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A Visco-hyperelastic Constitutive Model for Rubber Considering the Strain Level and One Case Study in the Sealing Packer

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Abstract

The rubber cylinder is a key component for maintaining the sealing pressure of the packer, particularly in deep underground wells. The stress relaxation of materials, as a typical feature of viscoelasticity, has become one of the main factors causing the failure of rubber cylinders in service. In the present study, a visco-hyperelastic model for the sealing rubber considering different strain levels is proposed based on the Prony series. Subsequently, the uniaxial compression stress relaxation experiments are conducted on the sealing rubber under different temperatures and strain levels, and the model parameters are thereby identified. As a case study, the proposed model is incorporated into the ABAQUS software via the UMAT subroutine, and the finite element simulation of the sealing packer is carried out. The results show that the sealing performance of the packer improves with a decrease in temperature or an increase in strain level. It is also noted that a large strain level can lead to the protrusion of the shoulder of the rubber cylinder.

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All data generated during this study are publicly available.

References

  1. Yeoh OH. Some forms of the strain energy function for rubber. Rubber Chem Technol. 2012;66(5):754–71.

    Article  Google Scholar 

  2. Khajehsaeid H, Arghavani J, Naghdabadi R. A hyperelastic constitutive model for rubber-like materials. Eur J Mech A Solid. 2013;38:144–51.

    Article  MathSciNet  MATH  Google Scholar 

  3. Horgan CO, Murphy JG. On the volumetric part of strain-energy functions used in the constitutive modeling of slightly compressible solid rubbers. Int J Solids Struct. 2009;46(16):3078–85.

    Article  MATH  Google Scholar 

  4. Fereidoonnezhad B, Naghdabadi R, Arghavani J. A hyperelastic constitutive model for fiber-reinforced rubber-like materials. Int J Eng Sci. 2013;71:36–44.

    Article  Google Scholar 

  5. Laine E, Grandidier JC, Benoit G, et al. Non-contact method used to determine the swelling/shrinking coefficients under CO2 sorption/desorption on an HNBR O-ring–Study of coupling with temperature and pressure. Polym Test. 2020;85(1):106411.

    Article  Google Scholar 

  6. Dal H, Gueltekin O, Acikgoz K. An extended eight-chain model for hyperelastic and finite viscoelastic response of rubberlike materials: Theory, experiments and numerical aspects. J Mech Phys Solids. 2020;145:104159.

    Article  MathSciNet  Google Scholar 

  7. Gong Y, Liu F, Zou R, et al. A simple anisotropic visco-hyperelastic constitutive model for cord-rubber composites. Compos Commun. 2021;28:100957.

    Article  Google Scholar 

  8. Zhong D, Xiang Y, Wang Z, et al. A visco-hyperelastic model for hydrogels with tunable water content. J Mech Phys Solids. 2023;173:105206.

    Article  MathSciNet  Google Scholar 

  9. Li C, Lua J. A hyper-viscoelastic constitutive model for polyurea. Mater Lett. 2009;63(11):877–80.

    Article  Google Scholar 

  10. Peng Q, Zhu Z, Jiang C, et al. Effect of stress relaxation on accelerated physical aging of hydrogenated nitrile butadiene rubber using time-temperature-strain superposition principle. Adv Ind Eng Polym Res. 2019;2(2):61–8.

    Google Scholar 

  11. Khajehsaeid H, Arghavani J, Naghdabadi R, et al. A visco-hyperelastic constitutive model for rubber-like materials: a rate-dependent relaxation time scheme. Int J Eng Sci. 2014;79:44–58.

    Article  MathSciNet  MATH  Google Scholar 

  12. Fazekas B, Goda TJ. Constitutive modelling of rubbers: mullins effect, residual strain, time-temperature dependence. Int J Mech Sci. 2021;210:106735.

    Article  Google Scholar 

  13. Wang B, Kari L. Constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency, magnetic and temperature dependence under a continuum mechanics basis. Polym Basel. 2020;13:472–87.

    Google Scholar 

  14. Janbaz M, Googarchin HS. Experimental and numerical analysis on magneto-hyper-viscoelastic constitutive responses of magnetorheological elastomers: a characterization procedure. Mech Mater. 2021;154:1–18.

    Article  Google Scholar 

  15. Xu X, Yan H, Xiao C, et al. An anisotropic hyper-visco-pseudo-elastic model and explicit stress solutions for fabric reinforced rubber composites. Int J Solids Struct. 2022;242:111519.

    Article  Google Scholar 

  16. Tada T, Urayama K, Mabuchi T, et al. Nonlinear stress relaxation of carbon black-filled rubber vulcanizates under various types of deformation. J Polym Sci Pol Phys. 2010;48(12):1380–7.

    Article  Google Scholar 

  17. Zhang X, Wu J, Xu Z, et al. Comparative study on the molecular chain orientation and strain-induced crystallization behaviors of HNBR with different acrylonitrile content under uniaxial stretching. Polymer. 2021;219:123520.

    Article  Google Scholar 

  18. Dong L, Li K, Zhu X, et al. Study on high temperature sealing behavior of packer rubber tube based on thermal aging experiments. Eng Fail Anal. 2020;108:104321.

    Article  Google Scholar 

  19. Amin AFMS, Alam MS, Okui Y. An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification. Mech Mater. 2002;34(2):75–95.

    Article  Google Scholar 

  20. Salimi A, Abbassi-Sourki F, Karrabi M, et al. Investigation on viscoelastic behavior of virgin EPDM/ reclaimed rubber blends using Generalized Maxwell Model (GMM). Polym Test. 2021;93:106989.

    Article  Google Scholar 

  21. Rangarajan SE, Ramarathnam KK. Viscoelastic properties of natural rubber with fatigue damage. Int J Fatigue. 2021;150:106344.

    Article  Google Scholar 

  22. Hoo Fatt MS, Ouyang X. Integral-based constitutive equation for rubber at high strain rates. Int J Solids Struct. 2007;44(20):6491–506.

    Article  MATH  Google Scholar 

  23. Gamonpilas C, McCuiston R. A non-linear viscoelastic material constitutive model for polyurea. Polymer. 2012;53(17):3655–8.

    Article  Google Scholar 

  24. Ghoreishy MHR. Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method. Mater Design. 2012;35:791–7.

    Article  Google Scholar 

  25. Yang H, Yao XF, Yan H, et al. Anisotropic hyper-viscoelastic behaviors of fabric reinforced rubber composites. Compos Struct. 2018;187:116–21.

    Article  Google Scholar 

  26. Jin L, Li S, Cheng Y, et al. A time-dependent Yeoh model to predict the corrosion effect of supercritical CO2 on the HNBR sealing rubber. J Mech Sci Technol. 2022;36(5):2461–70.

    Article  Google Scholar 

  27. Zhang J, Xia P. An improved PSO algorithm for parameter identification of nonlinear dynamic hysteretic models. J Sound Vib. 2017;389:153–67.

    Article  Google Scholar 

  28. Veivers H, Bermingham M, Dunn M, et al. Layup optimisation of laminated composite tubular structures under thermomechanical loading conditions using PSO. Compos Struct. 2021;276:114483.

    Article  Google Scholar 

  29. Leng DX, Huang C, Xu K, et al. Experimental mechanics and numerical prediction on stress relaxation and unrecoverable damage characteristics of rubber materials. Polym Test. 2021;98:107183.

    Article  Google Scholar 

  30. Huang Y, Li Y, Zhao H, et al. Research on constitutive models of hydrogenated nitrile butadiene rubber for packer at different temperatures. J Mech Sci Technol. 2020;34(1):155–64.

    Article  Google Scholar 

  31. Dong L, Li K, Li B, et al. Study in deep shale gas well to prevent shoulder protruding packer with high pressure sealing. Eng Fail Anal. 2020;118:104871.

    Article  Google Scholar 

  32. Zheng X, Li B. Study on sealing performance of packer rubber based on stress relaxation experiment. Eng Fail Anal. 2021;129:105692.

    Article  Google Scholar 

  33. Wang H, Chen S, Liu Y, et al. Numerical simulation and experimental validation for design improvement of packer rubber. Int J Simul Process Model. 2017;12(5):419–28.

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11972375, 12211530028), the Natural Science Foundation of Shandong Province (ZR202011050038, ZR2022MA086), the Science and Technology Project in Qingdao Developing Zone (2020-81), and Special Funds for the Basic Scientific Research Expenses of Central Government Universities (2472022X03006A).

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Authors and Affiliations

  1. College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Lan Jin, Demin Zhao & Jianlin Liu

Authors
  1. Lan Jin
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  2. Demin Zhao
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  3. Jianlin Liu
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Contributions

LJ contributed to methodology and writing original draft; DZ contributed to review and funding; JL contributed to formal analysis, review, and funding.

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Correspondence to Jianlin Liu.

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Jin, L., Zhao, D. & Liu, J. A Visco-hyperelastic Constitutive Model for Rubber Considering the Strain Level and One Case Study in the Sealing Packer. Acta Mech. Solida Sin. 36, 710–723 (2023). https://doi.org/10.1007/s10338-023-00397-w

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  • DOI: https://doi.org/10.1007/s10338-023-00397-w

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