Method for testing fatigue threshold value of elastomer through elastic limit strain point
Through Mullins testing and elastic limit strain point method, the problems of long test time and large sample size in the prior art are solved, and the elastomer fatigue threshold is quickly and accurately obtained, and the accuracy of material design and safety assessment is improved.
Patent Information
- Application Number
- CN202410470376.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-18
- Publication Date
- 2025-05-30
AI Technical Summary
The prior art has limitations on long time and large sample size when testing elastomer fatigue thresholds, and simplified methods may not accurately reflect fatigue thresholds in actual applications, affecting the accuracy of material design and safety assessment.
By performing Mullins test on the Gaussian chain model elastomer, the elastic limit strain point is measured, and the fatigue test strain is gradually reduced from this point, and a curve of cyclic test and energy release rate (G-N curve) is obtained to obtain the ultimate fatigue threshold.
This method can quickly and accurately obtain elastomer fatigue thresholds, reduce test time and sample size requirements, and improve the accuracy of material design and safety assessment.
Smart Images
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Abstract
Description
Technical Field
[0001] The present application relates to a method for testing the fatigue threshold of an elastomer, which determines the fatigue threshold of the elastomer through the elastic limit strain point of the elastomer. Background Art
[0002] Elastomers possess good mechanical properties and durability. The durability and lifespan assessment of this material rely on fatigue testing, which reveals the material's performance under long-term stress by simulating cyclic stress conditions in actual applications and evaluates the degree of material damage by monitoring crack propagation. Traditional fatigue testing methods have limitations in terms of long testing time (15 days) and large sample size (0.5m 2 ), and it is unrealistic or uneconomical to complete the test in some cases. Therefore, researchers have been seeking more efficient methods to determine the fatigue threshold, including simplifying the fatigue threshold to a certain percentage of the fracture energy (such as 5%-10%) to reduce the computational complexity. However, this simplified method may not accurately reflect the true fatigue threshold of the elastomer in actual applications, affecting the accuracy of material design and safety assessment. Therefore, obtaining a method for quickly obtaining the fatigue threshold of an elastomer has important practical application value. Summary of the Invention
[0003] The present application relates to a method for testing the fatigue threshold of an elastomer, which determines the fatigue threshold of the elastomer through the elastic limit strain point of the elastomer. It has the advantages of rapid testing and low requirements for the number of test samples.
[0004] The test scheme provided by the present application is to perform Mullins testing on a Gaussian chain model elastomer to obtain the elastic limit strain point of the elastomer. Starting from the elastic limit strain point, the fatigue limit strain is found by gradually reducing the fatigue test strain, and the curve of the cyclic test and energy release rate of the elastomer (G-N curve) is obtained and the limit of this curve is calculated to obtain the fatigue threshold. Brief Description of the Drawings
[0005] Figure 1 is a diagram of the Mullins effect and fatigue mechanism.
[0006] Figure 2 is the stress-strain curve in Mullins testing (a) infinitely low loading speed; (b) infinitely high loading speed; (c) actual loading speed.
[0007] Figure 3 is the Mullins test curve of (a) PMA; (b) PDMS and (c) IDNE and its (d) hysteresis.
[0008] Figure 4are Mullins curves of (a) PMA, (b) PDMS, and (c) IDNE with a 24-hour interval between two loadings.
[0009] Figure 5 is the stress-strain curve in a typical cycle of (a 1 ) PDMS at a strain of 0.1; (a 2 ) overall stress-strain curve of PDMS at a strain of 0.1; (a 3 ) fitted curve of the fatigue threshold of PDMS; (b 1 ) stress-strain curve in a typical cycle of IDNE; (b 2 ) overall stress-strain curve of PDMS at a strain of 0.1; (b 3 ) fitted curve of the fatigue threshold of PDMS.
[0010] Figure 6 Schematic diagram of fatigue principle: (a) schematic diagram of a cracked specimen when not stretched; (b) schematic diagram of a cracked specimen with crack closure; (c) clamped photo of the crack when not stretched; (d) clamped photo of the crack opening during the first stretching; (e) clamped photo of the crack closure during the 10,000th stretching; (f) clamped photo of the crack opening during the 10,000th stretching.
[0011] Figure 7 is, at 0 °C and a strain of 0.1, the stress-strain curve in a typical cycle of (a 1 ) PDMS; (a 2 ) overall stress-strain curve of PDMS at a strain of 0.1; (a 3 ) fitted curve of the fatigue threshold of PDMS; (b 1 ) stress-strain curve in a typical cycle of IDNE; (b 2 ) overall stress-strain curve of PDMS at a strain of 0.1; (b 3 ) fitted curve of the fatigue threshold of PDMS. Detailed implementation manners
[0012] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the embodiments of this application. Obviously, the described embodiments are some, rather than all, of the embodiments of this application. The components of the embodiments of this application described and illustrated here can generally be arranged and designed in various different configurations.
[0013] The following is a detailed example of the solution of this application: In traditional Mullins tests, the calculation of energy density is crucial for evaluating material properties. The area under the loading curve represents the total work done by the external force on the material ( Figure 1c), i.e., the energy stored in the material during loading. The area under the unloading curve, on the other hand, reflects the elastic energy that the material can recover after unloading. Figure 1 d), representing the elastic resilience ability of the material. The area difference between the two curves is usually regarded as energy dissipation Figure 1 (the red area in d), which is often considered to be caused by the breakage of internal molecular chains in the material and other irreversible deformation mechanisms (such as plastic deformation). Figure 1 (the red chain segments in ab). However, the traditional calculation method of energy dissipation ignores this important factor of the relaxation phenomenon. In actual polymer materials, not all molecular chains remain unchanged or break during loading and unloading. Those molecular chains that do not slip Figure 1 (the yellow chain segments in ab) contribute to the generation of elastic work, thus promoting the rebound effect of the material, while the slippage of some other molecular chains Figure 1 (the green chain segments in ab) is part of the relaxation process. However, considering the energy loss during the relaxation process as energy dissipation may lead to a deviation in the understanding of the energy loss mechanism within the material. In fact, the relaxation phenomenon largely reflects the viscoelastic properties of the material, rather than simply energy dissipation. The energy loss of viscoelastic materials during loading and unloading not only stems from the breakage of molecular chains or plastic deformation, but also includes the energy loss caused by the slippage and rearrangement between molecular chains.
[0014] One of the innovative ideas of this application to solve the problem of viscoelastic work in the Mullins test is to regard the work generated by molecular slippage as frictional work, and this part of the work is stored as viscoelastic energy and gradually released inside the material through the relaxation process. In continuous Mullins tests, due to the lack of sufficient relaxation time, this results in the viscoelastic energy not being completely released between each loading-unloading cycle, forming a hysteresis phenomenon on the curve, which is manifested in the form of an area difference Figure 1 (the green area in e). To minimize the problem of the influence of viscoelastic work on the hysteresis curve, this study proposes a new method, that is, to calculate energy dissipation by comparing the area differences between two consecutive loading curves Figure 1 (the red area in e). This method can more accurately distinguish the energy loss of the material in the pure elastic deformation and plastic deformation stages, rather than wrongly including the hysteresis effect caused by viscoelasticity in the energy dissipation.
[0015] In-depth analysis and improvement of the Mullins test method and the calculation method of energy dissipation are the key to solving the influence of viscoelastic work on energy dissipation. In actual operation, since the loading speed cannot be infinitely low or infinitely high, the storage and dissipation of viscoelastic work become an inevitable phenomenon, which poses a challenge to the accurate calculation of energy dissipation.
[0016] Ideally, if the loading speed is infinitely low, a hysteresis curve close to the influence of non-viscoelasticity can be obtained, and the theoretical energy dissipation can be clearly observed from the hysteresis curve ( Figure 2 a). In another extreme, that is, when an extremely high loading speed is applied, the hysteresis curve is mainly determined by the viscoelastic response ( Figure 2 b), and at this time, the viscoelastic work can be directly calculated from the curve. However, the loading speed in reality is between these two extremes, resulting in the storage of viscoelastic work during loading and unloading, and thus generating test errors that cannot be directly calculated ( Figure 2 c). To eliminate this error, a 10% error value is set for the hysteresis, that is, if the hysteresis is less than 10%, it is considered that there will be no significant energy dissipation, and the behavior of the material is mainly elastic. This criterion helps researchers more accurately distinguish the elastic stage and the viscoelastic stage of the material, and then use it to determine the elastic limit strain point, more accurately evaluate the fatigue performance and durability of the material. This method provides an effective solution for accurately calculating energy dissipation.
[0017] The stress-strain curves of three typical elastomers, PMA, PDMS, and IDNE, measured by Mullins test are as Figure 3 a, Figure 3 b, Figure 3 c shown, where all adjacent loading curves are above the unloading curves. This phenomenon indicates that there is a certain degree of energy recovery in these materials. However, since these materials are chemically cross-linked elastomers, they do not have self-healing ability. This energy recovery mechanism can only be due to the viscoelastic characteristics inside the material, resulting in part of the energy being temporarily stored in the relative displacement of polymer chains.
[0018] Figure 4 Shown are two loading and unloading experiments at strains of 0.5 and 0.75, but there is an interval of 24 h between the two loading and unloading processes. Compared with Figure 3 that, the hysteresis area has significantly decreased, especially for PDMS and IDNE samples ( Figure 4 b and 4c). At a strain of 0.75, no energy dissipation occurs in the elastomers. This proves that the relaxation time mentioned above is crucial for the Mullins test of elastomers.
[0019] From Figure 3It can be seen from abc that in the Mullins test, the different performances of the three materials, PMA, PDMS, and IDNE, reveal their respective unique viscoelastic properties and internal structural differences. In particular, due to its significant viscoelastic properties, PMA exhibits a large amount of energy dissipation during loading and unloading, and its hysteresis percentage is always higher than 10% throughout the strain range, indicating that PMA lacks a clear elastic limit strain point. In contrast, PDMS and IDNE show smaller hysteresis values at lower strain levels (such as a strain of 0.25), suggesting that at these strain levels, the two materials mainly exhibit elastic responses and relatively less energy dissipation. However, when the strain increases to 0.5, the hysteresis values of PDMS and IDNE both exceed 10%, indicating that at higher strain levels, the viscoelastic effect becomes more significant, resulting in more energy dissipation. Based on this observation, it can be inferred that the elastic limit strain points of PDMS and IDNE may be in the strain range of 0.25 to 0.5.
[0020] By using samples with artificial cracks and calculating the energy release rate of the material at different strains and performing a linear fit, the fatigue threshold similar to that under long-term use conditions can be approximately obtained ( Figure 5 a 3 and b 3 ).
[0021] As mentioned above, in the Mullins test, a hysteresis of more than 10% in elastic materials is indeed regarded as an important indicator for the viscoelasticity to start contributing to energy dissipation. This phenomenon indicates that once this hysteresis percentage is reached, the molecular chains inside the material begin to respond to external loading in a non-fully elastic form, resulting in partial loss of energy. Accordingly, the elastic limit strain point of the material, that is, the strain point where the material changes from a pure elastic response to a response including significant viscoelasticity, can be located between the strain points of two consecutive Mullins tests.
[0022] By analyzing the typical process in 10,000 cycles and calculating the energy release rate at different strains and performing a curve fit, it is found that the fatigue threshold of IDNE reaches 364 J / m 2 , significantly higher than 81 kJ / m of PDMS 2 . In addition, by calculating the fatigue threshold using traditional methods, that is, by determining the strain point (λc) at which crack propagation occurs ( Figure 5 a 3 and b 3 the black line segment in), the results show that the fatigue thresholds of IDNE and PDMS are 385 J / m 2 and 85 J / m 2 respectively, with an error of only 6% compared to the results calculated by the elastic limit strain point method. At the same time, this accuracy is much higher than that based on 5% fracture energy of 5.2 kJ / m2 and 1.23 kJ / m 2 The fatigue thresholds estimated by the standard method show the advantages of the elastic limit strain point method in terms of accuracy and efficiency. Therefore, as a method for obtaining fatigue thresholds, the elastic limit strain point method is not only more accurate but also faster, providing an effective new approach for fatigue performance evaluation. The application of this method is of great practical significance, especially for those occasions that require accurate evaluation of fatigue thresholds to guide engineering design and material selection ( Figures 5 - 7 indicating the artificial crack propagation of the material).
[0023] To verify the applicability and sensitivity of the newly proposed method in this chapter under different conditions, fatigue experiments on PDMS and IDNE materials were carried out under ice-water conditions (0 °C), and the influence of low-temperature environment on the fatigue performance of materials was further explored. By analyzing the typical cycles in 10,000 cycles, it was found that under ice-water conditions, the fatigue thresholds of PDMS and IDNE were 66 kJ / m 2 and 125 J / m 2 ( Figure 7 a 2 and b 2 ). By comparing the fatigue thresholds obtained based on the elastic limit strain point with those obtained by the traditional method (calculated based on the strain point λc where crack propagation occurs), it can be observed that the fatigue thresholds of IDNE and PDMS are 123 J / m 2 and 64 J / m 2 . This result shows that the fatigue thresholds obtained using the elastic limit strain point method have higher accuracy in error control, with an error of only 3%, much lower than the fatigue thresholds estimated based on the 5% fracture energy standard (985 J / m 2 and 1.23 kJ / m 2 ). This not only further proves the effectiveness of the proposed method but also highlights its advantages in terms of reliability. The effectiveness of the method proposed in this application was also verified under the low-temperature ice-water environment.
Claims
1. A method for testing the fatigue threshold of an elastic body, characterized in that A method for determining the fatigue threshold of an elastomer by the elastic limit strain point of the elastomer. The method is specifically to obtain the elastic limit strain point of the elastomer by performing a Mullins test on a Gaussian chain model elastomer. And taking the elastic limit strain point as the starting point, the fatigue limit strain is found by gradually reducing the fatigue test strain, and a curve (GN curve) of the elastomer cyclic test and energy release rate is obtained and the curve is limited to obtain the fatigue threshold.
2. The fatigue threshold test method according to claim 1, characterized in that: The method for obtaining the elastic limit strain point is Mullins test.
3. The fatigue threshold test method according to claim 1, characterized in that: The Mullins test environment is 0 degrees Celsius to room temperature.
4. The fatigue threshold test method according to claim 1, characterized in that: When the elastic limit strain point is obtained, the hysteresis error obtained by the Mullins test is less than 10%.
5. The mechanical fatigue threshold in hydrogel and liquid crystal is obtained by the fatigue threshold testing method described in claim 1.