Skip to main content
SpringerLink
Log in

Strain rate influence on hardening and damage characteristics of composite materials

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The paper presents models to characterize the dependence of hardening and strength characteristics of composite materials on damage and strain rate. The results of experimental studies of the behavior of composite materials in a wide range of strain rates are analyzed, and some regularities are determined. On the base of a failure criterion which includes the dependence of failure characteristics on damage and the rate of damage as well, taking into account the dependence of stiffness characteristics on the damage parameters, the stress–strain curves are determined for different strain rates, and they correlate quite well with the results of experimental studies. A method for the experimental determination of the material’s parameters is proposed. Some cases of complex, non-monotonic loading and unloading of composite materials are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Hsiao, H.M., Daniel, I.M.: Strain rate behavior of composite materials. Compos. Part B Eng. 29, 521–533 (1998)

    Google Scholar 

  2. Hsiao, H.M., Daniel, I.M., Cordes, R.D.: Strain Rate Effects on the Transverse Compressive and Shear Behavior of Unidirectional Composites. J. Compos. Mater. 33, 1620–1642 (1999)

    Google Scholar 

  3. Vogler, T.J., Kyriakides, S.: Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. Part I Exp. Int. J. Plast. 15, 783–806 (1999)

    MATH  Google Scholar 

  4. Koerber, H., Xavier, J., Camanho, P.P.: High strain rate characterisation of unidirectional carbon-epoxy IM7-8552 in transverse compression and in-plane shear using digital image correlation. Mech. Mater. 42, 1004–1019 (2010)

    Google Scholar 

  5. Koerber, H., Camanho, P.P.: High strain rate characterisation of unidirectional carbon-epoxy IM7-8552 in longitudinal compression. Compos. Part A Appl. Sci. Manuf. 42, 462–470 (2011)

    Google Scholar 

  6. Kuhn, P., Catalanotti, G., Xavier, J., Camanho, P.P., Koerber, H.: Fracture toughness and crack resistance curves for fiber compressive failure mode in polymer composites under high rate loading. Compos. Struct. 182, 164–175 (2017)

    Google Scholar 

  7. Seifoori, S., Izadi, R., Yazdinezhad, A.R.: Impact damage detection for small- and large-mass impact on CFRP and GFRP composite laminate with different striker geometry using experimental, analytical and FE methods. Acta Mech. 230, 4417–4433 (2019)

    Google Scholar 

  8. González, E.V., Maimí, P., Camanho, P.P., Turon, A., Mayugo, J.A.: Simulation of drop-weight impact and compression after impact tests on composite laminates. Compos. Struct. 94, 3364–3378 (2012)

    Google Scholar 

  9. Hongkarnjanakul, N., Bouvet, C., Rivallant, S.: Validation of low velocity impact modelling on different stacking sequences of CFRP laminates and influence of fibre failure. Compos. Struct. 106, 549–559 (2013)

    Google Scholar 

  10. Tan, W., Falzon, B.G., Chiu, L.N.S., Price, M.: Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates. Compos. Part A Appl. Sci. Manuf. 71, 212–226 (2015)

    Google Scholar 

  11. Jacob, G.C., Fellers, J.F., Simunovic, S., Starbuck, J.M.: Energy absorption in polymer composites for automotive crashworthiness. J. Compos. Mater. 36, 813–850 (2002)

    Google Scholar 

  12. Xu, J., Ma, Y., Zhang, Q., Sugahara, T., Yang, Y., Hamada, H.: Crashworthiness of carbon fiber hybrid composite tubes molded by filament winding. Compos. Struct. 139, 130–140 (2016)

    Google Scholar 

  13. Kakogiannis, D., Chung Kim Yuen, S., Palanivelu, S., Van Hemelrijck, D., Van Paepegem, W., Wastiels, J., Vantomme, J., Nurick, G.N.: Response of pultruded composite tubes subjected to dynamic and impulsive axial loading. Compos. Part B Eng 55, 537–547 (2013)

    Google Scholar 

  14. Kim, J.S., Yoon, H.J., Shin, K.B.: A study on crushing behaviors of composite circular tubes with different reinforcing fibers. Int. J. Impact Eng. 38, 198–207 (2011)

    Google Scholar 

  15. Zhou, G., Sun, Q., Fenner, J., Li, D., Zeng, D., Su, X., Peng, Y.: Crushing behaviors of unidirectional carbon fiber reinforced plastic composites under dynamic bending and axial crushing loading. Int. J. Impact Eng. 140, 103539 (2020)

    Google Scholar 

  16. Obradovic, J., Boria, S., Belingardi, G.: Lightweight design and crash analysis of composite frontal impact energy absorbing structures. Compos. Struct. 94, 423–430 (2012)

    Google Scholar 

  17. Xiao, X., McGregor, C., Vaziri, R., Poursartip, A.: Progress in braided composite tube crush simulation. Int. J. Impact Eng. 36, 711–719 (2009)

    Google Scholar 

  18. Huang, J., Wang, X.: Numerical and experimental investigations on the axial crushing response of composite tubes. Compos. Struct. 91, 222–228 (2009)

    Google Scholar 

  19. Matsuo, T., Kan, M., Furukawa, K., Sumiyama, T., Enomoto, H., Sakaguchi, K.: Numerical modeling and analysis for axial compressive crushing of randomly oriented thermoplastic composite tubes based on the out-of-plane damage mechanism. Compos. Struct. 181, 368–378 (2017)

    Google Scholar 

  20. Waimer, M., Siemann, M.H., Feser, T.: Simulation of CFRP components subjected to dynamic crash loads. Int. J. Impact Eng. 101, 115–131 (2017)

    Google Scholar 

  21. Lukaszewicz, D., Blok, L., Kratz, J., Ward, C., Kassapoglou, C.: Experimental and numerical investigation of full scale impact test on fibre-reinforced plastic sandwich structure for automotive crashworthiness. Int. J. Autom. Compos. 3(2–4), 339–353 (2017)

    Google Scholar 

  22. Israr, H.A., Rivallant, S., Bouvet, C., Barrau, J.J.: Finite element simulation of 0/90 CFRP laminated plates subjected to crushing using a free-face-crushing concept. Compos. Part A Appl. Sci. Manuf. 62, 16–25 (2014)

    Google Scholar 

  23. Hull, D.: A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos. Sci. Technol. 40, 377–421 (1991)

    Google Scholar 

  24. Boria, S., Obradovic, J., Belingardi, G.: Experimental and numerical investigations of the impact behaviour of composite frontal crash structures. Compos. Part B Eng. 79, 20–27 (2015)

    Google Scholar 

  25. Chiu, L.N.S., Falzon, B.G., Ruan, D., Xu, S., Thomson, R.S., Chen, B., Yan, W.: Crush responses of composite cylinder under quasi-static and dynamic loading. Compos. Struct. 131, 90–98 (2015)

    Google Scholar 

  26. Palanivelu, S., Van Paepegem, W., Degrieck, J., Van Ackeren, J., Kakogiannis, D., Van Hemelrijck, D., Wastiels, J., Vantomme, J.: Experimental study on the axial crushing behaviour of pultruded composite tubes. Polym. Test. 29, 224–234 (2010)

    Google Scholar 

  27. Farley, G.L.: The Effects of Crushing Speed on the Energy-Absorption Capability of Composite Tubes. J. Compos. Mater. 25, 1314–1329 (1991)

    Google Scholar 

  28. Ataabadi, P.B., Karagiozova, D., Alves, M.: Crushing and energy absorption mechanisms of carbon fiber-epoxy tubes under axial impact. Int. J. Impact Eng. 131, 174–189 (2019)

    Google Scholar 

  29. Wang, Y., Feng, J., Wu, J., Hu, D.: Effects of fiber orientation and wall thickness on energy absorption characteristics of carbon-reinforced composite tubes under different loading conditions. Compos. Struct. 153, 356–368 (2016)

    Google Scholar 

  30. Fallahi, H., Taheri-Behrooz, F., Asadi, A.: Nonlinear Mechanical Response of Polymer Matrix Composites: A Review. Polym. Rev. 60, 42–85 (2020)

    Google Scholar 

  31. Gupta, A.K., Patel, B.P., Nath, Y.: Nonlinear static analysis of composite laminated plates with evolving damage. Acta Mech. 224, 1285–1298 (2013)

    MathSciNet  MATH  Google Scholar 

  32. Thiruppukuzhi, S.V., Sun, C.T.: Models for the strain-rate-dependent behavior of polymer composites. Compos. Sci. Technol. 61, 1–12 (2001)

    Google Scholar 

  33. Sun, C.T., Chen, J.L.: A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites. J. Compos. Mater. 23, 1009–1020 (1989)

    Google Scholar 

  34. Vogler, M., Rolfes, R., Camanho, P.P.: Mechanics of Materials Modeling the inelastic deformation and fracture of polymer composites - Part I?: Plasticity model. Mech. Mater. 59, 50–64 (2013)

    Google Scholar 

  35. Koerber, H., Kuhn, P., Ploeckl, M., Otero, F., Gerbaud, P.W., Rolfes, R., Camanho, P.P.: Experimental characterization and constitutive modeling of the non-linear stress-strain behavior of unidirectional carbon-epoxy under high strain rate loading. Adv. Model. Simul. Eng. Sci. 5, (2018)

  36. Vasiukov, D., Panier, S., Hachemi, A.: Non-linear material modeling of fiber-reinforced polymers based on coupled viscoelasticity-viscoplasticity with anisotropic continuous damage mechanics. Compos. Struct. 132, 527–535 (2015)

    Google Scholar 

  37. Hashin, Z.: Failure criteria for unidirectional fibre composites. J. Appl. Mech. 47, 329–334 (1980)

    Google Scholar 

  38. Daniel, I.M., Werner, B.T., Fenner, J.S.: Strain-rate-dependent failure criteria for composites. Compos. Sci. Technol. 71, 357–364 (2011)

    Google Scholar 

  39. Fedulov, B., Fedorenko, A., Safonov, A., Lomakin, E.: Nonlinear shear behavior and failure of composite materials under plane stress conditions. Acta Mech. 228, (2017)

  40. Fedulov, B.N., Fedorenko, A.N., Kantor, M.M., Lomakin, E.V.: Failure analysis of laminated composites based on degradation parameters. Meccanica. 53, 359–372 (2017)

    MathSciNet  Google Scholar 

  41. Lomakin, E.V., Fedulov, B.N., Fedorenko, A.N.: Nonlinear effects in the behavior and fracture of composite materials. IOP Conf. Ser. Mater. Sci. Eng. 581, 012015 (2019)

    Google Scholar 

  42. Fedorenko, A.N., Fedulov, B.N., Lomakin, E.V.: Failure analysis of laminated composites with shear nonlinearity and strain-rate response. Procedia Struct. Integr. 18, 432–442 (2019)

    Google Scholar 

  43. Bondarchuk, D.A., Fedulov, B.N., Fedorenko, A.N.: The effect of residual stress induced by manufacturing on strength on free edge of carbon-epoxy composite with \([0^{\circ } /90^{\circ } ]\)n layup. Procedia Struct. Integr. 18, 353–367 (2019)

    Google Scholar 

  44. Kachanov, L.: Introduction to Continuum Damage Mechanics. Springer, Berlin (1986)

    MATH  Google Scholar 

  45. Lemaitre, Jean, Chaboche, Jean-Louis: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  46. Totry, E., González, C., Llorca, J.: Mechanisms of shear deformation in fiber-reinforced polymers?: experiments and simulations. 197–209 (2009)

  47. Zinoviev, P.A., Grigoriev, S.V., Lebedeva, O.V., Tairova, L.P.: The strength of multilayered composites under a plane-stress state Fail. Criteria Fibre-Reinforced-Polymer Compos. 3538, 379–401 (2004)

    Google Scholar 

  48. Faggiani, A., Falzon, B.G.: Predicting low-velocity impact damage on a stiffened composite panel. Compos. Part A Appl. Sci. Manuf. 41, 737–749 (2010)

    Google Scholar 

  49. Johnson, G.R., Cook, W.H.: Fracture characteristics of three metals subjected to various strains. strain rates, temperatures and pressures 21, 31–48 (1985)

    Google Scholar 

  50. Cash, J.R.: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459, 797–815 (2003)

    MathSciNet  MATH  Google Scholar 

  51. Byrne, G.D., Hindmarsh, A.C.: Stiff ODE solvers: a review of current and coming attractions. J. Comput. Phys. 70, 1–62 (1987)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was carried out in the Lomonosov Moscow State University and supported by the Russian Science Foundation, grant no. 20-11-20230.

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia, 119991

    Evgeny Lomakin & Boris Fedulov

  2. Moscow Aviation Institute, National Research University, Moscow, Russia, 125993

    Evgeny Lomakin

  3. Center for Design, Manufacturing and Materials, Skolkovo Institute of Science and Technology, Moscow, Russia, 143025

    Boris Fedulov & Alexey Fedorenko

Authors
  1. Evgeny Lomakin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boris Fedulov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexey Fedorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Evgeny Lomakin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lomakin, E., Fedulov, B. & Fedorenko, A. Strain rate influence on hardening and damage characteristics of composite materials. Acta Mech 232, 1875–1887 (2021). https://doi.org/10.1007/s00707-020-02806-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02806-4

Search

Navigation