Multi-Scale Modeling of Curing Residual Stresses in Composite with Random Fiber Distribution into Consideration

  • Zhenyi YuanEmail author
  • Ben Zhang
  • Guigeng Yang
  • ZhenchaoYang
  • Aofei Tang
  • Shujuan Li
  • Yan Li
  • Pengkang Zhao
  • Yongjun Wang


During curing process of composites, residual stresses inevitably develop and play an important role in the final mechanical properties of composites. Therefore, the consideration of residual stresses when designing composite structure is necessary. The causes of residual stresses are well known on the part and fiber-matrix level. However, the influence of the part level factors on micro residual stresses is less known and rarely investigated. This work aims at a better understanding of the effects of macro-level factors, including temperature variation and mechanical strains on micro-scale stresses. To this end, a multi-scale method is developed, which consists of a macro-scale model to capture temperature variation and mechanical strains field under a given cycle condition, and a RVE (Representative Volume Element) to predict residual stresses in matrix. The results demonstrate that the maximum micro residual stress in matrix presents about almost 52% reduction in the model with part-level information into consideration as compared with the results without considering the multi-scale effect. It can be also seen that with multi-scale effect into account, the matrix in the RVE experienced tensile residual stresses in the matrix-poor locations and compressive residual stresses in the matrix-poor locations.


Thermosetting resin Residual stress Finite element analysis Multi-scale modeling 



The authors would like to acknowledge the financial supports by National Nature Science Foundation of China (51575442, 51805430), China Postdoctoral Science Foundation (2017 M613172) and Natural Science Foundation of Shaanxi Provincial Department of Education (17JK0562).


  1. 1.
    Zhou, J., Li, Y., Li, N., Liu, S., Cheng, L., Sui, S., Gao, J.: A multi-pattern compensation method to ensure even temperature in composite materials during microwave curing process. Compos. A: Appl. Sci. Manuf. 107, 10–20 (2017)CrossRefGoogle Scholar
  2. 2.
    Svanberg, J.M., Holmberg, J.A.: An experimental investigation on mechanisms for manufacturing induced shape distortions in homogeneous and balanced laminates. Compos. A: Appl. Sci. Manuf. 32, 827–838 (2001)CrossRefGoogle Scholar
  3. 3.
    Yuan, Z.Y., Wang, Y.J., Peng, X.Q., Wang, J.B., Wei, S.M.: An analytical model on through-thickness stresses and warpage of composite laminates due to tool-part interaction. Compos. Part B. 55, 408–413 (2016)CrossRefGoogle Scholar
  4. 4.
    Zhao, L.G., Warrior, N.A., Long, A.C.: A micromechanical study of residual stress and its effect on transverse failure in polymer–matrix composites. Int. J. Solids Struct. 43, 5449–5467 (2006)CrossRefGoogle Scholar
  5. 5.
    Shokrieh, M.M., Safarabadi, M.: Three-dimensional analysis of micro-residual stresses in fibrous composites based on the energy method: a study including interphase effects. J. Compos. Mater. 46, 727–735 (2012)CrossRefGoogle Scholar
  6. 6.
    Ma, H.L., Lau, K.T., Hui, D., Shi, S.Q., Poon, C.K.: Theoretical analysis on the pullout behavior of carbon nanotube at cryogenic environment with the consideration of thermal residual stress. Compos. Part B. 128, 67–75 (2017)CrossRefGoogle Scholar
  7. 7.
    Crasto, A.S., Ran, Y.K., Russell, J.D.: In situ monitoring of residual strain development during composite cure. Polym. Compos. 23, 454–463 (2002)CrossRefGoogle Scholar
  8. 8.
    Colpo, F., Humbert, L., Botsis, J.: Characterisation of residual stresses in a single fibre composite with FBG sensor. Compos. Sci. Technol. 67, 1830–1841 (2007)CrossRefGoogle Scholar
  9. 9.
    Shokrieh, M.M., Akbari, S., Daneshvar, A.: A comparison between the slitting method and the classical lamination theory in determination of macro-residual stresses in laminated composites. Compos. Struct. 96, 708–715 (2013)CrossRefGoogle Scholar
  10. 10.
    Ersoy, N., Vardar, O.: Measurement of residual stresses in layered composites by compliance method. J. Compos. Mater. 34, 575–598 (2000)CrossRefGoogle Scholar
  11. 11.
    Jannotti, P., Subhash, G., Zheng, J., Halls, V.: Measurement of microscale residual stresses in multi-phase ceramic composites using Raman spectroscopy. Acta Mater. 129, 482–491 (2017)CrossRefGoogle Scholar
  12. 12.
    Zhang, X.X., Ni, D.R., Xiao, B.L., Andra, H., Gan, W.M., Hofmann, M., Ma, Z.Y.: Determination of macroscopic and microscopic residual stresses in friction stir welded metal matrix composites via neutron diffraction. Acta Mater. 87, 161–173 (2015)CrossRefGoogle Scholar
  13. 13.
    Bahmani, A., Li, G., Willett, T.L., Montesano, J.: Three-dimensional microscopic assessment of randomly distributed representative volume elements for high fiber volume fraction unidirectional composites. Compos. Struct. 192, 153–164 (2018)CrossRefGoogle Scholar
  14. 14.
    Arafath, A.R.A., Vaziri, R., Poursartip, A.: Closed-form solution for process-induced stresses and deformation of a composite part cured on a solid tool: part I – flat geometries. Compos. A: Appl. Sci. Manuf. 39, 1106–1117 (2008)CrossRefGoogle Scholar
  15. 15.
    Nelson, S., Hanson, A., Briggs, T., Werner, B.: Verification and validation of residual stresses in composite structures. Compos. Struct. 194, 662–673 (2018)CrossRefGoogle Scholar
  16. 16.
    Zhao, L.G., Warrior, N.A., Long, A.C.: A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer–matrix composites. Mater. Sci. Eng. A. 452, 483–498 (2007)CrossRefGoogle Scholar
  17. 17.
    Maligno, A.R., Warrior, N.A., Long, A.C.: Effects of interphase material properties in unidirectional fibre reinforced composites. Compos. Sci. Technol. 70, 36–44 (2010)CrossRefGoogle Scholar
  18. 18.
    Maligno, A.R., Warrior, N.A., Long, A.C.: Effects of inter-fibre spacing on damage evolution in unidirectional (UD) fibre-reinforced composites. Eur. J. Mech. A. Solid. 28, 768–776 (2009)CrossRefGoogle Scholar
  19. 19.
    Shokrieh, M.M., Safarabadi, M.: Effects of imperfect adhesion on thermal micro-residual stresses in polymer matrix composites. Int. J. Adhes. Adhes. 31, 490–497 (2011)CrossRefGoogle Scholar
  20. 20.
    Yang, L., Yan, Y., Ma, J., Liu, B.: Effects of inter-fiber spacing and thermal residual stress on transverse failure of fiber-reinforced polymer-matrix composites. Comput. Mater. Sci. 68, 255–262 (2013)CrossRefGoogle Scholar
  21. 21.
    Herráez, M., González, C., Lopes, C.S., Villoria, R.G.D., Llorca, J., Sánchez, T.V.: Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: an approach to virtual materials design. Compos. A: Appl. Sci. Manuf. 91, 484–492 (2016)CrossRefGoogle Scholar
  22. 22.
    Ghayoor, H., Hoa, S.V., Marsden, C.C.: A micromechanical study of stress concentrations in composites. Compos. Part B. 132, 115–124 (2018)CrossRefGoogle Scholar
  23. 23.
    Elnekhaily, S.A., Talreja, R.: Damage initiation in unidirectional fiber composites with different degrees of nonuniform fiber distribution. Compos. Sci. Technol. 155, 22–32 (2018)CrossRefGoogle Scholar
  24. 24.
    Yuan, Z., Wang, Y., Yang, G., Tang, A., Yang, Z., Li, S., Li, Y., Song, D.: Evolution of curing residual stresses in composite using multi-scale method. Compos. Part B. 155, 49–61 (2018)CrossRefGoogle Scholar
  25. 25.
    Bogetti, T.A., Gillespie, J.W.J.: Two-dimensional cure simulation of thick thermosetting composites. J. Compos. Mater. 25, 239–273 (1991)CrossRefGoogle Scholar
  26. 26.
    Johnston, A., Vaziri, R., Poursartip, A.: A plane strain modelfor process-induced deformationof laminated composite structures. J. Compos. Mater. 35, 1435–1469 (2001)CrossRefGoogle Scholar
  27. 27.
    White, S.R., Kim, Y.K.: Process-induced residual stress analysis of AS4/3501-6 composite material. Mech. Compos. Mater. 5, 153–186 (1998)Google Scholar
  28. 28.
    Lee, W.I., Loos, A.C., Springer, G.S.: Heat of reaction, degree of cure, and viscosity of Hercules 3501-6 resin. J. Compos. Mater. 16, 510–520 (1982)CrossRefGoogle Scholar
  29. 29.
    Ersoy, N., Garstka, T., Potter, K., Wisnom, M.R., Porter, M.C., Stringer, G.: Development of the properties of a carbon fibre reinforced thermosetting composite through cure. Compos. A: Appl. Sci. Manuf. 41, 401–409 (2010)CrossRefGoogle Scholar
  30. 30.
    Kim, Y.K., White, S.R.: Stress relaxation behavior of 3501-6 epoxy resin during cure. Polym. Eng. Sci. 36, 2852–2862 (2010)CrossRefGoogle Scholar
  31. 31.
    Kim, Y.K., White, S.R.: Viscoelastic analysis of processing-induced residual stresses in thick composite laminates. Mech. Compos. Mater. 4, 361–387 (1997)Google Scholar
  32. 32.
    Li, G., Sharifpour, F., Bahmani, A., Montesano, J.: A new approach to rapidly generate random periodic representative volume elements for microstructural assessment of high volume fraction composites. Mater. Des. 150, 124–138 (2018)CrossRefGoogle Scholar
  33. 33.
    Naya, F., Pappas, G., Botsis, J.: Micromechanical study on the origin of fiber bridging under interlaminar and intralaminar mode I failure. Compos. Struct. 210, 877–891 (2019)CrossRefGoogle Scholar
  34. 34.
    Lina, R., Lenaïk, B., Joliff, Y.: Validation of a representative volume element for unidirectional fiber-reinforced composites: case of a monotonic traction in its cross section. Compos. Struct. 154, 14–16 (2016)Google Scholar
  35. 35.
    Pathan, M.V., Tagarielli, V.L., Patsias, S.: Effect of fibre shape and interphase on the anisotropic viscoelastic response of fibre composites. Compos. Struct. 162, 156–163 (2017)CrossRefGoogle Scholar
  36. 36.
    Pathan, M.V., Tagarielli, V.L., Patsias, S.: Numerical predictions of the anisotropic viscoelastic response of uni-directional fibre composites. Compos. A: Appl. Sci. Manuf. 93, 18–32 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Zhenyi Yuan
    • 1
    Email author
  • Ben Zhang
    • 1
  • Guigeng Yang
    • 1
  • ZhenchaoYang
    • 1
  • Aofei Tang
    • 1
  • Shujuan Li
    • 1
  • Yan Li
    • 1
  • Pengkang Zhao
    • 1
  • Yongjun Wang
    • 2
  1. 1.School of Mechanical and Instrument EngineeringXi’an University of TechnologyXi′anChina
  2. 2.School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi′anChina

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