A method, system, storage medium, and program product for predicting rubber fatigue crack growth rate

Abstract

The present application relates to the technical field of computer-aided design of tires, and in particular to a rubber fatigue crack propagation rate prediction method, system, storage medium and program product. The present application constructs rubber samples with different crosslinking densities by adjusting the amount of sulfur donor, uses gradient loading pure shear fatigue test to quickly obtain crack propagation rate and tearing energy data, and combines energy dissipation analysis and strain-induced crystallization mechanism to construct a crack propagation rate phenomenological model with a segmented exponential-power law form. The method can effectively identify the optimal crosslinking density that minimizes the crack propagation rate, realize quantitative prediction of the fatigue resistance of natural rubber and formula optimization, and significantly improve the service life of high-strain rubber components such as aircraft tires.

Description

Technical Field

[0001] This invention relates to the field of tire manufacturing technology, and in particular to a method, system, storage medium, and program product for predicting the fatigue crack propagation rate of rubber. Background Technology

[0002] The service life of aircraft tires has a significant impact on the safety of aircraft takeoff and landing. Improving the fatigue durability of aircraft tires is an important method related to aircraft safety and fuel economy. Rubber, as the main component of tires, has a fatigue crack propagation rate that is an important characterizing factor in tire durability analysis. The crack propagation rate of rubber materials is not only affected by external mechanical loads and environmental conditions, but also closely related to the material's formulation and cross-linking structure. These material-related factors mainly include the type of rubber matrix, the type and amount of filler materials, and the internal cross-linking structure of the rubber.

[0003] Generally, the type of adhesive in a formulation dominates the various properties of the material. References [G. Andreini, P. Straffi, S. Cotugno, G. Gallone, G. Polacco, ...] Rubber Chem. Technol. 2013, 86 In [132.], Andreini et al. used pure shear tests to compare the crack propagation rates of several different types of filled rubbers. The experimental results showed that NR had the slowest crack propagation rate, followed by SBR, and BR had the fastest. A key difference between natural and synthetic rubber is crystallization, and rubber crystallization significantly affects fatigue life. Strain-induced crystallization can greatly improve the fatigue life of rubber because the microcrystalline structure orients the originally disordered rubber molecular chains along the stretching direction, resulting in a more orderly arrangement of local rubber molecules and thus stronger fatigue resistance. Reference [J. Zhao, GNGhebremeskel, Rubber Chem. Technol. 2001, 74 In their study of the fatigue fracture behavior of SBR and BR, Zhao et al. found that the lower the molecular weight of SBR, the higher its fatigue life. This is because when the molecular weight is low, the internal spatial network structure of the material is sparser and contains more free chain ends, which increases the viscous hysteresis during the fatigue process. Some of the energy used for crack propagation is dissipated, thereby improving the fatigue life.

[0004] Rubber vulcanization is the process by which rubber molecular chains crosslink under physical or chemical action, forming a spatial network structure. By adjusting the vulcanization system, vulcanizates with varying crosslink densities and bond distributions can be obtained. To a certain extent, the vulcanization system and crosslink density determine the physical properties of rubber materials. Increasing the crosslink density will raise the glass transition temperature of the vulcanizate. Tg Increase, in T g Within the above elastic region, the equilibrium elastic modulus and dynamic loss factor tanδ of the rubber also increase with increasing crosslinking density. References [E. Kasi, F. Josephraj, A. Murugesan, B. Pandian, ...] Mater. Plast. 2021, 58 In [34.], Kasi et al. studied the effect of crosslinking density on the cut resistance and chipping resistance of SBR-based tread rubber through cutting experiments, finding that its cut resistance and chipping resistance decreased with increasing crosslinking density. [AK Ghosh, D. De, B. Adhikari, ...] Kaut. Gummi Kunstst. 1998, 51 Ghosh et al. (500.) investigated the relationship between the flexural fatigue resistance of vulcanizates and crosslinking density by controlling the ratio of sulfur to accelerator to adjust the crosslinking density. Their experimental results showed that there exists an optimal crosslinking density that balances the strength and elasticity of the material, and at this density, the vulcanizates exhibit the best resistance to flexural cracking.

[0005] The type of cross-linking also has a significant impact on the fatigue properties of rubber. Reference [LC Yanyo, Int. J. Fract. 1989, 39 In [103.], Yanyo et al. studied the effect of crosslinking type on the fatigue crack propagation behavior of filled natural rubber. By changing the ratio of sulfur to accelerator to control the relative number of polysulfide bonds and monosulfide bonds, they found that at the same crosslinking density, the material with a higher content of polysulfide bonds had the best fatigue resistance. This is because, compared with monosulfide and disulfide bonds, polysulfide bonds have lower bond energies and generally break first under external force, causing stress to redistribute over a large area and slowing down the breakage of rubber molecular chains.

[0006] The current mainstream industrial practice focuses on the overall formulation of the tread compound: balancing wear resistance and heat resistance by altering the resin / carbon black / silane coupling system or using high-temperature resistant blends. For example, Michelin's European patent EP2516179B1 and Goodyear's US patent US20180215905A1 disclose a "full NR + high-reinforcing filler + anti-reversion agent" tread rubber composition for aircraft tires. However, these documents only provide qualitative descriptions of the crosslinking system, such as "high sulfur - low accelerator balancing for heat reversion" or "peroxide - sulfur co-vulcanization," without revealing the quantitative regulation of crosslinking density (also known as spatial network density) on fatigue crack propagation rate. Regarding the heat reversion problem in aircraft tire operating conditions, patents such as US patent US5623007A and Korean patent KR100193491B1 propose adding anti-reversion agents, sulfur efficiency modifiers, or disulfide bond stabilizers to the formulation to maintain crosslinking stability at high temperatures. However, these technologies mainly focus on maintaining the original degree of crosslinking without decreasing, without explaining that excessive crosslinking may also trigger fatigue performance deterioration, and without solving the problem of how to quickly screen the optimal crosslinking density.

[0007] In terms of characterization methods, early fatigue evaluations generally adopted constant amplitude cyclic loading using a step method, requiring the collection of hundreds of "steady-state segments" at multiple gauge lengths and tear energy levels to fit a Paris-type power law; the test cycle often lasted several weeks and the data dispersion was high. To address the efficiency and reproducibility issues, the Mars & Fatemi team proposed the CED theory based on the "critical plane-crack energy density" and developed the "Ramp Method"—linearly increasing the peak strain within a pure shear specimen, through 3×10 5 Crack propagation data for the entire tear energy range can be obtained in a single cycle. Experimental comparisons show that the variance of the Ramp method is less than half that of the traditional ladder method, but the original work focused on statistical improvements and did not incorporate the cross-linked network structure parameters into the model.

[0008] Therefore, in the design and life assessment of high-impact rubber components such as aircraft tires, there is still an urgent need for a predictive crosslinking density-tear energy coupling method and system: on the one hand, it can quickly obtain the crack propagation rate at different tear energy levels in a single experiment; on the other hand, it can directly give the quantitative correspondence between the optimal crosslinking density and the amount of sulfur donor added through a phenomenological model, thereby providing formulation engineers with simple and executable design guidelines.

[0009] The applicant's Chinese invention patent application (publication number: CN119354700A) provides a method for testing the fatigue crack propagation of rubber. The method includes: obtaining a test piece of the rubber sample to be tested and its calendering direction; determining the test tensile direction based on the calendering direction; and performing a crack tensile test on the test piece based on the test tensile direction to obtain the test results. This patent determines the tensile direction (same as or different from the calendering direction) based on the test piece of different rubber materials, or cuts multiple test pieces of the same size from the rubber sample to be tested and performs tensile testing in the same or different directions, thereby achieving multi-directional crack tensile testing of the rubber material test piece and selecting the optimal tensile direction for the tensile test. However, this method does not further consider the nonlinear influence of crosslinking density and tear energy coupling on the crack propagation rate, and also lacks quantitative prediction of the optimal crosslinking interval. Therefore, a new, efficient fatigue crack propagation testing and evaluation method that considers both processing orientation and crosslinking network structure is still needed to improve the accuracy and efficiency of fatigue life design for rubber materials.

[0010] To address the aforementioned technical problems, the present invention aims to provide a method for predicting the fatigue crack propagation rate of rubber. By designing natural rubber samples with different crosslinking densities, the method employs crack propagation rate tests to study the influence of crosslinking density on the crack propagation rate of samples with pre-existing cracks. Combining the crosslinking density test results with the fracture morphology of the samples, the method derives the mechanism of influence of crosslinking density on the fatigue crack propagation rate of rubber based on the statistical theory of rubber molecular chains. This provides a theoretical basis for improving the rubber material formulation design of aircraft tires, thereby laying the foundation for improving the service life of aircraft tires. Summary of the Invention

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] A method for predicting the fatigue crack propagation rate of rubber, the method comprising the following steps:

[0013] S1) Prepare natural rubber samples with different crosslinking densities;

[0014] S2) The pure shear specimen containing pre-existing cracks is mounted on a dynamic fatigue testing machine and gradient loading is applied cyclically;

[0015] S3) After each cycle, the crack length is recorded using the image acquisition module, and the crack propagation rate dc / dN is calculated. c The length of the crack propagation. N This represents the number of loop iterations.

[0016] S4) Integrate the stress-strain curves of the loading and unloading sections respectively to obtain the average maximum tear of the unloading section. T max_unloadingAverage maximum tear energy of the loaded segment T max_loading And obtain the viscous tearing energy: T E-loss = T max-loading - T max-unloading ;

[0017] S5) The crosslinking density of the sample was determined using the equilibrium swelling method. v ;

[0018] S6) Substitute the data obtained in steps S3-S5 into the following piecewise phenomenological model:

[0019] ;

[0020] The parameters were obtained by fitting using the least squares method. A , B , λ , f , m 1 , m 2 and critical crosslinking density v 0 ;

[0021] S7) Based on the model, output the predicted crack propagation rate curves for formulations with different crosslinking densities, and automatically determine the optimal crosslinking density that minimizes dc / dN.

[0022] Preferably, the crosslinking density in step S1 is controlled by adjusting the amount of sulfur donor, and the amount of sulfur donor is in the range of 3.25 phr-11.25 phr.

[0023] Preferably, in step S2, the gradient loading process maintains the strain valley value at 0 in each cycle, and the strain peak increases once every 500 cycles, for a total of 300,000 cycles and 600 cycles. The strain peak value in the first cycle is 10%, and the strain peak value in the 600th cycle is 50%.

[0024] As a preferred option, in step S3, the camera takes a photo before the start of the experiment and after each cycle. The length of the crack propagation is determined based on the photo, and the crack propagation rate is calculated by fitting the crack propagation length and the number of cycles using a power function.

[0025] The relationship between crack propagation rate and the number of load cycles is as follows:

[0026] ;

[0027] α and β are constants in the power function of crack propagation length, obtained by data fitting.

[0028] Preferably, in step S4, the stress and strain in each cycle are recorded, and the maximum tearing energy of each cycle is calculated accordingly. T The tear energy of a pure shear specimen is calculated using the following formula:

[0029] T= W × h 0 ;

[0030] in W For strain energy density, h 0 represents the clamping height of the sample when no deformation occurs.

[0031] Preferably, the equilibrium swelling method described in step S5 is carried out at 23±2℃ for 48 hours, using toluene as a solvent, and the crosslinking density is calculated based on the Flory-Rehner equation.

[0032] Preferably, the method is specifically used for evaluating the fatigue life of aircraft tire tread rubber, with the principal strain range limited to 10%-50% and the frequency limited to 5Hz±1Hz.

[0033] Furthermore, the present invention also provides a fatigue performance evaluation system for natural rubber for implementing the method, comprising:

[0034] The dynamic fatigue loading module is electromagnetically driven and can provide gradient sinusoidal loading within the range of 0-50% principal strain.

[0035] The image acquisition module, located on the side of the sample, has automatic focusing and crack tracking functions to acquire crack propagation images; the force-displacement acquisition module is used to synchronously record stress-strain data during the loading and unloading phases.

[0036] Data processing unit, built-in:

[0037] a) Image recognition algorithm used to calculate crack length;

[0038] b) Energy integration algorithm, used to obtain energy in real time. T max-loading , T max-unloading as well as T E-loss ;

[0039] c) Crosslinking density calculation module, used to call equilibrium swelling parameters and output v ;

[0040] d) Piecewise phenomenological model fitting module, used to solve for model parameters and optimal crosslinking density. vopt ;

[0041] The results are displayed in the formulation recommendation module, which outputs the crack propagation rate-tear energy curve and corresponding formulation optimization suggestions.

[0042] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement steps S3-S7 of the method.

[0043] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement steps S3-S7 of the method.

[0044] This invention, employing the aforementioned technical solution, investigates the influence of crosslinking density on the crack propagation rate of samples with pre-existing cracks. It provides an explanation of the nonlinear relationship between crosslinking density and the fatigue crack propagation rate of rubber from two aspects: energy dissipation mechanism and crack tip inhibition. Based on this, a phenomenological model of crack propagation rate with crosslinking density and tear energy as variables is proposed. This model can effectively fit the relationship between crack propagation rate and tear energy under different crosslinking densities. Using this model, the fatigue resistance of natural rubber formulations with different crosslinking densities can be quickly evaluated. It also provides an effective demonstration for further exploring the influence of the microscopic molecular chain network structure of natural rubber on macroscopic mechanical properties, laying the foundation for improving the lifespan of aircraft tires under harsh service conditions. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the sample's geometric dimensions.

[0046] Figure 2 A programmed tensile strain history plot for crack propagation rate measurement.

[0047] Figure 3 The crosslinking density of the six materials is given.

[0048] Figure 4 The results are the static mechanical property test results for six materials; among them: Figure 4 In the middle (a), the tensile stress-strain curve is shown. Figure 4 (b) shows the stress diagrams at 50% and 100% constant elongation (M50 and M100); Figure 4 (c) is a graph showing the relationship between tensile strength at break and elongation at break; Figure 4 The middle (d) diagram shows the tear strength.

[0049] Figure 5 Photographs of fatigue crack propagation tests.

[0050] Figure 6The length of crack propagation ( c） With the number of cycles ( N The graph shows the changes in the number of characters; among them, Figure 6 (a) represents the crack propagation length within the first 150,000 cycles. Figure 6 (b) represents the crack propagation length over the next 150,000 cycles.

[0051] Figure 7 The stress-strain curve obtained from the experiment.

[0052] Figure 8 The results are the crack growth rate (CGR) test results; among which, Figure 8 (a) CGR curves of each composite material; Figure 8 (b) when T max-unloading The CGR values ​​are 300 Jm⁻², 500 Jm⁻², 1000 Jm⁻², and 1500 Jm⁻², respectively.

[0053] Figure 9 For viscous tearing energy T E,loss With maximum strain Max The curve of change; where, Figure 9 (a) T of each composite material E,loss curve, Figure 9 (b) is a bar chart of the maximum tear energy of samples with different crosslinking densities under different principal strains.

[0054] Figure 10 The curves show the viscous tear energy versus crack propagation rate for NR samples with different crosslinking densities; among them, Figure 10 In the middle (a), the relationship curves between crack propagation rate and viscous tear energy are shown for natural rubber samples with different crosslinking densities. Figure 10 (b) is a bar chart of crack propagation rate for samples with different crosslinking densities at different viscous tear energy levels.

[0055] Figure 11 The curves showing the variation of residual strain (SetStrain) with strain for NR samples with different crosslinking densities.

[0056] Figure 12 Fit a curve to the experimental data; where, Figure 12 In the middle (a), the fitted curves of the experimental data corresponding to NR-2.25, NR-4.7, NR-6.25, and NR-7.8 are shown. Figure 12 In the middle (b), the fitting curves of the experimental data corresponding to NR-7.8, NR-9.375 and NR11.25 are shown.

[0057] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention. Detailed Implementation

[0058] 1. Experimental Design

[0059] 1.1 Preparation of Natural Rubber Composite Materials

[0060] The main formulation of the NR composite material of this invention is expressed as a percentage of NR (phr). Natural rubber (NR) is produced in Thailand; carbon black is produced by Shanghai Cabot Chemical Co., Ltd.; carbon black coupling agent is from Tongcheng New Materials Group Co., Ltd.; antioxidant is a product of Jiangsu Shengao Chemical Technology Co., Ltd.; accelerator is a product of Zibo Huamei Chemical Co., Ltd.; zinc oxide is a product of Shandong Xingya New Materials Co., Ltd.; stearic acid is produced in Malaysia; vulcanizing agent is a product of Jiangsu Qixiang High-Tech Materials Co., Ltd. Unless otherwise specified, all the above raw materials are purchased from the conventional market. The corresponding types of additives, their proportions, and the naming of the NR composite materials obtained according to different formulations are shown in Table 1 below.

[0061] Table 1. Formulation composition per 100 parts of natural rubber (phr)

[0062]

[0063] Among them, the proportions of carbon black (46.5%), coupling agent (1%), antioxidant (1%), accelerator (1.3%), ZnO (4%), and stearic acid (2%) are the same for all six materials. The material preparation mainly includes the following three steps:

[0064] Raw rubber plasticizing: Raw rubber is added into an internal mixer (GK255 internal mixer, Yiyang Rubber & Plastics Machinery Group Co., Ltd.), the rotation speed is 30 rpm / min, the top plug is pressed down, and the rubber is discharged when the temperature reaches 130℃;

[0065] First stage of mixing: Add plasticized rubber, carbon black, and other fines to the internal mixer at a speed of 25 rpm / min for approximately 90 seconds. When the temperature reaches 130℃, raise the top bolt to remove the carbon black fines. Once the temperature drops to 100℃, lower the top bolt and increase the speed to 35 rpm / min. When the temperature rises back to 130℃, increase the speed to 60 rpm / min. Discharge the rubber when the temperature reaches 150℃.

[0066] Vulcanization section: Add a section of masterbatch, vulcanizing agent and accelerator to the open mill (XK-550 open mill, Yiyang Rubber & Plastics Machinery Group Co., Ltd.), make three cuts in total, make 3 triangular bundles and 2 long strips, then adjust the roller gap to 2mm, and pass through the thin sheet;

[0067] After the final rubber compound has been left to stand for a certain period of time, it is vulcanized for 30 minutes using a flat vulcanizing machine (XLB-D flat vulcanizing machine, Huzhou Hongqiao Rubber Machinery Co., Ltd.) at a temperature of 151℃ and a pressure of 10MPa.

[0068] 1.2 Crack propagation rate test

[0069] The fatigue crack propagation rate test follows the ISO-17727 standard. The test specimens used are pure shear specimens containing a pre-existing crack. Variable amplitude loading allows for faster testing of the crack propagation rate in rubber. To ensure the effective area of ​​the specimen is under pure shear, the specimen needs to meet a suitable length-to-height ratio. In this test, the specimen is 150 mm long, the working area is 10 mm high, the thickness is 1.5 mm, and the pre-existing crack length is 25 mm. Figure 1 As shown.

[0070] The test was conducted using a dynamic fatigue performance testing machine (MK-3000 electromagnetic dynamic fatigue performance testing machine, Eribo Technology (Tianjin) Co., Ltd.). The displacement was controlled by the load, which was in the form of a horizontal sine wave with a frequency of 5Hz. The test temperature was room temperature of 23℃.

[0071] The experiment was conducted using a dynamic fatigue performance testing machine (MK-3000 electromagnetic dynamic fatigue performance testing machine, Eribo Technology (Tianjin) Co., Ltd.). Displacement control was implemented, with the load in the form of a horizontal sinusoidal wave at a frequency of 5Hz, and the test temperature was room temperature (23℃). To improve experimental efficiency, a gradient loading method was adopted for the fatigue crack propagation test, where the strain applied to the sample increased linearly with the number of load cycles. The specific experimental scheme is as follows: During cyclic loading, the strain valley value in each cycle was kept at 0, and the strain peak value increased every 500 cycles (1 lap). The test consisted of 300,000 cycles (600 laps). The strain peak value in the first lap was 10%, and the strain peak value in the 600th lap was 50%. Figure 2 As shown in (a), the testing equipment system records the stress and strain in each cycle, from which the maximum tear energy of each cycle can be calculated. T Equation (1) is the formula for calculating the tear energy of a pure shear specimen:

[0072] T = W × h 0 (1)

[0073] in W For strain energy density,h 0 represents the clamping height of the sample when no deformation occurs.

[0074] Before the experiment begins and after each lap, the camera takes a photograph of the crack tip, such as... Figure 2 The crack propagation length can be determined from the photograph at the location shown in (b). The crack propagation rate can be obtained by fitting the crack propagation length and number of cycles using a power function, as described in the literature [Shangguan Wenbin, Wang Xiaoli, Duan Xiaocheng, et al. Test and modeling method for crack propagation in rubber materials of vibration isolators under variable amplitude load [J]. Journal of Mechanical Engineering, 2015, 51(8):9.].

[0075] 1.3 Determination of crosslinking density

[0076] The crosslinking density of rubber was tested using the equilibrium swelling method. v A certain mass (m0) of dried sample was placed in a sealed container containing toluene and soaked at room temperature for 48 hours to allow it to swell to equilibrium. The sample was then removed, the surface solvent was quickly blotted dry with filter paper, and the mass of the swollen sample (m1) was measured. The swollen sample was then placed in a vacuum drying oven and dried to constant weight, and the mass of the dried sample (m2) was measured. The crosslinking density was calculated using the Flory-Rehner equation.

[0077] (2)

[0078] (3);

[0079] In the formula x This represents the interaction parameter between rubber and toluene solvent. ρ r and ρ s The densities are those of natural rubber and toluene solvent, respectively. V 0 represents the molar volume of toluene solvent.

[0080] 1.4 Mechanical property testing of rubber materials

[0081] Tensile properties of the material were tested according to ISO 37:2017. The specimens were dumbbell-shaped (gauge length 25 mm, width 6 mm), cut along the calendering direction from 2 mm thick vulcanized rubber using a cutter. The specimens were stretched at 500 mm / min until fracture using a tensile testing machine (GT-TCS-2000 tensile testing machine, Dongguan High-Speed ​​Railway Testing Instruments Co., Ltd.). Tear strength of the material was tested according to ISO 34-1:2004. The specimens were crescent-shaped, 110 mm long, 25 mm wide, and 2 mm thick, with a 1 mm notch pre-made on the inner side of the concave area. The specimens were stretched along their length at 500 mm / min using a tensile testing machine until tearing.

[0082] 2. Results Analysis

[0083] 2.1 Mechanical properties

[0084] Figure 3 The results show the crosslinking density test results for six materials. Figure 4 The results of the mechanical property tests are shown in the figure, with the data points representing the median values ​​from three experiments. The data table reveals a complex nonlinear relationship between the material's static mechanical properties and crosslinking density.

[0085] In this test, the tensile modulus is expressed as the stress at a specified elongation. For example, M50 represents the tensile stress at 50% elongation. Figure 4 (a) and Figure 4 As can be seen in (b), with the increase of crosslinking density, the elastic modulus of the material shows a trend of first increasing and then decreasing, reaching its maximum at a crosslinking density of NR-9.375, and then starting to decrease, reaching its minimum at NR-11.25. With the increase of crosslinking density, the tensile strength at break gradually decreases; the elongation at break decreases first, reaching its minimum at a crosslinking density of NR-9.375, and then increases again. Figure 4 (c) Generally, the higher the crosslinking density of a material, the stronger the entanglement between its internal molecular chains, which hinders the slippage between molecular chains, thus increasing the tensile stress at a given elongation and decreasing the elongation at break.

[0086] Furthermore, there is no significant correlation between the tear strength of the material and its crosslinking density. Figure 4 (d) The tear strengths of NR-3.25, NR-4.7 and NR-6.25 are similar, at approximately 130 kN / m. NR-7.8 has the lowest tear strength, NR-11.25 has a relatively small tear strength of approximately 81 kN / m, and NR-9.375 has a tear strength in between, at approximately 108 kN / m.

[0087] 2.2 Crack propagation rate test

[0088] In the fatigue crack propagation test, the equipment's photographic system takes an initial photograph as a reference before the test begins, and then takes another photograph after each lap. The crack length and crack profile shape can be obtained from these photographs. Table 2 shows the photographs taken for each composite material before the test begins, and at the end of the 200th, 400th, and 600th laps of the test.

[0089] Figure 6 The length of crack propagation ( c ) with the number of cycles ( N The relationship between crack propagation length and number of cycles can be described using a power function. The derivative of equation (4) can be used to obtain the relationship between crack propagation rate and number of load cycles.

[0090] (4);

[0091] In the above formula α and β These are constants in the power function of crack propagation length, which can be obtained by data fitting.

[0092] A total of 300,000 trials were conducted. cycle . Figure 6 In Figure (a), the crack propagation length varies with the number of cycles during the first 150,000 cycles. Figure 6 Figure (b) shows the crack propagation length as a function of the number of cycles in the last 150,000 cycles. It can be observed that the crack propagation length of NR-7.8 is relatively small throughout the process, while the crack propagation length of NR-11.25 is generally larger. In the first 150,000 cycles, the curves of NR-3.25 and NR-4.7 show similar trends, with the propagation length of NR-3.25 slightly greater than that of NR-4.7; the curves of NR-6.25 and NE-9.375 show similar trends. In the last 150,000 cycles, the curves of NR-3.25, NR-4.7, and NR-6.25 have similar shapes, and the final crack propagation lengths are also relatively close, with the propagation length of NR-3.25 greater than that of NR-4.7, which in turn is greater than that of NR-6.25. The crack propagation length of NR-9.375 suddenly increases near the 220,000th cycle, showing a clear abrupt change. The overall trend of NR-11.25 is very similar to that of NR-9.375.

[0093] Within the small circulation range (0.8×10 5 Within one cycle, the crack propagation length changes little with crosslinking density. This may be related to the weak van der Waals forces between molecular chains; in the early stages of fatigue, when strain is applied for a short period, the effect of crosslinking density on crack propagation length is not significant. When the cycle period is within 0.8 × 10⁻⁶ cycles... 5 -1.5×10 5During the subsequent cycles, as the crosslinking density continuously increases, an optimal crosslinking density point NR-7.8 emerges, minimizing the crack propagation length of the sample. However, the regularity of other methods is not strong. When the cycle period is greater than 1.5 × 10⁻⁶, 5 At that time, there exists an optimal crosslinking density inflection point NR-7.8 that minimizes the crack propagation length, and the pattern is obvious.

[0094] also, Figure 5 The experiment showed the crack path and profile during the experiment. The propagation paths of NR-7.8 and NR-6.25 showed significant deflection, and the crack profile edges were uneven. Based on the data, it can be determined that the deflection of NR-7.8 is a macroscopic manifestation affecting the overall low crack propagation rate, while the deflection of NR-6.25 occurred in cycles of 1.5 × 10⁻⁶. 5 While the crack propagation rate is around 100%, its overall crack propagation rate is much higher than that of NR-7.8. Conversely, the crack opening edges of NR-9.375 and NR-11.25 are relatively smooth.

[0095] 2.3 Relationship between crack propagation rate and maximum tearing energy

[0096] Based on the fatigue crack propagation tests described above, the relationship between crack propagation rate and maximum cyclic tear energy of samples with different crosslinking densities was further analyzed. The method described in the literature [Goossens, JR and Mars, WV, 2018. Finitely scoped, high reliability fatigue crack growth measurements. Rubber Chemistry and Technology, 91(4), pp.644-650.] was used to obtain continuously varying tear energy and corresponding crack propagation rate data during the tests. Because the stress-strain behavior of filled rubber exhibits significant hysteresis, the strain energy density is typically calculated using the unloading section curve when calculating the tear energy. W ,like Figure 7 As shown. Then, calculate the average maximum tearing energy per circumference according to equation (1). T max-unloading By combining the crack propagation rate results, the curve of crack propagation rate versus tearing energy can be obtained, such as... Figure 8 As shown.

[0097] from Figure 8 It can be seen that when the tearing energy is less than 500 J / m 2 At this point, the crack propagation rates of the six materials were relatively similar, indicating that the effect of crosslinking density was not significant within this range. When the tearing energy was greater than 600 J / m... 2 At that time, significant differences began to appear in the crack propagation rates. Observation Figure 8 The results for NR-3.25, NR-4.7, NR-6.25 and NR-7.8 in (a) show that the slope of the curves for these four materials gradually decreases, and the curves for NR-9.375 and NR11.25 are above NR-7.8. Figure 8 (b) is when T max-unloading 300J / m 2 500J / m 2 1000J / m 2 and 1500J / m 2 The crack propagation rate of each material at that time was calculated. The results show that when... T max-unloading 300J / m 2 At that time, the crack propagation rates of the six materials were relatively similar, with NR-7.8 exhibiting the lowest crack propagation rate; when T max-unloading 500J / m 2 1000J / m 2 and 1500J / m 2 At this time, the crack propagation rate generally showed a trend of first decreasing and then increasing, with the minimum value at NR-7.8. The greater the tear energy, the more obvious the difference. Combining the crosslinking density test results, it can be concluded that, under the same tear energy, the crack propagation rate first decreases and then increases with the increase of crosslinking density. That is, for the crack propagation rate of rubber materials, there is an optimal crosslinking density that minimizes the crack propagation rate.

[0098] 2.4 Fatigue Mechanism Analysis Based on Crack Propagation

[0099] To further investigate the changes in crack propagation rate caused by variations in crosslinking density, the data generated during the experiment were further analyzed. In the aforementioned fatigue crack propagation test, except for the average maximum tear rate in the unloading section... T max_unloading In addition, the average maximum tear energy of the loaded segment was calculated from the stress-strain data of the loaded segment using dynamic cyclic load records. T max_loading and calculated T E_loss = T max_loading - T max_unloading We put T E_loss Defined as viscous tear energy, it represents the portion of tear energy dissipated per unit area of ​​the crack plane due to the viscoelastic properties of the material when an external load is applied to the crack plane. Figure 9 for T E_lossThe curve shows the variation of the maximum strain value (StrainMax), where StrainMax is the average of the maximum strain values ​​in each cycle within the same loop. The figure shows that as the crosslinking density increases, under the same strain conditions, during the process of increasing the vulcanizing agent content from 3.25% to 6.25%, and from 7.8% to 11.25%, the strain values ​​decrease. T E_loss The concentration gradually increases; however, when the vulcanizing agent content is 7.8%, T E_loss It is at a low level.

[0100] Figure 10 (a) shows T E_loss The curve shows the relationship between crack propagation rate and crack extension rate. It is generally believed that filled natural rubber can effectively dissipate the tearing energy applied to the crack tip by external load through the viscous loss of the molecular chains; therefore, materials with high viscous loss should have a lower crack propagation rate. However, from... Figure 10 As can be clearly seen in (b), for the tested samples with different crosslinking densities, the crack propagation rate increases with... T E-loss The variation pattern and crack propagation rate with T max_unloading The change pattern is consistent; when the vulcanizing agent content is 7.8%, T E-loss The crack propagation rate is at its minimum, which is also the minimum at this point. This phenomenon cannot be explained from the perspective of viscous loss.

[0101] Another supplementary theory is needed to explain the phenomenon that the crack propagation rate initially increases and then decreases with increasing crosslinking density. Considering the prevalent strain crystallization effect in NR (Natural Curing Agent), as the crosslinking density increases, the density of molecular chains that orient and crystallize at the crack tip during the tensile stage also increases, further increasing the resistance to crack propagation. This can explain the phenomenon that, under the same tearing energy conditions, the crack propagation rate decreases with increasing crosslinking density when the vulcanizing agent content increases from 3.25% to 7.8%. On the other hand, for the vulcanizing agent content increasing from 7.8% to 11.25%, the increased crosslinking density leads to a greater frictional effect caused by the relative movement between the molecular chain network and the filling network during cyclic loading-unloading, resulting in increased energy loss due to friction. T E-loss The gradual increase in viscous energy loss rate, under the same tearing energy conditions during dynamic cyclic alternating loading, indicates an increase in the viscous heat generation rate per unit time. This leads to an increase in crack tip temperature (e.g., from room temperature to 50°C). Since the crystallinity of strain-induced crystallization decreases significantly at high temperatures, the crack propagation rate will actually increase when the crosslinking density further increases.

[0102] The low crack propagation rate of NR-7.8 is mainly due to the hindering effect of strain-induced crystallization on crack propagation rather than viscous loss. Another indirect evidence for this is the reduced tearing energy at the crack tip, which comes from the tear strength test results. Figure 4 (d) Since the tear strength test is calculated from data of a single tensile loading process, the viscous dissipation effect at the crack tip plays a major role in reducing crack propagation caused by the external load input energy during the tearing process. The tear strength test data shows that, compared to NR-3.25 and NR-4.7, in fatigue tests… T E_loss Among the high-level specimens, the NR-7.8 specimen exhibited the lowest tear strength among all tested materials, which is consistent with the performance of this type of specimen in fatigue tests. T E_loss The lowest possible scenario matches.

[0103] The residual stress (SetStrain) of the NR-7.8 specimen during cyclic loading was also at a high level. SetStrain is the average deformation of the specimen when the stress returns to zero during the unloading phase of each cycle in the fatigue crack propagation test. SetStrain measures the change in inelastic deformation of the specimen during dynamic fatigue testing. During cyclic loading, the stretched and oriented rubber molecular chains in the specimen require a certain amount of time to return to a non-oriented state during unloading. When the frequency of the alternating load is high (e.g., 5Hz), the molecular chains cannot completely return to a non-oriented state within the limited unloading time. Therefore, the specimen exhibits a certain degree of inelastic deformation during the test. The magnitude of the inelastic deformation of the specimen can indirectly reflect the number and degree of orientation of the molecular chains that become oriented during loading.

[0104] from Figure 11 It can be seen that for NR samples with different crosslinking densities, SetStrain increases with increasing strain. Comparing several samples with vulcanization accelerator content gradually increasing from NR-3.25 to NR-7.8, it is found that with the increase of crosslinking density, the SetStrain of NR-3.25, NR-4.7, and NR-6.25 samples gradually decreases, that is, the inelastic deformation of the material decreases. This is consistent with the hypothesis that the increase of crosslinking density causes the increase of material elasticity. At the same time, the SetStrain of NR-9.375 and NR-11.25 is at a lower level, while the SetStrain of NR-7.8 is only slightly smaller than that of NR-3.25, but is at a higher level among all samples.

[0105] 2.5 Model for Crack Propagation Rate of Natural Rubber Based on Crosslinking Density and Tear Energy

[0106] The actual molecular chain network of filled rubber materials is very complex, containing both cross-linked networks formed by randomly cross-linked entangled molecular chains and filled networks formed by filler components. Furthermore, there are complex interactions between these cross-linked and filled networks. Regarding fatigue resistance, filled rubber materials exhibit resistance to applied fatigue loads through two different mechanisms: one is through the elastic deformation of the molecular chain network to resist external forces, storing the energy applied by the external force within the molecular chain network; the other is through the viscous properties of the molecular chain network to dissipate the energy applied by the external force as internal energy. The cross-linking density of the rubber material plays a crucial role in these two fatigue resistance mechanisms. Under the premise that other factors remain constant, filled rubber materials with different cross-linking densities exhibit different elastic deformation capabilities and viscous dissipation capabilities. Therefore, it can be inferred that the fatigue crack propagation performance of filled rubber materials with different cross-linking densities will have significant differences.

[0107] The above experimental data and analysis show that, during the stable crack propagation stage, the crack propagation rate of the NR rubber sample first decreases and then increases with the increase of crosslinking density. During the process of crosslinking density changing from low to high, there exists a critical value that results in the lowest crack propagation rate. That is, under otherwise constant conditions, by changing the amount of vulcanization accelerator, an optimal crosslinking density can be obtained, resulting in the NR rubber formulation having the best fatigue resistance. Based on the above experimental phenomena, we constructed a phenomenological model of crack propagation rate regarding crosslinking density, as shown in equation (5):

[0108] (5)

[0109] In the formula v 0 represents the critical crosslinking density, A, B, m1, m2, λ, f is a material constant.

[0110] This model uses crosslinking density as a new variable and a critical crosslinking density as the dividing point to divide the crack propagation rate model into two parts. Below the critical crosslinking density, the crack propagation rate decreases exponentially with increasing crosslinking density; above the critical crosslinking density, the crack propagation rate and crosslinking density are defined as a power-law relationship. According to this model definition, when the crosslinking density of the material reaches the critical crosslinking density, the crack propagation rate of the sample is at its lowest level under any tearing energy condition.

[0111] Based on the experimental results above, assuming that the crosslinking density corresponding to NR-7.8 is the critical crosslinking density of the target formulation, the sample crosslinking density data obtained in the above experiments, as well as the crack propagation rate and tearing energy, are used. T max_unloadingThe relationship data was used to fit the above model. The experimental data corresponding to NR-3.25, NR-4.7, NR-6.25, and NR-7.8 were used to fit the formula used for the low crosslinking density range, and the experimental data corresponding to NR-7.8, NR-9.375, and NR11.25 were used to fit the formula used for the high crosslinking density range. The resulting fitting curves and fitting parameters are shown below. Figure 12 As shown in Table 2.

[0112] Table 2 Fitting parameters

[0113]

[0114] The fitted curves show that the above model can well describe the change of crack propagation rate with tearing energy, and can reflect the change of crack propagation rate with crosslinking density in different crosslinking density ranges. According to equation (5), with crosslinking density as the independent variable, the optimal crosslinking density that minimizes crack propagation rate can be approximately obtained.

[0115] Comparative Examples and Implementation Examples

[0116] I. Common Experimental Conditions (Shared by Comparative and Specific Examples)

[0117] Sample systems: NR-3.25, NR-4.7, NR-6.25, NR-7.8, NR-9.375, NR-11.25 (sulfur donor 3.25–11.25 phr), other formulations are the same.

[0118] Geometry / Loading: Pure shear specimen (150×10×1.5mm, pre-cracked 25mm), 5Hz, room temperature 23℃; Ramp gradient loading (10%→50%, increasing every 500 cycles, for a total of 3×10⁵ cycles, 600 cycles).

[0119] Measurement: Crack length c is calculated by imaging at the end of the cycle, and CGR (da / dN) is obtained by power function fitting; T is obtained by integrating from the unloading section. max-unloading (Tearing energy); crosslinking density v is obtained by equilibrium swelling method.

[0120] Evaluation point: Select T max-unloading The four representative energy levels =300 / 500 / 1000 / 1500 J•m⁻² are compared.

[0121] Statistics: Leave-one-out cross-validation (LOO-CV) was performed on the four energy levels according to the formulation, and MAPE, RMSE, R², and AIC were calculated.

[0122] Note: The comparative example only changed the prediction formula; other data collection and preprocessing were completely consistent to ensure comparability.

[0123] II. Comparative Example 1 (Benchmark Model: Thomas)

[0124] Model: da / dN=CT m

[0125] Independent variable: Tear energy T only (using the maximum tear energy T at the unloading section) max-unloading ).

[0126] Fitting: Linear least squares fitting of log(da / dN)–logT is performed according to the formula to obtain C,m.

[0127] Features and limitations: It does not include crosslinking density v, and cannot express the non-monotonic CGR–v relationship that decreases first and then increases.

[0128] Example 1 (Model of the Invention)

[0129] Model (piecewise exponential-power law, including crosslink density):

[0130] ;

[0131] Independent variables: tearing energy T and crosslinking density v, with the breakpoint being the critical crosslinking density v0 (measured to NR-7.8).

[0132] Fitting: Joint least squares estimation of A, B, λ, f, m1, m2, v0 over all formulation data; parameter examples and... Figure 12 Consistent with Table 3.

[0133] Advantages: It can simultaneously characterize the competing mechanisms of strain-induced crystallization retardation (exponential decay in low-crosslinked segments) and viscous heat-induced acceleration (power-law increase in high-crosslinked segments), and analytically obtain v. opt .

[0134] III. Comparison of Data and Statistical Results

[0135] Table 4 Comparison of prediction accuracy at typical energy levels (unit: m / cycle)

[0136] NR-3.25 500 <![CDATA[2.50×10⁻ 5 ]]> <![CDATA[2.30×10⁻ 5 ]]> −8.0 <![CDATA[2.55×10⁻ 5 ]]> +2.0 1000 <![CDATA[3.10×10⁻ 5 ]]> <![CDATA[2.60×10⁻ 5 ]]> −16.1 <![CDATA[3.05×10⁻ 5 ]]> −1.6 NR-7.8 500 <![CDATA[1.40×10⁻ 5 ]]> <![CDATA[2.10×10⁻ 5 ]]> +50.0 <![CDATA[1.46×10⁻ 5 ]]> +4.3 1000 <![CDATA[1.80×10⁻ 5 ]]> <![CDATA[2.65×10⁻ 5 ]]> +47.2 <![CDATA[1.87×10⁻ 5 ]]> +3.9 NR-11.25 500 <![CDATA[3.20×10⁻ 5 ]]> <![CDATA[2.90×10⁻ 5 ]]> −9.4 <![CDATA[3.15×10⁻ 5 ]]> −1.6 1000 <![CDATA[4.40×10⁻ 5 ]]> <![CDATA[3.35×10⁻ 5 ]]> −23.9 <![CDATA[4.80×10⁻ 5 ]]> +9.1

[0137] IV. Mechanism of Difference and Evidence of Effect

[0138] 1. Non-monotonic relations are reproducible

[0139] Actual observations: CGR first decreases and then increases with crosslinking density v, with NR-7.8 showing the lowest plateau in the total tear energy range. Thomas's single power law only changes monotonically with T, failing to produce a minimum value, resulting in a systematic overestimation (maximum +50%) of NR-7.8. The low crosslinking region Ae of this invention... -λv This demonstrates SIC hindrance, with high cross-linking region Bv α The acceleration is reflected by viscous heat generation, and an analytical minimum is given at v=v0, which is consistent with the actual measurement.

[0140] 2. The necessity of energy channel decomposition

[0141] Using T max-unloading (Elasticity) and T Eloss (Viscous) distinguishes between driving and dissipative processes; Thomas did not model T. Eloss The cracking rate was underestimated in the highly crosslinked-high temperature rise region (see NR-11.25, −23.9%). The model parameters λ and α of this invention are sensitive to the SIC effect and viscous temperature rise, respectively, and can predict stability across energy levels and formulations.

[0142] 3. Engineering availability (optimal crosslinking density)

[0143] Thomas could not derive the optimal crosslinking density; repeated formulation trials were required. This invention obtains v opt =v0 (corresponding to NR-7.8) can be directly mapped to a process window of 7.4–8.2 phr for sulfur donors; the average CGR is reduced by 28–41% in the 500–1500 J•m⁻² range (compared to non-optimal formulations).

[0144] 4. Efficiency and stability

[0145] A single Ramp experiment can cover 300-1500 J•m⁻², and combined with a unified model for joint fitting, the experimental cycle is reduced from 2-3 weeks to <3 days; the results show that the cross-energy level consistency (single data source) is better than multiple constant amplitude experiments.

[0146] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

[0147] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0148] This application may be described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0149] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0150] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0151] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0152] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0153] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

Claims

1. A method for predicting the fatigue crack propagation rate of rubber, characterized in that, The method includes the following steps: S1) Prepare natural rubber samples with different crosslinking densities; S2) The pure shear specimen containing pre-existing cracks is mounted on a dynamic fatigue testing machine and gradient loading is applied cyclically; S3) After each cycle, the crack length is recorded using the image acquisition module, and the crack propagation rate dc / dN is calculated. c The length of the crack propagation. N This represents the number of loop iterations. S4) Integrate the stress-strain curves of the loading and unloading sections respectively to obtain the average maximum tear energy of the unloading section. T max_unloading Average maximum tear energy of the loaded segment T max_loading And obtain the viscous tearing energy: T E-loss = T max-loading - T max-unloading， draw T E-loss Curve showing the relationship between crack propagation rate and crack speed; T E-loss It is used to represent the portion of tearing energy dissipated per unit area of ​​the crack plane due to the viscoelastic properties of the material when an external load is applied to the crack plane; S5) The crosslinking density of the sample was determined using the equilibrium swelling method. ; S6) Substitute the data obtained in steps S3-S5 into the following piecewise phenomenological model: ； The parameters were obtained by fitting using the least squares method. A , B , λ , f , m 1 , m 2 and critical crosslinking density ; S7) Based on the model, output the predicted crack propagation rate curves for formulations with different crosslinking densities, and automatically determine the optimal crosslinking density that minimizes dc / dN.

2. The method according to claim 1, characterized in that, The crosslinking density mentioned in step S1 is controlled by adjusting the amount of sulfur donor, and the amount of sulfur donor ranges from 3.25 phr to 11.25 phr.

3. The method according to claim 1, characterized in that, In step S2, the gradient loading process maintains the strain valley value at 0 in each cycle during the cyclic loading process. The strain peak value increases once every 500 cycles, and the experiment consists of 300,000 cycles and 600 laps. The strain peak value in the first lap is 10%, and the strain peak value in the 600th lap is 50%.

4. The method according to claim 1, characterized in that, In step S3, the camera takes a picture before the experiment begins and after each lap. The length of the crack propagation is determined based on the picture. The crack propagation rate is calculated by fitting the crack propagation length and the number of cycles using a power function. The relationship between crack propagation rate and the number of load cycles is as follows: ； α and β are constants in the power function of crack propagation length, obtained by data fitting.

5. The method according to claim 1, characterized in that, In step S4, the stress and strain in each cycle are recorded, and the maximum tearing energy per cycle is calculated accordingly. T The tear energy of a pure shear specimen is calculated using the following formula: T= W × h 0 ； in W For strain energy density, h 0 represents the clamping height of the sample when no deformation occurs.

6. The method according to claim 1, characterized in that, The equilibrium swelling method described in step S5 was carried out at 23±2℃ for 48 hours, using toluene as a solvent, and the crosslinking density was calculated based on the Flory-Rehner equation.

7. The method according to any one of claims 1-6, characterized in that, The method is specifically used for evaluating the fatigue life of aircraft tire tread rubber, with the principal strain range limited to 10%-50% and the frequency limited to 5Hz±1Hz.

8. A fatigue performance evaluation system for natural rubber used in implementing the method according to any one of claims 1-6, characterized in that, include: The dynamic fatigue loading module is electromagnetically driven and can provide gradient sinusoidal loading within the range of 0-50% principal strain. The image acquisition module, located on the side of the sample, has automatic focusing and crack tracking functions to acquire images of crack propagation. Force-displacement acquisition module is used to synchronously record stress-strain data of the loading and unloading sections; Data processing unit, built-in: a) Image recognition algorithm used to calculate crack length; b) Energy integration algorithm, used to obtain energy in real time. T max-loading , T max-unloading as well as T E-loss ; c) Crosslinking density calculation module, used to call equilibrium swelling parameters and output ; d) Piecewise phenomenological model fitting module, used to solve for model parameters and optimal crosslinking density. v opt ; The results are displayed in the formulation recommendation module, which outputs the crack propagation rate-tear energy curve and corresponding formulation optimization suggestions.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by the processor, they implement steps S3-S7 of the method according to any one of claims 1-6.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement steps S3-S7 of the method according to any one of claims 1-6.

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