Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics
Full Article - Open Access.
SIZE EFFECTS ON THE STRENGTH AND TOUGHNESS OF FIBRE–REINFORCED COMPOSITES
This paper presents an analytical model for size effects on the longitudinal tensile strength of composite fibre bundles. The strength of individual fibres is modelled by a Weibull distribution, while the matrix (or fibre–matrix interface) is represented through a perfectly– plastic shear–lag model. A probabilistic analysis of the failure process in hierarchical bundles (bundles of bundles) is performed, so that a scaling law relating the strength distributions of consecutive bundle levels is derived. An efficient numerical scheme (based on asymptotic limits) is proposed, hence coupon–sized bundle strength distributions are obtained almost instantaneously. Parametric and sensitivity studies show that both fibre and matrix properties are critical for bundle strength; model predictions at different scales are validated against experimental results available in the literature.
Palavras-chave: Size effect, Tensile strength, Hierarchical bundles, Fibre–reinforced composites,
-  M. R. Wisnom, “Size effects in the testing of fibre–composite materials,” Composites Science and Technology, 59, 1937–1957, 1999.
-  G. W. Weibull, “A statistical distribution function of wide applicability,” Journal of Applied Mathematics, 293–297, 1951.
-  Z. P. Ba?zant, “Size effect on structural strength: a review,” Archive of Applied Mechanics, 69, 703–725, 1999.
-  A. Carpinteri, “Scaling laws and renormalization–groups for strength and toughness of disordered materials,” International Journal of Solids and Structures, 31, 291–302, 199
-  M. R. Wisnom, S. R. Hallett, and C. Soutis, “Scaling effects in notched composites,” Journal of Composite Materials, 44, 195–210, 2010.
-  L. Mishnaevsky and P. Brondsted, “Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: A review,” Computational Materials Science, 44, 1351–1359, 2009.
-  S. Pradhan, A. Hansen, and B. K. Chakrabarti, “Failure processes in elastic fiber bundles,” Reviews of Modern Physics, 82, 499–555, 2010.
-  C. P. Beetz, “The analysis of carbon–fiber strength distributions exhibiting multiple– modes of failure,” Fibre Science and Technology, 16, 45–59, 1982.
-  I. J. Beyerlein and S. L. Phoenix, “Statistics for the strength and size effects of microcomposites with four carbon fibers in epoxy resin,” Composites Science and Technology, 56, 75–92, 1996.
-  E. G. Stoner, D. D. Edie, and S. D. Durham, “An end–effect model for the single– filament tensile test,” Journal of Materials Science, 29, 6561–6574, 1994.
-  M. Kazanci, “Carbon fiber reinforced microcomposites in two different epoxies,” Polymer Testing, 23, 747–753, 2004.
-  T. Okabe and N. Takeda, “Size effect on tensile strength of unidirectional CFRP composites— experiment and simulation,” Composites Science and Technology, 62, 2053– 2064, 2002.
-  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,” Composites Science and Technology, 71, 1471–1477, 2011.
-  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 tow filamentisation,” Composites Part A — Applied Science and Manufacturing, 38, 755– 770, 2007.
-  S. Pimenta, S. T. Pinho, P. Robinson, K. H.Wong, and S. J. Pickering, “Mechanical analysis and toughening mechanisms of a multiphase recycled CFRP,” Composites Science and Technology, 70, 1713–1725, 2010.
-  H. E. Daniels, “The statistical theory of the strength of bundles of threads. I,” Proceeedings of the Royal Society A — Mathematical, Physical and Andamp; Engineering Science, 183, 405–435, 1945.
-  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,” Composites Science and Technology, 70, 614–621, 2010.
-  W. I. Newman and A. M. Gabrielov, “Failure of hierarchical distributions of fiber– bundles. 1,” International Journal of Fracture, 50, 1–14, 1991.
-  T. Hobbiebrunken, B. Fiedler, M. Hojo, and M. Tanaka, “Experimental determination of the true epoxy resin strength using micro-scaled specimens,” Composites Part A — Applied Science and Manufacturing, 38, 814–818, 2007.
-  A. B. de Morais, “Stress distribution along broken fibres in polymer–matrix composites,” Composites Science and Technology, 61, 1571–1580, 2001.
-  M. R. Nedele and M. R. Wisnom, “3-dimensional finite–element analysis of the stress– concentration at a single–fiber break,” Composites Science and Technology, 51, 517– 524, 1994.
-  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,” Journal of the Mechanics and Physics of Solids, 44, 1997–2039, 1996.
-  S. Pimenta and S. T. Pinho, “Hierarchical scaling law for the strength of composite fibre bundles,” submitted to the Journal of the Mechanics and Physics of Solids, 2012.
-  Dow Plastics, “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, 1999.
Pinho, S. T.; Pimenta, S.; "SIZE EFFECTS ON THE STRENGTH AND TOUGHNESS OF FIBRE–REINFORCED COMPOSITES", p. 4394-4413 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1].
São Paulo: Blucher,
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19865
últimos 30 dias | último ano | desde a publicação