Skip to main content
Log in

Tough–brittle transition in unidirectional composites with fibre breakage and fibre–matrix interfacial failure

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Fracture of three-dimensional unidirectional composites is studied through Monte Carlo fracture simulations on model composites. Fracture develops in the model composites by the failure of fibre segments wherein the tensile stress exceeds a Weibull-distributed random strength, and by the failure of the fibre–matrix interfaces wherein the shear stress exceeds a deterministic interfacial strength, \(T_0\). The size of the weakest-link failure event is inferred from empirical strength distributions obtained from the simulations. It is found to diverge or converge with composite size for \(T_0\) below or above a threshold value, respectively. The threshold is identified as the tough–brittle fracture mode transition. The mechanistic cause underlying the transition is also identified.

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

Access this article

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  • Banholzer B, Brameshuber W (2001) Eine methode zur beschreibung des verbundes zwischen faser und zementgebundener matrix. Beton Stahlbetonbau 96(10):663–669

    Article  Google Scholar 

  • Beyerlein IJ, Phoenix SL (1997) Statistics of fracture for an elastic notched composite lamina containing Weibull fibers I. Features from Monte-Carlo simulation. Eng Fract Mech 57(2–3):241–265

    Article  Google Scholar 

  • Binder K (2003) Overcoming the limitation of finite size in simulations: From the phase transition of the Ising model to polymers, spin glasses, etc. In: AIP conference proceedings, vol 690. American Institute of Physics, pp 74–84

  • Cook J, Gordon J (1964) A mechanism for the control of crack propagation in all-brittle systems. Proc R Soc Lond A 282(1391):508–520

    Article  Google Scholar 

  • Curtin W (1993) The tough to brittle transition in brittle matrix composites. J Mech Phys Solids 41(2):217–245

    Article  Google Scholar 

  • Curtin W (1998) Size scaling of strength in heterogeneous materials. Phys Rev Lett 80(7):1445

    Article  Google Scholar 

  • Curtin W (2000) Dimensionality and size effects on the strength of fiber-reinforced composites. Compos Sci Technol 60(4):543–551

    Article  Google Scholar 

  • Daniels HE (1945) The statistical theory of the strength of bundles of threads. Proc R Soc Lond A 183(995):405–435

    Article  MathSciNet  Google Scholar 

  • Dzenis YA, Qian J (2001) Analysis of microdamage evolution histories in composites. Int J Solids Struct 38(10–13):1831–1854

    Article  Google Scholar 

  • Epstein B (1948) Statistical aspects of fracture problems. J Appl Phys 19(2):140–147

    Article  MathSciNet  Google Scholar 

  • Goree JG, Gross RS (1980) Analysis of a unidirectional composite containing broken fibers and matrix damage. Eng Fract Mech 13(3):563–578

    Article  Google Scholar 

  • Gücer D, Gurland J (1962) Comparison of the statistics of two fracture modes. J Mech Phys Solids 10(4):365–373

    Article  Google Scholar 

  • Gupta A, Mahesh S, Keralavarma SM (2017) Strength distribution of large unidirectional composite patches with realistic load sharing. Phys Rev E 96(4):043002

    Article  Google Scholar 

  • Gupta A, Mahesh S, Keralavarma SM (2018) A fast algorithm for the elastic fields due to interacting fibre breaks in a periodic fibre composite. Int J Fract 211(1–2):295–303

    Article  Google Scholar 

  • Habeeb CI, Mahesh S (2015) Strength distribution of planar local load-sharing bundles. Phys Rev E 92(2):022125

    Article  Google Scholar 

  • Hansen A, Hemmer P, Pradhan S (2015) The fiber bundle model: modeling failure in materials. Statistical physics of fracture and breakdown. Wiley

  • Harlow DG, Phoenix S (1981a) Probability distributions for the strength of composite materials I: two-level bounds. Int J Fract 17(4):347–372

  • Harlow DG, Phoenix SL (1981b) Probability distributions for the strength of composite materials II: a convergent sequence of tight bounds. Int J Fract 17(6):601–630

  • He M, Evans AG, Curtin WA (1993) The ultimate tensile strength of metal and ceramic-matrix composites. Acta Metall Mater 41(3):871–878

    Article  Google Scholar 

  • Hedgepeth JM (1961) Stress concentrations in filamentary structures. Tech. Rep. RN D-882, NASA

  • Hedgepeth JM, Van Dyke P (1967) Local stress concentrations in imperfect filamentary composite materials. J Compos Mater 1(3):294–309

    Article  Google Scholar 

  • Herrera-Franco P, Drzal L (1992) Comparison of methods for the measurement of fibre/matrix adhesion in composites. Composites A 23(1):2–27

    Article  Google Scholar 

  • Hull D, Clyne TW (1996) An introduction to composite materials. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Ibnabdeljalil M, Curtin W (1997) Strength and reliability of fiber-reinforced composites: localized load-sharing and associated size effects. Int J Solids Struct 34(21):2649–2668

    Article  Google Scholar 

  • Ibnabdeljalil M, Curtin W (1997) Strength and reliability of notched fiber-reinforced composites. Acta Mater 45(9):3641–3652

    Article  Google Scholar 

  • Kachhwah US, Mahesh S (2020) Tough-brittle transition in the planar fracture of unidirectional fiber composites. Phys Rev E 101(6):063002

    Article  Google Scholar 

  • Karger-Kocsis J, Mahmood H, Pegoretti A (2015) Recent advances in fiber/matrix interphase engineering for polymer composites. Prog Mater Sci 73:1–43

    Article  Google Scholar 

  • Kumar MS, Raghavendra K, Venkataswamy MA, Ramachandra HV (2012) Fractographic analysis of tensile failures of aerospace grade composites. Mater Res 15(6):990–997

    Article  Google Scholar 

  • Landis CM, Beyerlein IJ, McMeeking RM (2000) Micromechanical simulation of the failure of fiber reinforced composites. J Mech Phys Solids 48(3):621–648

    Article  Google Scholar 

  • Ma Y, Yang Y, Sugahara T, Hamada H (2016) A study on the failure behavior and mechanical properties of unidirectional fiber reinforced thermosetting and thermoplastic composites. Composites B 99:162–172

    Article  Google Scholar 

  • Ma Y, Ueda M, Yokozeki T, Sugahara T, Yang Y, Hamada H (2017) A comparative study of the mechanical properties and failure behavior of carbon fiber/epoxy and carbon fiber/polyamide 6 unidirectional composites. Compos Struct 160:89–99

    Article  Google Scholar 

  • Mahesh S (2020) A fast algorithm for fracture simulations representing fibre breakage and matrix failure in three-dimensional fibre composites. Int J Fract 222(1):75–109

    Article  MathSciNet  Google Scholar 

  • Mahesh S, Phoenix SL, Beyerlein IJ (2002) Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix. Int J Fract 115(1):41–85

    Article  Google Scholar 

  • Mahesh S, Gupta A, Kachhwah US, Sheikh N (2019) A fast algorithm to simulate the failure of a periodic elastic fibre composite. Int J Fract 217(1):127–135

    Article  Google Scholar 

  • McCartney L, Smith R (1983) Statistical theory of the strength of fiber bundles. J Appl Mech 50(3):601–608

    Article  Google Scholar 

  • Nishimori H, Ortiz G (2010) Elements of phase transitions and critical phenomena. OUP, Oxford

    Book  Google Scholar 

  • Robinson P, Greenhalgh E, Pinho S (2012) Failure mechanisms in polymer matrix composites: criteria, testing and industrial applications. Elsevier, London

    Book  Google Scholar 

  • Scott A, Mavrogordato M, Wright P, Sinclair I, Spearing S (2011) In situ fibre fracture measurement in carbon-epoxy laminates using high resolution computed tomography. Compos Sci Technol 71(12):1471–1477

  • Sket F, Seltzer R, Molina-Aldareguía J, Gonzalez C, LLorca J (2012) Determination of damage micromechanisms and fracture resistance of glass fiber/epoxy cross-ply laminate by means of x-ray computed microtomography. Compos Sci Technol 72(2):350–359

    Article  Google Scholar 

  • Smith R (1980) A probability model for fibrous composites with local load sharing. Proc R Soc Lond A 372(1751):539–553

    Article  MathSciNet  Google Scholar 

  • Smith R, Phoenix S, Greenfield M, Henstenburg R, Pitt R (1983) Lower-tail approximations for the probability of failure of three-dimensional fibrous composites with hexagonal geometry. Proc R Soc Lond A 388(1795):353-391

    Article  MathSciNet  Google Scholar 

  • Weibull W (1952) A statistical distribution function of wide applicability. J Appl Mech 19(2):233–234

    Article  Google Scholar 

  • Zhandarov S, Mäder E (2005) Characterization of fiber/matrix interface strength: applicability of different tests, approaches and parameters. Compos Sci Technol 65(1):149–160

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sivasambu Mahesh.

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

Mahesh, S. Tough–brittle transition in unidirectional composites with fibre breakage and fibre–matrix interfacial failure. Int J Fract 233, 39–70 (2022). https://doi.org/10.1007/s10704-021-00609-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-021-00609-9

Keywords

Navigation