Method and system for predicting damage-containing viscoelastic poisson's ratio of particle reinforced polymer

Abstract

The application discloses a kind of particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method and system.The method first obtains the damage parameter of high solid content polymer creep process, determines the damage evolution model of creep process;Damage decoupling is then carried out, the linear creep process of high solid content polymer is obtained, and the creep compliance time domain variation data of linear creep process is obtained;Then, the relaxation modulus is inverted based on the creep compliance of linear creep process;Finally, based on the determined damage evolution model and relaxation modulus, the viscoelastic Poisson's ratio time domain variation model considering damage is established to predict the damage-containing viscoelastic Poisson's ratio.The application can simultaneously obtain the damage-containing viscoelastic Poisson's ratio, undamaged creep response and relaxation modulus by only needing creep test data, which greatly reduces the test cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of material mechanical property characterization, and particularly relates to a particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method and system. BACKGROUND

[0002] Particle-reinforced polymer is a kind of multiphase composite material taking polymer as a matrix and rigid particles as a reinforcing phase. It realizes performance complementation and synergistic effect by combining two or more materials with different properties together, thereby obtaining excellent comprehensive performance that single polymer does not have, and meeting various harsh engineering application requirements. The Poisson's ratio of solid propellant as a typical polymer-based particle-reinforced viscoelastic composite material has a decisive influence on the structural integrity of the grain of a solid rocket engine. During the ignition and pressure building process of the engine, the grain is in a three-way compression state, and a relative change of 1% in the Poisson's ratio of the propellant can cause a change of more than 10% in the stress and strain response of the grain; when the Poisson's ratio changes from the incompressible state (≈0.5) to the compressible state (<0.5), the structural analysis error will be further significantly magnified. At the mesoscopic level, damage evolution (such as pore growth and interface debonding) has a strong coupling relationship with the Poisson's ratio, and directly affects the volume expansion behavior and long-term mechanical properties of the material.

[0003] Some existing technologies derive the mutual integral equation relationship of the tensile relaxation modulus K(t), the volume relaxation modulus (t) and the viscoelastic Poisson's ratio v(t) and the numerical integral algorithm for solving v(t). The research results show that the viscoelastic Poisson's ratio v(t) increases in the direction of 1 / 2 as the temperature increases or the load action time increases, and decreases in the direction of 1 / 3 as the temperature decreases or the load action time decreases. In addition, some existing technologies study the viscoelastic Poisson's ratio of high-filled composite propellant (Ф>0.6) by theoretical derivation, and find that the initial viscoelastic Poisson's ratio (0.01~10s) of the composite solid propellant may be less than 0.4, and the viscoelastic Poisson's ratio will develop to more than 0.45 only when the load time is long enough and no damage occurs.

[0004] In addition, some existing technologies study the influence of loading rate on the Poisson's ratio of solid propellant by using the digital image correlation method, and the research results show that the initial Poisson's ratio is larger as the temperature increases and the loading rate increases, and the Poisson's ratio is larger as the initial strain is larger in the relaxation test. However, the test results are all carried out under a small strain of 6%, and the influence of damage on the Poisson's ratio under large strain is not considered. The test results of the linear viscoelastic Poisson's ratio of the composite solid propellant show that the viscoelastic Poisson's ratio of the solid propellant increases with time and approaches 0.5.

[0005] The above research meets the theory that the viscoelastic Poisson's ratio of incompressible material gradually tends to 0.5 with the increase of load time. Although the above method promotes the characterization of viscoelastic Poisson's ratio, there is still a fundamental defect. Since the composite solid propellant is a polymer-based particle reinforced composite material, during the long time of loading, with the continuous increase of strain, damage behavior such as pore will inevitably occur in the material, and the propellant will also be converted from incompressible material to compressible material. Related research shows that nonlinear behavior also occurs when the strain is small during the creep process of viscoelastic material. However, the above method does not consider the influence of damage, especially when testing and obtaining the Poisson's ratio during the creep process. Although the creep strain is obtained based on the creep test, the relaxation modulus is obtained based on the relaxation test, which causes the parameters in the formula for calculating the viscoelastic Poisson's ratio during the creep process to be obtained by different tests, and the accuracy is limited. Moreover, related research shows that the larger the initial strain is, the larger the Poisson's ratio is in the relaxation test. Therefore, different types of tests will cause additional errors. How to solve the above shortcomings of the existing method is a problem that needs to be solved at present. SUMMARY

[0006] The purpose of the present application is to solve the limitations of the existing technology in the characterization of viscoelastic Poisson's ratio without coupling the influence of damage evolution, and the dependence on additional relaxation test when obtaining the viscoelastic Poisson's ratio during the creep process, and to provide a particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method and system.

[0007] The specific technical solutions adopted by the present application are as follows:

[0008] In a first aspect, the present application provides a particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method, which comprises:

[0009] S1, based on the creep rupture test data of the target polymer under different creep stresses, fitting an exponential relationship model of creep stress and rupture time to obtain the linear cumulative damage index and Lebesgue stress norm of the target polymer, and then assigning the two damage parameters to the damage evolution model of the creep process with creep stress and creep time as independent variables;

[0010] S2, decoupling the longitudinal tensile creep test data of the target polymer under different creep stresses to obtain the linear creep process of the target polymer, and then obtaining the creep compliance time domain variation data of the linear creep process;

[0011] S3, fitting the generalized Voigt model using the creep compliance time domain variation data of the linear creep process, and then inversely obtaining the relaxation modulus time domain variation model based on the conversion model between creep compliance and relaxation modulus;

[0012] S4, based on the tensile creep test data of the target polymer under the target creep stress, a transverse strain time domain variation model is fitted, and then combined with the creep process damage evolution model and the relaxation modulus time domain variation model, a damage considering viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress is established, which is used to predict the viscoelastic Poisson's ratio of the target polymer at any time during the creep process.

[0013] As a preferred embodiment of the first aspect, in the exponential relationship model of the creep stress and the rupture time, the creep stress is obtained by multiplying the Lebesgue stress norm and the reciprocal of the exponential term, and the exponential term takes the rupture time as the base and the reciprocal of the linear cumulative damage index as the power. Further, the exponential relationship model of the creep stress and the rupture time is expressed by the formula as follows:

[0014]

[0015] In the formula, σ is the creep stress, t is the rupture time, and D is the linear cumulative damage index. D is the linear cumulative damage index. σ is the Lebesgue stress norm.

[0016] As a preferred embodiment of the first aspect, the creep process damage evolution model adopts a nonlinear model taking the creep damage variable as the dependent variable, the Lebesgue stress norm and the linear cumulative damage index of the target polymer as the fixed coefficients, and the creep stress and the creep time as the independent variables. Further, the creep process damage evolution model is expressed by the formula as follows:

[0017]

[0018] In the formula, σ is the creep stress, t is the creep time, and D is the linear cumulative damage index. D is the creep damage variable of the target polymer calculated by the creep process damage evolution model, which is determined by the creep stress σ and the creep time t. D and σ are the values fitted by the least square method using the exponential relationship model. D and σ are the values fitted by the least square method using the exponential relationship model. D and σ are the values fitted by the least square method using the exponential relationship model.

[0019] As a preferred embodiment of the first aspect, in the method for decoupling damage of the longitudinal tensile creep test data of the target polymer under each creep stress in S2, the current creep stress is substituted into the creep process damage evolution model to obtain a time domain variation model of the creep damage variable, and then the creep damage variable corresponding to each creep time in the longitudinal strain time domain data is calculated, the longitudinal strain at each creep time is multiplied by the difference between 1 and the creep damage variable at the creep time to obtain the longitudinal strain without damage at each creep time, and the damage decoupling is completed; and then the longitudinal strain without damage in the time domain variation data is divided by the current creep stress to obtain the creep compliance time domain variation data of the linear creep process under the current creep stress.

[0020] As a preferred embodiment of the first aspect, in the S3, the relaxation modulus time-domain variation model adopts a generalized Maxwell model, wherein the relaxation modulus of each Maxwell unit is obtained by solving a conversion model between the creep compliance and the relaxation modulus.

[0021] As a preferred embodiment of the first aspect, the conversion model between the creep compliance and the relaxation modulus is in the form of:

[0022]

[0023] wherein: N is the number of Maxwell units in the generalized Maxwell model, τi is the relaxation time of the i-th Maxwell unit, Gi is the relaxation modulus of the i-th Maxwell unit, E is the equilibrium modulus, t is the creep time; J is the instantaneous compliance, the retardation compliance of the j-th Voigt unit, τj is the retardation time of the j-th Voigt unit , Nv is the number of Voigt units, , and are obtained by fitting the generalized Voigt model using the creep compliance time-domain variation data of the linear creep process under different creep stresses as fitting data.

[0024] Further, the relaxation modulus time-domain variation model based on the generalized Maxwell model is expressed by the formula:

[0025]

[0026] wherein: t is the creep time corresponding relaxation modulus; E is the equilibrium modulus, which can be calculated from the fitted instantaneous compliance and the retardation compliances of the Voigt units , the calculation formula of which is ; Gi is the relaxation modulus of the i-th Maxwell unit; τi is the relaxation time of the i-th Maxwell unit, which is a preset value; N is the number of Maxwell units, which is a preset value.

[0027] As the preferred of the above first aspect, the time-domain variation model of the viscoelastic Poisson's ratio considering damage is:

[0028]

[0029] Wherein: is the viscoelastic Poisson's ratio considering damage, is the creep time calculated by the creep process damage evolution model is the corresponding creep damage variable, is the creep time calculated by the relaxation modulus time-domain variation model is the corresponding relaxation modulus, is the instantaneous moment calculated by the transverse strain time-domain variation model is the corresponding transverse strain, is the target creep stress.

[0030] In the second aspect, the present application provides a particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system, which comprises:

[0031] A prediction time specifying module is configured to input a target time at which the viscoelastic Poisson's ratio needs to be predicted;

[0032] A prediction result generating module is configured to call the time-domain variation model of the viscoelastic Poisson's ratio considering damage of the target polymer under the target creep stress according to the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method as described in any one of the above first aspect, and obtain the prediction result of the viscoelastic Poisson's ratio according to the target time.

[0033] In the third aspect, the present application provides a computer program product comprising computer programs / instructions, which, when executed by a processor, can realize the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method as described in any one of the above first aspect, or realize the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system as described in the above second aspect.

[0034] In the fourth aspect, the present application provides a computer electronic device comprising a memory and a processor;

[0035] The memory is configured to store computer programs;

[0036] The processor is configured to, when executing the computer programs, realize the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method as described in any one of the above first aspect, or realize the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system as described in the above second aspect.

[0037] Compared with the prior art, the present application has the following beneficial effects:

[0038] 1. The present application breaks through the limitations of traditional tests and realizes the simultaneous analysis of multiple parameters in a single test. The present application first proposes a technical path based on damage decoupling-creep compliance inversion relaxation modulus, which completely eliminates the dependence on independent relaxation tests. The present application can simultaneously obtain the viscoelastic Poisson's ratio of the damaged material, the creep response without damage, and the relaxation modulus only by using the creep test data, greatly reducing the test cost.

[0039] 2. The present application realizes precise quantification of damage evolution and improves the accuracy of Poisson's ratio representation. The present application decouples the damage effect in the creep process through a nonlinear damage evolution model, eliminates the interference of damage on Poisson's ratio calculation, and can realize high-precision calculation of Poisson's ratio under large strain conditions, significantly improving the prediction accuracy of volume deformation of particle reinforced polymers (such as solid propellants) during creep.

[0040] 3. The present application designs a new mathematical inversion algorithm to ensure parameter consistency. The present application realizes strict mathematical inversion of creep compliance to relaxation modulus based on the generalized Voigt model and the relaxation modulus analytical matrix. This algorithm avoids the Poisson's ratio drift problem caused by the difference in initial strain in traditional relaxation tests, ensuring the consistency of modulus parameters and creep data.

[0041] 4. The present application has strong engineering applicability and supports the structural integrity evaluation of key fields. For typical application scenarios of particle reinforced polymers such as solid propellant grain structure integrity analysis, the present application can solve the stress prediction distortion problem caused by the deviation of Poisson's ratio from 0.5 under damage state, and is verified by rocket engine solid propellant, providing support for the structural integrity evaluation of solid propellant grain during long-term storage.

[0042] 5. The present application has high universality and is compatible with multiple models for expansion. The present application supports various creep models such as generalized Voigt model and Burgers model, meeting the creep modeling needs of different material systems. After decoupling with the nonlinear damage model in the embodiment, the creep compliance under different stresses has high coincidence, verifying the robustness of the present application to the linear viscoelasticity assumption after damage decoupling. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 Figure 1 is a schematic diagram of the steps of the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method;

[0044] Figure 2 Figure 2 is a module composition diagram of the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system;

[0045] Figure 3 Figure 3 is a structural schematic diagram of a computer electronic device;

[0046] Figure 4Creep stress vs. time to failure plot for the example;

[0047] Figure 5 Damage curve comparison plot for the example under different stress loading;

[0048] Figure 6 Creep compliance comparison plot for the example after damage decoupling;

[0049] Figure 7 Relaxation modulus inversion result plot for the example from creep compliance;

[0050] Figure 8 Poisson's ratio vs. time plot for the example under 0.0241 MPa and 0.0492 MPa stress for 30 days;

[0051] Figure 9 Long-term (10 years) Poisson's ratio prediction vs. damage evolution comparison plot for the example. DETAILED DESCRIPTION

[0052] In order to make the above objectives, characteristics and advantages of the present application more apparent, specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. It will be apparent, however, to one skilled in the art that the present application can be practiced without using some or all of these specific details. In other instances, well-known process steps have not been described in detail in order to avoid unnecessarily obscuring the present application. Wherever possible, any aspects of the present application not recited in the above Summary are intended to be covered by the description and drawings.

[0053] The existing method does not consider the damage effect, and needs to obtain the relaxation modulus through an independent relaxation test, so that the damage-free creep response cannot be reconstructed directly based on the creep test data containing damage, and then only the relaxation modulus can be analyzed by relying on the creep compliance through mathematical inversion. The present application aims to break through this limitation and proposes a technical path that only needs single creep test data, decouples the damage and inverts the relaxation modulus through the creep compliance, and finally realizes the goal of accurately obtaining the damaged viscoelastic Poisson's ratio based on the creep test.

[0054] In a preferred embodiment of the present application, the specific process of the particle reinforced polymer damaged viscoelastic Poisson's ratio prediction method includes steps S1-S4. The specific implementation of each step will be described in detail below.

[0055] S1, based on the creep rupture test data of the target polymer under different creep stresses, fitting the exponential relationship model of the creep stress and the rupture time, obtaining the linear cumulative damage index and Lebesgue stress norm of the target polymer, and then assigning the two damage parameters to the creep process damage evolution model with the creep stress and the creep time as the independent variables.

[0056] It should be noted that the target polymer in the present application refers to a particulate reinforced polymer which needs to be predicted for the damage-containing viscoelastic Poisson's ratio, such as a solid propellant for a rocket engine. The creep rupture test data of the target polymer under different creep stresses refers to continuously applying a tensile stress to the target polymer to cause creep until rupture, and recording the creep stress and the rupture time in pairs during the process. The creep rupture test can be implemented by referring to the prior art, which belongs to the prior art, and will not be described in detail.

[0057] In addition, in the embodiment of the present application, the exponential relationship model of the creep stress and the rupture time is The Lebesgue stress norm is multiplied by the reciprocal of the exponential term to obtain, wherein the exponential term takes the rupture time as the base, and the reciprocal of the linear cumulative damage index as the power. The exponential relationship model of the creep stress and the rupture time is expressed by the formula as follows:

[0058]

[0059] In the formula, is the linear cumulative damage index, and the Lebesgue stress norm.

[0060] The exponential relationship model of the creep stress and the rupture time can use the creep rupture test data under different creep stresses as fitting data, and obtain the parameters and in the model by least squares fitting.

[0061] In addition, in the embodiment of the present application, the creep process damage evolution model uses a nonlinear model with the creep damage variable as the dependent variable, the linear cumulative damage index and the Lebesgue stress norm of the target polymer as fixed coefficients, and the creep stress and the creep time as independent variables. The creep process damage evolution model is expressed by the formula as follows:

[0062]

[0063] Wherein: The creep damage variable of the target polymer is calculated by the creep damage evolution model, which is composed of creep stress. The creep time t determines the model's... and The values ​​obtained by fitting the above exponential relationship model using the least squares method.

[0064] S2. Damage decoupling is performed on the longitudinal tensile creep test data of the target polymer under different creep stresses to obtain the linear creep process of the target polymer, and then the time-domain variation data of creep compliance of the linear creep process are obtained.

[0065] It should be noted that the longitudinal tensile creep test data of the target polymer under different creep stresses refers to the time-domain variation data of longitudinal strain continuously recorded during the process of continuously applying tensile stress to induce creep in the target polymer. The longitudinal tensile creep test can be implemented with reference to existing technology and is therefore considered prior art, so it will not be described in detail here. Furthermore, the longitudinal tensile creep test can actually be completed in the same test as the aforementioned creep rupture test.

[0066] In an embodiment of the present invention, the method for damage decoupling of the longitudinal tensile creep test data of the target polymer under each creep stress (hereinafter referred to as the current creep stress for damage decoupling) is as follows: substitute the current creep stress into the creep process damage evolution model described in formula (2) above, and fix the creep stress. Afterwards, the only independent variable remaining in the model is the creep time t, thus obtaining the time-domain variation model of the creep damage variable. Then, the creep damage variable corresponding to each creep time in the longitudinal strain time-domain data is calculated. The difference between multiplying the longitudinal strain at each creep moment by 1 and the creep damage variable at that creep moment is obtained, yielding the longitudinal strain without damage at each creep moment, thus completing damage decoupling. This damage decoupling process can be expressed by the formula:

[0067]

[0068] In the formula: This represents the longitudinal strain under the current creep stress, while This refers to the creep damage variable of the target polymer calculated using a creep damage evolution model. It's important to note that `t` in actual longitudinal tensile creep test data is a discrete value. Therefore, for each data point in the longitudinal tensile creep test data, it's necessary to calculate the corresponding creep damage variable based on a time-domain variation model of the creep damage variable after fixing the creep stress to the current creep stress, according to the creep time `t` corresponding to the data point. The value is then used to obtain the longitudinal strain corresponding to the data point through formula (3). The longitudinal strain The damage is eliminated by the factor (1-D), and thus the longitudinal strain without damage is obtained which represents the longitudinal strain without damage, and the longitudinal tensile creep test data under the current creep stress which can represent the linear creep process of the target polymer under the current creep stress.

[0069] In addition, after obtaining the linear creep process of the target polymer under each creep stress in S2, the longitudinal strain without damage time domain variation data can be further divided by the current creep stress to obtain the creep compliance time domain variation data of the linear creep process under the current creep stress. For each creep stress, the process of extracting the creep compliance time domain variation data from the corresponding linear creep process can be represented by the formula:

[0070]

[0071] In the formula: which represents the creep compliance corresponding to the creep time t (i.e., the creep compliance of the linear creep), and the longitudinal tensile creep test data under the current creep stress which can constitute the creep compliance time domain variation data of the linear creep process under the current creep stress. In the process of extracting the creep compliance time domain variation data for each creep stress, the creep stress in formula (4) is the current creep stress needs to be used.

[0072] S3, the creep compliance time domain variation data of the linear creep process is used to fit the generalized Voigt model, and based on the conversion model between the creep compliance and the relaxation modulus, the relaxation modulus time domain variation model is inversely obtained.

[0073] In the embodiments of the present application, the relaxation modulus time domain variation model adopts a generalized Maxwell model, wherein the relaxation modulus of each Maxwell unit is obtained by solving the conversion model between the creep compliance and the relaxation modulus.

[0074] Further, the conversion model between the creep compliance and the relaxation modulus can be represented as follows:

[0075]

[0076] wherein: N is the number of Maxwell units in the generalized Maxwell model, is the relaxation time of the i th Maxwell unit, is the relaxation modulus of the i th Maxwell unit, is the equilibrium modulus, is the creep time, is the instantaneous compliance, is the retardation compliance of the jth Voigt unit, is the retardation time of the jth Voigt unit , is the number of Voigt units, , and The generalized Voigt model is fitted by using the creep compliance time-domain variation data of the linear creep process under different creep stresses as fitting data.

[0077] In order to better understand the principle of the above S3 step, the derivation process of the conversion model described in the above formula (5) and the specific solving method are described in detail below.

[0078] 1) Based on the creep compliance time-domain variation data of the linear creep process under different creep stresses, that is, the aforementioned creep compliance data of the undamaged material The generalized Voigt model described in formula (6) is fitted by using these data as fitting data:

[0079]

[0080] Wherein: is the instantaneous compliance, and is the fitting coefficient; is the viscosity coefficient, and is the fitting coefficient; is the creep time; is the retardation compliance of the jth Voigt unit, and is the fitting coefficient; is the retardation time of the jth Voigt unit, and is a preset value; is the number of Voigt units, and is a preset value.

[0081] 2) The target polymer is a viscoelastic material, and due to its complex mechanical properties, a plurality of models in series and parallel combination are required to comprehensively describe its mechanical properties, so the generalized Maxwell model is required to be used for description. The relaxation modulus expression based on the generalized Maxwell model is:

[0082]

[0083] Wherein: represents the creep time corresponding relaxation modulus; is the equilibrium modulus, which can be calculated by the instantaneous compliance and the retardation compliance of each Voigt unit calculated, and the calculation formula is ; is the relaxation modulus of the i-th Maxwell unit; is the relaxation time of the i-th Maxwell unit, which is a preset value; is the number of Maxwell units, which is a preset value.

[0084] 3) Derivation and solution of the relationship between the creep compliance and the relaxation modulus are as follows:

[0085] Since the creep compliance and the relaxation modulus satisfy the following formula:

[0086]

[0087] In the formula: represents the instantaneous time for integration, which is the integral variable.

[0088] Derivation of the creep compliance expression can obtain:

[0089]

[0090] At the same time, can be expressed as:

[0091]

[0092] Thus, formula (9) and formula (10) are substituted into formula (8), and the relationship between the creep compliance and the relaxation modulus is obtained:

[0093]

[0094] Wherein, is the Dirac function.

[0095] In addition, when , the above formula (11) can be transformed into the following form:

[0096]

[0097] The above formula (12) is the transformation model based on the relationship between the creep compliance and the relaxation modulus that needs to be solved. Solving the transformation model can obtain the relaxation modulus of all Maxwell units .

[0098] In order to facilitate the solution, when the time is , two intermediate variables and are introduced, and the expressions of are set as follows:

[0099]

[0100] Setting The expression is as follows:

[0101]

[0102] The above formula (12) can be rewritten as follows:

[0103]

[0104] As described above, when the creep compliance time domain variation data of the linear creep process under different creep stresses is used as fitting data to complete the fitting of the generalized Voigt model, the following can be obtained: , and , and and are preset values or known quantities, so for each Maxwell unit, the two intermediate variables and can be calculated, and then can be solved.

[0105] Finally, in actual application, the present embodiment can convert all the to-be-solved formula (15) into a matrix form convenient for batch solving:

[0106]

[0107] As can be seen from formula (16), to solve , only the corresponding and at the same time points as the Voigt unit number need to be obtained, and then the relaxation modulus, i.e., the parameters E1~E m , can be batch solved through formula (16). After E1~E m is solved, it is substituted into the relaxation modulus expression of the generalized Maxwell model shown in formula (7), and then the relaxation modulus at any time can be calculated according to the expression.

[0108] S4, based on the tensile creep test data of the target polymer under the target creep stress, a transverse strain time domain variation model is fitted, and then combined with the creep process damage evolution model and the relaxation modulus time domain variation model, a damage-considered viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress is established, which is used to predict the viscoelastic Poisson's ratio of the target polymer at any time during the creep process.

[0109] ​It should be noted that the tensile creep test data of the target polymer under the target creep stress refers to the time-domain variation data of the longitudinal strain and the transverse strain recorded continuously during the process of continuously applying a specified tensile stress to the target polymer to make it creep. The tensile creep test can be implemented according to the prior art, which belongs to the prior art and will not be described in detail. Moreover, the tensile creep test can actually be completed through the same test as the aforementioned creep rupture test and the longitudinal tensile creep test, that is, the time-domain variation data of the longitudinal strain and the transverse strain under different creep stresses and the final rupture time are recorded in the same test.

[0110] In the embodiments of the present application, the data of the creep compliance coincident time period part can be extracted from the tensile creep test data of the target polymer under the target creep stress (i.e. the creep stress required in actual application) as fitting data for fitting the time-domain variation model of the transverse strain. The creep compliance coincident time period is generally the stage of smaller strain occurring in the creep process, and the judgment method is as follows:

[0111] Firstly, the creep compliance under different stresses is directly calculated based on the creep test data under different stresses , which is . The damage decoupling is not required, and the longitudinal strain of the target polymer in the tensile creep test data under different creep stresses can be divided by the respective corresponding creep stress, and the calculation formula is as follows:

[0112]

[0113] Then, the deviation between the creep compliances under different creep stresses in the time domain is obtained, and the time period in which the deviation between each two is less than a threshold value (which can be set to 5%) is the creep compliance coincident time period.

[0114] The above-mentioned time-domain variation model of the transverse strain can be represented by the following formula (18):

[0115]

[0116] In the formula, t represents the creep time, corresponding transverse strain, is an initial transverse strain parameter, is the th transverse strain parameter, is a delay time parameter, and all of them are obtained by fitting; is the number of transverse strain parameters, which can be set according to the fitting requirement.

[0117] ​Finally, when the transverse strain time-domain variation model is obtained, it can be used to predict the transverse strain at any time, so the damage evolution model in the creep process and the relaxation modulus time-domain variation model are combined to establish the damage-considered viscoelastic Poisson's ratio time-domain variation model of the target polymer under the target creep stress as shown in the following formula (19), and the model form is:

[0118]

[0119] Wherein: is the damage-considered viscoelastic Poisson's ratio, is the creep time calculated by the creep process damage evolution model corresponding to the creep damage variable, is the creep time calculated by the relaxation modulus time-domain variation model corresponding to the relaxation modulus, is the instantaneous time calculated by the transverse strain time-domain variation model corresponding to the transverse strain, is the target creep stress.

[0120] It should be noted that the damage-considered viscoelastic Poisson's ratio time-domain variation model described in the above formula (19) needs to be constructed separately for each target creep stress, and the and in the model under different creep stresses are only related to the target polymer, so as long as the target polymer is unchanged, the and in formula (19) under different creep stresses are the same, but the transverse strain in the transverse strain time-domain variation model is not only related to the target polymer, but also related to the creep stress received, so for the target creep stress actually needed to be predicted, the corresponding transverse strain time-domain variation model needs to be fitted separately, and then substituted into formula (19) to form the damage-considered viscoelastic Poisson's ratio time-domain variation model under the target creep stress.

[0121] In another embodiment of the present application, based on the damage-considered viscoelastic Poisson's ratio time-domain variation model constructed for the target polymer and the target creep stress, a particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system can be further constructed, as shown in Figure 2 which comprises:

[0122] A prediction time specifying module for inputting a target time at which the viscoelastic Poisson's ratio needs to be predicted;

[0123] a prediction result generation module configured to invoke a time-domain variation model of the viscoelastic Poisson's ratio of the target polymer under the target creep stress and according to the target time to obtain a prediction result of the viscoelastic Poisson's ratio of the target polymer at the target time under the target creep stress.

[0124] It should be noted that the prediction time designation module can be configured to receive the target time for predicting the viscoelastic Poisson's ratio from a user through a GUI interface or other instruction input form, and the target time can be configured to be flexibly input according to a time point value or a time period as needed. Similarly, the prediction result generation module can also display the prediction result of the viscoelastic Poisson's ratio through a GUI interface or other result file output form.

[0125] It should be noted that the viscoelastic Poisson's ratio prediction method of the particle reinforced polymer with damage S1-S4 and the viscoelastic Poisson's ratio prediction system of the particle reinforced polymer with damage can be essentially realized in the form of a computer program or a software functional module.

[0126] Therefore, based on the same inventive concept, as shown in Figure 3 The present application also provides a computer electronic device corresponding to the viscoelastic Poisson's ratio prediction method of the particle reinforced polymer with damage provided in the above embodiments, which comprises a memory and a processor.

[0127] The memory is configured to store a computer program.

[0128] The processor is configured to implement the viscoelastic Poisson's ratio prediction method of the particle reinforced polymer with damage as described above, or implement the viscoelastic Poisson's ratio prediction system of the particle reinforced polymer with damage as described above when the computer program is executed.

[0129] In addition, the logical instructions in the memory described above can be realized in the form of a software functional unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the part of the prior art that contributes essentially or the part of the technical solutions can be embodied in the form of a software product, which is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application.

[0130] Therefore, based on the same inventive concept, the present application provides a computer readable storage medium corresponding to the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method, and the storage medium stores a computer program. When the computer program is executed by a processor, the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method or the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system as described above can be implemented.

[0131] Therefore, based on the same inventive concept, the present application provides a computer program product, which includes computer program / instructions that can be executed by a processor to implement the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method or the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system as described above.

[0132] Specifically, in the computer readable storage medium of the above three embodiments, the stored computer program is executed by a processor to execute the steps of S1-S4 or the two functional modules in the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system.

[0133] It can be understood that the storage medium can include a random access memory (RAM) and a non-volatile memory (NVM), such as at least one disk memory. Meanwhile, the storage medium can also be a U disk, a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0134] It can be understood that the processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; or a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component.

[0135] It should be noted that the skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system described above can refer to the corresponding process in the foregoing method embodiments, which will not be repeated here. In the embodiments provided in the present application, the division of steps or modules in the system and method described is only a logical functional division, and there can be another division manner in actual implementation, for example, multiple modules or steps can be combined or integrated together, or a module or step can be split.

[0136] The present application will further demonstrate the detailed implementation process and technical effects of the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method shown in the above S1-S4 steps on specific experimental data, so as to facilitate understanding of the essence of the present application.

[0137] Embodiment

[0138] The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of the present embodiment has the same steps as the foregoing S1-S4 steps, which will not be repeated here. The following mainly demonstrates the specific test data acquisition and the specific results of each step.

[0139] In the present embodiment, the creep rupture test of the target polymer under different creep stresses in S1 step, the longitudinal tensile creep test of the target polymer under different creep stresses in S2 step, and the tensile creep test of the target polymer under the target creep stress in S4 step are all obtained by the same test. The target polymer of the test is a certain type of rocket engine charge using HTPB / AP composite solid propellant with a solid content of 83%. The HTPB / AP composite solid propellant is subjected to a verification experiment in a controlled environment (SDJ705 high-low temperature and humidity test chamber) with a constant temperature of 20℃ and a humidity of less than 50%. The test is designed for 7 groups of creep stress levels (0.0241 MPa, 0.0492 MPa, 0.1022 MPa, 0.1372 MPa, 0.1862 MPa, 0.2205 MPa, 0.2403 MPa), and 7 groups of long-term creep test schemes under different creep stresses are designed: the HTPB / AP composite solid propellant is subjected to tension by hanging weight type multi-sample creep device under different creep stresses, the transverse strain and longitudinal strain are measured synchronously by vernier caliper at regular intervals under each creep stress, 60-day short-term creep full-cycle data are obtained, and the 10-year long-term evolution behavior is extrapolated based on the damage decoupling model. If creep rupture occurs during the creep process, the rupture time is recorded. Finally, creep rupture occurs at 31 days, 36 days and 66 days under 0.2403 MPa, 0.2205 MPa and 0.1862 MPa stress respectively, and no creep rupture occurs under the remaining stress levels.

[0140] 1) This embodiment refers to the aforementioned S1 step, based on the creep rupture test data of the target polymer under different creep stresses, the exponential relationship model of creep stress and fracture time is fitted, and the linear cumulative damage index and Lebesgue stress norm of the target polymer are obtained, and then the two damage parameters are assigned to the creep process damage evolution model with creep stress and creep time as independent variables.

[0141] In this embodiment, under the stresses of 0.2403 MPa, 0.2205 MPa and 0.1862 MPa, the specimen fracture times are 31 days, 36 days and 66 days respectively, so the exponential relationship model of creep stress and fracture time corresponding to the aforementioned formula (1) is fitted by least squares method using the three groups of data, and , The two fitting parameters are substituted into the creep process damage evolution model. It is verified that the prediction accuracy error of the creep process damage evolution model corrected by the fitting parameters is less than 5%, and the relationship between the creep stress and the fracture time is shown in Figure 4 , and the damage curves under different initial stress loading conditions are shown in Figure 5 .

[0142] 2) This embodiment refers to the aforementioned S2 step, the damage decoupling is performed on the longitudinal tensile creep test data of the target polymer under different creep stresses, and the linear creep process of the target polymer is obtained, and then the creep compliance time domain variation data of the linear creep process is obtained.

[0143] In this embodiment, 6 groups of different creep stresses respectively obtain the creep compliance time domain variation data of the linear creep process. The creep compliance time domain variation data under the stresses of 0.2403 MPa, 0.2205 MPa, 0.1862 MPa and 0.1372 MPa are visualized as Figure 6 , it can be seen that the coincidence degree of the creep compliance under the four stress levels is high, indicating that linear viscoelasticity is dominant and damage has been well decoupled.

[0144] 3) This embodiment refers to the aforementioned S3 step, the generalized Voigt model is fitted using the creep compliance time domain variation data of the linear creep process, and then the relaxation modulus time domain variation model is inversely obtained based on the conversion model between the creep compliance and the relaxation modulus.

[0145] In this embodiment, the generalized Voigt model described in formula (6) uses a 3-unit generalized Voigt model (Prony series), that is, the number of Voigt units n is 3, and this model is used to fit the undamaged creep compliance. When j=1, 2, 3, the delay times of the 3 Voigt units are respectively 、 、 And the generalized Maxwell model in the number of Maxwell unit m is also taken as 3, so the relaxation time of the i-th Maxwell unit is taken as , and the maximum relaxation time is 66. The matrix inversion algorithm based on formula (16) is used to solve the relaxation modulus E1~E m , so as to convert the creep compliance into the relaxation modulus, and the Laplace domain analytical method is also calculated in this embodiment. The relaxation modulus obtained by the two methods is shown in Figure 7 , wherein E represents the relaxation modulus solved by the matrix inversion algorithm based on formula (16) of the application, J represents the creep compliance, and laplaceE represents the relaxation modulus obtained by the Laplace domain analytical method.

[0146] 4) In this embodiment, referring to the S4 step described above, the transverse strain time domain variation model is fitted based on the tensile creep test data of the target polymer under the target creep stress, and then the damage evolution model and the relaxation modulus time domain variation model are combined to establish the damage considering viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress, which is used to predict the viscoelastic Poisson's ratio of the target polymer at any time during the creep process.

[0147] In this embodiment, the number of transverse strain parameters is set to =6. In order to verify the final prediction effect, the damage considering viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress shown in formula (19) is input into the transverse strain model and the inversion relaxation modulus E ( t ), and the Poisson's ratio test results under the stresses of 0.0241 MPa and 0.0492 MPa within 30 days are shown in Figure 8 . Figure 8 It is shown that, during the creep process, the Poisson's ratio continuously increases in the short term and tends to 0.5, which accords with the characteristics of incompressible viscoelastic materials. In addition, the comparison graph of the long-term (10 years) Poisson's ratio prediction result and the damage evolution result is shown in Figure 9 . Figure 9 It is shown that, with the accumulation of damage (the damage variable D >0.4 in the 10-year period), the Poisson's ratio continuously decreases to below 0.3, which reveals the transition mechanism of the material from the incompressible state to the compressible state.

[0148] Finally, it needs to be explained that the above-described embodiments are only some preferred implementation schemes of the present application, but are not intended to limit the present application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application. For example, the present application obtains the linear creep process of high solid content polymer by damage decoupling, and the model of damage in the damage decoupling process, the creep compliance model and the method of converting relaxation modulus through the creep compliance are not unique. For example, the damage model can adopt a nonlinear damage evolution model (but the creep compliance under different stresses obtained after damage decoupling should have a high coincidence degree, i.e. meet the linear viscoelastic process), the creep compliance fitting can adopt a Burgers model, and the method of converting relaxation modulus through the creep compliance can adopt Laplace transformation and inverse transformation. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the protection scope of the present application.

Claims

1. A method for predicting damage-containing viscoelastic Poisson's ratio of particle reinforced polymers, characterized by, The method comprises the following steps: S1. Based on the creep rupture test data of the target polymer under different creep stresses, an exponential relationship model of the creep stress and the rupture time is fitted to obtain a linear cumulative damage index and a Lebesgue stress norm of the target polymer, and then the two damage parameters are assigned to a creep process damage evolution model with the creep stress and the creep time as independent variables; S2. The longitudinal tensile creep test data of the target polymer under different creep stresses are damage decoupled to obtain a linear creep process of the target polymer, and then the creep compliance time domain variation data of the linear creep process are obtained; S3. The creep compliance time domain variation data of the linear creep process are used to fit a generalized Voigt model, and then a relaxation modulus time domain variation model is inversely obtained based on a conversion model between the creep compliance and the relaxation modulus; S4. Based on the tensile creep test data of the target polymer under a target creep stress, a transverse strain time domain variation model is fitted, and then a damage considered viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress is established by combining the creep process damage evolution model and the relaxation modulus time domain variation model, which is used to predict the viscoelastic Poisson's ratio of the target polymer at any time in the creep process. The damage considered viscoelastic Poisson's ratio time domain variation model is in the form of: ； wherein: is the viscoelastic Poisson's ratio considering damage, is the creep time calculated from the creep process damage evolution model is the corresponding creep damage variable, is the creep time calculated from the relaxation modulus time domain variation model is the corresponding relaxation modulus, is the instant time calculated from the transverse strain time domain variation model is the corresponding transverse strain, is the target creep stress.

2. The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of claim 1, wherein, In the exponential relationship model of the creep stress and the rupture time, the creep stress is obtained by multiplying the Lebesgue stress norm and the reciprocal of the exponential term, and the exponential term takes the rupture time as the base and the reciprocal of the linear cumulative damage index as the power.

3. The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of claim 1, wherein, The creep process damage evolution model adopts a nonlinear model with the creep damage variable as the dependent variable, the linear cumulative damage index and the Lebesgue stress norm of the target polymer as the fixed coefficients, and the creep stress and the creep time as the independent variables.

4. The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of claim 1, wherein, In S2, the method for damage decoupling of the longitudinal tensile creep test data of the target polymer under each creep stress is as follows: the current creep stress is substituted into the creep process damage evolution model to obtain a time domain variation model of the creep damage variable, and then the creep damage variable corresponding to each creep time in the longitudinal strain time domain data is calculated; the longitudinal strain at each creep time is multiplied by the difference between 1 and the creep damage variable at the creep time to obtain the longitudinal strain without damage at each creep time, and the damage decoupling is completed; Then, the longitudinal strain without damage in the time domain is divided by the current creep stress to obtain the creep compliance time domain variation data of the linear creep process under the current creep stress.

5. The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of claim 1, wherein, In S3, the relaxation modulus time domain variation model adopts a generalized Maxwell model, wherein the relaxation modulus of each Maxwell unit is obtained by solving the conversion model between the creep compliance and the relaxation modulus.

6. The particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method of claim 5, wherein, The conversion model between the creep compliance and the relaxation modulus is in the form of: ； wherein: is the number of Maxwell elements in the generalized Maxwell model, is the relaxation time of the i-th Maxwell element, is the relaxation modulus of the i-th Maxwell element, is the equilibrium modulus, is the creep time; is the instantaneous compliance, is the retarded compliance of the j-th Voigt element, is the retardation time of the j-th Voigt element , is the number of Voigt elements, , and are obtained by fitting the generalized Voigt model using the creep compliance time-domain variation data of the linear creep process under different creep stresses as fitting data.

7. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions can be executed by the processor to perform the particle reinforced polymer damage contained viscoelastic Poisson's ratio prediction method in any one of claims 1-6.

8. A computer electronic device, comprising: The computer program / instructions can be executed by the processor to perform the particle reinforced polymer damage contained viscoelastic Poisson's ratio prediction method in any one of claims 1-6. The computer program / instructions can be executed by the processor to perform the particle reinforced polymer damage contained viscoelastic Poisson's ratio prediction method in any one of claims 1-6. The processor is configured to perform the method for predicting the damage-containing viscoelastic Poisson's ratio of the particle-reinforced polymer as claimed in any one of claims 1-6 when executing the computer program.

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