Methods, apparatus, equipment, and media for constructing stress prediction models for semi-crystalline polymers

Abstract

This application relates to the field of mechanical technology and provides a method, apparatus, equipment, and medium for constructing a stress prediction model for semi-crystalline polymers. The construction method includes: determining target influencing factors associated with the stress behavior of semi-crystalline polymers; the target influencing factors include at least a temperature factor; constructing multiple theoretical expressions for stress behavior based on the target influencing factors; constructing a theoretical prediction model based on the multiple theoretical expressions for stress behavior, the theoretical prediction model including a comprehensive theoretical expression for characterizing the correlation between the theoretical expressions for stress behavior; performing discrete numerical analysis on each theoretical expression for stress behavior according to a preset numerical analysis method to obtain the corresponding engineering expressions for stress behavior; inputting each engineering expression for stress behavior into the comprehensive theoretical expression to obtain the engineering prediction model. This application achieves accurate prediction of the strain-stress behavior of semi-crystalline polymer materials over a wide temperature range.

Description

Technical Field

[0001] This application belongs to the field of mechanical technology, and in particular relates to the method, apparatus, equipment and medium for constructing stress prediction models for semi-crystalline polymers. Background Technology

[0002] For semi-crystalline polymer materials such as polyetheretherketone (PEEK), their mechanical properties determine their application scenarios. In the aerospace field, the development of components typically requires the use of high-performance materials. Predicting the mechanical properties of materials, especially their strain-stress behavior, is beneficial for accurately and efficiently assessing whether a material meets the requirements of a specific application scenario. This allows for the selection and optimized design of materials, thereby improving the performance and reliability of components using that material.

[0003] Most existing semi-crystalline constitutive models used to predict stress behavior are isothermal constitutive models. These models cannot capture the self-heating phenomenon of semi-crystalline polymer materials. Self-heating can cause the polymer to undergo a glass transition, reducing the lifespan of components. Summary of the Invention

[0004] This application provides a method, apparatus, equipment, and medium for constructing a stress prediction model for semi-crystalline polymers, which can solve the problem that existing models do not consider the influence of temperature during the prediction process, resulting in low prediction accuracy.

[0005] In a first aspect, embodiments of this application provide a method for constructing a stress prediction model for semi-crystalline polymers, comprising:

[0006] Identify target influencing factors associated with the stress behavior of semi-crystalline polymers; the target influencing factors include at least a temperature factor.

[0007] Based on the target influencing factor, multiple theoretical expressions for stress behavior are constructed;

[0008] Based on the multiple stress behavior theoretical expressions, a theoretical prediction model is constructed, which includes a comprehensive theoretical expression to characterize the correlation between the various stress behavior theoretical expressions;

[0009] According to the preset numerical analysis method, discrete numerical analysis is performed on each of the theoretical expressions of stress behavior to obtain the engineering expression of stress behavior corresponding to each of the theoretical expressions of stress behavior.

[0010] The engineering expressions for each stress behavior are input into the comprehensive theoretical expression to obtain the engineering prediction model.

[0011] Therefore, the method for constructing a stress prediction model for semi-crystalline polymers provided in this application can take into account the complex temperature environment in which the semi-crystalline polymer material is used. In at least one branch of the model, based on the temperature factor, an equivalent plastic strain rate update equation and a plastic deformation gradient update equation associated with it are constructed. Then, a plastic deformation gradient expression deeply associated with the temperature factor can be obtained. Based on the plastic deformation gradient expression, an elastic strain expression is obtained, so that the final engineering prediction model expression based on the elastic strain expression is deeply associated with the temperature factor. This enables accurate prediction of the strain and stress behavior of semi-crystalline polymer materials over a large temperature range, which is beneficial to ensuring the performance and reliability of parts manufactured using semi-crystalline polymer materials.

[0012] In one possible implementation of the first aspect, the plurality of stress behavior theoretical expressions include intermolecular resistance theoretical expressions, crystalline region resistance theoretical expressions, and molecular network resistance theoretical expressions; the construction method includes:

[0013] Based on the target influencing factors, theoretical expressions for intermolecular resistance, crystal region resistance, and molecular network resistance are constructed respectively.

[0014] A theoretical prediction model is constructed based on the theoretical expressions for intermolecular resistance, crystal region resistance, and molecular network resistance.

[0015] Based on the preset numerical analysis method, discrete numerical analysis is performed on the theoretical expressions of intermolecular resistance, crystal region resistance, and molecular network resistance respectively to obtain the engineering expressions of intermolecular resistance, crystal region resistance, and molecular network resistance.

[0016] The engineering expressions for intermolecular resistance, crystalline region resistance, and molecular network resistance are input into the theoretical prediction model to obtain the engineering prediction model; the engineering prediction model is used to characterize the correlation between the target influencing factor and the stress of the semi-crystalline polymer.

[0017] In one possible implementation of the first aspect, the engineering prediction model includes a first branch, a second branch, and a third branch in parallel; the first branch calculates a first stress using the intermolecular resistance engineering expression, the second branch calculates a second stress using the crystal region resistance engineering expression, and the third branch calculates a third stress using the molecular network resistance engineering expression; the output of the engineering prediction model is obtained by weighted calculation based on the first stress, the second stress, and the third stress.

[0018] In one possible implementation of the first aspect, the engineering prediction model includes multiple branches in parallel; the step of performing discrete numerical analysis on each of the theoretical expressions of stress behavior according to a preset numerical analysis method to obtain an engineering expression of stress behavior corresponding to each theoretical expression of stress behavior includes:

[0019] For at least one branch of the engineering prediction model, determine the initial plastic deformation gradient and establish the plastic deformation gradient update equation;

[0020] Based on the initial plastic deformation gradient and the plastic deformation gradient update equation, the plastic deformation gradient corresponding to the nth step is obtained; where n≤N, n represents the current iteration number of the engineering prediction model, and N represents the total iteration number of the engineering prediction model;

[0021] The elastic deformation gradient corresponding to the nth step is calculated based on the plastic deformation gradient corresponding to the nth step.

[0022] The elastic strain expression is calculated based on the elastic deformation gradient corresponding to the nth step.

[0023] The elastic strain expression is input into the stress behavior theoretical expression corresponding to the at least one branch to obtain the elastic stress expression corresponding to the at least one branch; the stress behavior engineering expression corresponding to the at least one branch includes the elastic stress expression.

[0024] In one possible implementation of the first aspect, establishing the plastic deformation gradient update equation includes:

[0025] Based on the temperature factor in the target influencing factors, an equivalent plastic strain rate update equation is established.

[0026] The equivalent plastic strain rate is calculated based on the updated equation for the equivalent plastic strain rate.

[0027] The plastic deformation rate is calculated based on the equivalent plastic strain rate.

[0028] Based on the plastic deformation rate, a plastic deformation gradient update equation is established.

[0029] In one possible implementation of the first aspect, calculating the equivalent plastic strain rate according to the equivalent plastic strain rate update equation includes:

[0030] A plastic resistance expression is constructed; the plastic resistance expression is used to characterize the relationship between plastic resistance and the equivalent plastic strain rate;

[0031] The plastic resistance expression is input into the equivalent plastic strain rate update equation to obtain the replaced equivalent plastic strain rate update equation;

[0032] The equivalent plastic strain rate is calculated based on the updated equation of the replaced equivalent plastic strain rate.

[0033] Secondly, embodiments of this application provide a method for predicting the stress-strain behavior of semi-crystalline polymers, including:

[0034] Obtain the factor values ​​corresponding to the target influencing factors under the current usage state of the semi-crystalline polymer;

[0035] The factor values ​​of the semi-crystalline polymer under its current use state are input into the engineering prediction model to obtain the elastic stress of each branch in the engineering prediction model; the engineering prediction model is obtained according to any of the above construction methods, and the engineering prediction model includes multiple branches in parallel; wherein, two branches of the multiple branches are used to calculate the plastic resistance based on the factor values, and the elastic stress is calculated based on the plastic resistance.

[0036] Based on the elastic stress of each branch in the engineering prediction model, the comprehensive stress value of the semi-crystalline polymer under the current use condition is calculated.

[0037] Therefore, the prediction method of the semi-crystalline polymer stress prediction model provided in this application embodiment can take into account the complex temperature environment in which the semi-crystalline polymer material is used. In at least one branch of the model, based on the temperature factor, an equivalent plastic strain rate update equation and a plastic deformation gradient update equation associated with it are constructed. Then, a plastic deformation gradient expression deeply associated with the temperature factor can be obtained. Based on the plastic deformation gradient expression, an elastic strain expression is obtained, so that the final engineering prediction model expression based on the elastic strain expression is deeply associated with the temperature factor. This enables accurate prediction of the strain and stress behavior of semi-crystalline polymer materials over a large temperature range, which is beneficial to ensuring the performance and reliability of parts manufactured using semi-crystalline polymer materials.

[0038] Thirdly, embodiments of this application provide an apparatus for constructing a stress prediction model for semi-crystalline polymers, comprising:

[0039] The target influence factor determination module determines the target influence factors associated with the stress behavior of the semi-crystalline polymer; the target influence factors include at least a temperature factor.

[0040] The theoretical expression construction module constructs multiple theoretical expressions for stress behavior based on the target influencing factor;

[0041] The theoretical prediction model construction module constructs a theoretical prediction model based on the multiple stress behavior theoretical expressions. The theoretical prediction model includes a comprehensive theoretical expression used to characterize the correlation between the various stress behavior theoretical expressions.

[0042] The engineering expression acquisition module performs discrete numerical analysis on each of the theoretical stress behavior expressions according to a preset numerical analysis method to obtain the engineering stress behavior expression corresponding to each of the theoretical stress behavior expressions.

[0043] The engineering prediction model acquisition module inputs the engineering expressions of each stress behavior into the comprehensive theoretical expression to obtain the engineering prediction model.

[0044] Fourthly, embodiments of this application provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for constructing a semi-crystalline polymer stress prediction model as described in any of the first aspects above.

[0045] Fifthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for constructing a semi-crystalline polymer stress prediction model as described in any of the first aspects above.

[0046] It is understood that the beneficial effects of the third to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart illustrating the method for constructing a stress prediction model for semi-crystalline polymers provided in this application embodiment;

[0049] Figure 2 This is a schematic diagram of the structure of the rheological model corresponding to the stress prediction model of the semi-crystalline polymer provided in the embodiments of this application;

[0050] Figure 3 This is a flowchart illustrating step S140 in the method for constructing a semi-crystalline polymer stress prediction model provided in this application embodiment;

[0051] Figure 4 This is a flowchart illustrating step S141 in the method for constructing a semi-crystalline polymer stress prediction model provided in this application embodiment;

[0052] Figure 5This is a flowchart illustrating the method for predicting the stress-strain behavior of semi-crystalline polymers provided in the embodiments of this application;

[0053] Figure 6 This is a schematic diagram of stress reference results and simulation results curves at different strain rates at 200 degrees Celsius, provided in the embodiments of this application;

[0054] Figure 7 This is a schematic diagram of stress reference results and simulation results curves at different strain rates at 100 degrees Celsius, provided in the embodiments of this application;

[0055] Figure 8 This is a schematic diagram of the stress reference results and simulation results curves at 100 degrees Celsius and a strain rate of 0.001 / s provided in the embodiments of this application for different crystallinities.

[0056] Figure 9 This is a schematic diagram of the structure of the apparatus for constructing a semi-crystalline polymer stress prediction model provided in the embodiments of this application;

[0057] Figure 10 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0058] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0059] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0060] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0061] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0062] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0063] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0064] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Figure 1 This is a schematic flowchart illustrating a method for constructing a stress prediction model for a semi-crystalline polymer, as provided in an embodiment of this application. Figure 1 As shown, the method includes:

[0066] S110, determine the target influencing factors associated with the stress behavior of the semi-crystalline polymer. The target influencing factors include at least a temperature factor. Specifically, the target influencing factors are factors associated with the strain-stress behavior of the semi-crystalline polymer material. In this embodiment, the target influencing factors include crystallinity, temperature factor, and strain rate, but this application is not limited thereto.

[0067] In practical engineering applications, PEEK is often used in conjunction with 3D printing to customize complex parts. However, the complex thermal history of 3D printing, coupled with the fact that temperature affects crystallinity (meaning crystallinity varies with temperature), makes it difficult to predict the mechanical properties of 3D-printed PEEK samples. This negatively impacts the widespread application of PEEK in the aerospace field. In contrast, existing isothermal constitutive models do not consider the influence of crystallinity on stress performance in semi-crystalline polymers. Since the crystallinity of semi-crystalline polymers directly affects the warpage and shrinkage rate of samples in additive manufacturing, controlling crystallinity is crucial for sample size and shape. The predictive model provided in this application considers crystallinity, thus overcoming this problem.

[0068] Since the mechanical properties of semi-crystalline polymer materials are also closely related to their strain rate, the strain rate of semi-crystalline polymers is also considered when constructing the engineering prediction model in this application embodiment. This is also beneficial to improving the accuracy of the above-mentioned engineering prediction model in predicting the stress of semi-crystalline polymer materials.

[0069] S120, Based on the aforementioned target influencing factors, multiple stress behavior theoretical expressions are constructed. This embodiment has three stress behavior theoretical expressions: intermolecular resistance, crystalline region resistance, and molecular network resistance. The subsequent prediction model has three branches, each corresponding one-to-one with one of the aforementioned stress behavior theoretical expressions. For example, the three branches are the first branch, the second branch, and the third branch. The first branch corresponds to the intermolecular resistance theoretical expression, the second branch to the crystalline region resistance theoretical expression, and the third branch to the molecular network resistance theoretical expression. The stress result for each branch is calculated based on the engineering expression derived from its corresponding stress behavior theoretical expression.

[0070] As an example and not a limitation, in this embodiment, the theoretical expression for intermolecular resistance described above can be as shown in formula (1):

[0071]

[0072] Among them, T A This represents the elastic stress corresponding to the first branch of the prediction model, also known as intermolecular resistance. J = det(F), where F represents the total deformation gradient corresponding to each branch of the prediction model. The total deformation gradient is the same for all branches. The total deformation gradient for each branch is the product of the plastic deformation gradient and the elastic deformation gradient of that branch. The plastic deformation gradient and the elastic deformation gradient are different for each branch. J represents the determinant of the total deformation gradient F. τA This represents the Kirchhoff stress corresponding to the first branch.

[0073] The above τ A The calculation formula is shown in formula (2):

[0074]

[0075] in, This represents the elastic right stretch tensor corresponding to the first branch. This represents the elastic strain corresponding to the first branch. The corresponding expression is also the expression for the elastic strain of the first branch. μ A (θ) represents the shear modulus related to the absolute temperature θ. Therefore, the expressions established in this application for calculating the elastic stress and Kirchhoff stress corresponding to the first branch comprehensively consider the strain rate and temperature factors of the semi-crystalline polymer material, enabling a more accurate prediction of the stress properties of the semi-crystalline polymer material.

[0076] The calculation formula for the above theoretical expression of crystal region resistance is shown in formula (3):

[0077]

[0078] Among them, T B This represents the elastic stress corresponding to the second branch of the prediction model, which is also the crystal region resistance. J = det(F), where F represents the total deformation gradient corresponding to each branch of the prediction model, and the total deformation gradient is the same for all branches. J represents the determinant of the total deformation gradient F. τ B This represents the Kirchhoff stress corresponding to the second branch. τ B The calculation formula is shown in formula (4):

[0079]

[0080] in, This represents the right stretch tensor corresponding to the second branch. This represents the elastic strain corresponding to the second branch. μ B k represents the shear modulus. B Indicates bulk modulus, Representation matrix The trace, I represents the second-order unit tensor, α represents the coefficient of thermal expansion, θ represents the absolute temperature, and θ0 represents the initial temperature.

[0081] Therefore, the expressions for calculating the elastic stress and Kirchhoff stress corresponding to the second branch established in this application embodiment are related to the strain factor and temperature factor. Since the strain rate is the ratio of strain to time, the prediction model comprehensively considers the strain rate and temperature factors of the semi-crystalline polymer material, enabling the model to more accurately predict the stress performance of the semi-crystalline polymer material under complex temperature and strain rate environments.

[0082] The calculation formula for the above molecular network resistance theoretical expression is shown in formula (5):

[0083]

[0084] Among them, T C This represents the elastic stress corresponding to the third branch of the prediction model, also known as the molecular network resistance. J = det(F), where F represents the total deformation gradient corresponding to each branch of the prediction model, and the total deformation gradient is the same for all branches. J represents the determinant of the total deformation gradient F. r This represents the rubber modulus. N represents the maximum tensile strength of the chain. L represents the stretch ratio of any single chain in a molecular network. -1 Let denote the inverse of the Langevin function, that is, the inverse function of the Langevin function. Let I denote the second-order identity tensor. This represents the isovolumetric portion of the left Cauchygreen tensor. F T Let F be the transpose of matrix F.

[0085] S130, Based on the above-mentioned multiple stress behavior theoretical expressions, a theoretical prediction model is constructed. This theoretical prediction model includes a comprehensive theoretical expression characterizing the relationships between the various stress behavior theoretical expressions. This theoretical prediction model is used to predict the stress results of components made of semi-crystalline polymer materials in certain operating environments. Figure 2 A schematic diagram of the rheological model corresponding to the theoretical prediction model is shown. It includes three parallel branches: a first branch 21, a second branch 22, and a third branch 23. The first branch 21 includes a first elastic stress module 211 and a first plastic resistance module 212. The first plastic resistance module 212 consists of two dampers. The first damper is related to the main chain motion of the molecule, involving the movement and rearrangement of molecular chain segments. The second damper is related to the side chain or branch motion of the molecule, simulating smaller motions in the molecular structure, such as local rotation of side chains or branches. The first damper has a significant impact on the macroscopic behavior of the polymer, determining the evolution of the yield stress of the polymer at high strain rates.

[0086] The second branch 22 includes a second elastic stress module 221 and a second plastic resistance module 222. The second plastic resistance module 222 consists of a damper. The third branch 23 includes only the third elastic stress module 231 and does not include the plastic resistance module. Since semi-crystalline polymers exhibit typical rubber-like behavior at high temperatures, they experience strain hardening. This strain hardening primarily stems from the orientation of the molecular chains, rather than the influence of the crystal structure. Therefore, in this embodiment, the third branch 23 utilizes a nonlinear rubber elastic spring unit, i.e., a Langevin spring, to simulate rubber elasticity and employs an eight-chain model to capture the resistance of molecular chain orientation, i.e., molecular network resistance. Figure 2 middle This represents the elastic deformation gradient corresponding to the first branch. F represents the elastic deformation gradient corresponding to the second branch. C This represents the elastic deformation gradient corresponding to the third branch.

[0087] As described above, the embodiments of this application involve three theoretical expressions for stress behavior. In this embodiment, the intermolecular resistance corresponding to the first branch 21 and the molecular network resistance corresponding to the third branch 23 are used to describe the mechanical behavior of the amorphous state, and the crystalline region resistance corresponding to the second branch 22 is used to describe the mechanical behavior of the crystalline state, thus obtaining a comprehensive theoretical expression. The comprehensive theoretical expression is a weighted combination of the various theoretical expressions for stress behavior. In this embodiment, the comprehensive theoretical expression is shown in formula (6):

[0088] T = (1-p)(T) A +T B )+pT C (6)

[0089] Where p represents crystallinity and T represents the comprehensive stress result output by the prediction model. As can be seen from formula (6), the comprehensive theoretical expression established in this application embodiment is related to crystallinity. Therefore, the expression established in this application embodiment for calculating comprehensive stress comprehensively considers the strain rate, temperature and crystallinity factors of the semi-crystalline polymer material, enabling the prediction model to more accurately predict the stress performance of the semi-crystalline polymer material under complex and changing target influencing factor environments.

[0090] Semicrystalline polymers exhibit different properties at different temperatures. At high temperatures, they show viscosity and low strength, while strain can reach 300%. At room temperature, semicrystalline polymers have higher strength. This application provides a thermo-mechanically coupled viscoelastic-plastic constitutive model considering crystallinity and temperature, implemented in the finite element software Abaqus. This model can predict stress over a wide temperature range and in multi-strain rate scenarios, which is of great significance for the widespread application of semicrystalline polymers in various fields.

[0091] S140, according to the preset numerical analysis method, perform discrete numerical analysis on each theoretical expression of stress behavior to obtain the engineering expression of stress behavior corresponding to each theoretical expression of stress behavior.

[0092] Specifically, there are three theoretical expressions for stress behavior and three engineering expressions for stress behavior. The aforementioned pre-defined numerical analysis method is based on a combination of the finite element method and the numerical difference method. Based on this pre-defined numerical analysis method, discrete numerical analysis is performed on the theoretical expressions for intermolecular resistance to obtain the engineering expressions for intermolecular resistance. Based on this pre-defined numerical analysis method, discrete numerical analysis is performed on the theoretical expressions for crystalline region resistance to obtain the engineering expressions for crystalline region resistance. Based on this pre-defined numerical analysis method, discrete numerical analysis is performed on the theoretical expressions for molecular network resistance to obtain the engineering expressions for molecular network resistance.

[0093] And S150, by inputting the engineering expressions for each stress behavior into the above comprehensive theoretical expression, an engineering prediction model is obtained. In specific implementation, the above engineering expressions for intermolecular resistance, crystalline region resistance, and molecular network resistance are input into the above comprehensive theoretical expression to obtain an engineering prediction model. The above engineering prediction model is used to characterize the correlation between the above target influencing factors and the stress of the semi-crystalline polymer.

[0094] The first branch of the engineering prediction model calculates the first stress using the above-mentioned engineering expression for intermolecular resistance. The second branch of the engineering prediction model calculates the second stress using the above-mentioned engineering expression for crystal region resistance. The third branch of the engineering prediction model calculates the third stress using the above-mentioned engineering expression for molecular network resistance. After the first, second, and third stresses are weighted and calculated based on the above formula (6), the final stress result predicted by the model, i.e., the comprehensive stress value, can be obtained.

[0095] The formulas (1) to (6) disclosed in the above embodiments of this application are only theoretical equations and cannot be directly used in engineering. They need to be converted into formulas that can be directly implemented by computer programming and used in engineering through the discrete numerical analysis steps disclosed in the subsequent embodiments of this application.

[0096] In this embodiment, for the first plastic resistance module 212 and the second plastic resistance module 222, the plastic flow is assumed to be incompressible. Therefore, in the theoretical implementation stage, the evolution equation of the plastic deformation gradient is as shown in formula (7):

[0097]

[0098] This represents the rate of change of the plastic deformation gradient corresponding to the second branch. This represents the plastic deformation gradient corresponding to the second branch. This represents the plastic deformation rate corresponding to the second branch, regarding The definition is shown in formula (8):

[0099]

[0100] in, Represents the equivalent plastic strain rate. Indicates the direction of plastic flow. The evolution equation can be expressed as formula (9):

[0101]

[0102] This represents the initial equivalent plastic strain rate, which is generated by a preset method. Updates are required during the iterative solution process. The equivalent shear stress is represented by m, which is a strain rate parameter and is generated by a preset value. S represents the internal variable, which determines the yield form of the curve, either softening or hardening. The evolution equation of the internal variable S can be expressed as formula (10). In this embodiment, the internal variable S is solved according to formula (10).

[0103]

[0104] in, It is the differential result of the internal variable S, where t represents the pre-factor, S sat This represents the saturation value of the internal variable S. It represents the equivalent plastic strain rate.

[0105] This can be expressed as formula (11):

[0106]

[0107] T′ B The elastic stress T corresponding to the second branch is represented by B The skewed portion, T′ B This can be expressed as formula (12):

[0108]

[0109] tr(T B ) represents the elastic stress T corresponding to the second branch. B The trace of the corresponding matrix, I represents the second-order identity tensor.

[0110] Equivalent shear stress This can be expressed as formula (13):

[0111]

[0112] Among them, (T′ B :T′ B ) indicates that for T′ B The double dot product operation.

[0113] Based on the above formulas (7) to (13), the plastic deformation gradient can be calculated in the theoretical stage. However, these formulas cannot realize the engineering application of the plastic deformation gradient. If engineering application is to be realized, subsequent engineering processing is required. Furthermore, the above formulas (7) to (13) are applicable to the solution process of the first branch and the second branch of the prediction model. The above formulas (7) to (13) only exemplarily list the calculation formula of the second branch B. When it is necessary to solve the relevant parameters of the first branch A, it is only necessary to replace the subscript B in formulas (7) to (13) with the subscript A. This embodiment will not be elaborated further.

[0114] In some alternative embodiments, for at least one branch of the engineering prediction model, the engineering of plastic deformation gradient calculation and branch elastic stress calculation can be achieved through the schemes shown in steps S141 to S145. Specifically, for these corresponding branches, such as Figure 3 As shown, step S140 includes:

[0115] S141, for at least one branch of the engineering prediction model, determine the initial plastic deformation gradient and establish the plastic deformation gradient update equation.

[0116] S142, based on the initial plastic deformation gradient and the plastic deformation gradient update equation described above, obtain the plastic deformation gradient corresponding to step n. Where n ≤ N, n represents the current iteration number of the engineering prediction model in the calculation process, and N represents the total number of iterations in the calculation process of the engineering prediction model. Both n and N are positive integers.

[0117] S143, based on the plastic deformation gradient corresponding to the nth step above, calculate the elastic deformation gradient corresponding to the nth step.

[0118] S144. Based on the elastic deformation gradient corresponding to the nth step above, the expression for elastic strain is calculated.

[0119] S145, input the above elastic strain expression into the stress behavior theoretical expression corresponding to the above at least one branch to obtain the elastic stress expression corresponding to the above at least one branch. The stress behavior engineering expression corresponding to the above at least one branch includes the above elastic stress expression.

[0120] Furthermore, such as Figure 4 As shown, in this embodiment, step S141 includes:

[0121] S1411, Based on the temperature factor in the above-mentioned target influencing factors, establish the equivalent plastic strain rate update equation.

[0122] S1412, the equivalent plastic strain rate is calculated based on the above-mentioned equivalent plastic strain rate update equation.

[0123] S1413, based on the above equivalent plastic strain rate, the plastic deformation rate is calculated.

[0124] And S1414, based on the above plastic deformation rate, establish the plastic deformation gradient update equation.

[0125] In this embodiment, step S1412 includes:

[0126] Construct an expression for plastic resistance. The above expression for plastic resistance is used to characterize the relationship between plastic resistance and the equivalent plastic strain rate.

[0127] Inputting the above plastic resistance expression into the above equivalent plastic strain rate update equation yields the replaced equivalent plastic strain rate update equation.

[0128] Furthermore, the equivalent plastic strain rate is calculated based on the updated equivalent plastic strain rate equation after the above replacement.

[0129] Specifically, the elastic stress T corresponding to the first branch can be obtained according to the above formula (1). A When the first branch is in the nth step of the engineering prediction model calculation and solution process, the equivalent stress is... When the value is greater than 0, the first branch enters the plastic state, at which point the equivalent plastic strain rate needs to be updated. Using the constitutive relation, the equivalent plastic strain rate update equation related to the temperature factor is obtained, as shown in equation (14):

[0130]

[0131] in, This represents the equivalent stress corresponding to the (n+1)th step in the calculation and solution process of the engineering prediction model for the first branch. This represents the plastic resistance corresponding to the (n+1)th step in the calculation and solution process of the first branch in the engineering prediction model. Wherein, and All are related to the temperature factor. The calculation formula is shown in formula (15):

[0132]

[0133] In the above formula (15), T A ′ ,n+1 T represents A,n+1The skewed portion, T A,n+1 This represents the elastic stress corresponding to the (n+1)th step in the calculation and solution process of the first branch in the engineering prediction model, (T) A ′ ,m+1 :T A ′ ,n+1 ) indicates that for T A ′ ,m+1 Perform a double dot product operation.

[0134] The above plastic resistance The calculation formula, i.e. the expression for plastic resistance, is shown in formula (16):

[0135]

[0136] Here, α represents the stress relaxation process related to the motion of the molecular backbone. β represents the stress relaxation process related to the motion of the molecular side chains or branches. B θ is Boltzmann's constant. θ is the absolute temperature. x This represents the activation volume corresponding to the independent variable x. This represents the initial rate constant. This represents the equivalent plastic strain rate at step (n+1) in the calculation and solution process of the first branch in the engineering prediction model. ΔH x Let x represent the activation energy corresponding to the independent variable x. R represents the gas constant. Represent the independent variable The corresponding inverse hyperbolic sine function.

[0137] Therefore, the expression for calculating the plastic resistance corresponding to the first branch established in this application embodiment takes into account the strain rate and temperature factors of the semi-crystalline polymer material, making it possible to more accurately predict the stress performance of the semi-crystalline polymer material.

[0138] In this embodiment, by substituting formulas (15) and (16) into formula (14) above, the updated equivalent plastic strain rate equation can be obtained. Based on this updated equivalent plastic strain rate equation, the equivalent plastic strain rate can be calculated. Then, by inputting the following formula (17), the plastic deformation rate corresponding to the (n+1)th step in the calculation and solution process of the first branch in the engineering prediction model can be calculated. Formula (17) is:

[0139]

[0140] Regarding step S141 above, since the material is not deformed in the initial state, the initial plastic deformation gradient corresponding to the first branch is a unit tensor, that is, an identity matrix. In this embodiment, the plastic deformation gradient update equation (i.e., the implicit solution equation) corresponding to the first branch is established as shown in formula (18):

[0141]

[0142] Where Δt represents the time step of the solution, based on the above initial plastic deformation gradient, the above formula (18), and the above plastic deformation rate. The plastic deformation gradient corresponding to the nth step in the calculation and solution process of the first branch in the engineering prediction model can then be obtained. Then, the total plastic deformation gradient F corresponding to the nth step in the calculation process of the first branch is obtained from the finite element software. A,n F A,n Given the quantities, the elastic deformation gradient corresponding to the nth step in the calculation and solution process of the first branch in the engineering prediction model is calculated according to formula (19). Formula (19) is:

[0143]

[0144] The above express The inverse matrix.

[0145] Then to Perform polar decomposition, as shown in equation (20):

[0146]

[0147] This represents the rotational component after polar decomposition, specifically the elastic rotation tensor corresponding to the nth step in the computational solution of the first branch. After polar decomposition, the elastic right-hand stretch tensor corresponding to the nth step in the computational solution of the first branch can be obtained. Then we can utilize The elastic strain corresponding to the nth step in the calculation process of the first branch is calculated. The expression for elastic strain. The expression is entered into the above formula (4) to replace Then input formula (4) into formula (3), and replace the subscripts in formulas (3) and (4) accordingly to calculate the elastic stress T corresponding to the first branch. A .

[0148] Therefore, as can be seen from the above description, the steps S141 to S145 disclosed in the embodiments of this application are applicable to solving the elastic stress corresponding to the first branch.

[0149] For the solution process of elastic stress corresponding to the second branch of the engineering prediction model, please refer to the following specific implementation plan description.

[0150] For the second branch, similar to the first branch, since the material is undeformed in the initial state, the initial plastic deformation gradient corresponding to the second branch is a unit tensor, that is, an identity matrix. Using the exponential mapping method, the plastic deformation gradient update equation (i.e., the implicit solution equation) corresponding to the second branch established in this embodiment is as shown in formula (21):

[0151]

[0152] Among them, the above This represents the plastic deformation gradient corresponding to the (n+1)th step in the calculation and solution process of the engineering prediction model in the second branch. This represents the plastic deformation gradient corresponding to the nth step in the calculation and solution process of the second branch in the engineering prediction model, where Δt represents the time step of the solution. This represents the plastic deformation rate corresponding to the (n+1)th step in the calculation and solution process of the second branch in the engineering prediction model. express The inverse matrix. express The inverse matrix.

[0153] Furthermore, embodiments of this application establish the experimental elastic deformation gradient corresponding to the second branch. The solution equation is shown in formula (22):

[0154]

[0155] The above F B,n+1 F represents the total plastic deformation gradient corresponding to the (n+1)th step in the calculation process of the second branch. Since the total deformation gradient corresponding to each branch is the same, therefore F B,n+1 And F in the first branch A,n The values ​​are equal.

[0156] The embodiments of this application refer to the above. Perform polar decomposition, as shown in equation (23):

[0157]

[0158] The above This represents the rotational component after pole decomposition, i.e., the experimental elastic rotational tensor corresponding to the second branch. After pole decomposition, the experimental elastic right-hand tensor corresponding to the second branch can be obtained.

[0159] This application embodiment is based on the above-described... Through polar decomposition and some algebraic operations, a solution equation for the elastic strain expression corresponding to the second branch was also established, as shown in formula (24):

[0160]

[0161] in, This represents the elastic right stretch tensor corresponding to the (n+1)th step in the calculation process of the second branch. Let represent the elastic strain corresponding to the (n+1)th step in the calculation process of the second branch, and let Δt and Δt represent the elastic strain. The meanings of the variables are described above and will not be repeated here.

[0162] Then, substituting the above formula (24) into the above formula (4), the Kirchhoff stress τ corresponding to the second branch can be obtained in this embodiment. B The update equation is shown in formula (25):

[0163]

[0164] τ B,n+1 τ represents the Kirchhoff stress corresponding to the (n+1)th step in the calculation process of the second branch. B,trial This represents the experimental Kirchhoff stress corresponding to the second branch. μ B This represents the shear modulus. This represents the equivalent plastic strain rate corresponding to the (n+1)th step in the calculation and solution process of the second branch in the engineering prediction model. Indicates the direction of plastic flow.

[0165] Based on the reverse flow rule, this application embodiment transforms the above formula (9) to obtain the expression characterizing the equivalent shear stress of the second branch. The equation (26) relating the relationship between the internal variable S and the variable S is shown below:

[0166]

[0167] The meaning of the relevant parameters in formula (26) can be found in the relevant description in formula (9), and will not be repeated here.

[0168] Then, by combining the above formulas (3), (11), and (25), we can obtain the relationship between elastic stress T and T. B The update equation is shown in formula (27):

[0169]

[0170] in, This represents the equivalent elastic stress corresponding to the (n+1)th step in the calculation and solution process of the engineering prediction model in the second branch. This represents the equivalent experimental elastic stress in the calculation process of the second branch. Combining the above formulas (26) and (27), the equivalent plastic strain rate can be obtained. The implicit equation is shown in formula (28):

[0171]

[0172] The meanings of each variable can be referred to the above description, and will not be repeated in this embodiment. Then, combining the above formulas (7) to (13) and formula (28), the equivalent plastic strain rate is obtained by updating the equation using the backward Euler method. The corresponding value. Substituting the corresponding values ​​into formula (24) above, the elastic strain corresponding to the second branch can be obtained. The expression for elastic strain Substituting the expression into formulas (4) and (3), the elastic stress T corresponding to the second branch can be calculated. B .

[0173] Regarding the third branch of the engineering prediction model, since its network resistance is nonlinear elastic and does not involve the plastic resistance part, there is no need to update the plastic deformation gradient. The elastic stress update equation of the third branch can be directly established according to the above formula (5), as shown in formula (29):

[0174]

[0175] Among them, T C,n+1 This represents the elastic stress corresponding to the (n+1)th step in the calculation and solution process of the engineering prediction model in the third branch. This represents the stretching ratio of any single chain in the molecular network during the (n+1)th step of the solution process. This represents the volumetric portion of the left Cauchy Green tensor during the (n+1)th step of the solution process. F n+1 This represents the total deformation gradient during the (n+1)th step of the solution process, which is equal to F. (F) n+1 ) T Represents matrix F n+1 The transpose of .

[0176] Based on the above technical solution, the embodiments of this application realize the elastic stress T of the first branch. A The elastic stress T corresponding to the second branch B And the elastic stress T corresponding to the third branch CThe discretization and numericalization of the stresses corresponding to the three branches after discretization and numericalization, along with the pre-obtained crystallinity parameter values, are substituted into the above formula (6) to obtain the predicted comprehensive stress, making the above prediction model usable in engineering applications. For example, during use, the relevant equations can be programmed into the user subroutines UMAT and UMTHT of the Abaqus software using Fortran language, and the obtained material parameters can be input to establish a 2D model, thereby obtaining the strain-stress relationship of the material.

[0177] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0178] Therefore, the stress prediction model for semi-crystalline polymers provided in this application adopts a three-parallel model, which accurately captures the amorphous phase, crystalline phase, and molecular network stress of semi-crystalline polymer materials, ensuring the adaptability and accuracy of the model under various physical conditions, realizing accurate prediction of the stress performance of semi-crystalline polymers in engineering applications, and expanding the application prospects of semi-crystalline polymer materials in the aerospace industry.

[0179] The semi-crystalline polymer stress prediction model provided in this application constructs, in at least one branch, an equivalent plastic strain rate update equation and a plastic deformation gradient update equation related to temperature and strain rate, based on temperature factor and elastic strain. Then, a plastic deformation gradient expression deeply correlated with temperature factor can be obtained, and an elastic strain expression is derived based on the plastic deformation gradient expression. Furthermore, the established comprehensive theoretical expression is correlated with crystallinity, enabling the final engineering prediction model expression based on this elastic strain expression to be deeply correlated with the target influencing factor. This allows for consideration of the complex environments in which semi-crystalline polymer materials are used, achieving accurate prediction of the strain-stress behavior of semi-crystalline polymer materials over a wide range of temperature, strain rate, and crystallinity, thus ensuring the performance and reliability of parts manufactured using semi-crystalline polymer materials.

[0180] In another embodiment of this application, a method for predicting the stress-strain behavior of semi-crystalline polymers is disclosed. For example... Figure 5 As shown, the prediction method includes the following steps:

[0181] S510, obtain the factor value corresponding to the target influencing factor under the current usage state of the semi-crystalline polymer.

[0182] S520, the factor values ​​of the semi-crystalline polymer under its current use state are input into the engineering prediction model to obtain the elastic stress of each branch in the engineering prediction model. The engineering prediction model is obtained according to the construction method disclosed in any of the above embodiments, and the engineering prediction model includes multiple branches in parallel. Among them, two branches of the multiple branches calculate the plastic resistance based on the factor values, and the elastic stress is calculated based on the plastic resistance.

[0183] S530, based on the elastic stress of each branch in the above engineering prediction model, the comprehensive stress value of the above semi-crystalline polymer under the current use state is calculated.

[0184] In practical implementation, the input parameters of the aforementioned engineering prediction model, namely the target influencing factors, are obtained and input into the model. The model then calculates and outputs the comprehensive stress value of the semi-crystalline polymer material under the current state. These target influencing factors include, but are not limited to, temperature, strain rate, and crystallinity. This prediction method repeats the steps in the aforementioned construction method during the calculation process to obtain the output result. The difference lies in that the results obtained from each step in the construction method are expressions, while the results output from each step in the prediction method are numerical.

[0185] This application also provides embodiments for verifying the effects of factors such as temperature, strain rate, and crystallinity on stress. Among them, Figure 6 and Figure 7 The effect of temperature and strain rate factors is verified. Figure 8 This study verifies the influence of crystallinity. In this embodiment, tensile simulation experiments were conducted at different temperatures using a universal testing machine equipped with an environmental chamber, and material strain was monitored using digital image correlation technology. The simulation experiments were performed at 100℃ and 200℃, simulating strain rates of 0.001 / s, 0.01 / s, and 0.1 / s, respectively. Before the simulation experiments began, the samples were kept at the environmental chamber for 30 minutes to ensure temperature uniformity. The first part of this embodiment will only show and briefly analyze the data from the three different strain rate experiments at 200℃ and 100℃, illustrating the model's predictive performance under the influence of temperature and strain rate factors. In this environment, the first part mainly focuses on the mechanical properties of the material at different temperatures and strain rates.

[0186] like Figure 6As shown, at 200 degrees Celsius, strain rates of 0.001 / s (corresponding to curve 63), 0.01 / s (corresponding to curve 62), and 0.1 / s (corresponding to curve 61) were simulated. The solid line represents the reference result, which is the preset real result. The scatter plot represents the simulation experimental results; the goal of the experiment is to fit the reference result with the simulation results. Observation shows that the simulation experimental results and the reference result curves exhibit good agreement. The simulation experimental results capture three deformation stages of the semi-crystalline polymer material at high temperature: linear elastic behavior in the small deformation stage, strain hardening phenomenon in the medium deformation stage, and rubbery behavior in the large deformation stage. The higher the strain rate, the greater the yield stress and the greater the overall stress of the semi-crystalline polymer material.

[0187] like Figure 7 As shown, strain rates of 0.001 / s (corresponding to curve 73), 0.01 / s (corresponding to curve 72), and 0.1 / s (corresponding to curve 71) were simulated at 100 degrees Celsius. The reference curves at 100 degrees Celsius show significant differences compared to those at 200 degrees Celsius. At 100 degrees Celsius, the Young's modulus of the semi-crystalline polymer material is significantly higher than that at 200 degrees Celsius. It also exhibits strain softening behavior, with a substantial reduction in strain. This strain softening phenomenon is mainly due to self-heating caused by the high strain rate at low temperatures, which is caused by friction and molecular chain movement within the material.

[0188] The simulation results in the first part of this embodiment demonstrate that the engineering prediction model provided in this embodiment has good prediction accuracy under the influence of different temperature and strain rate factors.

[0189] The second part of this embodiment performs predictive analysis on samples with different crystallinities. The tensile testing method for these samples is consistent with that in the first part. For example... Figure 8 As shown, experiments were conducted on samples with three different crystallinities at 100 degrees Celsius and a strain rate of 0.001 / s. The crystallinities were 21.11% (corresponding to curve 83), 24.01% (corresponding to curve 82), and 26.09% (corresponding to curve 81), respectively. Samples with different crystallinities were prepared using a sand-filled heat treatment annealing method. Specifically, sand-filled heat treatment involves placing the sample in sand and then heating it in an oven. This method effectively prevents warping and shrinkage of the sample during heat treatment.

[0190] like Figure 8As shown, the overall stress-strain behavior of semi-crystalline polymer materials at different crystallinities is somewhat similar to that at different strain rates, both exhibiting strain softening. Samples with higher crystallinity exhibit higher strength and yield stress. This is because increasing crystallinity means increasing the number of regions where polymer chains are neatly arranged, and crystalline regions have significantly higher load-bearing capacity than amorphous regions. The engineering prediction model provided in this application can accurately capture these changes in mechanical behavior at different crystallinities.

[0191] The simulation results in the second part of this embodiment demonstrate that the engineering prediction model provided in this embodiment maintains good prediction accuracy under the influence of different crystallinity factors.

[0192] Therefore, by comparing the experimental results under different strain rates, temperatures and crystallinities, it is demonstrated that the engineering prediction model provided in this application can effectively predict the stress properties of semi-crystalline polymer materials.

[0193] Therefore, the method for predicting the stress-strain behavior of semi-crystalline polymers provided in this application constructs, in at least one branch, an equivalent plastic strain rate update equation and a plastic deformation gradient update equation related to temperature and strain rate based on temperature factor and elastic strain. Then, a plastic deformation gradient expression deeply related to temperature factor can be obtained, and an elastic strain expression can be obtained based on the plastic deformation gradient expression. Furthermore, the established comprehensive theoretical expression is related to crystallinity, so that the engineering prediction model expression finally established based on the elastic strain expression is deeply related to the target influencing factor. This method can take into account the complex environment in which semi-crystalline polymer materials are used, and achieve accurate prediction of the strain-stress behavior of semi-crystalline polymer materials within a large temperature range, strain rate range, and crystallinity range. This is beneficial for ensuring the performance and reliability of parts manufactured using semi-crystalline polymer materials.

[0194] In other words, the model accurately captures the amorphous phase, crystalline phase, and molecular network stress of the semi-crystalline polymer material during the prediction process, ensuring the model's adaptability and accuracy under various physical conditions. This enables accurate prediction of the stress performance of semi-crystalline polymers in engineering applications and expands the application prospects of semi-crystalline polymer materials in the aerospace industry.

[0195] Corresponding to the method for constructing the stress prediction model for semi-crystalline polymers described in the above embodiments, Figure 9 A structural block diagram of the apparatus for constructing a stress prediction model for semi-crystalline polymers provided in the embodiments of this application is shown. For ease of explanation, only the parts related to the embodiments of this application are shown.

[0196] Reference Figure 9 The construction device includes:

[0197] The target influence factor determination module 91 determines the target influence factors associated with the stress behavior of the semi-crystalline polymer. These target influence factors include at least a temperature factor.

[0198] The theoretical expression construction module 92 constructs multiple theoretical expressions for stress behavior based on the aforementioned target influencing factors.

[0199] The theoretical prediction model construction module 93 constructs a theoretical prediction model based on the above multiple stress behavior theoretical expressions. The theoretical prediction model includes a comprehensive theoretical expression used to characterize the correlation between the various stress behavior theoretical expressions.

[0200] The engineering expression acquisition module 94 performs discrete numerical analysis on each of the above-mentioned theoretical expressions of stress behavior according to a preset numerical analysis method, and obtains the engineering expression of stress behavior corresponding to each of the above-mentioned theoretical expressions of stress behavior.

[0201] The engineering prediction model acquisition module 95 inputs the above-mentioned stress behavior engineering expressions into the above-mentioned comprehensive theoretical expression to obtain the engineering prediction model.

[0202] In some optional embodiments, the aforementioned multiple stress behavior theoretical expressions include intermolecular resistance theoretical expressions, crystalline region resistance theoretical expressions, and molecular network resistance theoretical expressions. The theoretical expression construction module 92 is used to construct intermolecular resistance theoretical expressions, crystalline region resistance theoretical expressions, and molecular network resistance theoretical expressions based on the aforementioned target influencing factors. The theoretical prediction model construction module 93 is used to construct theoretical prediction models based on the aforementioned intermolecular resistance theoretical expressions, crystalline region resistance theoretical expressions, and molecular network resistance theoretical expressions. The engineering expression acquisition module 94 performs discrete numerical analysis on the aforementioned intermolecular resistance theoretical expressions, crystalline region resistance theoretical expressions, and molecular network resistance theoretical expressions according to a preset numerical analysis method, obtaining engineering expressions for intermolecular resistance, crystalline region resistance, and molecular network resistance. The engineering prediction model acquisition module 95 is used to input the aforementioned intermolecular resistance engineering expressions, crystalline region resistance engineering expressions, and molecular network resistance engineering expressions into the aforementioned theoretical prediction models to obtain engineering prediction models; the engineering prediction models are used to characterize the correlation between the aforementioned target influencing factors and the stress of the aforementioned semi-crystalline polymer.

[0203] In some optional embodiments, the above-mentioned engineering prediction model includes a first branch, a second branch, and a third branch in parallel; the first branch calculates the first stress using the above-mentioned intermolecular resistance engineering expression, the second branch calculates the second stress using the above-mentioned crystal region resistance engineering expression, and the third branch calculates the third stress using the above-mentioned molecular network resistance engineering expression; the output of the above-mentioned engineering prediction model is obtained by weighted calculation based on the above-mentioned first stress, the above-mentioned second stress, and the above-mentioned third stress.

[0204] In some alternative embodiments, the above-mentioned engineering expression obtaining module 94 includes:

[0205] The first processing unit determines the initial plastic deformation gradient and establishes the plastic deformation gradient update equation for at least one branch of the above engineering prediction model.

[0206] The plastic deformation gradient acquisition unit obtains the plastic deformation gradient corresponding to the nth step based on the initial plastic deformation gradient and the plastic deformation gradient update equation described above. Here, n ≤ N, where n represents the current iteration number of the engineering prediction model and N represents the total number of iterations of the engineering prediction model.

[0207] The elastic deformation gradient calculation unit calculates the elastic deformation gradient corresponding to the nth step based on the plastic deformation gradient corresponding to the nth step above.

[0208] The elastic strain calculation unit calculates the elastic strain expression based on the elastic deformation gradient corresponding to the nth step above.

[0209] The elastic stress expression acquisition unit inputs the aforementioned elastic strain expression into the stress behavior theoretical expression corresponding to at least one of the aforementioned branches to obtain the elastic stress expression corresponding to at least one of the aforementioned branches. The stress behavior engineering expression corresponding to at least one of the aforementioned branches includes the aforementioned elastic stress expression.

[0210] In some alternative embodiments, the first processing unit includes:

[0211] The first equation establishment unit establishes an equivalent plastic strain rate update equation based on the temperature factor in the target influence factors.

[0212] The first calculation unit calculates the equivalent plastic strain rate based on the above-mentioned equivalent plastic strain rate update equation.

[0213] The second calculation unit calculates the plastic deformation rate based on the equivalent plastic strain rate mentioned above.

[0214] The second equation establishes the unit, and based on the above plastic deformation rate, establishes the plastic deformation gradient update equation.

[0215] In some alternative embodiments, the first computing unit described above includes:

[0216] The first processing sub-unit constructs the expression for plastic resistance. This expression characterizes the relationship between plastic resistance and the equivalent plastic strain rate.

[0217] The second processing subunit inputs the above plastic resistance expression into the above equivalent plastic strain rate update equation to obtain the replaced equivalent plastic strain rate update equation.

[0218] The third processing subunit calculates the equivalent plastic strain rate based on the updated equivalent plastic strain rate equation after the above replacement.

[0219] In another embodiment of this application, a device for predicting the stress-strain behavior of a semi-crystalline polymer is provided. The prediction device includes:

[0220] The factor value acquisition module obtains the factor values ​​corresponding to the target influencing factors under the current usage state of the semi-crystalline polymer.

[0221] The branched elastic stress calculation module inputs the factor values ​​of the semi-crystalline polymer under its current use state into the engineering prediction model to obtain the elastic stress of each branch in the engineering prediction model. The engineering prediction model is obtained according to the construction method disclosed in any of the above embodiments, and includes multiple branches in parallel; wherein, two of the multiple branches calculate the plastic resistance based on the factor values, and the elastic stress is calculated based on the plastic resistance.

[0222] The comprehensive stress value calculation module calculates the comprehensive stress value of the semi-crystalline polymer under its current use state based on the elastic stress of each branch in the above engineering prediction model.

[0223] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0224] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0225] This application also provides an electronic device, such as... Figure 10 As shown, the electronic device 30 includes: at least one processor 301, a memory 302, and a computer program 303 stored in the memory and executable on the at least one processor, wherein the processor executes the computer program to implement the steps in any of the above method embodiments.

[0226] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0227] This application provides a computer program product that, when run on a mobile terminal, enables the mobile terminal to implement the steps described in the above-described method embodiments.

[0228] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographic device / electronic device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0229] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0230] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0231] In the embodiments provided in this application, it should be understood that the disclosed apparatus / network devices and methods can be implemented in other ways. For example, the apparatus / network device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0232] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0233] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for constructing a stress prediction model for semi-crystalline polymers, characterized in that, include: Identify the target influencing factors associated with the stress behavior of semi-crystalline polymers; The target influencing factors include at least the temperature factor; Based on the target influencing factor, multiple theoretical expressions for stress behavior are constructed; Based on the multiple stress behavior theoretical expressions, a theoretical prediction model is constructed, which includes a comprehensive theoretical expression to characterize the correlation between the various stress behavior theoretical expressions; According to the preset numerical analysis method, discrete numerical analysis is performed on each of the theoretical expressions of stress behavior to obtain the engineering expression of stress behavior corresponding to each of the theoretical expressions of stress behavior. The engineering expressions for each stress behavior are input into the comprehensive theoretical expression to obtain the engineering prediction model; The multiple stress behavior theoretical expressions include intermolecular resistance theoretical expressions, crystal region resistance theoretical expressions, and molecular network resistance theoretical expressions. The construction method includes: Based on the target influencing factors, theoretical expressions for intermolecular resistance, crystal region resistance, and molecular network resistance are constructed respectively. A theoretical prediction model is constructed based on the theoretical expressions for intermolecular resistance, crystal region resistance, and molecular network resistance. Based on the preset numerical analysis method, discrete numerical analysis is performed on the theoretical expressions of intermolecular resistance, crystal region resistance, and molecular network resistance respectively to obtain the engineering expressions of intermolecular resistance, crystal region resistance, and molecular network resistance. The engineering expressions for intermolecular resistance, crystalline region resistance, and molecular network resistance are input into the theoretical prediction model to obtain the engineering prediction model; the engineering prediction model is used to characterize the correlation between the target influencing factor and the stress of the semi-crystalline polymer. The theoretical expression for intermolecular resistance is shown in formula (1): in, This represents the elastic stress corresponding to the first branch of the prediction model, which is also known as intermolecular resistance. , This represents the total deformation gradient corresponding to each branch of the prediction model. The total deformation gradient corresponding to each branch is the same. The total deformation gradient corresponding to each branch is the product of the plastic deformation gradient and the elastic deformation gradient of each branch. The plastic deformation gradient of each branch is different, and the elastic deformation gradient of each branch is also different. The determinant of the total deformation gradient F; This represents the Kirchhoff stress corresponding to the first branch; The The calculation formula is shown in formula (2): in, , This represents the elastic right stretch tensor corresponding to the first branch. This represents the elastic strain corresponding to the first branch. The corresponding expression is also the expression for the elastic strain in the first branch. Represents absolute temperature The relevant shear modulus; The calculation formula for the theoretical expression of the crystal region resistance is shown in formula (3): in, This represents the elastic stress corresponding to the second branch of the prediction model, which is also known as the crystal region resistance. This indicates the Kirchhoff stress corresponding to the second branch; The calculation formula is shown in formula (4): in, This represents the right stretch tensor corresponding to the second branch. This represents the elastic strain corresponding to the second branch. Indicates shear modulus, Indicates bulk modulus. Representation matrix traces, Represents the second-order unit tensor. Indicates the coefficient of thermal expansion. Represents absolute temperature. Indicates the initial temperature; The calculation formula for the theoretical expression of molecular network resistance is shown in formula (5): in, This represents the elastic stress corresponding to the third branch of the prediction model, which is also known as the molecular network resistance. Indicates the rubber modulus. Indicates the maximum stretching factor of the chain. Represents the stretch ratio of any single chain in a molecular network. Describe the inverse function of the Langevin function. Represents the second-order unit tensor. This represents the volumetric portion of the left Cauchygreen tensor. , Denotes the transpose of matrix F; The comprehensive theoretical expression is shown in formula (6): in, Indicates crystallinity. This represents the combined stress result output by the prediction model.

2. The construction method as described in claim 1, characterized in that, The engineering prediction model includes a first branch, a second branch, and a third branch connected in parallel; the first branch uses the intermolecular resistance engineering expression to calculate the first stress, and the second branch uses the crystal region resistance engineering expression to calculate the second stress. The third branch calculates the third stress using the molecular network resistance engineering expression; the output of the engineering prediction model is obtained by weighted calculation based on the first stress, the second stress, and the third stress.

3. The construction method as described in claim 1, characterized in that, The engineering prediction model includes multiple branches in parallel; the step of performing discrete numerical analysis on each of the theoretical expressions of stress behavior according to a preset numerical analysis method to obtain the engineering expression of stress behavior corresponding to each theoretical expression of stress behavior includes: For at least one branch of the engineering prediction model, determine the initial plastic deformation gradient and establish the plastic deformation gradient update equation. Based on the initial plastic deformation gradient and the plastic deformation gradient update equation, the plastic deformation gradient corresponding to the nth step is obtained; where n≤N, n represents the current iteration number of the engineering prediction model, and N represents the total iteration number of the engineering prediction model; The elastic deformation gradient corresponding to the nth step is calculated based on the plastic deformation gradient corresponding to the nth step. The elastic strain expression is calculated based on the elastic deformation gradient corresponding to the nth step. The elastic strain expression is input into the stress behavior theoretical expression corresponding to the at least one branch to obtain the elastic stress expression corresponding to the at least one branch; the stress behavior engineering expression corresponding to the at least one branch includes the elastic stress expression.

4. The construction method as described in claim 3, characterized in that, The establishment of the plastic deformation gradient update equation includes: Based on the temperature factor in the target influencing factors, an equivalent plastic strain rate update equation is established. The equivalent plastic strain rate is calculated based on the updated equation for the equivalent plastic strain rate. The plastic deformation rate is calculated based on the equivalent plastic strain rate. Based on the plastic deformation rate, a plastic deformation gradient update equation is established.

5. The construction method as described in claim 4, characterized in that, The step of calculating the equivalent plastic strain rate based on the updated equation includes: A plastic resistance expression is constructed; the plastic resistance expression is used to characterize the relationship between plastic resistance and the equivalent plastic strain rate; The plastic resistance expression is input into the equivalent plastic strain rate update equation to obtain the replaced equivalent plastic strain rate update equation; The equivalent plastic strain rate is calculated based on the updated equation of the replaced equivalent plastic strain rate.

6. A method for predicting the stress-strain behavior of a semi-crystalline polymer, characterized in that, include: Obtain the factor values ​​corresponding to the target influencing factors under the current usage state of the semi-crystalline polymer; The factor values ​​of the semi-crystalline polymer under its current use state are input into the engineering prediction model to obtain the elastic stress of each branch in the engineering prediction model; the engineering prediction model is obtained by the construction method according to any one of claims 1-5, and the engineering prediction model includes multiple branches in parallel; wherein, two branches of the multiple branches calculate plastic resistance based on the factor values, and calculate elastic stress based on the plastic resistance; Based on the elastic stress of each branch in the engineering prediction model, the comprehensive stress value of the semi-crystalline polymer under the current use condition is calculated.

7. A device for constructing a stress prediction model for semi-crystalline polymers, characterized in that, include: The target influence factor determination module identifies the target influence factors associated with the stress behavior of semi-crystalline polymers. The target influencing factors include at least the temperature factor; The theoretical expression construction module constructs multiple theoretical expressions for stress behavior based on the target influencing factor; The theoretical prediction model construction module constructs a theoretical prediction model based on the multiple stress behavior theoretical expressions. The theoretical prediction model includes a comprehensive theoretical expression used to characterize the correlation between the various stress behavior theoretical expressions. The engineering expression acquisition module performs discrete numerical analysis on each of the theoretical stress behavior expressions according to a preset numerical analysis method to obtain the engineering stress behavior expression corresponding to each of the theoretical stress behavior expressions. The engineering prediction model acquisition module inputs the engineering expressions of each stress behavior into the comprehensive theoretical expression to obtain the engineering prediction model; The multiple stress behavior theoretical expressions include intermolecular resistance theoretical expressions, crystal region resistance theoretical expressions, and molecular network resistance theoretical expressions. The theoretical expression construction module is used to construct theoretical expressions for intermolecular resistance, crystal region resistance, and molecular network resistance, respectively, based on the target influencing factor. The theoretical prediction model construction module is used to construct a theoretical prediction model based on the theoretical expression of intermolecular resistance, the theoretical expression of crystal region resistance, and the theoretical expression of molecular network resistance. The engineering expression acquisition module is used to perform discrete numerical analysis on the theoretical expressions of intermolecular resistance, crystal region resistance, and molecular network resistance respectively according to a preset numerical analysis method, so as to obtain the engineering expressions of intermolecular resistance, crystal region resistance, and molecular network resistance. The engineering prediction model acquisition module is used to input the engineering expressions for intermolecular resistance, crystal region resistance, and molecular network resistance into the theoretical prediction model to obtain the engineering prediction model; the engineering prediction model is used to characterize the correlation between the target influencing factor and the stress of the semi-crystalline polymer; The theoretical expression for intermolecular resistance is shown in formula (1): in, This represents the elastic stress corresponding to the first branch of the prediction model, which is also known as intermolecular resistance. , This represents the total deformation gradient corresponding to each branch of the prediction model. The total deformation gradient corresponding to each branch is the same. The total deformation gradient corresponding to each branch is the product of the plastic deformation gradient and the elastic deformation gradient of each branch. The plastic deformation gradient of each branch is different, and the elastic deformation gradient of each branch is also different. The determinant of the total deformation gradient F; This represents the Kirchhoff stress corresponding to the first branch; The The calculation formula is shown in formula (2): in, , This represents the elastic right stretch tensor corresponding to the first branch. This represents the elastic strain corresponding to the first branch. The corresponding expression is also the expression for the elastic strain in the first branch. Represents absolute temperature The relevant shear modulus; The calculation formula for the theoretical expression of the crystal region resistance is shown in formula (3): in, This represents the elastic stress corresponding to the second branch of the prediction model, which is also known as the crystal region resistance. This indicates the Kirchhoff stress corresponding to the second branch; The calculation formula is shown in formula (4): in, This represents the right stretch tensor corresponding to the second branch. This represents the elastic strain corresponding to the second branch. Indicates shear modulus, Indicates bulk modulus. Representation matrix traces, Represents the second-order unit tensor. Indicates the coefficient of thermal expansion. Represents absolute temperature. Indicates the initial temperature; The calculation formula for the theoretical expression of molecular network resistance is shown in formula (5): in, This represents the elastic stress corresponding to the third branch of the prediction model, which is also known as the molecular network resistance. Indicates the rubber modulus. Indicates the maximum stretching factor of the chain. Represents the stretch ratio of any single chain in a molecular network. Describe the inverse function of the Langevin function. Represents the second-order unit tensor. This represents the volumetric portion of the left Cauchygreen tensor. , Denotes the transpose of matrix F; The comprehensive theoretical expression is shown in formula (6): in, Indicates crystallinity. This represents the combined stress result output by the prediction model.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 6.

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