 2 : the stress to which the whole is subjected;
ε＝ε 1 +ε 2 +ε 3 : the strain experienced overall.
Further, step S5 specifically includes the following steps:
s501: on the basis of the step S4, canceling the constitutive equations of epsilon 1, epsilon 2 and epsilon 3 to obtain the following formulas:
and eliminating epsilon 1, epsilon 2 and epsilon 3 to obtain a Burgers model constitutive equation:
wherein:
ε＝C*t；
wherein: t =0, e =0, σ =0
Then, solving for:
in the formula, s is a transformation parameter;
Subjecting the formula (2) to inverse Laplace transform, and finishing to obtain a stretching speed v 0 The tensile stress σ (t) at direct drawing over time t is:
s502: maximum tensile strength to be solved, and E 1 ,E 3 ,η 2 ,η 3 In the calculation mode of the formula (1), solving to obtain the maximum elongation rate epsilon yc 。
Compared with the prior art, the invention has the beneficial effects that:
the invention adopts a theoretical calculation method, thereby shortening the total test time, reducing the test amount, reducing the cost of manpower and material resources, and solving the problems of long test time consumption, large test amount and large consumption of manpower and material resources in the prior art;
dividing the composite into a matrix phase, an interface phase, and a particle phase, thereby calculating tensile properties;
the tensile strength of the steel is calculated by combining a compound empirical formula with test data
Solving the maximum stretching rate through the built burger constitutive model;
the maximum tensile strength and the maximum elongation are calculated theoretically and compared with the test, so that the prediction test is guided.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
FIG. 1 is a viscoelastic constitutive model diagram of a theoretical calculation method for tensile property of a composite propellant, which is provided by the invention;
FIG. 2 is a three-phase tensile strength schematic diagram of a theoretical calculation method for tensile properties of a composite propellant.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Referring to fig. 1-2, the theoretical calculation method of the tensile property of the composite propellant comprises the following steps:
s1: determining the specific surface area S, the surface area average particle diameter D and the volume fraction phi f of the filling particles by using a particle size spectrometer;
s2: inquiring the empirical binding coefficient B of the particles on the surface of the substrate and the particle density phi ρ Carrying out a tensile test on the substrate according to the test formula to obtain the maximum tensile strength of the substrate;
s3: substituting the formula of the established empirical composite material, and calculating the maximum tensile strength of the composite material containing the particles;
the specific calculation method is as follows:
s4: introducing the related viscoelastic performance of each phase in three-phase viscoelasticity, establishing a three-phase viscoelasticity model, and performing stress-strain analysis on the model;
specifically, the stress-strain analysis is performed in the following manner: sigma 1 ＝E 3 ε 2 ；
σ＝σ 1 +σ 2 ＝ε 1 E 1 ；
ε＝ε 1 +ε 2 +ε 3 ；
Wherein E is 1 : particle phase elastic modulus;
E 3 : adhesive matrix elastic modulus;
η 2 : an intermediate adhesive viscosity coefficient;
η 3 : adhesive matrix adhesive viscosity coefficient;
ε 1 : the phase change experienced by the particle phase;
ε 2 : the phase change experienced by the mesophase;
ε 3 : the phase change suffered by the matrix phase;
σ 1 : the base spring portion is strained;
σ 2 : stress on the part of the substrate stuck to the pot;
σ＝σ 1 +σ 2 : the overall stress experienced;
ε＝ε 1 +ε 2 +ε 3 : the strain experienced by the population;
s5: the maximum tensile strength is obtained by calculation through the correlation of the time of the maximum tensile strength and the time of the maximum elongation, and the maximum elongation epsilon is obtained by solving the maximum tensile strength yc And completing the calculation.
The step S5 specifically includes the following steps:
s501: on the basis of the step S4, eliminating the constitutive equations of epsilon 1, epsilon 2 and epsilon 3 to obtain the following formulas:
and eliminating epsilon 1, epsilon 2 and epsilon 3 to obtain a Burgers model constitutive equation:
wherein:
ε＝C*t；
wherein: t =0, e =0, σ =0
Then, solving, according to the boundary conditions:
in the formula, s is a transformation parameter;
Subjecting the formula (2) to inverse Laplace transform, and finishing to obtain a stretching speed v 0 The tensile stress σ (t) at the time of direct drawing with time t is:
s502: maximum tensile strength to be solved, and E 1 ,E 3 ,η 2 ,η 3 In the calculation mode of the formula (1), the maximum elongation epsilon is obtained by solving yc 。
In order to better understand the technical solution of the present invention, the following description is further explained with reference to data and drawings.
Preferred embodiments of the same invention
The formulation (mass fraction) of the composite propellant table is shown in table 1.
TABLE 1
A theoretical calculation method for tensile property of a composite propellant comprises the following steps:
the method comprises the following steps: determining the specific surface area S, the surface area average particle diameter D and the volume fraction phi f of the filling particles by using a particle size spectrometer;
wherein, the physical signs of the granules are shown in Table 2.
| Name of particle | Specific surface area S (m) 2 /g) | Surface area average particle diameter D (. Mu.m) |
| AP (100-140 mesh) | 2.3 | 64.184 |
| AL powder (13 μm) | 345.6 | 11.9 |
TABLE 2
Step two: inquiring the empirical binding coefficient B of the particles on the surface of the substrate and the particle density phi ρ According to the experimental formula, carrying out a tensile experiment on the matrix to obtain the maximum tensile strength of the matrix;
the particle interfacial properties are shown in Table 3.
TABLE 3
Step three: substituting the formula of the established empirical composite material, and calculating the maximum tensile strength of the composite material containing the particles, wherein m is 0.67;
the specific calculation method is as follows:
as shown in fig. 1, step four: establishing three-phase viscoelasticity, and carrying out stress-strain analysis on the model;
specifically, the stress-strain analysis is performed in the following manner: sigma 1 ＝E 3 ε 2 ；
σ＝σ 1 +σ 2 ＝ε 1 E 1 ；
ε＝ε 1 +ε 2 +ε 3 ；
Wherein E is 1 : particle phase elastic modulus;
E 3 : adhesive matrix elastic modulus;
η 2 : an intermediate adhesive viscosity coefficient;
η 3 : adhesive matrix adhesive viscosity coefficient;
ε 1 : the phase change experienced by the particle phase;
ε 2 : the phase change experienced by the mesophase;
ε 3 : the phase change suffered by the matrix phase;
σ 1 : the base spring portion is strained;
σ 2 : stress on the part of the substrate stuck to the pot;
σ＝σ 1 +σ 2 : the overall stress experienced;
ε＝ε 1 +ε 2 +ε 3 : the strain experienced overall.
Step five: on the basis of the fourth step, eliminating the constitutive equation of epsilon 1, epsilon 2 and epsilon 3 to obtain the following formula:
elimination of epsilon 1 ,ε 2 And ε 3 Get the constitutive equation of Burgers model
Wherein the content of the first and second substances,
ε＝C*t；
where t =0, e =0, σ =0,
the original equation can be solved according to the boundary conditions
In the formula, s is a transformation parameter;
is the laplace transform of stress. Subjecting the formula (2) to inverse Laplace transform, and finishing to obtain a stretching speed v 0 The tensile stress sigma (t) in direct drawing is in relation to the time t
α＝(p1+sqrt(p1^2-4p2))/2*p2；
β＝(p1-sqrt(p1^2-4p2)/2*p2。
Step six: the maximum tensile strength solved for in the third step, and E 1 ,E 3 ,η 2 ,η 3 Substituting the formula (1), solving the equation to obtain the maximum elongation epsilon yc And finishing the calculation.
Wherein, the theoretical calculation is compared with the experiment, and the specific result is shown in the table 4.
TABLE 4
Compared with the experimental data, the error is in a small range, the calculation result can predict the test, the number of times of the test is minimized, the test efficiency is improved, unnecessary non-technical cost is avoided, powerful guidance and reference are provided for the current composite material tensile test, and a theoretical calculation method is adopted, so that the total test time is shortened, the test amount is reduced, the labor and material cost is reduced, and the problems of long test time consumption, large test amount and large consumption of manpower and material resources in the prior art are solved;
the maximum tensile strength and the maximum elongation are calculated by theory and compared with the test, thereby guiding the prediction test.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
Claims (4)
1. A theoretical calculation method for tensile property of a composite propellant is characterized by comprising the following steps:
s1: measuring the specific surface area S and the surface area average particle size D of the filling particles by using a particle size spectrometer;
s2: inquiring the empirical binding coefficient B of the particles on the surface of the substrate and the particle density phi ρ According to the experimental formula, carrying out a tensile experiment on the matrix to obtain the maximum tensile strength of the matrix;
s3: substituting the established empirical formula of the composite material, and calculating the maximum tensile strength of the composite material containing the particles;
s4: introducing the related viscoelastic performance of each phase in three-phase viscoelasticity, establishing a three-phase viscoelasticity model, and performing stress-strain analysis on the model;
s5: the maximum tensile strength is obtained by calculation through the correlation of the time of the maximum tensile strength and the time of the maximum elongation, and the maximum elongation epsilon is obtained by solving the maximum tensile strength yc And finishing the calculation.
2. The theoretical calculation method for tensile property of composite propellant according to claim 1 is used in step S3, and the specific calculation method is as follows:
3. the theoretical calculation method for tensile property of composite propellant according to claim 2, wherein the stress-strain analysis in step S4 is performed in the following manner:
σ 1 ＝E 3 ε 2 ；
σ＝σ 1 +σ 2 ＝ε 1 E 1 ；
9＝ε 1 +9 2 +9 3 ；
wherein E is 1 : particle phase elastic modulus;
E 3 : adhesive matrix elastic modulus;
η 2 : an intermediate adhesive viscosity coefficient;
η 3 : adhesive matrix adhesive viscosity coefficient;
ε 1 : the phase change experienced by the particle phase;
ε 2 : the phase change experienced by the mesophase;
ε 3 : the phase change suffered by the matrix phase;
σ 1 : the base spring portion is strained;
σ 2 : stress on the part of the substrate stuck to the pot;
σ＝σ 1 +σ 2 : the overall stress experienced;
ε＝ε 1 +ε 2 +ε 3 : the overall strain experienced.
4. The theoretical calculation method for tensile property of composite propellant according to claim 3, wherein the step S5 further comprises the following steps:
s501: on the basis of the step S4, canceling the constitutive equations of epsilon 1, epsilon 2 and epsilon 3 to obtain the following formulas:
and eliminating epsilon 1, epsilon 2 and epsilon 3 to obtain a Burgers model constitutive equation:
wherein:
ε＝C*t；
wherein: t =0, e =0, σ =0
Then, solving for:
in the formula, s is a transformation parameter;
Inverse Laplace transformation of formula (2)Alternatively, it is finished to a drawing rate v 0 The tensile stress σ (t) at the time of direct drawing with time t is:
s502: maximum tensile strength to be solved, and E 1 ,E 3 ,η 2 ,η 3 In the calculation mode of the formula (1), solving to obtain the maximum elongation rate epsilon yc 。
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| CN115906316A (en) * | 2022-11-21 | 2023-04-04 | 江苏科技大学 | Core-shell carrier design and preparation method without negative mechanical influence on matrix |
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| CN115906316A (en) * | 2022-11-21 | 2023-04-04 | 江苏科技大学 | Core-shell carrier design and preparation method without negative mechanical influence on matrix |
| CN115906316B (en) * | 2022-11-21 | 2023-09-22 | 江苏科技大学 | Design and preparation method of core-shell carrier without negative mechanical influence on matrix |
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