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A phenomenological aging-damage hyperelastic model based on configurational mechanics for short fiber-reinforced rubber composites

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Abstract

The damage and aging of short fiber-reinforced rubber composites (SFRCs) have a significant impact on the performance and stability of associated products. However, the presence of internal short fibers and the large deformation characteristics of rubber materials make it difficult to characterize the damage behavior. Therefore, it is imperative to investigate the material’s damage behavior, as well as the influence of aging on mechanical properties, and develop a precise constitutive model. This study extends configurational mechanics to hyperelastic materials and introduces the concept of equivalent configurational stress as a physically meaningful variable representing damage, thereby establishing a constitutive model that couples aging and damage. Uniaxial tensile tests were performed on samples in various aging states to analyze the damage behavior of SFRCs and validate the accuracy of the proposed constitutive model. Furthermore, this research highlights the prospective application of configuration mechanics in characterizing damage in composite materials.

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References

  1. Goettler, L., Shen, K.: Short fiber reinforced elastomers. Rubber Chem. Technol. 56(3), 619–638 (1983). https://doi.org/10.5254/1.3538144

    Article  Google Scholar 

  2. Abrate, S.: The mechanics of short fiber-reinforced composites: a review. Rubber Chem. Technol. 59(3), 384–404 (1986)

    Article  MATH  Google Scholar 

  3. Kashani, M.R.: Aramid-short-fiber reinforced rubber as a tire tread composite. J. Appl. Polym. Sci. 113(2), 1355–1363 (2009). https://doi.org/10.1002/app.30026

    Article  MATH  Google Scholar 

  4. Jayan, J.S., Appukuttan, S., Wilson, R., Joseph, K., George, G., Oksman, K.: 1 - an introduction to fiber reinforced composite materials. In: Joseph, K., Oksman, K., George, G., Wilson, R., Appukuttan, S. (eds.) Fiber Reinforced Composites. Woodhead Publishing Series in Composites Science and Engineering, pp. 1–24. Woodhead Publishing, England (2021). https://doi.org/10.1016/B978-0-12-821090-1.00025-9

  5. Patel, M., Soames, M., Skinner, A.R., Stephens, T.S.: Stress relaxation and thermogravimetric studies on room temperature vulcanised polysiloxane rubbers. Polym. Degrad. Stab. 83(1), 111–116 (2004). https://doi.org/10.1016/S0141-3910(03)00231-3

    Article  Google Scholar 

  6. Gillen, K.T., Celina, M.: Predicting polymer degradation and mechanical property changes for combined radiation-thermal aging environments. Rubber Chem. Technol. 91(1), 27–63 (2018). https://doi.org/10.5254/rct.18.81679

    Article  MATH  Google Scholar 

  7. Celina, M., Linde, E., Brunson, D., Quintana, A., Giron, N.: Overview of accelerated aging and polymer degradation kinetics for combined radiation-thermal environments. Polym. Degrad. Stab. 166, 353–378 (2019). https://doi.org/10.1016/j.polymdegradstab.2019.06.007

    Article  Google Scholar 

  8. Pan, Y., Zhong, Z.: Modeling the mullins effect of rubber-like materials. Int. J. Damage Mech 26(6), 933–948 (2017). https://doi.org/10.1177/1056789516635728

    Article  MATH  Google Scholar 

  9. Yang, Y., Zhou, Q., Deng, Y., Lin, J.: Compressive behaviors of ultra-low-weight foamed cement-based composite reinforced by polypropylene short fibers. Int. J. Damage Mech. 29(8), 1306–1325 (2020). https://doi.org/10.1177/1056789520908638

    Article  MATH  Google Scholar 

  10. Grandcoin, J., Boukamel, A., Lejeunes, S.: A micro-mechanically based continuum damage model for fatigue life prediction of filled rubbers. Int. J. Solids Struct. 51(6), 1274–1286 (2014). https://doi.org/10.1016/j.ijsolstr.2013.12.018

    Article  MATH  Google Scholar 

  11. Tan, K.T., Watanabe, N., Iwahori, Y.: Impact damage resistance, response, and mechanisms of laminated composites reinforced by through-thickness stitching. Int. J. Damage Mech. 21(1), 51–80 (2012). https://doi.org/10.1177/1056789510397070

    Article  MATH  Google Scholar 

  12. Garcea, S., Sinclair, I., Spearing, S., Withers, P.: Mapping fibre failure in situ in carbon fibre reinforced polymers by fast synchrotron x-ray computed tomography. Compos. Sci. Technol. 149, 81–89 (2017). https://doi.org/10.1016/j.compscitech.2017.06.006

    Article  MATH  Google Scholar 

  13. Zhang, B., Yu, X., Gu, B.: Modeling and experimental validation of interfacial fatigue damage in fiber-reinforced rubber composites. Polym. Eng. Sci. 58(6), 920–927 (2018). https://doi.org/10.1002/pen.24646

    Article  MATH  Google Scholar 

  14. Liu, R., Sancaktar, E.: Identification of crack progression in filled rubber by micro x-ray ct-scan. Int. J. Fatigue 111, 144–150 (2018). https://doi.org/10.1016/j.ijfatigue.2018.01.033

    Article  MATH  Google Scholar 

  15. Matsubara, M., Teramoto, S., Nagatani, A., Kawamura, S., Tsujiuchi, N., Ito, A., Kobayashi, M., Furuta, S.: Effect of fiber orientation on nonlinear damping and internal microdeformation in short-fiber-reinforced natural rubber. Exp. Tech. 45, 37–47 (2021). https://doi.org/10.1007/s40799-020-00404-6

    Article  Google Scholar 

  16. Akhtar, S., De, P., De, S.: Short fiber-reinforced thermoplastic elastomers from blends of natural rubber and polyethylene. J. Appl. Polym. Sci. 32(5), 5123–5146 (1986). https://doi.org/10.1002/app.1986.070320530

    Article  MATH  Google Scholar 

  17. Nguyen, B.N., Khaleel, M.A.: - prediction of damage in a randomly oriented short-fiber composite plate containing a central hole1. In: Bathe, K.J. (ed.) Computational Fluid and Solid Mechanics 2003, pp. 519–522. Elsevier Science Ltd, Oxford (2003). https://doi.org/10.1016/B978-008044046-0.50128-7

  18. Nguyen, B.N., Tucker, B.J., Khaleel, M.A.: A mechanistic approach to matrix cracking coupled with fiber-matrix debonding in short-fiber composites. J. Eng. Mater. Technol. 127(3), 337–350 (2005). https://doi.org/10.1115/1.1924565

    Article  MATH  Google Scholar 

  19. Al-Rub, R.K.A., Tehrani, A.H., Darabi, M.K.: Application of a large deformation nonlinear-viscoelastic viscoplastic viscodamage constitutive model to polymers and their composites. Int. J. Damage Mech 24(2), 198–244 (2015). https://doi.org/10.1177/1056789514527020

    Article  MATH  Google Scholar 

  20. Li, Q., Chen, Y.: Surface effect and size dependence on the energy release due to a nanosized hole expansion in plane elastic materials. J. Appl. Mech. 75(6), 061008 (2008). https://doi.org/10.1115/1.2965368

    Article  Google Scholar 

  21. Hu, Y., Li, Q., Shi, J., Chen, Y.: Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane. J. Appl. Phys. 112(3), 034302 (2012). https://doi.org/10.1063/1.4740224

    Article  Google Scholar 

  22. Li, Q., Lv, J., Guo, Y., Tian, X.: A consistent framework of material configurational mechanics in piezoelectric materials. Acta Mech. 229(1), 299–322 (2018). https://doi.org/10.1007/s00707-017-1966-5

    Article  MathSciNet  MATH  Google Scholar 

  23. Yuan, Z., Li, Q.: A configurational force based anisotropic damage model for original isotropic materials. Eng. Fract. Mech. 215, 49–64 (2019). https://doi.org/10.1016/j.engfracmech.2019.04.029

    Article  MATH  Google Scholar 

  24. Wang, R., Yuan, Z., Li, Q., Yang, B., Zuo, H.: Damage evolution of biodegradable magnesium alloy stent based on configurational forces. J. Biomech. 122, 110443 (2021). https://doi.org/10.1016/j.jbiomech.2021.110443

    Article  MATH  Google Scholar 

  25. Ishak, Z.M., Berry, J.: Hygrothermal aging studies of short carbon fiber reinforced nylon 6.6. J. Appl. Polym. Sci. 51(13), 2145–2155 (1994). https://doi.org/10.1002/app.1994.070511306

    Article  MATH  Google Scholar 

  26. Bradshaw, R., Brinson, L.: Physical aging in polymers and polymer composites: An analysis and method for time-aging time superposition. Polym. Eng. Sci. 37(1), 31–44 (1997). https://doi.org/10.1002/pen.11643

    Article  MATH  Google Scholar 

  27. Ishak, Z.M., Ishiaku, U., Karger-Kocsis, J.: Hygrothermal aging and fracture behavior of short-glass-fiber-reinforced rubber-toughened poly (butylene terephthalate) composites. Compos. Sci. Technol. 60(6), 803–815 (2000). https://doi.org/10.1016/S0266-3538(99)00193-1

    Article  Google Scholar 

  28. Sethi, S., Ray, B.C.: Environmental effects on fibre reinforced polymeric composites: Evolving reasons and remarks on interfacial strength and stability. Adv. Coll. Interface. Sci. 217, 43–67 (2015). https://doi.org/10.1016/j.cis.2014.12.005

    Article  MATH  Google Scholar 

  29. Zheng, T., Zheng, X., Zhan, S., Zhou, J., Liao, S.: Study on the ozone aging mechanism of natural rubber. Polym. Degrad. Stab. 186, 109514 (2021). https://doi.org/10.1016/j.polymdegradstab.2021.109514

    Article  MATH  Google Scholar 

  30. Lv, J., Li, Q.: Equivalent configurational stress to predict material yielding and crack propagation. Acta Mech. 227, 3055–3065 (2016). https://doi.org/10.1007/s00707-016-1665-7

    Article  MathSciNet  MATH  Google Scholar 

  31. Eshelby, J.D., Frank, F.C., Nabarro, F.R.: Xli. the equilibrium of linear arrays of dislocations. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42(327), 351–364 (1951). https://doi.org/10.1080/14786445108561060

  32. Kienzler, R., Herrmann, G.: On the properties of the Eshelly tensor. Acta Mech. 125(1–4), 73–91 (1997). https://doi.org/10.1007/BF01177300

    Article  MathSciNet  MATH  Google Scholar 

  33. Eischen, J., Herrmann, G.: Energy release rates and related balance laws in linear elastic defect mechanics. J. Appl. Mech. 54(2), 388–392 (1987). https://doi.org/10.1115/1.3173024

    Article  MATH  Google Scholar 

  34. Marino, M., Wriggers, P.: Nearly-constrained transversely isotropic linear elasticity: energetically consistent anisotropic deformation modes for mixed finite element formulations. Int. J. Solids Struct. 202, 166–183 (2020). https://doi.org/10.1016/j.ijsolstr.2020.05.011

    Article  MATH  Google Scholar 

  35. Mo, C., Jiang, Y., Raney, J.R.: Microstructural evolution and failure in short fiber soft composites: experiments and modeling. J. Mech. Phys. Solids 141, 103973 (2020). https://doi.org/10.1016/j.jmps.2020.103973

    Article  MathSciNet  MATH  Google Scholar 

  36. Ghassemieh, E., Nassehi, V.: Stiffness analysis of polymeric composites using the finite element method. Adv. Polym. Technol. 20(1), 42–57 (2001)

    Article  MATH  Google Scholar 

  37. Holzapfel, G.A.: Nonlinear solid mechanics: a continuum approach for engineering science. Kluwer Academic Publishers Dordrecht (2002)

  38. Khajehsaeid, H., Arghavani, J., Naghdabadi, R.: A hyperelastic constitutive model for rubber-like materials. Eur. J. Mech. -A/Solids 38, 144–151 (2013). https://doi.org/10.1016/j.euromechsol.2012.09.010

    Article  MathSciNet  MATH  Google Scholar 

  39. Mansouri, M., Darijani, H.: Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. Int. J. Solids Struct. 51(25–26), 4316–4326 (2014). https://doi.org/10.1016/j.ijsolstr.2014.08.018

    Article  MATH  Google Scholar 

  40. Chen, S., Wang, C., Lu, X., Li, M., Li, M., Li, Q.: A parameter identification scheme of the visco-hyperelastic constitutive model of rubber-like materials based on general regression neural network. Archive Appl. Mech. (2023). https://doi.org/10.1007/s00419-023-02434-z

    Article  MATH  Google Scholar 

  41. Deuri, A.S., Bhowmick, A.K.: Aging of EPDM rubber. J. Appl. Polym. Sci. 34(6), 2205–2222 (1987). https://doi.org/10.1002/app.1987.070340613

    Article  MATH  Google Scholar 

  42. Wang, X., Yang, K., Zhang, P.: Evaluation of the aging coefficient and the aging lifetime of carbon black-filled styrene-isoprene-butadiene rubber after thermal-oxidative aging. Compos. Sci. Technol. 220, 109258 (2022). https://doi.org/10.1016/j.compscitech.2021.109258

    Article  MATH  Google Scholar 

  43. Liu, J., Li, X., Xu, L., Zhang, P.: Investigation of aging behavior and mechanism of nitrile-butadiene rubber (NBR) in the accelerated thermal aging environment. Polym. Testing 54, 59–66 (2016). https://doi.org/10.1016/j.polymertesting.2016.06.010

    Article  MATH  Google Scholar 

  44. Li, Y., Liu, X., Hu, X., Luo, W.: Changes in tensile and tearing fracture properties of carbon-black filled rubber vulcanizates by thermal aging. Polym. Adv. Technol. 26(11), 1331–1335 (2015). https://doi.org/10.1002/pat.3683

    Article  MATH  Google Scholar 

  45. Wang, S., Xu, J., Li, H., Liu, J., Zhou, C.: The effect of thermal aging on the mechanical properties of ethylene propylene diene monomer charge coating. Mech. Time-Depend. Mater. 28(2), 321–336 (2024). https://doi.org/10.1007/s11043-022-09557-w

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos.12172270), the Fundamental Research Funds for the Central Universities in China. The author Qun Li gratefully acknowledges the support of K.C. Wong Education Foundation.

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  1. State Key Laboratory for Strength and Vibration of Mechanical Structure, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Shenghao Chen, Chunguang Wang & Qun Li

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Chen wrote the main manuscript text, Chen and Li completed the theoretical derivation, Chen and Wang carried out the experimental work. All authors reviewed the manuscript.

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Correspondence to Qun Li.

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Chen, S., Wang, C. & Li, Q. A phenomenological aging-damage hyperelastic model based on configurational mechanics for short fiber-reinforced rubber composites. Arch Appl Mech 95, 33 (2025). https://doi.org/10.1007/s00419-024-02746-8

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