Method and system for predicting damage-containing viscoelasticity Poisson's ratio of particle reinforced polymer

Abstract

The invention discloses a particle reinforced polymer damage-containing viscoelasticity Poisson's ratio prediction method and a particle reinforced polymer damage-containing viscoelasticity Poisson's ratio prediction system. The method comprises the following steps: firstly, acquiring creep process damage parameters of the high-solid-content polymer, and determining a creep process damage evolution model; then obtaining a linear creep process of the high-solid-content polymer through damage decoupling, and obtaining creep compliance time domain change data of the linear creep process; then, a relaxation modulus is inversed based on creep compliance of a linear creep process; and finally, based on the determined damage evolution model and relaxation modulus, establishing a viscoelastic Poisson's ratio time domain change model considering damage to predict the viscoelastic Poisson's ratio containing damage. According to the method, the viscoelastic Poisson's ratio containing damage, the non-damage creep response and the relaxation modulus can be synchronously obtained only through creep test data, and the test cost is greatly reduced.

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 urgently. 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 dependency 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: In a first aspect, the present application provides a particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method, which comprises: 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; 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 creep compliance time domain variation data of the linear creep process is obtained; S3, the creep compliance time domain variation data of the linear creep process is used to fit the generalized Voigt model, and then based on the transformation model between creep compliance and relaxation modulus, the relaxation modulus time domain variation model is obtained by inversion; 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.

[0008] 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:

[0009] In the formula, σ is the creep stress, σ is the Lebesgue stress norm, 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.

[0010] 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 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. Further, the creep process damage evolution model is expressed by the formula as follows:

[0011] In the formula, 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, and D and σ in the model are obtained by the least square fitting of the exponential relationship model. 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, and D and σ in the model are obtained by the least square fitting of the exponential relationship model. 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, and D and σ in the model are obtained by the least square fitting of the exponential relationship model.

[0012] As a preferred embodiment of the first aspect, in the method of damage decoupling 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.

[0013] ​​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.

[0014] As a preferred embodiment of the first aspect, the conversion model between the creep compliance and the relaxation modulus is in the form of:

[0015] 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, Gj is 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 Both of them are fitted by using the creep compliance time-domain variation data of the linear creep process under different creep stresses as fitting data.

[0016] Further, the relaxation modulus time-domain variation model based on the generalized Maxwell model is expressed by the formula:

[0017] 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.

[0018] As a preferred embodiment of the first aspect, the damage-considered viscoelastic Poisson's ratio time-domain variation model is in the form of:

[0019] wherein: viscoelastic Poisson's ratio considering damage, creep time calculated by the creep process damage evolution model corresponding creep damage variable, creep time calculated by the relaxation modulus time-domain variation model corresponding relaxation modulus, instantaneous moment calculated by the transverse strain time-domain variation model corresponding transverse strain, target creep stress.

[0020] In a second aspect, the present application provides a particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system, comprising: a prediction moment designation module, configured to input a target moment for which a viscoelastic Poisson's ratio needs to be predicted; a prediction result generation module, configured to call a viscoelastic Poisson's ratio time-domain variation model considering damage of a target polymer under a target creep stress according to the particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method in any one of the above-mentioned first aspect, and obtain a prediction result of the viscoelastic Poisson's ratio according to the target moment.

[0021] In a third aspect, the present application provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, can implement the particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method in any one of the above-mentioned first aspect, or implement the particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system in the above-mentioned second aspect.

[0022] In a fourth aspect, the present application provides a computer electronic device, comprising a memory and a processor; the memory, configured to store computer programs; the processor, configured to, when executing the computer programs, can implement the particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction method in any one of the above-mentioned first aspect, or implement the particle-reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system in the above-mentioned second aspect.

[0023] Compared with the prior art, the present application has the following beneficial effects: 1. The present application breaks through the traditional test limit and realizes the synchronous 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 test. 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, which greatly reduces the test cost.

[0024] 2. The present application realizes the 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 the calculation of Poisson's ratio, and can realize the high-precision calculation of Poisson's ratio under large strain conditions, which significantly improves the prediction accuracy of volume deformation of particle reinforced polymers (such as solid propellants) in the creep process.

[0025] 3. The present application designs a new mathematical inversion algorithm to ensure the consistency of parameters. The present application realizes the strict mathematical inversion of creep compliance to relaxation modulus based on the generalized Voigt model and the analytical matrix of relaxation modulus. This algorithm avoids the Poisson's ratio drift problem caused by the difference in initial strain in traditional relaxation test, and ensures the consistency of modulus parameters and creep data.

[0026] 4. The present application has strong engineering applicability and supports the structural integrity evaluation of key fields. For the typical application scenarios of particle reinforced polymers such as solid propellant grain structure integrity analysis, the present application can solve the problem of stress prediction distortion caused by the deviation of Poisson's ratio from 0.5 under damage state, and is verified by rocket engine solid propellant, which provides support for the structural integrity evaluation of solid propellant grain during long-term storage.

[0027] 5. The present application has high universality and is compatible with multiple models. The present application supports various creep models such as generalized Voigt model and Burgers model, which meets the creep modeling needs of different material systems. After decoupling with the nonlinear damage model in the embodiment, the coincidence degree of creep compliance under different stresses is high, which verifies the robustness of the present application to the linear viscoelasticity assumption after damage decoupling. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The steps of the particle reinforced polymer damage viscoelastic Poisson's ratio prediction method are shown in the figure; Figure 2 The module composition diagram of the particle reinforced polymer damage viscoelastic Poisson's ratio prediction system is shown in the figure; Figure 3 The structure of the computer electronic device is shown in the figure; Figure 4 The creep stress and fracture time graph in the embodiment is shown in the figure; Figure 5 The damage curve comparison graph under different stress loads in the embodiment is shown in the figure; Figure 6 Creep compliance comparison chart after damage decoupling for the example; Figure 7 Relaxation modulus result chart for the example of creep compliance inversion; Figure 8 Poisson's ratio change over time chart within 30 days under 0.0241 MPa and 0.0492 MPa stress for the example; Figure 9 Comparison chart of predicted change of Poisson's ratio and damage evolution for the example of long-term (10 years). DETAILED DESCRIPTION

[0029] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below in combination with the drawings. In the following description, a large number of specific details are set forth in order to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the concept of the present application, so the present application is not limited by the specific embodiments disclosed below. The technical features in each embodiment of the present application can be combined accordingly without conflict.

[0030] The existing method cannot directly reconstruct the undamaged creep response based on the creep test data containing damage, and further rely on the mathematical inversion of the creep compliance to analyze the relaxation modulus, because it does not consider the damage effect and needs to obtain the relaxation modulus through independent relaxation test. The present application aims to break through this limitation and proposes a technical path that only requires single creep test data, decouples damage and inverses relaxation modulus through creep compliance, and finally realizes the goal of accurately obtaining the damaged viscoelastic Poisson's ratio based on creep test.

[0031] In a preferred embodiment of the present application, the specific process of the damaged viscoelastic Poisson's ratio prediction method of the particle reinforced polymer includes S1~S4 steps. The specific implementation of each step is described below.

[0032] S1, based on the creep rupture test data of the target polymer under different creep stresses, the exponential relationship model of creep stress and rupture time is fitted, 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.

[0033] It should be noted that the target polymer in this invention refers to particle-reinforced polymers for which damage viscoelastic Poisson's ratio prediction is required, such as solid propellants used in rocket engines. The creep rupture test data of the target polymer under different creep stresses refers to the creep stress and rupture time recorded in pairs during the process of continuously applying tensile stress to induce creep until rupture. The creep rupture test can be implemented with reference to existing technologies and is therefore not described in detail here.

[0034] Furthermore, in the embodiments of the present invention, in the above-described exponential relationship model between creep stress and fracture time, creep stress Lebesgue stress norm It is obtained by multiplying the exponent by the inverse of the exponent, where the exponent is the break time. With the base as the linear cumulative damage index The reciprocal of the product is raised to the power of the product. The exponential relationship between creep stress and fracture time is expressed by the formula:

[0035] In the formula, It is a linear cumulative damage index. Let be the Lebesgue stress norm.

[0036] The exponential relationship model between creep stress and fracture time described above can be fitted using creep fracture test data under different creep stresses, and the parameters in the model can be obtained by least squares fitting. and .

[0037] Furthermore, in the embodiments of the present invention, the above-mentioned creep process damage evolution model adopts a linear cumulative damage index of the target polymer with creep damage variable as the dependent variable. and Lebesgue stress norm This is a nonlinear model with fixed coefficients and creep stress and creep time as independent variables. The damage evolution model during the creep process is expressed by the following formula:

[0038] in: 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.

[0039] 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.

[0040] 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.

[0041] 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:

[0042] 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 was eliminated by the factor (1-D), thus obtaining This represents the longitudinal strain without damage, and the longitudinal strain corresponding to all sampled creep times t in the longitudinal tensile creep test data under the current creep stress. This can represent the linear creep process of the target polymer under the current creep stress.

[0043] Furthermore, in S2 above, after obtaining the linear creep process of the target polymer under each creep stress, the time-domain variation data of the longitudinal strain without damage can be further divided by the current creep stress to obtain the time-domain variation data of the creep compliance during the linear creep process under the current creep stress. For each creep stress, the process of extracting the time-domain variation data of the creep compliance from the corresponding linear creep process can be expressed by the following formula:

[0044] In the formula: This represents the creep compliance without damage (i.e., the creep compliance of linear creep) corresponding to creep time t, and the creep time t corresponding to all samples in the longitudinal tensile creep test data under the current creep stress. This can be used to construct the time-domain variation data of creep compliance during the linear creep process under the current creep stress. For each type of creep stress, when extracting the time-domain variation data of creep compliance, the creep stress in formula (4) is... The current creep stress must be used.

[0045] S3. Fit the generalized Voigt model using the time-domain variation data of creep compliance during the linear creep process, and then invert the relaxation modulus time-domain variation model based on the transformation model between creep compliance and relaxation modulus.

[0046] In an embodiment of the present invention, the relaxation modulus time-domain variation model adopts the generalized Maxwell model, wherein the relaxation modulus of each Maxwell element is obtained by solving the transformation model between creep compliance and relaxation modulus.

[0047] Furthermore, the conversion model between the above-mentioned creep compliance and relaxation modulus can be expressed as follows:

[0048] in: This represents the number of Maxwell cells in the generalized Maxwell model. Let be the relaxation time of the i-th Maxwell element. Let i be the relaxation modulus of the i-th Maxwell element. To balance the modulus, Creep time; For instantaneous softness, The delay compliance of the j-th Voigt unit, The delay time of the j-th Voigt unit , The number of Voigt units. , and The generalized Voigt model is fitted by using the time-domain change data of the creep compliance of the linear creep process under different creep stresses as fitting data.

[0049] In order to better understand the principle of the above S3 step, the derivation process and specific solving method of the conversion model described in the above formula (5) are described in detail below.

[0050] 1) Based on the time-domain change data of the creep compliance of the linear creep process under different creep stresses, that is, the aforementioned creep compliance without damage Data, these data are used as fitting data to fit the generalized Voigt model described in formula (6):

[0051] Among them: is the instantaneous compliance, and is the fitting coefficient; is the viscosity coefficient, and is the fitting coefficient; is the creep time; The delay compliance of the jth Voigt unit is, and is the fitting coefficient; is the delay time of the jth Voigt unit, and is a preset value; is the number of Voigt units, and is a preset value.

[0052] 2) The target polymer is a viscoelastic material, and due to its complex mechanical properties, multiple 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:

[0053] Among them: represents the creep time Corresponding relaxation modulus; is the equilibrium modulus, which can be obtained from the instantaneous compliance And the delay compliance of each Voigt unit Calculated, and the calculation formula is ; is the relaxation modulus of the ith Maxwell unit; is the relaxation time of the ith Maxwell unit, and is a preset value; is the number of Maxwell units, and is a preset value.

[0054] 3) The relationship between the creep compliance and the relaxation modulus is derived and solved, and the specific solution is as follows: Since creep compliance and relaxation modulus satisfy the following equation:

[0055] In the formula: It represents the instantaneous moment used for integration and is the integration variable.

[0056] Differentiating the creep compliance expression yields:

[0057] at the same time, It can be represented as:

[0058] Substituting equations (9) and (10) into equation (8), we can obtain the relationship between creep compliance and relaxation modulus:

[0059] in, This is the Dirac function.

[0060] In addition, when Then, the above formula (11) can be transformed into the following form:

[0061] Formula (12) above is the transformation model between creep compliance and relaxation modulus that needs to be solved. Solving this transformation model will yield the relaxation modulus of all Maxwell elements. .

[0062] For ease of solution, when time is At time, two intermediate variables are introduced. and And set The expression is as follows:

[0063] set up The expression is as follows:

[0064] Therefore, the above formula (12) can be rewritten as follows:

[0065] As mentioned earlier, by using the time-domain variation data of creep compliance during linear creep processes under different creep stresses as fitting data to complete the fitting of the generalized Voigt model, we can obtain... , and ,and and are known quantities or preset values, so for each Maxwell unit, two intermediate variables and can be calculated, and then the .

[0066] Finally, in actual application, the present embodiment can convert all the to-be-solved formula (15) into a matrix form convenient for batch solving:

[0067] As can be seen from formula (16), to solve , only the corresponding and at the same time points as the number of Voigt units need to be selected, 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.

[0068] S4, based on the tensile creep test data of the target polymer under the target creep stress, a transverse strain time-domain change model is fitted, and then combined with a creep process damage evolution model and a relaxation modulus time-domain change model, a damage-considered viscoelastic Poisson's ratio time-domain change 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.

[0069] It should be noted that the tensile creep test data of the target polymer under the target creep stress refers to the time-domain change 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 by referring 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 by the same test as the aforementioned creep rupture test and longitudinal tensile creep test, that is, the longitudinal strain time-domain change data and the transverse strain time-domain change data under different creep stresses and the final rupture time are recorded in the same test.

[0070] In the embodiments of the present application, the data of the creep compliance coincidence 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 transverse strain time-domain change model. The creep compliance coincidence time period is generally the stage of smaller strain in the creep process, and the judgment method is as follows:​ Firstly, the creep compliance is directly calculated based on the creep test data under different stresses The creep compliance Without damage decoupling, the longitudinal strain of the target polymer in the tensile creep test data under different creep stresses is divided by the respective corresponding creep stress, and the calculation formula is as follows:

[0071] Then, the deviation between the creep compliances under different creep stresses in the time domain is obtained The time period in which the deviation between each other is less than a threshold value (which can be set to 5%) can be used as the creep compliance coincidence time period.

[0072] The above transverse strain time domain change model can be represented by the following formula (18):

[0073] In the formula: represents the creep time corresponding to the transverse strain, is the initial transverse strain parameter, is the th transverse strain parameter, is the delay time parameter, all of which are obtained by fitting; is the number of transverse strain parameters, which can be set according to the fitting needs.

[0074] Finally, when the transverse strain time domain change model is obtained, it can be used to predict the transverse strain at any time, so the viscoelastic Poisson's ratio time domain change model of the target polymer under the target creep stress considering damage can be established as shown in the following formula (19) by combining the creep process damage evolution model and the relaxation modulus time domain change model, and the model form is:

[0075] Wherein: is the viscoelastic Poisson's ratio considering damage, is the creep time corresponding to the creep damage variable calculated by the creep process damage evolution model, is the creep time corresponding to the relaxation modulus calculated by the relaxation modulus time domain change model, is the instantaneous time corresponding to the transverse strain calculated by the transverse strain time domain change model, is the target creep stress.

[0076] It should be noted that the damage considering viscoelastic Poisson's ratio time domain variation model described in formula (19) needs to be constructed separately for each target creep stress, and the model under different creep stresses and is only related to the target polymer, so as long as the target polymer does not change, the and in formula (19) under different creep stresses are the same, but the lateral strain in the lateral 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 lateral strain time domain variation model needs to be fitted separately, and then substituted into formula (19) to form the damage considering viscoelastic Poisson's ratio time domain variation model under the target creep stress.

[0077] In another embodiment of the present application, based on the damage considering viscoelastic Poisson's ratio time domain variation model constructed for the target polymer and the target creep stress described above, a particle reinforced polymer damage containing viscoelastic Poisson's ratio prediction system can be further constructed, as shown in Figure 2 , which comprises: a prediction time specifying module for inputting a target time at which the viscoelastic Poisson's ratio needs to be predicted; a prediction result generating module for calling the damage considering viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress according to the particle reinforced polymer damage containing viscoelastic Poisson's ratio prediction method described in the foregoing embodiments, and obtaining the prediction result of the viscoelastic Poisson's ratio at the target time under the target creep stress according to the target time.

[0078] It should be noted that the prediction time specifying module described above can be input by a user through a GUI interface or other instruction input form, and the target time at which the viscoelastic Poisson's ratio needs to be predicted can be flexibly input according to the time point value or time period as needed. Similarly, the prediction result generating module can also display the prediction result of the viscoelastic Poisson's ratio through a GUI interface or other result file output form.

[0079] It should be noted that the particle reinforced polymer damage containing viscoelastic Poisson's ratio prediction method shown in S1-S4 and the particle reinforced polymer damage containing viscoelastic Poisson's ratio prediction system described above can essentially be realized in the form of a computer program or a software functional module.

[0080] Therefore, based on the same inventive concept, as shown in Figure 3 , the present application also provides a computer electronic device corresponding to the particle reinforced polymer damage containing viscoelastic Poisson's ratio prediction method provided in the foregoing embodiments, which comprises a memory and a processor. the memory, configured to store a computer program; the processor, configured to, when executing the computer program, 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.

[0081] In addition, the logic instructions in the memory described above can be implemented in the form of a software functional unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number 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 methods described in the various embodiments of the present application.

[0082] 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.

[0083] Therefore, based on the same inventive concept, the present application provides a computer program product, including computer programs / instructions, which, when executed by a processor, can 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.

[0084] Specifically, in the computer readable storage medium of the above three embodiments, the computer program stored therein is executed by a processor, and the steps of S1-S4 or the two functional modules in the particle reinforced polymer damage-containing viscoelastic Poisson's ratio prediction system can be executed.

[0085] It can be understood that the storage medium described above can include a random access memory (RAM) and can also include 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.

[0086] It can be understood that the processor described above can be a general processor, including a central processing unit (CPU), a network processor (NP), etc.; can also be 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.

[0087] In addition, 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 mode in actual implementation, for example, a plurality of modules or steps can be combined or integrated together, or a module or step can be split.

[0088] The present application will be further illustrated by a specific embodiment below to show 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.

[0089] Embodiment 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 specific test data acquisition and the specific results of each step will be mainly shown below.

[0090] In this embodiment, the target polymer in S1 step is subjected to a creep rupture test under different creep stresses, the target polymer in S2 step is subjected to a longitudinal tensile creep test under different creep stresses, and the target polymer in S4 step is subjected to a tensile creep test under a target creep stress, and the test data are obtained through the same test. The target polymer in this test is a HTPB / AP composite solid propellant with a solid content of 83% used in a certain type of rocket engine charge. The HTPB / AP composite solid propellant is subjected to a verification test in a controlled environment (SDJ705 high-low temperature and humidity test chamber) with a constant temperature of 20°C and a humidity of less than 50%. The test is conducted at 7 groups of creep stress levels (0.0241 MPa, 0.0492 MPa, 0.1022 MPa, 0.1372 MPa, 0.1862 MPa, 0.2205 MPa, and 0.2403 MPa), and a long-term creep test scheme under 7 groups of creep stresses is designed: the HTPB / AP composite solid propellant is subjected to tension by applying different creep stresses through a hanging weight type multi-specimen creep device, the transverse strain and longitudinal strain are synchronously measured at regular intervals by using a vernier caliper under each group of creep stress, 60-day short-term creep full-cycle data are obtained, and a 10-year long-term evolution behavior is extrapolated based on a damage decoupling model. If creep rupture occurs during the creep process, the rupture time is recorded. Finally, creep rupture occurs at the 31st day, the 36th day, and the 66th day under the stresses of 0.2403 MPa, 0.2205 MPa, and 0.1862 MPa, respectively, and no creep rupture occurs under the remaining stress levels.

[0091] 1) In this embodiment, based on the creep rupture test data of the target polymer under different creep stresses, the exponential relationship model of the creep stress and the rupture time is fitted, the linear cumulative damage index and the Lebesgue stress norm of the target polymer are obtained, and the two damage parameters are assigned to the creep process damage evolution model with the creep stress and the creep time as the independent variables.

[0092] In this embodiment, the specimen rupture times under the stresses of 0.2403 MPa, 0.2205 MPa, and 0.1862 MPa are 31 days, 36 days, and 66 days, respectively. Therefore, the exponential relationship model of the creep stress and the rupture time corresponding to the foregoing formula (1) is fitted by the least square method using the three groups of data, and the following formula (2) is obtained. , 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 after the fitting parameter correction is less than 5%, the relationship between the creep stress and the rupture time is shown in Figure 4 , and the damage curves under different initial stress loading conditions are shown in Figure 5 .

[0093] 2) This embodiment refers to the foregoing S2 step, and damage decoupling is performed on longitudinal tensile creep test data of the target polymer under different creep stresses to obtain a linear creep process of the target polymer, and then creep compliance time domain variation data of the linear creep process are obtained.

[0094] In this embodiment, the creep compliance time domain variation data of the linear creep process are obtained under six different creep stresses. The creep compliance time domain variation data under four levels 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 relatively high, indicating that linear viscoelasticity is dominant and damage has been well decoupled.

[0095] 3) This embodiment refers to the foregoing S3 step, and a generalized Voigt model is fitted by using the creep compliance time domain variation data of the linear creep process, 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.

[0096] In this embodiment, the generalized Voigt model described in formula (6) adopts a 3-unit generalized Voigt model (Prony series), that is, the number n of Voigt units is 3, and the model is used for fitting the damage-free creep compliance. When j = 1, 2, 3, the delay times of the three Voigt units are respectively , , . The number m of Maxwell units in the generalized Maxwell model is also 3, so when i = 1, 2, 3, the relaxation times of the i th Maxwell unit are respectively , and the maximum relaxation time is 66. The relaxation modulus E1~E m is solved based on the matrix inversion algorithm of formula (16), so as to convert the creep compliance into the relaxation modulus, and in this embodiment, the Laplace domain analytical method is also calculated synchronously, and 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 of formula (16) of the present application, J represents the creep compliance, and laplaceE represents the relaxation modulus obtained by the Laplace domain analytical method.

[0097] 4) This embodiment refers to the foregoing S4 step, and a 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 a viscoelastic Poisson's ratio time domain variation model of the target polymer under the target creep stress considering damage is established by combining the damage evolution model of the creep process and the relaxation modulus time domain variation model, so as to predict the viscoelastic Poisson's ratio of the target polymer at any moment in the creep process.

[0098] In the present embodiment, the number of lateral strain parameters is set to = 6. To verify the final prediction effect, based on the time-domain variation model of the viscoelastic Poisson's ratio of the target polymer under the target creep stress considering damage shown in formula (19), the lateral strain model shown in formula (18) is input and the inverse relaxation modulus E ( t ), the Poisson's ratio test results within 30 days under 0.0241 MPa and 0.0492 MPa stress are shown in Figure 8 . Figure 8 It is shown that, in the creep process, the Poisson's ratio continuously increases in the short term and tends to 0.5, which is consistent with the characteristics of incompressible viscoelastic materials. In addition, the comparison chart of the long-term (10 years) Poisson's ratio prediction results and the damage evolution results 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, revealing the transition mechanism of the material from the incompressible state to the compressible state.

[0099] Finally, it should be noted that the above-described embodiments are only some of the preferred implementation schemes of the present application, but are not intended to limit the present application. Those of ordinary skill in the related art can make various changes and modifications without departing from the spirit and scope of the present application. For example, after obtaining the linear creep process of the high solid content polymer by damage decoupling, the model of damage in the damage decoupling process, the creep compliance model, and the method of converting the relaxation modulus through the creep compliance are not unique, such as the nonlinear damage evolution model (but the creep compliances under different stresses obtained after damage decoupling should have a high coincidence degree, i.e., meet the linear viscoelastic process) can be used for the damage model, the Burgers model can be used for the creep compliance fitting, and the Laplace transform and inverse transform can be used for the method of converting the relaxation modulus through the creep compliance. 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 the Poisson's ratio of damaged viscoelasticity in particle-reinforced polymers, characterized in that, include: S1. Based on the creep fracture test data of the target polymer under different creep stresses, the exponential relationship model between creep stress and fracture time is fitted to obtain the linear cumulative damage index and Lebesgue stress norm of the target polymer. Then, the two damage parameters are assigned to the creep process damage evolution model with creep stress and creep time as independent variables. S2. Decouple 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 obtain the time domain variation data of the creep compliance of the linear creep process. S3. Fit the generalized Voigt model using the time-domain variation data of creep compliance in the linear creep process, and then invert the relaxation modulus time-domain variation model based on the transformation model between creep compliance and relaxation modulus. 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. 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 to predict the viscoelastic Poisson's ratio of the target polymer at any time during the creep process.

2. The method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 1, characterized in that, In the exponential relationship model between creep stress and fracture time, creep stress is obtained by multiplying the Lebesgue stress norm by the reciprocal of the exponential term, where the exponential term is raised to the power of the reciprocal of the linear cumulative damage exponent with the fracture time as the base.

3. The method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 1, characterized in that, The creep damage evolution model adopts a nonlinear model with creep damage variables as dependent variables, linear cumulative damage index and Lebesgue stress norm of the target polymer as fixed coefficients, and creep stress and creep time as independent variables.

4. The method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 1, characterized in that, 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: substitute the current creep stress into the creep process damage evolution model to obtain the time domain variation model of the creep damage variable, then calculate the creep damage variable corresponding to each creep time in the longitudinal strain time domain data, multiply the longitudinal strain at each creep moment by 1 and the difference between the longitudinal strain at each creep moment and the creep damage variable at that creep moment to obtain the longitudinal strain without damage at each creep moment, thus completing the damage decoupling; Then, divide the longitudinal strain time-domain variation data without damage 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 method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 1, characterized in that, In S3, the relaxation modulus time-domain variation model adopts the generalized Maxwell model, where the relaxation modulus of each Maxwell element is obtained by solving the transformation model between creep compliance and relaxation modulus.

6. The method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 5, characterized in that, The conversion model between creep compliance and relaxation modulus is as follows: ； in: This represents the number of Maxwell cells in the generalized Maxwell model. Let i be the relaxation time of the i-th Maxwell cell. Let i be the relaxation modulus of the i-th Maxwell element. To balance the modulus, Creep time; For instantaneous softness, The delay compliance of the j-th Voigt unit, The delay time of the j-th Voigt unit , The number of Voigt units. , and All models were obtained by fitting the generalized Voigt model using time-domain variation data of creep compliance during linear creep processes under different creep stresses as fitting data.

7. The method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 1, characterized in that, The time-domain variation model of the viscoelastic Poisson's ratio considering damage is in the following form: ； in: To account for the viscoelastic Poisson's ratio of damage, The creep time is calculated by the creep process damage evolution model. The corresponding creep damage variable, The creep time is calculated by the relaxation modulus time-domain variation model. The corresponding relaxation modulus, The instantaneous time obtained by the transverse strain time-domain variation model The corresponding transverse strain, The target creep stress.

8. A system for predicting the Poisson's ratio of damaged viscoelasticity in particle-reinforced polymers, characterized in that, include: The prediction time specification module is used to input the target time at which the viscoelastic Poisson's ratio needs to be predicted; The prediction result generation module is used to call the time-domain variation model of the viscoelastic Poisson's ratio of the target polymer under the target creep stress, considering the damage, according to the particle-reinforced polymer damage viscoelastic Poisson's ratio prediction method as described in any one of claims 1 to 7, and obtain the prediction result of the viscoelastic Poisson's ratio based on the target time.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it can implement the method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in any one of claims 1 to 7, or implement the system for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 8.

10. A computer electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to, when executing the computer program, implement the method for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in any one of claims 1 to 7, or implement the system for predicting the damaged viscoelastic Poisson's ratio of particle-reinforced polymers as described in claim 8.

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