Hierarchical scaling law for the strength of composite fibre bundles

Journal of the Mechanics and Physics of Solids

Volumn 61, Issue 6, 2013, Pages 1337-1356

  Pimenta, Soraia ^a   Pinho, Silvestre T ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Fibre reinforced composite material; Probability and statistics; Size effects; Strengthening and mechanisms

Indexed keywords

EFFICIENT NUMERICAL SCHEMES; FIBRE REINFORCED COMPOSITES; LONGITUDINAL TENSILE STRENGTHS; PROBABILISTIC ANALYSIS; PROBABILITY AND STATISTICS; SIZE EFFECTS; STRENGTH DISTRIBUTION; STRENGTHENING AND MECHANISMS;

FIBERS; STRESS ANALYSIS; WEIBULL DISTRIBUTION;

TENSILE STRENGTH;

EID: 84876282815     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2013.02.004     Document Type: Article

References (51)

1. M.L. Accorsi, A. Pegoretti, and A.T. Dibenedetto Dynamic analysis of fibre breakage in single- and multiple-fibre composites J. Mater. Sci. 31 1996 4181 4187
2. Z.P. Bažant Size effect on structural strength a review Arch. Appl. Mech. 69 1999 703 725
3. Z.P. Bažant, and S.D. Pang Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture J. Mech. Phys. Solids 55 2007 91 131
4. C.P. Beetz The analysis of carbon-fiber strength distributions exhibiting multiple-modes of failure Fibre Sci. Technol. 16 1982 45 59
5. S. Behzadi, P.T. Curtis, and F.R. Jones Improving the prediction of tensile failure in unidirectional fibre composites by introducing matrix shear yielding Compos. Sci. Technol. 69 2009 2421 2427
6. I.J. Beyerlein, and S.L. Phoenix Statistics for the strength and size effects of microcomposites with four carbon fibers in epoxy resin Compos. Sci. Technol. 56 1996 75 92
7. I.J. Beyerlein, and S.L. Phoenix Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition J. Mech. Phys. Solids 44 1996 1997 2039
8. A. Carpinteri Scaling laws and renormalization-groups for strength and toughness of disordered materials Int. J. Solids Struct. 31 1994 291 302
9. W.A. Curtin Theory of mechanical properties of ceramic-matrix composites J. Am. Ceram. Soc. 74 1991 2837 2845
10. W.A. Curtin The tough to brittle transition in brittle matrix composites J. Phys. Mech. Solids 41 1993 217 245
11. W.A. Curtin Stochastic damage evolution and failure in fiber-reinforced composites Adv. Appl. Mech. 36 1999 163 253
12. W.A. Curtin, and N. Takeda Tensile strength of fiber-reinforced composites I. Model and effects of local fiber geometry J. Compos. Mater. 32 1998 2042 2059
13. P.S. Curtis A computer model of the tensile failure process in unidirectional fibre composites Compos. Sci. Technol. 27 1986 63 86
14. H.E. Daniels The statistical theory of the strength of bundles of threads. I Proc. R. Soc. A - Math. Phys. Eng. Sci. 183 1945 405 435
15. Dow Plastics, 1999. Dow liquid epoxy resins. Form No. 296-00224-0199 WC+M 〈 http://epoxy.dow.com/epoxy/tech/index.htm 〉, last accessed on 29 January 2011.
16. H. Fukuda, and K. Kawata On the strength distribution of unidirectional fibre composites Fibre Sci. Technol. 10 1977 53 63
17. R. Gulino, P. Schwartz, and S. Phoenix Experiments on shear deformation, debonding and local load transfer in a model graphite/glass/epoxy microcomposite J. Mater. Sci. 26 1991 6655 6672
18. D.G. Harlow, and S.L. Phoenix The chain-of-bundles probability model for the strength of fibrous materials. I analysis and conjectures J. Compos. Mater. 12 1978 195 214
19. D.G. Harlow, and S.L. Phoenix The chain-of-bundles probability model for the strength of fibrous materials. II a numerical study of convergence J. Compos. Mater. 12 1978 314 334
20. L.T. Harper, T.A. Turner, N.A. Warrior, and C.D. Rudd Characterisation of random carbon fibre composites from a directed fibre preforming process the effect of two filamentisation Composites Part A - Appl. Sci. Manuf. 38 2007 755 770
21. Hedgepeth, J.M.; 1961. Stress Concentrations in Filamentary Structures. Technical Report TN D 882. NASA, Washington, DC, USA.
22. T. Hobbiebrunken, B. Fiedler, M. Hojo, and M. Tanaka Experimental determination of the true epoxy resin strength using micro-scaled specimens Composites Part A - Appl. Sci. Manuf. 38 2007 814 818
23. M. Kazanci Carbon fiber reinforced microcomposites in two different epoxies Polym. Test. 23 2004 747 753
24. A. Kelly, and W. Tyson Tensile properties of fibre-reinforced metals copper/tungsten and copper/molybdenum J. Mech. Phys. Solids 13 1965 329 338
25. M.J. Laffan, S.T. Pinho, P. Robinson, and L. Iannucci Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II size and lay-up effects Compos. Sci. Technol. 70 2010 614 621
26. C.M. Landis, I.J. Beyerlein, and R.M. McMeeking Micromechanical simulation of the failure of fiber reinforced composites J. Phys. Mech. Solids 48 2000 621 648
27. C.M. Landis, and R.M. McMeeking A shear-lag model for a broken fiber embedded in a composite with a ductile matrix Compos. Sci. Technol. 59 1999 447 457
28. S. Mahesh, S.L. Phoenix, and I.J. Beyerlein Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix Int. J. Fract. 115 2002 41 85
29. A.B. de Morais Stress distribution along broken fibres in polymer-matrix composites Compos. Sci. Technol. 61 2001 1571 1580
30. A.B. de Morais Prediction of the longitudinal tensile strength of polymer matrix composites Compos. Sci. Technol. 66 2006 2990 2996
31. J.A. Nairn On the use of shear-lag methods for analysis of stress transfer unidirectional composites Mech. Mater. 26 1997 63 80
32. M.R. Nedele, and M.R. Wisnom 3-Dimensional finite-element analysis of the stress-concentration at a single-fiber break Compos. Sci. Technol. 51 1994 517 524
33. W.I. Newman, and A.M. Gabrielov Failure of hierarchical distributions of fiber-bundles. 1 Int. J. Fract. 50 1991 1 14
34. T. Okabe, and N. Takeda A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites Compos. Sci. Technol. 61 2001 1773 1787
35. T. Okabe, and N. Takeda Size effect on tensile strength of unidirectional CFRP composites - experiment and simulation Compos. Sci. Technol. 62 2002 2053 2064
36. S.L. Phoenix, M. Ibnabdeljalil, and C.Y. Hui Size effects in the distribution for strength of brittle matrix fibrous composites Int. J. Solids Struct. 34 1997 545 568
37. S.L. Phoenix, P. Schwartz, and H.H. Robinson Statistics for the strength and lifetime in creep-rupture of model carbon epoxy composites Compos. Sci. Technol. 32 1988 81 120
38. S.L. Phoenix, and R.L. Smith A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers Int. J. Solids Struct. 19 1983 479 496
39. Pimenta, S.; Pinho, S.T. An analytical model for the translaminar tensile toughness of fibre composites with stochastic fractal fracture surfaces. J. Mech. Phys. Solids, submitted for publication.
40. S. Pimenta, S.T. Pinho, P. Robinson, K.H. Wong, and S.J. Pickering Mechanical analysis and toughening mechanisms of a multiphase recycled CFRP Compos. Sci. Technol. 70 2010 1713 1725
41. S. Pradhan, A. Hansen, and B.K. Chakrabarti Failure processes in elastic fiber bundles Rev. Mod. Phys. 82 2010 499 555
42. A.E. Scott, M. Mavrogordato, P. Wright, I. Sinclair, and S.M. Spearing In situ fibre fracture measurement in carbon-epoxy laminates using high resolution computed tomography Compos. Sci. Technol. 71 2011 1471 1477
43. S. Sihn, R.Y. Kim, K. Kawabe, and S.W. Tsai Experimental studies of thin-ply laminated composites Compos. Sci. Technol. 67 2007 996 1008
44. E.G. Stoner, D.D. Edie, and S.D. Durham An end-effect model for the single-filament tensile test J. Mater. Sci. 29 1994 6561 6574
45. Y. Swolfs, L. Gorbatikh, V. Romanov, S. Orlova, S.V. Lomov, and I. Verpoest Stress concentrations in an impregnated fibre bundle with random fibre packing Compos. Sci. Technol. 74 2013 113 120
46. A. Wada, and H. Fukuda Approximate upper and lower bounds for the strength of unidirectional composites Compos. Sci. Technol. 59 1999 89 95
47. G.W. Weibull A statistical distribution function of wide applicability J. Appl. Math. 1951 293 297
48. M.R. Wisnom Size effects in the testing of fibre-composite materials Compos. Sci. Technol. 59 1999 1937 1957
49. M.R. Wisnom, and D. Green Tensile failure due to interaction between fibre breaks Composites 26 1995 499 508
50. M.R. Wisnom, S.R. Hallett, and C. Soutis Scaling effects in notched composites J. Compos. Mater. 44 2010 195 210
51. S. Zhandarov, E. Pisanova, and B. Lauke Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part I. Crack initiation Stress-controlled or energy-controlled? Compos. Interfaces 5 1998 387 404