Abstract
Based on the rate-dependent non-aging constitutive model and the rate-independent aging constitutive model, a rate-dependent aging constitutive model is proposed to explain the changes in mechanical properties of ethylene propylene diene monomer (EPDM) rubber under different strain rates and aging states. In order to simulate the actual use state of rubber, accelerated aging tests are conducted on the samples in a hot air aging environment. The grey wolf algorithm is utilized to accurately fit the engineering stress–strain curve obtained from the experiment, obtaining specific coefficient values that represent the effects of strain rate, aging time, and aging temperature in the constitutive model. The results confirm the effectiveness of the proposed rate-dependent aging constitutive model in accurately predicting the mechanical property changes of EPDM rubber under different strain rates and aging states. The consistency between the experimental data and the calculated results is within the acceptable error range. It is worth noting that the stress in the model shows the dependence on strain rate, aging time and aging temperature, emphasizing the mechanical property changes of EPDM rubber at high temperatures and low strain rates simulated in the uniaxial tensile state.
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Obata Y, Kawabata S, Kawai H (1970) Mechanical properties of natural rubber Vulcanizates in finite deformation. J Polym Sci Part A-2: Polymer Physics 8(6):903–919. https://doi.org/10.1002/pol.1970.160080607
Liu Y, Zhang Q, Liu R, Chen M, Zhang C, Li X, Li W, Wang H (2022) Compressive stress-hydrothermal aging behavior and constitutive model of shield tunnel EPDM rubber material. Constr Build Mater 320:126298. https://doi.org/10.1016/j.conbuildmat.2021.126298
Gong C, Ding W, Xie D (2020) Parametric investigation on the sealant behavior of tunnel segmental joints under water pressurization. Tunn Undergr Space Technol 97:103231. https://doi.org/10.1016/j.tust.2019.103231
Guo M, Li J, Xi K, Liu Y, Ji J (2019) Effect of multi-walled carbon nanotubes on thermal stability and ablation properties of EPDM insulation materials for solid rocket motors. Acta Astronaut 159:508–516. https://doi.org/10.1016/j.actaastro.2019.01.047
Rallini M, Puri I, Torre L, Natali M (2018) Thermal and ablation properties of EPDM based heat shielding materials modified with density reducer fillers. Compos A 112:71–80. https://doi.org/10.1016/j.compositesa.2018.05.031
Li K, Zheng J, Zhi J, Zhang K (2018) Aging constitutive model of hydroxyl-terminated polybutadiene coating in solid rocket motor. Acta Astronaut 151:555–562. https://doi.org/10.1016/j.actaastro.2018.06.060
Gregori A, Castoro C, Marano GC, Greco R (2019) Strength reduction factor of concrete with recycled rubber aggregates from tires. Am Soc Civil Eng 31(8):04019146. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002783
Premarathna W, Jayasinghe J, Wijesundara KK, Gamage P, Ranatunga RRMSK, Senanayake CD (2021) Investigation of design and performance improvements on solid resilient tires through numerical simulation. Eng Fail Anal 128:105618. https://doi.org/10.1016/j.engfailanal.2021.105618
Lai D, Demartino C, Xiao Y (2022) High-strain rate compressive behavior of fiber-reinforced rubberized concrete. Constr Build Mater 319:125739. https://doi.org/10.1016/j.conbuildmat.2021.125739
Mendis ASM, Al-Deen S, Ashraf M (2018) Flexural shear behaviour of reinforced Crumbed Rubber Concrete beam. Constr Build Mater 166:779–791. https://doi.org/10.1016/j.conbuildmat.2018.01.150
He H, Zheng Q, Zhang Y, Chen J, Zhang L, Li F (2022) A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material. Nano Mater Sci 4:64–82. https://doi.org/10.1016/j.nanoms.2021.07.003
Rivlin RS, Saunders DW (1951) Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber. Phi Trans Royal Soc London Series A 243(865):251–288. https://doi.org/10.1098/rsta.1951.0004
Mooney M (1940) A theory of large elastic deformation. Appl Phys 11(9):582. https://doi.org/10.1063/1.1712836
Rivlin RS (1948) Large elastic deformations of isotropic materials. IV. Further developments of the general theory Philosophical Transactions of the Royal Society A. Math Phys Sci 241(835):379–397. https://doi.org/10.1098/rsta.1948.0024
Ogden RW (1972) Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society A. Math Phys Sci 326(1567):565–584. https://doi.org/10.1098/rspa.1972.0026
Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66(5):754–771. https://doi.org/10.5254/1.3538343
Li C, Ding Y, Yang Z, Yuan Z, Ye L (2020) Compressive stress-thermo oxidative ageing behaviour and mechanism of EPDM rubber gaskets for sealing resilience assessment. Polym Testing 84:106366. https://doi.org/10.1016/j.polymertesting.2020.106366
Pourmanda P, Hedenqvista MS, Furó I, Geddea UW (2017) Deterioration of highly filled EPDM rubber by thermal ageing in air: Kinetics and non-destructive monitoring. Polym Testing 64:267–276. https://doi.org/10.1016/j.polymertesting.2017.10.019
Redline EM, Celina MC, Harris CE, Giron NH, Sugama T, Pyatina T (2017) Anomalous aging of EPDM and FEPM under combined thermooxidative and hydrolytic states. Polym Degrad Stab 146:317–326. https://doi.org/10.1016/j.polymdegradstab.2017.09.010
Wang Z, Shen S, Zhou A, Xu Y (2020) Experimental evaluation of aging characteristics of EPDM as a Sealant for Undersea Shield Tunnels. J Mater Civ Eng 32(7):04020182. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003242
LeGac PY, LeSaux V, Paris M, Marco Y (2012) Ageing mechanism and mechanical degradation behaviour of polychloroprene rubber in a marine environment: Comparison of accelerated ageing and long-term exposure. Polym Degrad Stab 97:288–296. https://doi.org/10.1016/j.polymdegradstab.2011.12.015
Du Y, Zheng J, Yu G (2021) Storage life prediction under pre-strained thermally-accelerated aging of HTPB coating using the change of crosslinking density. Def Technol 17:1387–1394. https://doi.org/10.1016/j.dt.2020.07.008
Zhou W, Zhao M, Liu B, Ma Y, Zhang Y, Wang X (2021) Investigation of hydroxyl-terminated polybutadiene propellant breaking characteristics and mechanism impacted by subjected cavitation water jet. Def Technol 397:117021. https://doi.org/10.1016/j.powtec.2021.11.065
Zhao F, Bi W, Zhao S (2011) Influence of crosslink density on mechanical properties of natural rubber vulcanizates. J Macromol Sci Part B Phys 50(7):1460–1469. https://doi.org/10.1080/00222348.2010.507453
Chen G, Gupta A, Mekonnen TH (2022) Silane-modified wood fiber filled EPDM bio-composites with improved thermomechanical properties. Compos A 159:107029. https://doi.org/10.1016/j.compositesa.2022.107029
Du Y, Zheng J, Xiong C (2020) Cross-linking density and aging constitutive model of HTPB coating under prestrain thermal accelerated aging. Def Technol 16:439–446. https://doi.org/10.1016/j.dt.2019.07.007
Logan SR (1982) The origin and status of the Arrhenius equation. J Chem Educ 59:279–281. https://doi.org/10.1021/ed059p279
Shi C, Cao C, Lei M, Peng L, Shen J (2015) Time-dependent performance and constitutive model of EPDM rubber gasket used for tunnel segment joints. Tunn Undergr Space Technol 50:490–498. https://doi.org/10.1016/j.tust.2015.09.004
Zhu Z, Jiang C, Cheng Q, Zhang J, Guo S, Xiong Y, Fu B, Yang W, Jiang H (2015) Accelerated aging test of hydrogenated nitrile butadiene rubber using the time-temperature-strain superposition principle. RSC Adv 5:90178–90183. https://doi.org/10.1039/C5RA18528A
Wang S, Xu J, Li H, Liu J, Zhou C (2022) The effect of thermal aging on the mechanical properties of ethylene propylene diene monomer charge coating. Mech Time-Dependent Mater 7:1–16. https://doi.org/10.1007/s11043-022-09557-w
Wang S, Zhou C, Han C (2023) The aging property and storage life prediction of EPDM. J Phys: Conf Ser 2478:032046. https://doi.org/10.1088/1742-6596/2478/3/032046
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Nah C, Lee GB, Lim JY, Kim YH, SenGupta R, Gent AN (2010) Problems in determining the elastic strain energy function for rubber. Int J Non-Linear Mech 45:232–235. https://doi.org/10.1016/j.ijnonlinmec.2009.11.004
Horgan CO, Murphy JG (2009) Compression tests and constitutive models for the slight compressibility of elastic rubber-like materials. Int J Eng Sci 47:1232–1239. https://doi.org/10.1016/j.ijengsci.2008.10.009
Khajehsaeid H, Arghavani J, Naghdabadi R (2013) A hyperelastic constitutive model for rubber-like materials. Euro J Mech A/Solids 38:144–151. https://doi.org/10.1016/j.euromechsol.2012.09.010
Kommling A, Jaunich M, Wolff D (2016) Effects of heterogeneous aging in compressed HNBR and EPDM O-ring seals. Polym Degrad Stab 126:39–46. https://doi.org/10.1016/j.polymdegradstab.2016.01.012
Dong L, Li K, Zhu X, Li Z, Zhang D, Pan Y, Chen X (2020) Study on high temperature sealing behavior of packer rubber tube based on thermal aging experiments. Eng Fail Anal 108:104321. https://doi.org/10.1016/j.engfailanal.2019.104321
Liu J, Li X, Xu L, He T (2017) Service lifetime estimation of EPDM rubber based on accelerated aging tests. J Mater Eng Perform 26(4):1735. https://doi.org/10.1007/s11665-017-2519-8
Song B, Chen W (2004) Dynamic compressive behavior of EPDM rubber under nearly Uniaxial Strain States. J Eng Mater Technol 126(2):213. https://doi.org/10.1115/1.1651097
Mao Y, Li Y, Chen Y, Miao Y, Deng Q, Niu W (2015) Hyper-elastic behavior of two rubber materials under quasistatic and dynamic compressive loadings —testing, modeling and application. Polimery 60:7–8. https://doi.org/10.14314/polimery.2015.516
Jiang J, Xu J, Zhang Z, Chen X (2016) Rate-dependent compressive behavior of EPDM insulation: Experimental and constitutive analysis. Mech Mater 96:30–38. https://doi.org/10.1016/j.mechmat.2016.02.003
Shergold OA, Fleck NA, Radford D (2006) The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. Int J Impact Eng 32:1384–1402. https://doi.org/10.1016/j.ijimpeng.2004.11.010
Ghorbanoghli A, Narooei K (2019) A new hyper-viscoelastic model for investigating rate dependent mechanical behavior of dual cross link self-healing hydrogel. Int J Mech Sci 159:278–286. https://doi.org/10.1016/j.ijmecsci.2019.06.019
Kommling A, Jaunich M, Wolff D (2016) Revealing effects of chain scission during ageing of EPDM rubber using relaxation and recovery experiment. Polym Testing 56:261–268. https://doi.org/10.1016/j.polymertesting.2016.10.026
Liao Z, Yao X, Zhang L, Hossain M, Wang J, Zhang S (2019) Temperature and strain rate dependent large tensile deformation and tensile failure behavior of transparent polyurethane at intermediate strain rates. Int J Impact Eng 129:152–167. https://doi.org/10.1016/j.ijimpeng.2019.03.005
Funding
This work is supported by National Key R&D Program of China (Grant No.2022YFB3401901) and Sichuan Science and Technology Program (Grant Nos.2023NSFSC0394 and 2023NSFSC1988).
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Zhanjiang W. designed the research; Xiaoyang W. prepared all figures and prepared the initial draft of the manuscript; Xiaoyang W. and Dianjie J. carried out the experiments; and Xiaoyang W., Zhanjiang W., and Dianjie J. contributed to the analysis of the results, reviewing the manuscript, and revising the manuscript.
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Wang, X., Wang, Z. & Jiang, D. A rate-dependent aging constitutive model of EPDM rubber. Colloid Polym Sci (2024). https://doi.org/10.1007/s00396-024-05250-1
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DOI: https://doi.org/10.1007/s00396-024-05250-1