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TECHNICAL PAPERS

Size Effect on Flexural Strength of Fiber-Composite Laminates

[+] Author and Article Information
Zdeněk P. Bažant

Northwestern University, 2145 Sheridan Road (CEE), Evanston, IL 60208

Yong Zhou, Drahomı́r Novák, Isaac M. Daniel

Northwestern University, 2145 Sheridan Road (CEE), Evanston, IL 60208

J. Eng. Mater. Technol 126(1), 29-37 (Jan 22, 2004) (9 pages) doi:10.1115/1.1631031 History: Received December 02, 2002; Revised August 01, 2003; Online January 22, 2004
Copyright © 2004 by ASME
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References

Baz̆ant, Z. P., 1999, “Size Effect on Structural Strength: A Review,” Archives of Applied Mechanics (Ingenieur-Archiv, Springer Verlag) 69 , pp. 703–725; Reprinted with updates in Handbook of Materials Behavior, 1 , J. Lemaitre, ed., Academic Press, San Diego 2001, 30–68.
Baz̆ant, Z. P., 2002, Scaling of Structural Strength, Hermes Penton Science (Kogan Page Science), London.
Baz̆ant, Z. P., 2002, “Size effect theory and its application to fracture of fiber composites and sandwich plates,” Continuum Damage Mechanics of Materials and Structures, O. Allix and F. Hild, eds., Elsevier, Amsterdam, pp. 353–381.
Baz̆ant,  Z. P., and Chen,  E.-P., 1997, “Scaling of structural failure,” Appl. Mech. Rev., 50(10), pp. 593–627.
Baz̆ant,  Z. P., 1999, “Size effect,” Int. J. Solids Struct., 37(200), pp. 69–80.
Baz̆ant, Z. P., and Planas, J., 1998, Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton and London.
Baz̆ant,  Z. P., Daniel,  I. M., and Li,  Zhengzhi, 1996, “Size Effect and Fracture Characteristics of Composite Laminates,” ASME J. Eng. Mater. Technol., 118(3), pp. 317–324.
Baz̆ant,  Z. P., Kim,  J.-J. H., Daniel,  I. M., Becq-Giraudon,  E., and Zi,  Goangseup, 1999, “Size Effect on Compression Strength of Fiber Composites Failing by Kink Band Propagation,” Int. J. Fract., 95, pp. 103–141.
Baz̆ant, Z. P., Zhou, Y., Novák, D., and Daniel, I. M., 2001, “Size effect in fracture of sandwich structure components: foam and laminate,” Proc., ASME Intern. Mechanical Engrg. Congress, Vol. AMD-TOC (paper 25413), Am. Soc. of Mech. Engrs., New York, pp. 1–12.
Baz̆ant, Z. P., and Novák, D., 2000, “Probabilistic Nonlocal Theory for Quasi-Brittle Fracture Initiation and Size Effect. I. Theory and II. Application,” ASCE Journal of Engineering Mechanics, 126 (2), pp. 166–185.
Baz̆ant,  Z. P., and Novák,  D., 2000, “Energetic-Statistical Size Effect in Quasi-Brittle Failure at Crack Initiation,” ACI Mater. J., 97(3), pp. 381–392.
Baz̆ant, Z. P., 1984, “Size effect in blunt fracture: Concrete, rock, metal,” Journal of Engineering Mechanics ASCE, 110 , pp. 518–535.
Mahesh,  S., Phoenix,  S. L., and Beyerlein,  I. J., 2002, “Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix,” Int. J. Fract., 115, pp. 41–85.
Phoenix,  S. L., and Beyerlein,  I. J., 2000, “Distribution and size scalings for strength in a one-dimensional random lattice with load redistribution to nearest and next nearest neighbors,” Phys. Rev. E, 62(2), pp. 1622–1645.
Jackson,  K. E., 1992, “Scaling Effects in the Flexural Response and Failure of Composite Beams,” AIAA J., 30(8), pp. 2099–2105.
Johnson,  D. P., Morton,  J., Kellas,  S., and Jackson,  K. E., 2000, “Size Effect in Scaled Fiber Composites Under Four-Point Flexural Loading,” AIAA J., 38(6), pp. 1047–1054.
Wisnom,  M. R., 1991, “The Effect of Specimen Size on the Bending Strength of Unidirectional Carbon Fiber-Epoxy,” Composite Structures, 18, pp. 47–63.
Wisnom,  M. R., and Atkinson,  J. A., 1997, “Reduction in Tensile and Flexural Strength of Unidirectional Glass Fiber-Epoxy with Increasing Specimen Size,” Composite Structures, 38, pp. 405–412.
Lavoie,  J. A., Soutis,  C., and Morton,  J., 2000, “Apparent Strength Scaling in Continuous Fiber Composite Laminates,” Compos. Sci. Technol., 60, pp. 283–299.
Bullock,  R. E., 1974, “Strength ratios of composite materials in flexure and torsion,” J. Compos. Mater., 8, pp. 200–206.
Weibull, W., 1939, “The Phenomenon of Rupture in Solids,” Proc., Royal Swedish Institute of Engineering Research (Ingenioersvetenskaps Akad. Handl.), 153 , pp. 1–55.
Weibull,  W., 1951, “A Statistical Distribution Function of Wide Applicability,” ASME J. Appl. Mech., 18, pp. 293–297.
Fisher,  R. A., and Tippett,  L. H. C., 1928, “Limiting Frequency Distribution of the Largest and Smallest Member of a Sample,” Proc. Cambridge Philos. Soc., 24, pp. 180–190.
Fréchet, M., 1927, “Sur la loi de probabilité de l’ écart maximum,” Ann. soc. polon. math., 6 , p. 93.
von Mises, P., 1936, “La distribution de la plus grande de n valeurs,” Rev. math. Union interbalcanique, 1 , p. 1.
Baz̆ant, Z. P., 1998, “Size effect in tensile and compression fracture of concrete structures: computational modeling and design,” Fracture Mechanics of Concrete Structures, Proc., 3rd Int. Conf., FraMCoS-3, held in Gifu, Japan, H. Mihashi and K. Rokugo, eds., Aedificatio Publishers, Freiburg, Germany, pp. 1905–1922.
Baz̆ant, Z. P., and Li, Zhengzhi, 1995, “Modulus of Rupture: Size Effect due to Fracture Initiation in Boundary Layer,” ASCE Journal of Structural Engineering, 121 (4), pp. 739–746.
Barenblatt, G. I., 1979, Similarity, Self-Similarity and Intermediate Asymptotics, Plenum Press, New York.
Barenblatt, G. I., 1996, Scaling, Self-similarity and Intermediate Asymptotics, Cambridge University Press.
Bender, M. C., and Orszag, S. A., 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw Hill, New York, Chap. 9–11.
Hinch, E. J., 1991, Perturbation Methods, Cambridge University Press, Cambridge, UK.
Baz̆ant, Z. P., and Xi, Y., 1991, “Statistical size effect in quasi-brittle structures: II. Nonlocal theory,” ASCE J. of Engineering Mechanics, 117 (11), pp. 2623–2640.
Baz̆ant, Z. P., 2001, “Probabilistic modeling of quasibrittle fracture and size effect,” Proc., 8th Int. Conf. on Structural Safety and Reliability (ICOSSAR), R. B. Corotis, ed., Swets and Zeitinger, Balkema, pp. 1–23.
Baz̆ant, Z. P., and Novák, D., 2003, “Stochastic models for deformation and failure of quasibrittle structures: recent advances and new directions,” Computational Modelling of Concrete Structures (Proc., EURO-C Conf., St. Johann im Pongau, Austria), N. Bićanić, R. de Borst, H. Mang and G. Meschke, eds., A. A. Balkema Publ., Lisse, Netherlands, pp. 583–598.
Jackson, K. E., 1990, “Scaling Effects in the Static and Dynamic Response of Graphite-Epoxy Beam Columns,” NASA TM, 102697.
Baz̆ant, Z. P., and Cedolin, L., 1991, Stability of Structures: Elastic, Fracture and Damage Theories, Oxford University Press, New York, Chap. 1.
Baz̆ant, Z. P., and Skupin, L., 1967, “Méthode d’essai de viellissement des plastiques renforcées sous contrainte (Testing Method for Aging of Reinforced Plastics Under Stress),” Plastiques renforcées-Verre textile (Paris), 5 , pp. 27–30.
Baz̆ant, Z. P., and Skupin, L., 1968, “Material Properties for the Design of Polyvinylchloride Structural Members (in Czech),” Plastické Hmoty a Kauc̆uk, 5 , pp. 161–166.
Wisnom,  M. R., 1999, “Size Effect in the Testing of Fiber-Composite Materials,” Compos. Sci. Technol., 59, pp. 1937–1957.
Daniel, I. M., and Weil, N. A., 1963, “The Influence of Stress Gradient upon Fracture of Brittle Materials,” Paper ASME 63-WA-228.
Wisnom,  M. R., 1991, “Relationship between Size Effect and Strength Variability in Unidirectional Carbon Fiber-Epoxy,” Composites, 22, pp. 47–52.
Atkins,  A. G., and Caddell,  R. M., 1974, “The Law of Similitude and Crack Propagation,” Int. J. Mech. Sci., 16(8), pp. 541–548.
Daniels,  H. E., 1945, “The statistical theory of the strength of bundles and threads,” Proc. R. Soc. London, Ser. A, pp. 405–435.
Curtin,  W. A., and Takeda,  N., 1998, “Tensile strength of fiber composites. II. Model and effects of local geometry,” J. Compos. Mater., 32, pp. 2060–2091.
Landis,  C. M., Beyerlein,  I. J., and McMeeking,  R. M., 2000, “Micromechanical simulation of the failure of fiber reinforced composites,” J. Mech. Phys. Solids, 48, pp. 621–648.
Leath,  P. L., and Duxbury,  P. M., 1994, “Fracture of heterogeneous materials with continuous distribution of local breaking strengths,” Phys. Rev. B, 49, pp. 14905–14917.
Baz̆ant, Z. P., 2003, “Probability Distribution of Energetic-Statistical Size Effect in Quasibrittle Fracture,” Probabilistic Engineering Mechanics, in press.

Figures

Grahic Jump Location
Stress redistribution in flexure caused by a boundary layer of cracking
Grahic Jump Location
Optimum fits of existing test data on modulus of rupture versus relative size, in dimensionless coordinates, by (a) deterministic energetic formula; (b) energetic-statistical formula; (c) Weibull size effect formula with m=5; and (d) Weilbull size effect formula with m=30
Grahic Jump Location
Optimum fits of individual data sets by different formulas. (a) deterministic energetic size effect formula; (b) energetic-statistical size effect formula; (c) Weibull theory for m=5; and (d) Weibull theory for m=30. Numbers from 1 to 9 correspond to the data sets showed in Fig. 2.
Grahic Jump Location
Energetic-statistical formula of Jackson’s angle-ply data (actual scale)
Grahic Jump Location
The curve of elastica used in calculations for Table 5

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