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Damage modelling of epoxy material under uniaxial tension based on micromechanics and experimental analysis

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Abstract

Epoxy is a widely used thermosetting polymer in various engineering fields to develop composites. Studying its damage and fracture behaviour under various loading conditions is highly important. In this work, a micromechanics-based damage model is developed for understanding the damage initiation and growth in epoxy. To support this damage model, tests are performed for obtaining mechanical properties and to study the damage behaviour of epoxy. Diglycidyl ether of bisphenol A (DGEBA) resin with triethylenetetramine (TETA) hardener in 10:1 ratio are mixed and cured to make the epoxy. To give a physical meaning to damage, the model quantifies the damage as volume fraction of a spherical void in a unit representative volume element (RVE) of epoxy material. Degraded effective properties are computed for damaged RVE using standard mechanics-based micromechanical approach. A second-degree polynomial is established for effective stiffness with damage at any loading instance. This functional form of degraded stiffness in terms of damage is used in constitutive relations. A strain energy- based approach is used to compute thermodynamic forces, a state variable used for the evolution of damage. A damage evolution model is proposed with two material-specific parameters which are determined using experimental tests. The model is implemented by user material subroutine (UMAT) in commercial finite element software, Abaqus/Standard. The proposed model accurately captures the tensile behaviour of the epoxy material and gives capability to simulate an epoxy material’s damage behaviour from its initiation till failure or macrolevel rupture under uniaxial tensile loading. The developed model predicts the behaviour of the material in agreement with experimental results.

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References

  1. Kachanov, L.: Time of the rupture process under creep conditions. Isv. Akad. Nauk. SSR. Otd Tekh. Nauk 8, 26–31 (1958)

    Google Scholar 

  2. Rabotnov, Y.N.: Creep Rupture, in: Applied mechanics, pp. 342–349. Springer, Berlin (1969)

    Google Scholar 

  3. Chaboche, J.-L.: Continuous damage mechanics—a tool to describe phenomena before crack initiation. Nuclear Eng. Des. 64(2), 233–247 (1981)

    Article  Google Scholar 

  4. Janson, J.: Damage model of crack growth and instability. Eng. Fract. Mech. 10(4), 795–806 (1978)

    Article  Google Scholar 

  5. Mazars, J., Pijaudier-Cabot, G.: From damage to fracture mechanics and conversely: a combined approach. Int. J. Solids Struct. 33(20), 3327–3342 (1996)

    Article  MATH  Google Scholar 

  6. Daudeville, L., Allix, O., Ladeveze, P.: Delamination analysis by damage mechanics: some applications. Compos. Eng. 5(1), 17–24 (1995)

    Article  Google Scholar 

  7. Allix, O., Leveque, D., Perret, L.: Identification and forecast of delamination in composite laminates by an interlaminar interface model. Compos. Sci. Technol. 58(5), 671–678 (1998)

    Article  Google Scholar 

  8. Ladevèze, P., Allix, O., Gornet, L., Lévêque, D., Perret, L.: A computational damage mechanics approach for laminates: identification and comparison with experimental results. Stud. Appl. Mech. 46, 481–500 (1998)

    Article  Google Scholar 

  9. Ladeveze, P., Allix, O., Daudeville, L.: Mesomodeling of Damage for Laminate Composites: Application to Delamination, in: Inelastic Deformation of Composite Materials. Springer, New York (1991)

    Google Scholar 

  10. Ladevèze, P., Lubineau, G.: On a damage mesomodel for laminates: micro–meso relationships, possibilities and limits. Compos. Sci. Technol. 61(15), 2149–2158 (2001)

    Article  Google Scholar 

  11. Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11(5), 357–372 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hill, R.: Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour. J. Mech. Phys. Solids 12(4), 199–212 (1964)

    Article  MathSciNet  Google Scholar 

  13. Dassault Systèmes.: Abaqus 6.10 online documentation. Dassault Systèmes, Providence, Rhode Island (2010)

  14. Hibbitte, K.: Abaqus user subroutines reference manual. HKS INC (2005)

  15. Allaoui, A., Bai, S., Cheng, H.-M., Bai, J.: Mechanical and electrical properties of a MWNT/epoxy composite. Compos. Sci. Technol. 62(15), 1993–1998 (2002)

    Article  Google Scholar 

  16. Schadler, L.S., Giannaris, S.C., Ajayan, P.M.: Load transfer in carbon nanotube epoxy composites. Appl. Phys. Lett. 73(26), 3842–3844 (1998). doi:10.1063/1.122911. http://scitation.aip.org/content/aip/journal/apl/73/26/10.1063/1.122911

  17. Gojny, F.H., Wichmann, M.H.G., Köpke, U., Fiedler, B., Schulte, K.: Carbon nanotube-reinforced epoxy-composites: enhanced stiffness and fracture toughness at low nanotube content. Compos. Sci. Technol. 64(15) 2363–2371 (2004)

  18. Alvarez, V., Valdez, M., Vzquez, A.: Dynamic mechanical properties and interphase fiber/matrix evaluation of unidirectional glass fiber/epoxy composites. Polym. Test.22(6), 611–615 (2003). doi:10.1016/S0142-9418(02)00164-2. http://www.sciencedirect.com/science/article/pii/S0142941802001642

  19. Yang, B., Kozey, V., Adanur, S., Kumar, S.: Bending, compression, and shear behavior of woven glass fiber–epoxy composites. Compos. Part B Eng. 31(8), 715–721 (2000). doi:10.1016/S1359-8368(99)00052-9. http://www.sciencedirect.com/science/article/pii/S1359836899000529

  20. W. Goertzen, M. Kessler, Creep behavior of carbon fiber/epoxy matrix composites. Mater. Sci. Eng. A 421(12) (2006) 217–225. In: Internal Stress and Thermo-Mechanical Behavior in Multi-component Materials Systems, (TMS) Annual Meeting, 2004. doi:10.1016/j.msea.2006.01.063. http://www.sciencedirect.com/science/article/pii/S0921509306001390

  21. Dong, S., Gauvin, R.: Application of dynamic mechanical analysis for the study of the interfacial region in carbon fiber/epoxy composite materials. Polym. Compos. 14(5), 414–420 (1993). doi:10.1002/pc.750140508

    Article  Google Scholar 

  22. Choi, N., Kinloch, A., Williams, J.: Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode i, mode ii and mixed-mode i/ii loading. J. Compos. Mater. 33(1), 73–100 (1999)

    Article  Google Scholar 

  23. Yokozeki, T., Aoki, Y., Ogasawara, T.: Experimental characterization of strength and damage resistance properties of thin-ply carbon fiber/toughened epoxy laminates. Compos. Struct. 82(3), 382–389 (2008). doi:10.1016/j.compstruct.2007.01.015. http://www.sciencedirect.com/science/article/pii/S0263822307000219

  24. Wang, X., Chung, D.D.L.: Short-carbon-fiber-reinforced epoxy as a piezoresistive strain sensor. Smart Mater. Struct. 4(4), 363 (1995). http://stacks.iop.org/0964-1726/4/i=4/a=017

  25. Wang, X., Chung, D.D.L.: Real-time monitoring of fatigue damage and dynamic strain in carbon fiber polymer-matrix composite by electrical resistance measurement. Smart Mater. Struct. 6(4), 504 (1997). http://stacks.iop.org/0964-1726/6/i=4/a=017

  26. Chevalier, J., Morelle, X., Bailly, C., Camanho, P., Pardoen, T., Lani, F.: Micro-mechanics based pressure dependent failure model for highly cross-linked epoxy resins. Eng. Fract. Mech. 158, 1–12 (2016)

    Article  Google Scholar 

  27. Thomas, G.K.: Progressive delamination in unidirectional composites. unpublished M.Tech. thesis (2013)

  28. Suquet, P.: Elements of homogenization for inelastic solid mechanics. Homog. Tech. Compos. Media 272, 193–278 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  29. Herakovich, C.T.: Mechanics of fibrous composites. Wiley, New York (1998)

    Google Scholar 

  30. Ward, I.M., Sweeney, J.: Mechanical Properties of Solid Polymers. Wiley, Hoboken (2012)

    Book  Google Scholar 

  31. Li, F., Pan, J.: Plane-stress crack-tip fields for pressure-sensitive dilatant materials. Eng. Fract. Mech. 35(6), 1105–1116 (1990)

    Article  Google Scholar 

  32. Chang, W., Pan, J.: Effects of yield surface shape and round-off vertex on crack-tip fields for pressure-sensitive materials. Int. J. Solids Struct. 34(25), 3291–3320 (1997)

    Article  MATH  Google Scholar 

  33. Hsu, S.-Y., Vogler, T., Kyriakides, S.: Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. part ii: modeling. Int. J. Plast. 15(8), 807–836 (1999)

    Article  MATH  Google Scholar 

  34. Khan, A.S., Huang, S.: Continuum Theory of Plasticity. Wiley, Hoboken (1995)

    MATH  Google Scholar 

  35. Montazeri, A., Khavandi, A., Javadpour, J., Tcharkhtchi, A.: Viscoelastic properties of multi-walled carbon nanotube/epoxy composites using two different curing cycles. Mater. Des. 31(7), 3383–3388 (2010)

    Article  Google Scholar 

  36. ASTM D638: Standard Test Method for Tensile Properties of Plastics. American Society for Testing and Materials, Philadelphia (1998)

  37. Davis, J.R.: Tensile Testing. ASM International, Ohino (2004)

    Google Scholar 

  38. Gilat, A., Goldberg, R.K., Roberts, G.D.: Strain rate sensitivity of epoxy resin in tensile and shear loading. J. Aerosp. Eng. 20(2), 75–89 (2007)

    Article  Google Scholar 

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Acknowledgements

Authors thank technical staff of Aeromodeling Lab and Structures lab from Department of Aerospace Engineering, Indian Institute of Technology Kanpur, India for helping in the development of molds and materials.

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  1. Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh, 208016, India

    Gurmeet Singh, David Kumar & P. M. Mohite

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  1. Gurmeet Singh
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  2. David Kumar
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  3. P. M. Mohite
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Correspondence to P. M. Mohite.

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Singh, G., Kumar, D. & Mohite, P.M. Damage modelling of epoxy material under uniaxial tension based on micromechanics and experimental analysis. Arch Appl Mech 87, 721–736 (2017). https://doi.org/10.1007/s00419-016-1219-4

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  • DOI: https://doi.org/10.1007/s00419-016-1219-4

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