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A probabilistic micromechanical framework for self-healing polymers containing microcapsules

  • D.W. Jin (Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST)) ;
  • Taegeon Kil (Applied Science Research Institute, Korea Advanced Institute of Science and Technology (KAIST)) ;
  • H.K. Lee (Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST))
  • Received : 2023.04.04
  • Accepted : 2023.09.22
  • Published : 2023.09.25

Abstract

A probabilistic micromechanical framework is proposed to quantify numerically the self-healing capabilities of polymers containing microcapsules. A two-step self-healing process is designed in this study: A probabilistic micromechanical framework based on the ensemble volume-averaging method is derived for the polymers, and a hitting probability model combined with a crack nucleation model is then utilized for encountering microcapsules and microcracks. Using this framework, a series of parametric investigations are performed to examine the influence of various model parameters (e.g., the volume fraction of microcapsules, microcapsule radius, radius ratio of microcracks to microcapsules, microcrack aspect ratio, and scale parameter) on the self-healing capabilities of the polymers. The proposed framework is also implemented into a finite element code to solve the self-healing behavior of tapered double cantilever beam specimens.

Keywords

Acknowledgement

This study is supported by the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science & ICT) [Grant Number: 2017R1A5A1014883] through Smart Submerged Floating Tunnel System Research Center.

References

  1. Awaja, F., Zhang, S., Tripathi, M., Nikiforov, A. and Pugno, N. (2016), "Cracks, microcracks and fracture in polymer structures: Formation, detection, autonomic repair", Prog. Mater. Sci., 83, 536-573. https://doi.org/10.1016/j.pmatsci.2016.07.007
  2. Bagheri, R. and Pearson, R.A. (2000), "Role of particle cavitation in rubber-toughened epoxies: II. Inter-particle distance", Polymer (Guildf)., 41(1), 269-276. https://doi.org/10.1016/S0032-3861(99)00126-3
  3. Barbero, E.J., Greco, F. and Lonetti, P. (2005), "Continuum Damage-Healing Mechanics with application to self-healing composites", Int. J. Damage Mech., 14(1), 51-81. https://doi.org/10.1177/1056789505045928
  4. Bian, P.L., Liu, T.L., Qing, H. and Gao, C.F. (2018), "2D micromechanical modeling and simulation of Ta-particles reinforced bulk metallic glass matrix composite", Appl. Sci., 10(11). https://doi.org/10.3390/app8112192
  5. Blaiszik, B.J., Kramer, S.L.B., Olugebefola, S.C., Moore, J.S., Sottos, N.R. and White, S.R. (2010), "Self-healing polymers and composites", Annu. Rev. Mater. Res., 40, 179-211. https://doi.org/10.1146/annurev-matsci-070909-104532
  6. Brown, E.N. (2011), "Use of the tapered double-cantilever beam geometry for fracture toughness measurements and its application to the quantification of self-healing", J. Strain Anal. Eng. Des., 46(3), 167-186. https://doi.org/10.1177/0309324710396018
  7. Brown, E.N., Sottos, N.R. and White, S.R. (2002), "Fracture testing of a self-healing polymer composite", Exp. Mech., 42(4), 372-379. https://doi.org/10.1007/bf02412141
  8. Brown, E.N., Moore, J.S., White, S.R. and Sottos, N.R. (2003), "Fracture and fatigue behavior of a self-healing polymer composite", Mater. Res. Soc. Symp. - Proc., 735(January), 101-106. https://doi.org/10.1557/proc-735-c11.22
  9. Brown, E.N., White, S.R. and Sottos, N.R. (2004), "Microcapsule induced toughening in a self-healing polymer composite", J. Mater. Sci., 39(5), 1703-1710. https://doi.org/10.1023/B:JMSC.0000016173.73733.dc
  10. Brown, E.N., White, S.R. and Sottos, N.R. (2005), "Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite - Part II: In situ self-healing", Compos. Sci. Technol., 65(15-16 SPEC. ISS.), 2474-2480. https://doi.org/10.1016/j.compscitech.2005.04.053
  11. Chandrasekhar, S. (1943), "Stochastic problems in physics and astronomy", In: Reviews of Modern Physics (Vol. 15, Issue 1, pp. 1-89). https://doi.org/10.1103/RevModPhys.15.1
  12. Chen, T., Fang, L., Li, X., Gao, D., Lu, C. and Xu, Z. (2020), "Self-healing polymer coatings of polyurea-urethane/epoxy blends with reversible and dynamic bonds", Prog. Org. Coatings, 147, 105876. https://doi.org/10.1016/J.PORGCOAT.2020.105876
  13. Davies, R. and Jefferson, A. (2017), "Micromechanical modelling of self-healing cementitious materials", Int. J. Solids Struct., 113-114, 180-191. https://doi.org/10.1016/j.ijsolstr.2017.02.008
  14. Faravelli, L. and Marzi, A. (2010), "Coupling shape-memory alloy and embedded informatics toward a metallic self-healing material", Smart Struct. Syst., Int. J., 6(9), 1041-1056. https://doi.org/10.12989/sss.2010.6.9.1041
  15. Fifo, O., Ryan, K. and Basu, B. (2015), "Application of self-healing technique to fibre reinforced polymer wind turbine blade", Smart Struct. Syst., Int. J., 16(4), 593-606. https://doi.org/10.12989/sss.2015.16.4.593
  16. Gamstedt, E.K. and Talreja, R. (1999), "Fatigue damage mechanisms in unidirectional carbon-fibre-reinforced plastics", J. Mater. Sci., 34(11), 2535-2546. https://doi.org/10.1023/A:1004684228765
  17. Gao, C., Ruan, H., Yang, C. and Wang, F. (2021), "Investigation on microcapsule self-healing mechanism of polymer matrix composites based on numerical simulation", Polym. Compos., 42(7), 3619-3631. https://doi.org/10.1002/pc.26083
  18. Garoz Gomez, D., Gilabert, F.A., Tsangouri, E., Van Hemelrijck, D., Hillewaere, X.K.D., Du Prez, F.E. and Van Paepegem, W. (2015), "In-depth numerical analysis of the TDCB specimen for characterization of self-healing polymers", Int. J. Solids Struct., 64, 145-154. https://doi.org/10.1016/j.ijsolstr.2015.03.020
  19. Grellmann, W. and Langer, B. (2010), "Deformation and Fracture Behaviour of Polymer Materials", In: Springer Series in Materials Science (Vol. 70, Issue 4).
  20. Huseien, G.F., Nehdi, M.L., Faridmehr, I., Ghoshal, S.K., Hamzah, H.K., Benjeddou, O. and Alrshoudi, F. (2022), "Smart bioagents-activated sustainable self-healing cementitious materials: An all-inclusive overview on progress, benefits and challenges", Sustain., 14(4), p. 1980. https://doi.org/10.3390/su14041980
  21. Jang, D., Yoon, H.N., Nam, I.W. and Lee, H.K. (2020), "Effect of carbonyl iron powder incorporation on the piezoresistive sensing characteristics of CNT-based polymeric sensor", Compos. Struct., 244, 112260. https://doi.org/10.1016/J.COMPSTRUCT.2020.112260
  22. Jang, D., Yoon, H.N., Seo, J., Park, S., Kil, T. and Lee, H.K. (2021), "Improved electric heating characteristics of CNT-embedded polymeric composites with an addition of silica aerogel", Compos. Sci. Technol., 212, 108866. https://doi.org/10.1016/J.COMPSCITECH.2021.108866
  23. Ju, J.W. and Chen, T.M. (1994), "Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities", Acta Mech., 103(1-4), 103-121. https://doi.org/10.1007/BF01180221
  24. Ju, J.W. and Sun, L.Z. (2001), "Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: Micromechanics-based formulation", Int. J. Solids Struct., 38(2), 183-201. https://doi.org/10.1016/S0020-7683(00)00023-8
  25. Jud, K. and Kausch, H.H. (1979), "Load transfer through chain molecules after interpenetration at interfaces", Polym. Bull., 1(10), 697-707. https://doi.org/10.1007/BF00255445
  26. Karihaloo, B. and Fu, D. (1989), "A damage-based constitutive law for plain concrete in tension", Eur. J. Mech. A-Solids, 8, 373-384.
  27. Keller, M.W. and Sottos, N.R. (2006), "Mechanical properties of microcapsules used in a self-healing polymer", Exp. Mech., 46(6), 725-733. https://doi.org/10.1007/s11340-006-9659-3
  28. Khalid, H.R., Choudhry, I., Jang, D., Abbas, N., Salman Haider, M. and Lee, H.K. (2021), "Facile synthesis of sprayed CNTs layer-embedded stretchable sensors with controllable sensitivity", Polymers (Basel)., 13(2), 1-7. https://doi.org/10.3390/POLYM13020311
  29. Kil, T., Jin, D.W., Yang, B. and Lee, H.K. (2021), "A comprehensive micromechanical and experimental study of the electrical conductivity of polymeric composites incorporating carbon nanotube and carbon fiber", Compos. Struct., 268, 114002. https://doi.org/10.1016/J.COMPSTRUCT.2021.114002
  30. Kil, T., Jin, D.W., Yang, B. and Lee, H.K. (2022), "A combined experimental and micromechanical approach to investigating PTC and NTC effects in CNT-polypropylene composites under a self-heating condition", Compos. Struct., 289, 115440. https://doi.org/10.1016/J.COMPSTRUCT.2022.115440
  31. Kil, T., Bae, J.H., Yang, B. and Lee, H.K. (2023), "Multi-level micromechanics-based homogenization for the prediction of damage behavior of multiscale fiber-reinforced composites", Compos. Struct., 303, 116332. https://doi.org/10.1016/J.COMPSTRUCT.2022.116332
  32. Kim, J.S., Nam, I.W. and Lee, H.K. (2020), "Piezoelectric characteristics of urethane composites incorporating piezoelectric nanomaterials", Compos. Struct., 241, 112072. https://doi.org/10.1016/j.compstruct.2020.112072
  33. Lee, H.K. and Pyo, S.H. (2009), "3D-Damage Model for Fiber-Reinforced Brittle Composites with Microcracks and Imperfect Interfaces", J. Eng. Mech., 135(10), 1108-1118. https://doi.org/10.1061/(asce)em.1943-7889.0000039
  34. Lee, J.Y., Buxton, G.A. and Balazs, A.C. (2004), "Using nanoparticles to create self-healing composites", J. Chem. Phys., 121(11), 5531-5540. https://doi.org/10.1063/1.1784432
  35. Lin, J., Chen, H., Lv, Z. and Wang, Y. (2018), "Analytical solution on dosage of self-healing capsules in materials with two-dimensional multi-shaped crack patterns", IEEE J. Sel. Top. Quantum Electron., 25(6), 1229-1239. https://doi.org/10.1515/secm-2017-0256
  36. Lv, Z. and Chen, H. (2013), "Analytical models for determining the dosage of capsules embedded in self-healing materials", Comput. Mater. Sci., 68, 81-89. https://doi.org/10.1016/j.commatsci.2012.09.032
  37. Lv, Z. and Chen, H. (2014), "A probabilistic method for determining the volume fraction of pre-embedded capsules in self-healing materials", Smart Mater. Struct., 23(11). https://doi.org/10.1088/0964-1726/23/11/115009
  38. Meure, S., Wu, D.Y. and Furman, S. (2009), "Polyethylene-co-methacrylic acid healing agents for mendable epoxy resins", Acta Mater., 57(14), 4312-4320. https://doi.org/10.1016/j.actamat.2009.05.032
  39. Moghadam, A.A.A., Kouzani, A., Zamani, R., Magniez, K. and Kaynak, A. (2015), "Nonlinear large deformation dynamic analysis of electroactive polymer actuators", Smart Struct. Syst., Int. J., 15(6), 1601-1623. https://doi.org/10.12989/sss.2015.15.6.1601
  40. Munoz-Abella, B., Rubio, L. and Rubio, P. (2012), "A nondestructive method for elliptical cracks identification in shafts based on wave propagation signals and genetic algorithms", Smart Struct. Syst., Int. J., 10(1), 47-65. https://doi.org/10.12989/sss.2012.10.1.047
  41. Pang, J.W.C. and Bond, I.P. (2005), "'Bleeding composites'-damage detection and self-repair using a biomimetic approach", Compos. Part A Appl. Sci. Manuf., 36(2 SPEC. ISS.), 183-188. https://doi.org/10.1016/j.compositesa.2004.06.016
  42. Perelmuter, M. (2020), "Cracks self-healing-Physical and mathematical modelling", In: AIP Conference Proceedings (Vol. 2310, No. 1), pp. 109-110. https://doi.org/10.17223/9785946219242/69
  43. Rule, J.D., Sottos, N.R. and White, S.R. (2007), "Effect of microcapsule size on the performance of self-healing polymers", Polymer (Guildf)., 48(12), 3520-3529. https://doi.org/10.1016/j.polymer.2007.04.008
  44. Taheri, M.N., Sabet, S.A. and Kolahchi, R. (2020), "Experimental investigation of self-healing concrete after crack using nanocapsules including polymeric shell and nanoparticles core", Smart Struct. Syst., Int. J., 25(3), 337-343. https://doi.org/10.12989/sss.2020.25.3.337
  45. Talreja, R. (1989), "Damage development in composites: Mechanisms and modelling", J. Strain Anal. Eng. Des., 24(4), 215-222. https://doi.org/10.1243/03093247V244215
  46. Tsang, W.L. (2020), "The use of tapered double cantilever beam (TDCB) in investigating fracture properties of particles modified epoxy", SN Appl. Sci., 2(4), 1-10. https://doi.org/10.1007/s42452-020-2487-8
  47. Vallons, K.A.M., Drozdzak, R., Charret, M., Lomov, S.V. and Verpoest, I. (2015), "Assessment of the mechanical behaviour of glass fibre composites with a tough polydicyclopentadiene (PDCPD) matrix", Compos. Part A Appl. Sci. Manuf., 78, 191-200. https://doi.org/10.1016/J.COMPOSITESA.2015.08.016
  48. Verberg, R., Dale, A.T., Kumar, P., Alexeev, A. and Balazs, A.C. (2007), "Healing substrates with mobile, particle-filled microcapsules: Designing a 'repair and go' system", J. Royal Soc. Interf., 4(13), 349-357. https://doi.org/10.1098/rsif.2006.0165
  49. Wang, M., Hu, X. and Zhao, Y. (2021), "Probabilistic analysis models to determine capsule dosage for healing of cracks in concrete", Adv. Struct. Eng., 24(1), 52-64. https://doi.org/10.1177/1369433220942868
  50. White, S.R., Sottos, N.R., Geubelle, P.H., Moore, J.S., Kessler, M.R., Sriram, S.R., Brown, E.N. and Viswanathan, S. (2001), "Autonomic healing of polymer composites", Nature, 409(6822), 794. https://doi.org/10.1038/35057232
  51. Yang, S., Caggiano, A., Yi, M., Ukrainczyk, N. and Koenders, E. A.B. (2019), "Modelling autogenous self-healing with dissoluble encapsulated particles using a phase field approach", Mecanica Comput., 37(34), 1457-1467.
  52. Yang, S., Aldakheel, F., Caggiano, A., Wriggers, P. and Koenders, E. (2020), "A review on cementitious self-healing and the potential of phase-field methods for modeling crack-closing and fracture recovery", Materials (Basel), 13(22), 1-31. https://doi.org/10.3390/ma13225265
  53. Zhang, Y., Wang, Y., Li, Y., Huang, Z., Zheng, R. and Tan, Y. (2021), "Self-healing of mechanical damage of polyethylene/microcapsules electrical insulation composite material", J. Mater. Sci. Mater. Electron., 32(22), 26329-26340. https://doi.org/10.1007/s10854-021-06953-9.