Skip to main content
SpringerLink
Log in

A fast algorithm to simulate the failure of a periodic elastic fibre composite

  • Brief Note
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Monte-Carlo simulations of the fracture of elastic unidirectional model fibre composites are an important tool to understand composite reliability. On account of being computationally intensive, fracture simulations reported in the literature have been limited to simulation patches comprised of a few thousand fibres. While these limited patch sizes suffice to capture the dominant failure event when the fibre strength variability is low (synthetic fibres), they suffer from edge effects when the fibre strength variability is high (natural fibres). On the basis of recent algorithmic developments based on Fourier acceleration, a novel bisection based Monte Carlo failure simulation algorithm is presently proposed. This algorithm is used to obtain empirical strength distributions for model composites comprised of up to \(2^{20} \approx 10^6\) fibres, and spanning a wide range of fibre strength variabilities. These simulations yield empirical weakest-link strength distributions well into the lower tail. A stochastic model is proposed for the weakest-link event. The strength distribution predicted by this model fits the empirical distributions for any fibre strength variability.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Alava MJ, Nukala PK, Zapperi S (2006) Statistical models of fracture. Adv Phys 55(3–4):349–476

    Article  Google Scholar 

  • ASTM (2017) Standard test methods for tensile properties of polymer matrix composite materials. Standard D 3039, ASTM international, West Conshohocken, PA

  • Batrouni GG, Hansen A, Nelkin M (1986) Fourier acceleration of relaxation processes in disordered systems. Phys Rev Lett 57(11):1336

    Article  Google Scholar 

  • Beyerlein IJ, Phoenix SL, Sastry AM (1996) Comparison of shear-lag theory and continuum fracture mechanics for modeling fiber and matrix stresses in an elastic cracked composite lamina. Int J Solids Struct 33(18):2543–2574

    Article  Google Scholar 

  • Cormen T, Leiserson C, Rivest R, Stein C (2001) Introduction To algorithms. MIT Press, Cambridge

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

    Article  Google Scholar 

  • Eaton JW, Bateman D, Hauberg S, Wehbring R (2015) GNU octave version 4.0.0 manual: a high-level interactive language for numerical computations. CreateSpace Independent Publishing Platform. URL http://www.gnu.org/software/octave/doc/interpreter

  • Fidelis MEA, Pereira TVC, Gomes OdFM, de Andrade Silva F, Toledo Filho RD (2013) The effect of fiber morphology on the tensile strength of natural fibers. J Mater Res Technol 2(2):149–157

    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 (2017a) A fast algorithm for the elastic fields due to a single fiber break in a periodic fiber-reinforced composite. Int J Fract 204(1):121–127

    Article  Google Scholar 

  • Gupta A, Mahesh S, Keralavarma SM (2017b) Strength distribution of large unidirectional composite patches with realistic load sharing. Phys Rev E 96:043,002

    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):022,125

    Article  Google Scholar 

  • Hedgepeth JM (1961) Stress concentrations in filamentary structures. Technical report TN 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 

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

    Book  Google Scholar 

  • Jawaid M, Khalil HA (2011) Cellulosic/synthetic fibre reinforced polymer hybrid composites: a review. Carbohydr Polym 86(1):1–18

    Article  Google Scholar 

  • Landis C, McMeeking R (1999) Stress concentrations in composites with interface sliding, matrix stiffness and uneven fiber spacing using shear lag theory. Int J Solids Struct 36(28):4333–4361

    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 

  • Mahesh S, Mishra A (2018) Strength distribution of Ti/SiC metal-matrix composites under monotonic loading. Eng Fract Mech 194:86–104

    Article  Google Scholar 

  • Mahesh S, Phoenix S (2004) Absence of a tough-brittle transition in the statistical fracture of unidirectional composite tapes under local load sharing. Phys Rev E 69(2):026,102

    Article  Google Scholar 

  • Mahesh S, Beyerlein IJ, Phoenix SL (1999) Size and heterogeneity effects on the strength of fibrous composites. Physica D Nonlinear Phenom 133(1):371–389

    Article  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 

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

    Article  Google Scholar 

  • Mishra A, Mahesh S (2017) A deformation-theory based model of a damaged metal matrix composite. Int J Solids Struct 121:228–239

    Article  Google Scholar 

  • Okabe T, Takeda N (2002) Elastoplastic shear-lag analysis of single-fiber composites and strength prediction of unidirectional multi-fiber composites. Compos A 33(10):1327–1335

    Article  Google Scholar 

  • Okabe T, Takeda N, Kamoshida Y, Shimizu M, Curtin W (2001) A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites. Compos Sci Technol 61(12):1773–1787

    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  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  Google Scholar 

  • Tange O (2011) Gnu parallel–the command-line power tool. Login USENIX Mag 36(1):42–47. https://doi.org/10.5281/zenodo.16303

    Google Scholar 

  • Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 103(730):293–297

    Google Scholar 

  • Zhang J, Wang F (2009) Modeling of progressive failure in ductile matrix composites including local matrix yielding. Mech Adv Mater Struct 16(7):522–535

    Article  Google Scholar 

  • Zhou S, Curtin W (1995) Failure of fiber composites: a lattice green function model. Acta Metall Mater 43(8):3093–3104

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    Sivasambu Mahesh, Ankit Gupta, Uttam S. Kachhwah & Najam Sheikh

Authors
  1. Sivasambu Mahesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ankit Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Uttam S. Kachhwah
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Najam Sheikh
    View author publications

    You can also search for this author in PubMed Google Scholar

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., Gupta, A., Kachhwah, U.S. et al. A fast algorithm to simulate the failure of a periodic elastic fibre composite. Int J Fract 217, 127–135 (2019). https://doi.org/10.1007/s10704-019-00374-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-019-00374-w

Keywords

Search

Navigation