Method for evaluating influence of radiation-induced microstructure evolution on macroscopic performance

Abstract

The invention provides a method for evaluating the influence of radiation-induced microstructure evolution on macroscopic performance. The method comprises the following steps: constructing a dual-network constitutive model; calculating the initial shear modulus and average chain length of the rubber network based on the chemical crosslinking density; based on the engineering stress-stretch rate data and the initial shear modulus and the average chain length of the rubber network, a dual-network constitutive model is adopted for fitting, and the initial shear modulus, the average chain length and filler aggregate distribution correlation constants of the filling network are obtained; based on the relationship between the initial shear modulus and the average chain length of the rubber network and the chemical crosslinking density, the relationship between the average chain length of the filling network and the interface layer content, and the relationship between the filler aggregate distribution correlation constant and the radiation dose, the relationship between the microstructure evolution and the macroscopic performance change in the radiation environment is determined. According to the method, the influence of radiation-induced microstructure evolution on the macroscopic performance can be more effectively researched, and the service life of related equipment filled with silicone rubber in a radiation industrial environment can be accurately evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of radiation aging of filled silicone rubber, and particularly to a method for evaluating the influence of radiation-induced microstructural evolution on macroscopic properties. Background Art

[0002] Silicone rubber is widely used in fields such as nuclear facilities and the aerospace industry due to its excellent chemical stability. However, in these application fields, silicone rubber may be affected by radiation aging, resulting in performance degradation and shortening the service life of equipment. Therefore, it is necessary to study the degradation mechanism of silicone rubber under radiation to understand the performance changes of equipment and ensure the safe use of equipment.

[0003] A large number of radiation tests have been carried out on polymers, such as gamma rays, neutrons, ultraviolet rays, and electrons, indicating that different types of high-energy radiation have similar effects on the aging of silicone rubber, and the degree of aging is related to the total dose. Generally, at lower doses, radiation causes a cross-linking effect, resulting in an increase in the hardness of silicone rubber. However, at higher doses, radiation-induced degradation dominates, which reduces the tensile strength and hardness.

[0004] Through a detailed analysis of the radiation products, the structural evolution of pure rubber under irradiation can be well explained. Free radicals detected by EPR (Electron Paramagnetic Resonance) indicate that silicon radicals, methylene radicals, and terminal oxygen radicals are generated under radiation. The combination of free radicals leads to new cross-linking and gas release, and H2, CH4, CO2, and CO are detected in the generated gas. Figure 1 It is a schematic diagram of the radiation aging mechanism of silicone rubber in the prior art, from which the radiation aging mechanism of silicone rubber can be inferred with reference to Figure 1 as shown.

[0005] The performance of pure rubber is poor and it is difficult to meet engineering requirements. Therefore, fillers are usually added to improve its mechanical properties. The structure and performance of filled silicone rubber will be affected by radiation during use. However, there is currently no effective method to study the correlation between radiation-induced microstructural evolution and macroscopic properties, resulting in difficulty in effectively evaluating the influence of radiation-induced microstructural evolution on macroscopic properties, and further leading to the inability to accurately evaluate the service life of filled silicone rubber-related equipment in an industrial radiation environment, affecting its industrial application. Summary of the Invention

[0006] The present invention provides a method for evaluating the influence of radiation-induced microstructural evolution on macroscopic properties, which is used to more effectively study the influence of radiation-induced microstructural evolution on macroscopic properties and accurately evaluate the service life of filled silicone rubber-related equipment in a radiation industrial environment.

[0007] The present invention provides a method for evaluating the influence of radiation-induced microstructure evolution on macroscopic properties, and the method includes: Constructing a double-network constitutive model corresponding to filled silicone rubber; the filled silicone rubber is silica-filled silicone rubber, and the double-network constitutive model includes a rubber network part and a filled network part; Based on the chemical crosslinking density of the filled silicone rubber at each radiation dose, calculating the initial shear modulus and average chain length of the rubber network in the filled silicone rubber at each radiation dose; Based on the engineering stress-strain rate data of the filled silicone rubber at each radiation dose, the initial shear modulus and average chain length of the rubber network, using the double-network constitutive model for fitting, to obtain the initial shear modulus, average chain length of the filled network in the filled silicone rubber at each radiation dose, and a constant related to the filler aggregate distribution; Based on the correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density, the correlation between the average chain length of the filled network and the interfacial layer content, and the correlation between the constant related to the filler aggregate distribution and the radiation dose, determining the relationship between the microstructure evolution and macroscopic property changes of the filled silicone rubber in a radiation environment, so as to evaluate the influence of the microstructure evolution of the filled silicone rubber on macroscopic properties in a radiation environment.

[0008] According to the method for evaluating the influence of radiation-induced microstructure evolution on macroscopic properties provided by the present invention, the double-network constitutive model is: ; wherein, δ is the engineering stress, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, , , , I1 is the first strain invariant, i is the Taylor series, i = 1, 2, 3, and λ is the elongation rate.

[0009] According to the method for evaluating the influence of radiation-induced microstructure evolution on macroscopic properties provided by the present invention, the constructing of the double-network constitutive model corresponding to the filled silicone rubber includes: Based on the free energy of the rubber network and the free energy of the filled network, constructing a generalized strain energy function of the filled silicone rubber; Based on the survival chain cumulative probability distribution function of the filled network during the stretching process, determining a deformation function for characterizing the evolution of the filled network during the stretching process; Based on the generalized strain energy function of the filled silicone rubber and the deformation function, constructing a double-network constitutive model corresponding to the filled silicone rubber.

[0010] An evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, the cumulative probability distribution function of the surviving chains of the filler network during the stretching process is determined by the following method: Based on the average functionality of the active absorption sites on the aggregate filler, the maximum chain length in the filler network, and the Kuhn length, determine the probability of chains of length l in the filler network; Based on the stretching length and the maximum chain length in the filler network, perform a length integration on the probability of chains of length l in the filler network to determine the initial cumulative probability distribution function of the surviving chains; Simplify the exponential content in the initial cumulative probability distribution function of the surviving chains to obtain the cumulative probability distribution function of the surviving chains of the filler network during the stretching process.

[0011] An evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, the cumulative probability distribution function of the surviving chains of the filler network during the stretching process is: ; wherein, is the strain, , z is a constant related to the filler aggregate distribution, is the cumulative probability distribution function of the surviving chains of the filler network during the stretching process; The deformation function used to characterize the evolution of the filler network during the stretching process is: ; wherein, μ2 is the initial shear modulus of the filler network, z is a constant related to the filler aggregate distribution, is the strain, is the modulus of the filler network.

[0012] An evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, constructing a double-network constitutive model corresponding to the filled silicone rubber based on the generalized strain energy function and the deformation function of the filled silicone rubber, includes: Substitute the deformation function into the generalized strain energy function of the filled silicone rubber, and perform a series expansion on the generalized strain energy function of the filled silicone rubber to obtain the generalized strain energy function after series expansion; Based on the derivative of the generalized strain energy function after series expansion with respect to the first strain invariant, determine the double-network constitutive model corresponding to the filled silicone rubber.

[0013] An evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, the generalized strain energy function of the filled silicone rubber is: ; Among them, W is the generalized strain energy function of the filled silicone rubber, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, 、 is the inverse Langevin function, , , is the microscopic chain stretching, , λ1, λ2 and λ3 are the macroscopic principal stretch ratios of the filled silicone rubber in three orthogonal directions; The generalized strain energy function after the series expansion is: ; Among them, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, , , , I1 is the first strain invariant, i is the Taylor series, , for uniaxial tension .

[0014] According to an evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, the correlation between the initial shear modulus and the average chain length of the rubber network and the chemical crosslinking density is: ; ; Among them, μ1 is the initial shear modulus of the rubber network, v chem is the chemical crosslinking density, K is the Boltzmann constant, T is the absolute temperature, N is the average chain length of the rubber network, C is a constant.

[0015] According to an evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties provided by the present invention, the correlation between the average chain length of the filled network and the interfacial layer content is determined by the correlation between the average chain length of the filled network and the radiation dose and the correlation between the interfacial layer content and the radiation dose; The correlation between the average chain length of the filled network and the radiation dose is: ; The correlation between the interfacial layer content and the radiation dose is: A inter = 1.179×(1 - e -D / 229.5 ) + 1.851; where M is the average chain length of the filler network, A inter is the content of the interfacial layer, and D is the radiation dose; The correlation between the constant related to the filler aggregate distribution and the radiation dose is as follows: ; where z is the constant related to the filler aggregate distribution and D is the radiation dose.

[0016] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the evaluation method of the influence of radiation-induced microstructure evolution on macroscopic properties as described in any one of the above.

[0017] The evaluation method of the influence of radiation-induced microstructure evolution on macroscopic properties provided by the present invention decomposes the strain energy of the filled rubber into a rubber network part and a filler network part by constructing a double-network constitutive model, and analyzes based on the relationships between the model parameters of the double-network constitutive model and the chemical crosslinking density and the interfacial layer content. Thus, the influence of changes in the chemical crosslinking density and the interfacial layer content on the stress-strain curve is comprehensively considered, and the changes in the microstructure and macroscopic properties during the radiation aging process are successfully linked, which is beneficial to a deeper understanding of the radiation aging mechanism of filled silicone rubber, more accurately and effectively studying the influence of radiation-induced microstructure evolution on macroscopic properties, accurately evaluating the service life of filled silicone rubber-related devices in a radiation industrial environment, and thus better realizing the application of silica-filled silicone rubber in the industrial field, especially in an industrial radiation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 is a schematic diagram of the radiation aging mechanism of silicone rubber in the prior art.

[0020] Figure 2 is a flowchart of the evaluation method of the influence of radiation-induced microstructure evolution on macroscopic properties provided by the embodiments of the present invention.

[0021] Figure 3 is a decomposition diagram of the filled silicone rubber provided by the embodiments of the present invention.

[0022] Figure 4It is a schematic diagram of the engineering stress-strain curve and data fitting of SR under different irradiation doses provided by the embodiments of the present invention.

[0023] Figure 5 It is the influence of the change in the average chain length of the filler network on the mechanical properties provided by the embodiments of the present invention.

[0024] Figure 6 It is the influence of the change in the constant related to the filler aggregate distribution provided by the embodiments of the present invention on the mechanical properties.

[0025] Figure 7 It is the chain length distribution curve of the filled silicone rubber during the deformation process provided by the embodiments of the present invention.

[0026] Figure 8 It is a schematic diagram comparing the fitting effects of the experimental data of the double-network constitutive model, Arruda-Boyce model, and extended tube model under 0 kGy and 385 kGy radiation doses provided by the embodiments of the present invention.

[0027] Figure 9 It is a schematic diagram of the correlation between the average chain length M of the filler network and the radiation dose D provided by the embodiments of the present invention.

[0028] Figure 10 It is a schematic diagram of the structure of the electronic device provided by the embodiments of the present invention. Detailed implementation manners

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0030] In the description of the embodiments of the present invention, the terms "include", "comprise", or any other variant thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or device including a series of elements not only includes those elements but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article, or device. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0031] Silica is widely used as a filler in silicone rubber. There are differences in the radiation aging behaviors between filled rubber and pure rubber. Paramagnetic substances will be generated in the irradiated silica, and these substances migrate to the interface of the composite material. These paramagnetic substances will react with the material matrix to form covalent bonds or enhance physical adsorption, thereby changing the interaction between the filler and the matrix, and further affecting the macroscopic properties of the rubber.

[0032] So far, the following methods can be used to study the influence of radiation on the mechanical properties of rubber: (1) Establish the relationship between radiation and mechanical properties through a phenomenological constitutive model: The Ogden model is adopted within the framework of Tobolsky's double-network scheme to describe the mechanical changes of silicone rubber with radiation dose; (2) The Hyperfoam model is extended, that is, it is assumed that the model parameters corresponding to the initial modulus and hardness are linearly related to the radiation dose, so as to predict the radiation aging trend of the mechanical properties of silicone rubber. However, although the above-mentioned phenomenological constitutive models can explain the influence of radiation on mechanical properties, the phenomenological constitutive models do not contain microstructure information, so it is difficult to establish the relationship from microstructure to macroscopic characteristics. Therefore, it is necessary to develop a constitutive model containing microstructure information to explain the influence of radiation on mechanical properties.

[0033] The constitutive models based on statistical mechanics can be used to correlate the relationship between microstructure and macroscopic mechanical properties, such as: the strain energy function of Gaussian chain network, the James-Guth 3-chain strain energy function, the Flory 4-chain strain energy function, the Arrude-Boyce 8-chain strain energy function, the Tomita affine model and the tube model. However, the above-mentioned constitutive models based on statistical mechanics ignore the contributions of the filler network and the interaction between the filler and the matrix to mechanical properties, which play an important role in mechanical behavior. Moreover, the research work on developing constitutive models based on statistical mechanics under radiation conditions is also very limited.

[0034] In summary, the common method to study the mechanical changes during the rubber aging process at present is to establish the relationship between aging and mechanical properties through phenomenological constitutive models. However, these models lack the understanding of the microscopic mechanism; different from the phenomenological constitutive models, the constitutive models based on statistical mechanics are based on the physical and statistical methods of polymer chain networks and material microstructures, and their parameters have physical interpretations, but their fitting accuracy for filled rubber is poor. Therefore, it is necessary to extend the constitutive models based on statistical mechanics to make them suitable for studying the influence of the evolution of interfacial interactions on macroscopic mechanical properties during the radiation aging process of filled rubber.

[0035] In the embodiments of the present invention, by constructing a double-network constitutive model, the strain energy of the filled rubber is decomposed into a rubber network part and a filler network part, and based on the relationships between the various model parameters of the double-network constitutive model and the chemical crosslinking density and the interfacial layer content, the influence of the changes in the chemical crosslinking density and the interfacial layer content on the stress-strain curve is comprehensively considered, successfully linking the changes in the microstructure and macroscopic properties during the radiation aging process, which is beneficial to a deeper understanding of the radiation aging mechanism of the filled silicone rubber, more accurately and effectively studying the influence of radiation-induced microstructure evolution on the macroscopic properties, accurately evaluating the service life of the equipment related to the filled silicone rubber in the radiation industrial environment, and thus better realizing the application of silica-filled silicone rubber in the industrial field, especially in the industrial radiation environment.

[0036] Figure 2 It is a schematic flowchart of the evaluation method for the influence of radiation-induced microstructure evolution on macroscopic properties provided by the embodiments of the present invention. Referring to Figure 2 , the embodiments of the present invention provide an evaluation method for the influence of radiation-induced microstructure evolution on macroscopic properties, and the method may specifically include the following steps: Step 201, construct a double-network constitutive model corresponding to the filled silicone rubber; the filled silicone rubber is silica-filled silicone rubber, and the double-network constitutive model includes a rubber network part and a filler network part.

[0037] It should be noted that the execution subject of the evaluation method for the influence of radiation-induced microstructure evolution on macroscopic properties provided by the embodiments of the present invention may be an electronic device, a component in the electronic device, an integrated circuit or a chip. The electronic device may be a mobile electronic device or a non-mobile electronic device. Exemplarily, the mobile electronic device may be a mobile phone, a tablet computer, a notebook computer, a handheld computer, a wearable device, an Ultra-mobile Personal Computer (UMPC), a netbook or a Personal Digital Assistant (PDA), etc., and the non-mobile electronic device may be a server, a Network Attached Storage (NAS), a Personal Computer (PC), a television (TV), a teller machine or a self-service machine, etc. The embodiments of the present invention do not make specific limitations in this regard. Hereinafter, the embodiments of the present invention will be described with a server as the execution subject.

[0038] The Arruda-Boyce model is one of the most successful constitutive models based on statistical mechanics and is widely cited in engineering. Although the Arruda-Boyce model can accurately predict the mechanical behavior of unfilled elastomers, for filled elastomers, it cannot accurately reflect the mechanical behavior of composites because it ignores the influence of filling on the mechanical response.

[0039] Figure 3 is a schematic diagram of the decomposition of filled silicone rubber provided by an embodiment of the present invention. Referring to Figure 3 , considering the microstructure rearrangement of the filler network during deformation, the embodiment of the present invention extends the Arruda-Boyce model, decomposes the microstructure of the elastic particle composite material (i.e., silica-filled silicone rubber) into a rubber network and a filler network, that is, it is set that the filled rubber consists of two networks, a rubber network and a filler network, and considers the evolution of the filler network during the stretching process, so as to effectively study the influence of the microstructure evolution of the filled rubber on the macroscopic mechanical properties during radiation aging.

[0040] In a specific implementation, the generalized strain energy function of the filled silicone rubber can be decomposed into the superposition of the free energies of the rubber network and the filler network, and can be expressed as: ; (1) where W R represents the free energy of the rubber network, W F represents the free energy of the interaction network between the filler and the rubber (i.e., the filler network), and W is the generalized strain energy function of the filled silicone rubber.

[0041] Step 202, based on the chemical crosslinking density of the filled silicone rubber under each radiation dose, calculate the initial shear modulus and the average chain length of the rubber network in the filled silicone rubber under each radiation dose.

[0042] In the embodiment of the present invention, the equilibrium swelling method can be used to measure the chemical crosslinking density of the filled silicone rubber under each radiation dose.

[0043] In a specific implementation, for the filled silicone rubber under each radiation dose, the vulcanized filled silicone rubber sample can be swollen in toluene at room temperature for a predetermined time, and the first sample mass m1 is obtained after reaching swelling equilibrium; ammonia water is added to the sample swollen in toluene for modification and continued for a predetermined time to decompose the hydrogen bond between the filler and the silicone rubber, and the second sample mass m2 is obtained; the sample modified with ammonia water is dried to a constant mass m3 under vacuum at a predetermined temperature.

[0044] The chemical crosslinking density can be calculated by the following formula: ; (2) where V Sis the molar volume of toluene, χ is the interaction parameter between the filled silicone rubber and toluene, and v f is the volume fraction, and v e is the chemical crosslinking density (the chemical crosslinking density can also be expressed as v chem ).

[0045] The volume fraction can be calculated by the following formula: ; (3) where ρ p is the density of the silicone rubber block without filler, ρ s is the density of toluene, m3 is the constant mass, m k = m2, and v f is the volume fraction, m1 is the mass of the first sample, and m2 is the mass of the second sample.

[0046] The constitutive model proposed in the embodiments of the present invention comprehensively considers the influence of the rubber network and the filler network on the macroscopic mechanical properties. According to the physical meaning of the model parameters, the initial shear modulus of the rubber network is proportional to the chemical crosslinking density ν Chem , and the product of the average chain length N of the rubber network and ν Chem is a constant. Therefore, after measuring the chemical crosslinking density data of the filled silicone rubber at each radiation dose, the embodiments of the present invention can calculate the initial shear modulus data of the rubber network in the filled silicone rubber at each radiation dose through the proportional relationship between the initial shear modulus of the rubber network and the chemical crosslinking density, and calculate the average chain length data of the rubber network in the filled silicone rubber at each radiation dose through the relationship between the average chain length of the rubber network and the chemical crosslinking density.

[0047] The embodiments of the present invention can determine the contribution of the rubber network to the macroscopic properties by calculating the initial shear modulus data and the average chain length data of the rubber network in the filled silicone rubber at different radiation doses, and use them to fit the model parameters of the filler network.

[0048] Step 203: Based on the engineering stress-strain rate data of the filled silicone rubber at each radiation dose, the initial shear modulus and the average chain length of the rubber network, use the double-network constitutive model for fitting to obtain the initial shear modulus, the average chain length, and the constant related to the filler aggregate distribution in the filled silicone rubber at each radiation dose.

[0049] In the embodiments of the present invention, engineering stress-strain rate data of silica-filled silicone rubber, initial shear modulus data of the rubber network, and average chain length data can be obtained at different radiation doses. Curve fitting is performed using the constructed double-network constitutive model. Based on the curve fitting results, the initial shear modulus data, average chain length data, and constant data related to the filler aggregate distribution in the silica-filled silicone rubber at different radiation doses are determined.

[0050] Figure 4 is a schematic diagram of the engineering stress-strain curve and data fitting of SR at different irradiation doses provided by the embodiments of the present invention. Referring to Figure 4 , the data points can represent the original engineering stress-strain rate data, and the solid line can represent the fitting curve. The results show that the extended Arruda-Boyce model provided by the embodiments of the present invention can accurately reproduce the stress-strain curves of silicone rubber at different radiation doses.

[0051] The model parameters of the double-network constitutive model obtained by extending the Arruda-Boyce model in the embodiments of the present invention can be shown in Table 1: Table 1

[0052] Among them, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filler network, M is the average chain length of the filler network, z is a constant related to the filler aggregate distribution, and R 2 is used to measure the goodness of fit.

[0053] Among them, 0 kGy refers to silica-filled silicone rubber with a radiation dose of 0 (i.e., unirradiated rubber). Curve fitting can be performed with reference to the stress-strain curve of the unirradiated rubber to obtain various parameters.

[0054] Step 204: Based on the correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density, the correlation between the average chain length of the filler network and the interfacial layer content, and the correlation between the constant related to the filler aggregate distribution and the radiation dose, determine the relationship between the microstructure evolution and macroscopic property changes of the silica-filled silicone rubber in a radiation environment to evaluate the influence of the microstructure evolution of the silica-filled silicone rubber on the macroscopic properties in a radiation environment.

[0055] Figure 5 is the influence of the change in the average chain length of the filler network on the mechanical properties provided by the embodiments of the present invention. Referring to Figure 5 , when only changing the average chain length parameter M of the filler network, as the average chain length of the filler network decreases, the constraint of the silica filler on the rubber matrix is enhanced, resulting in the silica-filled silicone rubber being harder.

[0056] Figure 6 This is the effect of the change in the constant related to the filler aggregate distribution provided by the embodiments of the present invention on the mechanical properties. Referring to Figure 6 , when only the constant z related to the filler aggregate distribution is changed, an increase in the constant z related to the filler aggregate distribution can indicate that the chain length distribution in the filler network is more concentrated, resulting in a significant decrease in the modulus in the high-strain region.

[0057] During radiation aging, radiation enhances the interaction between the filler and the matrix, causing more chains to adsorb onto the interface layer, making the movement of molecular chains more difficult, resulting in a decrease in the average chain length of the filler network and a more concentrated chain length distribution, that is, M decreases and z increases. The combined effect of the two makes the SR stiffer. The embodiments of the present invention can be used to analyze the relationship between the microscopic structure evolution and the macroscopic property change of filled silicone rubber in a radiation environment by further analyzing the quantitative relationship between the average chain length M of the filler network and the radiation dose D, and the quantitative relationship between the constant z related to the filler aggregate distribution and the radiation dose D.

[0058] The double-network constitutive model provided by the embodiments of the present invention includes the relevant parameters of the rubber network and the filler network (the initial shear modulus and average chain length of the rubber network, the initial shear modulus, average chain length of the filler network, and the constant related to the filler aggregate distribution). Therefore, through the variation relationships between these model parameters and the chemical crosslinking density and the interfacial layer content (the correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density, the correlation between the average chain length of the filler network and the interfacial layer content, and the correlation between the constant related to the filler aggregate distribution and the radiation dose, etc.), the influence of the changes in the chemical crosslinking density and the interfacial layer content on the stress-strain curve is comprehensively considered, and the changes in the microscopic structure and macroscopic properties during the radiation aging process are successfully linked, which is conducive to a deeper understanding of the radiation aging mechanism of filled silicone rubber.

[0059] The embodiments of the present invention decompose the strain energy of the filled rubber into the rubber network part and the filler network part by constructing a double-network constitutive model, and analyze based on the relationships between the various model parameters of the double-network constitutive model and the chemical crosslinking density and the interfacial layer content. Therefore, the influence of the changes in the chemical crosslinking density and the interfacial layer content on the stress-strain curve is comprehensively considered, and the changes in the microscopic structure and macroscopic properties during the radiation aging process are successfully linked, which is conducive to a deeper understanding of the radiation aging mechanism of filled silicone rubber, more accurately and effectively studying the influence of radiation-induced microscopic structure evolution on macroscopic properties, accurately evaluating the service life of filled silicone rubber-related equipment in a radiation industrial environment, and thus better realizing the application of silica-filled silicone rubber in the industrial field, especially in an industrial radiation environment.

[0060] In an alternative embodiment, constructing the corresponding double-network constitutive model of the filled silicone rubber may specifically include: Step S11: Based on the free energy of the rubber network and the free energy of the filled network, construct a generalized strain energy function of the filled silicone rubber; Step S12: Based on the cumulative probability distribution function of the surviving chains of the filled network during the stretching process, determine a deformation function for characterizing the evolution of the filled network during the stretching process; Step S13: Based on the generalized strain energy function of the filled silicone rubber and the deformation function, construct the corresponding double-network constitutive model of the filled silicone rubber.

[0061] For the filled network, during the deformation process, due to the slipping, debonding, and breaking of the rubber chains on the surface of the filler, the filled network will be damaged. In the embodiment of the present invention, in order to analyze the change of the filled network during the loading process, it can be assumed that the system has a wide chain length distribution, so as to determine the cumulative probability distribution function of the surviving chains of the filled network during the stretching process.

[0062] During the deformation process, the modulus of the filled network can be determined by the cumulative contribution of the surviving chains. In the embodiment of the present invention, through the cumulative probability distribution function of the surviving chains of the filled network during the stretching process, the modulus of the filled network can be used as a deformation function, so as to determine the deformation function for characterizing the evolution of the filled network during the stretching process.

[0063] In the embodiment of the present invention, the generalized strain energy function of the filled silicone rubber can be decomposed into the superposition of the free energy of the rubber network and the free energy of the filled network, that is, based on the free energy of the rubber network and the free energy of the filled network, construct the generalized strain energy function of the filled silicone rubber.

[0064] In the embodiment of the present invention, the deformation function can be substituted into the generalized strain energy function of the filled silicone rubber, so as to construct the corresponding double-network constitutive model of the filled silicone rubber.

[0065] In an alternative embodiment, the cumulative probability distribution function of the surviving chains of the filled network during the stretching process can be determined through the following steps: Step S21: Based on the average functionality of the active absorption sites on the aggregate filler, the maximum chain length in the filled network, and the Kuhn length, determine the probability of the chain with length l in the filled network; Step S22: Based on the stretching length and the maximum chain length in the filled network, perform a length integration on the probability of the chain with length l in the filled network to determine the initial cumulative probability distribution function of the surviving chains; Step S23: Simplify the exponential content in the initial cumulative probability distribution function of the surviving chains to obtain the cumulative probability distribution function of the surviving chains of the filled network during the stretching process.

[0066] For the filled network, during the deformation process, due to the slipping, debonding, and breaking of the rubber chains on the surface of the filler, the filled network will be damaged. In the embodiments of the present invention, in order to analyze the changes in the filled network during the loading process, it can be assumed that the system has a wide chain length distribution, and the probability of a chain with a length of l can be expressed as: ; (4) where α is the average functionality of the active absorption sites on the aggregate filler, M max is the maximum chain length in the filled network, β is the Kuhn length, and P(l) is the probability of a chain with a length of l in the filled network.

[0067] Figure 7 is the chain length distribution curve of the filled silicone rubber during the deformation process provided by the embodiments of the present invention. Referring to Figure 7 , the shaded area represents the molecular chains that break at the elongation of λ. During deformation, the short chains break first, while the long chains still bear the mechanical load. During the deformation process, when the chain with a length of l is shorter than the tensile length it can be considered that the chain breaks (L is the equilibrium length of the chain), and it no longer contributes to the network entropy. Therefore, the initial survival chain cumulative probability distribution function can be expressed as: ; (5) where is the tensile length, M max is the maximum chain length in the filled network, N is the average chain length of the rubber network, α is the average functionality of the active absorption sites on the aggregate filler, β is the Kuhn length, P(l) is the probability of a chain with a length of l in the filled network, A is a normalization constant, and Φ( ) is the initial survival chain cumulative probability distribution function.

[0068] After the chain breaks, the role of the broken chain in the network entropy is completely lost, but the actual situation is more complex. Referring to the situation 1 and situation 2 in Figure 3 , the polymer chains may have multiple adsorption points on the aggregate, resulting in their evolution into longer molecular chains after debonding. The separation of the chains from the surface of the aggregate does not necessarily lead to the complete loss of their role in the network entropy energy. Therefore, the embodiments of the present invention can simplify the exponential form of the survival chain cumulative probability distribution function to obtain the survival chain cumulative probability distribution function of the filled network during the stretching process.

[0069] In an alternative embodiment, after simplifying the exponential content in the initial survival chain cumulative probability distribution function, the survival chain cumulative probability distribution function of the filled network during the stretching process can be expressed as: ; (6) Among them, is the strain, , z is a constant related to the filler aggregate distribution, is the cumulative probability distribution function of the surviving chains of the filler network during the stretching process.

[0070] During the deformation process, the modulus of the filler network can be determined by the cumulative contribution of the surviving chains, so as to obtain the modulus of the filler network as a function of deformation. The deformation function used to characterize the evolution of the filler network during stretching can be expressed as: ; (7) Among them, μ2 is the initial shear modulus of the filler network, z is a constant related to the filler aggregate distribution, is the strain, is the modulus of the filler network.

[0071] In an alternative embodiment, based on the generalized strain energy function of the filled silicone rubber and the deformation function, a double-network constitutive model corresponding to the filled silicone rubber is constructed, which may specifically include: Step S31, substituting the deformation function into the generalized strain energy function of the filled silicone rubber, and performing a series expansion on the generalized strain energy function of the filled silicone rubber to obtain the generalized strain energy function after series expansion; Step S32, determining the double-network constitutive model corresponding to the filled silicone rubber based on the derivative of the generalized strain energy function after series expansion with respect to the first strain invariant.

[0072] The presence of silica fillers has an amplifying effect on the strain of the composite material, and the strain amplification effect is also affected by the interaction between the fillers and the rubber. In the embodiments of the present invention, in order to avoid introducing too many parameters during the analysis and resulting in multiple local optimal values, the strain amplification effect is implicit in and M. In the embodiments of the present invention, the deformation function used to characterize the evolution of the filler network during stretching can be substituted into the generalized strain energy function of the filled silicone rubber, and the generalized strain energy function of the filled silicone rubber is expanded in series to obtain the generalized strain energy function after series expansion.

[0073] After obtaining the generalized strain energy function after series expansion, in order to directly compare with the experimental results (engineering stress), the embodiments of the present invention can perform a derivative of the generalized strain energy function after series expansion with respect to the first strain invariant, so as to calculate the engineering stress.

[0074] In an alternative embodiment, the generalized strain energy function of the filled silicone rubber can be expressed as: ; (8) Among them, W is the generalized strain energy function of the filled silicone rubber, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, and M is the average chain length of the filled network. and is the inverse Langevin function. , , is the microscopic chain stretching. , where λ1, λ2, and λ3 are the macroscopic principal stretch ratios of the filled silicone rubber in three orthogonal directions. After substituting the deformation function into the generalized strain energy function of the filled silicone rubber and performing a series expansion on the generalized strain energy function of the filled silicone rubber, the generalized strain energy function after the series expansion can be expressed as: ; (9) Among them, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, and M is the average chain length of the filled network. , , , I1 is the first strain invariant, i is the Taylor series, , which is used for uniaxial tension .

[0075] In an alternative embodiment, the constructed double-network constitutive model can be expressed as: ; (10) Among them, δ is the engineering stress, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, and M is the average chain length of the filled network. , , , I1 is the first strain invariant, i is the Taylor series, and λ is the elongation ratio.

[0076] Figure 8 is a schematic diagram comparing the fitting effects of the double-network constitutive model, Arruda-Boyce model, and extended tube model provided by the embodiments of the present invention on experimental data under radiation doses of 0 kGy and 385 kGy. Referring to Figure 8 , it can be seen from the fitting results that the double-network constitutive model provided by the embodiments of the present invention has good adaptability to SR (Silicon Rubber).

[0077] In an alternative embodiment, the correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density can be expressed as: ; (11) ; (12) where μ1 is the initial shear modulus of the rubber network, v chem is the chemical crosslinking density, K is the Boltzmann constant, T is the absolute temperature, N is the average chain length of the rubber network, and C is a constant.

[0078] In an alternative embodiment, the correlation between the average chain length of the filler network and the interfacial layer content can be determined by the correlation between the average chain length of the filler network and the radiation dose and the correlation between the interfacial layer content and the radiation dose.

[0079] The correlation between the average chain length of the filler network and the radiation dose can be expressed as: ; (13) where M is the average chain length of the filler network, A inter is the interfacial layer content, and D is the radiation dose.

[0080] The correlation between the interfacial layer content and the radiation dose can be expressed as: A inter = 1.179×(1 - e -D / 229.5 ) + 1.851; (14) where A inter is the interfacial layer content and D is the radiation dose.

[0081] Figure 9 is a schematic diagram of the correlation between the average chain length M of the filler network and the radiation dose D provided by the embodiments of the present invention. Referring to Figure 9 , in the embodiments of the present invention, the average chain length M of the filler network is related to the strength of the interaction between the filler and the matrix. Based on the linear correlation between the physical adsorption crosslinking density ν Phy and the interfacial layer content, the interaction between the filler and the matrix can be determined is positively correlated, and then it can be analyzed and determined that there is a linear negative correlation between the average chain length M of the filler network and .

[0082] Based on the initial survival chain cumulative probability distribution function (5), it can be seen that the constant z related to the filler aggregate distribution is related to the α-active absorption sites on the aggregate surface and is comprehensively affected by the interfacial interaction strength and the active sites (free radicals) of the polymer chain. Therefore, the constant z related to the filler aggregate distribution shows a linear correlation with the radiation dose: ; (15) Where z is a constant related to the filler aggregate distribution and D is the radiation dose.

[0083] In a specific implementation, the physical adsorption crosslinking density of the filled silicone rubber at each radiation dose can be determined based on the equilibrium swelling method; based on each radiation dose and the physical adsorption crosslinking density of the filled silicone rubber at each radiation dose, a charging model is used for fitting to obtain the functional relationship between the physical adsorption crosslinking density and the radiation dose; the interfacial layer content of the filled silicone rubber at each radiation dose is determined based on low-field nuclear magnetic resonance technology; based on each radiation dose and the interfacial layer content of the filled silicone rubber at each radiation dose, a charging model is used for fitting to obtain the functional relationship between the interfacial layer content and the radiation dose; based on the functional relationship between the physical adsorption crosslinking density and the radiation dose and the functional relationship between the interfacial layer content and the radiation dose, the linear correlation between the physical adsorption crosslinking density and the interfacial layer content of the filled silicone rubber in a radiation environment is determined.

[0084] The functional relationship between the physical adsorption crosslinking density and the radiation dose can be expressed as: ; (16) Where D is the radiation dose and v phy is the physical adsorption crosslinking density.

[0085] In the embodiment of the present invention, the change in the crosslinking density of silica-filled silicone rubber during radiation aging is decomposed into physical adsorption and chemical adsorption by the equilibrium swelling method, the change in the physical adsorption crosslinking density with the radiation dose is fitted by a charging model, the interfacial layer content is quantified using low-field nuclear magnetic resonance technology, the change in the interfacial layer content with the radiation dose is fitted by a charging model, and the linear correlation between the interfacial layer content and the physical adsorption strength of silica-filled silicone rubber in different radiation environments can be determined through the relationship between the physical adsorption strength and the change in the interfacial layer content with the radiation dose. Based on the correlation, it is beneficial to accurately evaluate the change in the interfacial content of silica-filled silicone rubber in different radiation environments, and further beneficial to evaluate the influence of the radiation environment on the macroscopic properties of the material.

[0086] Figure 10 Illustrates a schematic diagram of the physical structure of an electronic device, such as Figure 10As shown in the figure, the electronic device may include: a processor 1010, a communications interface 1020, a memory 1030, and a communication bus 1040. Among them, the processor 1010, the communications interface 1020, and the memory 1030 complete mutual communication through the communication bus 1040. The processor 1010 may call the logical instructions in the memory 1030 to execute an evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties. The method includes: constructing a double-network constitutive model corresponding to the filled silicone rubber; the filled silicone rubber is silica-filled silicone rubber, and the double-network constitutive model includes a rubber network part and a filled network part; based on the chemical crosslinking density of the filled silicone rubber at each radiation dose, calculating the initial shear modulus and average chain length of the rubber network in the filled silicone rubber at each radiation dose; based on the engineering stress-strain rate data of the filled silicone rubber at each radiation dose, the initial shear modulus and average chain length of the rubber network, using the double-network constitutive model for fitting to obtain the initial shear modulus, average chain length of the filled network in the filled silicone rubber at each radiation dose, and a constant related to the filler aggregate distribution; based on the correlation relationship between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density, the correlation relationship between the average chain length of the filled network and the interfacial layer content, and the correlation relationship between the constant related to the filler aggregate distribution and the radiation dose, determining the relationship between the microstructural evolution and macroscopic property changes of the filled silicone rubber in a radiation environment to evaluate the influence of the microstructural evolution of the filled silicone rubber on macroscopic properties in a radiation environment.

[0087] In addition, when the logical instructions in the above-mentioned memory 1030 can be implemented in the form of software functional units and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0088] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative work.

[0089] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. These modifications or replacements 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 the present invention.

Claims

1. An evaluation method for the influence of radiation-induced microstructural evolution on macroscopic properties, characterized in that, The method includes: Constructing a double-network constitutive model for the filled silicone rubber; the filled silicone rubber is silica-filled silicone rubber, and the double-network constitutive model includes a rubber network part and a filled network part; Based on the chemical crosslinking density of the filled silicone rubber at each radiation dose, calculating the initial shear modulus and average chain length of the rubber network in the filled silicone rubber at each radiation dose; Based on the engineering stress-strain rate data of the filled silicone rubber at each radiation dose, the initial shear modulus and average chain length of the rubber network, fitting using the double-network constitutive model to obtain the initial shear modulus, average chain length of the filled network in the filled silicone rubber at each radiation dose, and a constant related to the filler aggregate distribution; Based on the correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density, the correlation between the average chain length of the filled network and the interfacial layer content, and the correlation between the constant related to the filler aggregate distribution and the radiation dose, determining the relationship between the microstructural evolution and macroscopic property changes of the filled silicone rubber in a radiation environment to evaluate the influence of the microstructural evolution of the filled silicone rubber on macroscopic properties in a radiation environment.

2. The method according to claim 1, wherein The double-network constitutive model is: ； where δ is the engineering stress, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, , , , I1 is the first strain invariant, i is the Taylor series, i = 1, 2, 3, and λ is the elongation ratio.

3. The method according to claim 1, characterized in that The constructing of the double-network constitutive model corresponding to the filled silicone rubber includes: Based on the free energy of the rubber network and the free energy of the filled network, constructing a generalized strain energy function of the filled silicone rubber; Based on the survival chain cumulative probability distribution function of the filled network during the stretching process, determining a deformation function for characterizing the evolution of the filled network during the stretching process; Based on the generalized strain energy function of the filled silicone rubber and the deformation function, constructing a double-network constitutive model corresponding to the filled silicone rubber.

4. The method according to claim 3, wherein The survival chain cumulative probability distribution function of the filled network during the stretching process is determined by the following method: Based on the average functionality of the active absorption sites on the aggregate fillers, the maximum chain length in the filler network, and the Kuhn length, determine the probability of chains of length l in the filler network; Based on the stretching length and the maximum chain length in the packing network, perform a length integration on the probability of the chains with length l in the packing network to determine the initial survival chain cumulative probability distribution function; Simplifying the exponential content in the initial survival chain cumulative probability distribution function to obtain the survival chain cumulative probability distribution function of the filled network during the stretching process.

5. The method according to claim 3, characterized in that The survival chain cumulative probability distribution function of the filled network during the stretching process is: ； wherein, is the strain, , z is a constant related to the filler aggregate distribution, is the cumulative probability distribution function of the surviving chains of the filler network during the stretching process; The deformation function for characterizing the evolution of the filled network during the stretching process is: ； Among them, μ2 is the initial shear modulus of the filled network, z is a constant related to the distribution of filler aggregates, is the strain, is the modulus of the filled network.

6. The method according to claim 3, characterized in that, The constructing of the double-network constitutive model corresponding to the filled silicone rubber based on the generalized strain energy function of the filled silicone rubber and the deformation function includes: Substituting the deformation function into the generalized strain energy function of the filled silicone rubber and performing a series expansion on the generalized strain energy function of the filled silicone rubber to obtain the generalized strain energy function after series expansion; Based on the derivative of the generalized strain energy function after series expansion with respect to the first strain invariant, determining the double-network constitutive model corresponding to the filled silicone rubber.

7. The method according to claim 6, characterized in that, The generalized strain energy function of the filled silicone rubber is: ； where W is the generalized strain energy function of the filled silicone rubber, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, and is the inverse Langevin function, , , is the stretching of the microscopic chain, , and λ1, λ2, and λ3 are the macroscopic principal stretch ratios of the filled silicone rubber in three orthogonal directions; The generalized strain energy function after series expansion is: ； Among them, μ1 is the initial shear modulus of the rubber network, N is the average chain length of the rubber network, μ2 is the initial shear modulus of the filled network, M is the average chain length of the filled network, , , , I1 is the first strain invariant, i is the Taylor series, , for uniaxial tension .

8. The method according to claim 1, wherein, The correlation between the initial shear modulus and average chain length of the rubber network and the chemical crosslinking density is: ； ； where μ1 is the initial shear modulus of the rubber network, v chem is the chemical crosslink density, K is the Boltzmann constant, T is the absolute temperature, N is the average chain length of the rubber network, and C is a constant.

9. The method according to claim 1, wherein The correlation between the average chain length of the filled network and the interfacial layer content is determined by the correlation between the average chain length of the filled network and the radiation dose and the correlation between the interfacial layer content and the radiation dose; The correlation between the average chain length of the filled network and the radiation dose is: ； The correlation between the content of the interface layer and the radiation dose is as follows: A inter =1.179×(1- e -D / 229.5 )+1.851； where M is the average chain length of the filling network, A inter is the content of the interfacial layer, and D is the radiation dose; The correlation between the constant related to the filler aggregate distribution and the radiation dose is as follows: ； where z is the constant related to the filler aggregate distribution, and D is the radiation dose.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method for evaluating the influence of radiation-induced microstructural evolution on macroscopic properties according to any one of claims 1 to 9.

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