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Effective transverse elastic moduli of three-phase hybrid fiber-reinforced composites with randomly located and interacting aligned circular fibers of distinct elastic properties and sizes

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Abstract

A higher-order multi-scale structure for three-phase hybrid fiber-reinforced composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. Two non-equivalent formulations are considered in detail to derive effective transverse elastic moduli of three-phase composites leading to new higher-order bounds. Numerical examples and comparisons among our theoretical predictions and other analytical predictions are rendered to illustrate the potential capability of the present method.

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References

  1. Banthia N., Nandakumar N.: Crack growth resistance of hybrid fiber reinforced cement composites. Cem. Concr. Compos. 25(1), 3–9 (2003)

    Article  Google Scholar 

  2. Banthia N., Gupta R.: Hybrid fiber reinforced concrete (HyFRC): fiber synergy in high strength matrices. Mater. Struct. 37(10), 707–716 (2004)

    Article  Google Scholar 

  3. Banthia N., Soleimani S.: Flexural response of hybrid fiber reinforced cementitious composites. ACI Mater. J. 102(6), 382–389 (2005)

    Google Scholar 

  4. Blunt J., Ostertag C.P.: Performance-based approach for the design of a deflection hardened hybrid fiber-reinforced concrete. J. Eng. Mech. ASCE 135(9), 978–986 (2009)

    Article  Google Scholar 

  5. Soliman E., Al-Haik M., Taha M.R.: On and off-axis tension behavior of fiber reinforced polymer composites incorporating multi-walled carbon nanotubes. J. Compos. Mater. 46(14), 1661–1675 (2012)

    Article  Google Scholar 

  6. Wang M.C., Zhang Z.G., Sun Z.: The hybrid model and mechanical properties of hybrid composites reinforced with different diameter fibers. J. Reinf. Plast. Compos. 28(3), 257–264 (2009)

    Article  MathSciNet  Google Scholar 

  7. Hashin Z., Shtrikman S.: On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335–342 (1962)

    Article  MathSciNet  Google Scholar 

  8. Hashin Z., Shtrikman S.: A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11, 127–140 (1962)

    Article  MathSciNet  Google Scholar 

  9. Hill R.: Theory of mechanical properties of fiber-strengthened materials: I. elastic behavior. J. Mech. Phys. Solids 12, 199–212 (1964)

    Article  MathSciNet  Google Scholar 

  10. Hill R.: Theory of mechanical properties of fiber-strengthened materials: II. inelastic behavior. J. Mech. Phys. Solids 12, 213–218 (1964)

    Article  MathSciNet  Google Scholar 

  11. Hashin Z., Rosen B.W.: The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 31, 223–232 (1964)

    Article  Google Scholar 

  12. Hashin Z.: On elastic behavior of fiber reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids 13, 119–134 (1965)

    Article  Google Scholar 

  13. Walpole L.J.: On bounds for overall elastic moduli of inhomogeneous systems: I. J. Mech. Phys. Solids 14, 151–162 (1966)

    Article  MATH  Google Scholar 

  14. Walpole L.J.: On bounds for overall elastic moduli of inhomogeneous Systems: II. J. Mech. Phys. Solids 14, 289–301 (1966)

    Article  Google Scholar 

  15. Walpole L.J.: On the overall elastic moduli of composite materials. J. Mech. Phys. Solids 17, 235–251 (1969)

    Article  MATH  Google Scholar 

  16. Hashin, Z.: Theory of fiber reinforced materials. NASA CR-1974 (1972)

  17. Silnutzer, N.: Effective Constants of Statistically Homogeneous Materials. Ph.D. Thesis, University of Pennsylvania (1972)

  18. Milton G.W.: Bounds on the elastic and transport properties of two-component composites. J. Mech. Phys. Solids 30, 177–191 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  19. Milton G.W., Phan-Thien N.: New bounds on effective elastic moduli of two-component materials. Proc. R. Soc. A380, 305–331 (1982)

    Google Scholar 

  20. Torquato S., Lado F.: Improved bounds of the effective elastic moduli of random arrays of cylinders. J. Appl. Mech. 59, 1–6 (1992)

    Article  MathSciNet  Google Scholar 

  21. Hill R.: Theory of mechanical properties of fiber-strengthened materials: III. self-consistent model. J. Mech. Phys. Solids 13, 189–198 (1965)

    Article  Google Scholar 

  22. Hill R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965)

    Article  Google Scholar 

  23. Christensen R.M., Lo K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)

    Article  MATH  Google Scholar 

  24. Mori T., Tanaka K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973)

    Article  Google Scholar 

  25. Benveniste Y.: A new approach to the application of Mori-Tanaka’s theory in composite materials. Mech. Mater. 6, 147–157 (1987)

    Article  Google Scholar 

  26. Weng G.J.: The theoretical connection between Mori-Tanaka’s theory and the Hashin-Shtrikman-Walpole bounds. Int. J. Eng. Sci. 28, 1111–1120 (1990)

    Article  MATH  Google Scholar 

  27. Eshelby J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A241, 376–396 (1957)

    MathSciNet  Google Scholar 

  28. Mura T.: Micromechanics of Defects in Solids. 2nd edn. Kluwer, The Netherlands (1987)

    Book  Google Scholar 

  29. Honein, E.: Multiple Inclusions in Elastostatics. Ph.D. Dissertation at Stanford University (1991)

  30. Nemat-Nasser S., Hori M.: Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier Science Publisher B. V., Netherlands (1993)

    MATH  Google Scholar 

  31. Ju J.W., Chen T.M.: Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities. Acta Mech. 103, 103–121 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ju J.W., Chen T.M.: Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities. Acta Mech. 103, 123–144 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  33. Ju J.W., Zhang X.D.: Micromechanics and effective transverse elastic moduli of composites with randomly located aligned circular fibers. Int. J. Solids Struct. 35(9–10), 941–960 (1998)

    Article  MATH  Google Scholar 

  34. Ju J.W., Yanase K.: Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions. Acta Mech. 215(1), 135–153 (2010)

    Article  MATH  Google Scholar 

  35. Ju J.W., Yanase K.: Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions. Acta Mech. 216(1–4), 87– 103 (2011)

    Article  MATH  Google Scholar 

  36. Lin P.J., Ju J.W.: Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties. Acta Mech. 208, 11–26 (2009)

    Article  MATH  Google Scholar 

  37. Adams D.F., Crane D.A.: Finite element micromechanical analysis of a unidirectional composite including longitudinal shear loading. Comput. Struct. 18(6), 1153–1165 (1984)

    Article  MATH  Google Scholar 

  38. Nimmer R.P., Bankert R.J., Russell E.S., Smith G.A., Wright P.K.: Micromechanical modeling of fiber/matrix interface effects in transversely loaded SiC/Ti-6-4 metal matrix composites. J. Comp. Tech. Res 13, 3–13 (1991)

    Article  Google Scholar 

  39. Doghri I., Friebel C.: Effective elasto-plastic properties of inclusion-reinforced composites. Study of shape, orientation and cyclic response. Mech. Mater. 37, 45–68 (2005)

    Article  Google Scholar 

  40. Ju J.W., Chen T.M.: Micromechanics and effective elastoplastic behavior of two-phase metal matrix composites. Trans. ASME J. Eng. Mater. Tech. 116, 310–318 (1994)

    Article  Google Scholar 

  41. Ju J.W., Tseng K.H.: Effective elastoplastic behavior of two-phase ductile matrix composites: a micromechanical framework. Int. J. Solids Struct. 33, 4267–4291 (1996)

    Article  MATH  Google Scholar 

  42. Ju J.W., Tseng K.H.: Effective elastoplastic algorithms for ductile matrix composites. J. Eng. Mech. ASCE 123, 260–266 (1997)

    Article  Google Scholar 

  43. Ju J.W., Zhang X.D.: Effective elastoplastic behavior of ductile matrix composites containing randomly located aligned circular fibers. Int. J. Solids Struct. 38, 4045–4069 (2001)

    Article  MATH  Google Scholar 

  44. Ju J.W., Sun L.Z.: Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation. Int. J. Solids Struct. 38(2), 183–201 (2001)

    Article  MATH  Google Scholar 

  45. Sun L.Z., Ju J.W.: Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part II: applications. Int. J. Solids Struct. 38(2), 203–225 (2001)

    Article  Google Scholar 

  46. Ju J.W., Sun L.Z.: A novel formulation for the exterior-point Eshelby’s tensor of an ellipsoidal inclusion. J. Appl. Mech. ASME 66, 570–574 (1999)

    Article  Google Scholar 

  47. Ju J.W., Lee H.K.: A micromechanical damage model for effective elastoplastic behavior of ductile matrix composites considering evolutionary complete particle debonding. Comput. Methods Appl. Mech. Eng. 183, 201–222 (2000)

    Article  MATH  Google Scholar 

  48. Ju J.W., Lee H.K.: A micromechanical damage model for effective elastoplastic behavior of partially debonded ductile matrix composites. Int. J. Solids Struct. 38, 6307–6332 (2001)

    Article  MATH  Google Scholar 

  49. Sun L.Z., Ju J.W., Liu H.T.: Elastoplastic modeling of metal matrix composites with evolutionary particle debonding. Mech. Mater. 35, 559–569 (2003)

    Article  Google Scholar 

  50. Sun L.Z., Liu H.T., Ju J.W.: Effect of particle cracking on elastoplastic behaviour of metal matrix composites. Int. J. Numer. Meth. Eng. 56, 2183–2198 (2003)

    Article  MATH  Google Scholar 

  51. Liu H.T., Sun L.Z., Ju J.W.: An interfacial debonding model for particle-reinforced composites. Int. J. Damage Mech. 13, 163–185 (2004)

    Article  Google Scholar 

  52. Liu H.T., Sun L.Z.: Effects of thermal residual stresses on effective elastoplastic behavior of metal matrix composites. Int. J. Solids Struct. 41, 2189–2203 (2004)

    Article  MATH  Google Scholar 

  53. Ko, Y.F.: Effective Elastoplastic-Damage Model for Fiber-Reinforced Metal Matrix Composites with Evolutionary Fibers Debonding. Ph.D. Dissertation, University of California, Los Angeles (2005)

  54. Ju J.W., Ko Y.F., Ruan H.N.: Effective elastoplastic damage mechanics for fiber reinforced composites with evolutionary complete fiber debonding. Int. J. Damage Mech. 15(3), 237–265 (2006)

    Article  Google Scholar 

  55. Liu H.T., Sun L.Z., Ju J.W.: Elastoplastic modeling of progressive interfacial debonding for particle-reinforced metal matrix composites. Acta Mech. 181(1–2), 1–17 (2006)

    Article  MATH  Google Scholar 

  56. Ju J.W., Ko Y.F., Ruan H.N.: Effective elastoplastic damage mechanics for fiber reinforced composites with evolutionary partial fiber debonding. Int. J. Damage Mech. 17(6), 493–537 (2008)

    Article  Google Scholar 

  57. Ju J.W., Ko Y.F.: Micromechanical elastoplastic damage modeling of progressive interfacial arc debonding for fiber reinforced composites. Int. J. Damage Mech. 17, 307–356 (2008)

    Article  Google Scholar 

  58. Ju J.W., Yanase K.: Elastoplastic damage micromechanics for elliptical fiber composites with progressive partial fiber debonding and thermal residual stresses. Theor. Appl. Mech. 35(1–3), 137–170 (2008)

    Article  MATH  Google Scholar 

  59. Lee H.K., Ju J.W.: 3-D micromechanics and effective moduli for brittle composites with randomly located interacting microcracks and inclusions. Int. J. Damage Mech. 17(5), 377–417 (2008)

    Article  MathSciNet  Google Scholar 

  60. Ju J.W., Ko Y.F., Zhang X.D.: Multi-level elastoplastic damage mechanics for elliptical fiber reinforced composites with evolutionary complete fiber debonding. Int. J. Damage Mech. 18(5), 419–460 (2009)

    Article  Google Scholar 

  61. Ju J.W., Yanase K.: Micromechanical elastoplastic damage mechanics for elliptical fiber-reinforced composites with progressive partial fiber debonding. Int. J. Damage Mech. 18(7), 639–668 (2009)

    Article  Google Scholar 

  62. Ju J.W., Yanase K.: Size-dependent probabilistic micromechanical damage mechanics for particle reinforced metal matrix composites. Int. J. Damage Mech. 20(7), 1021–1048 (2011)

    Article  Google Scholar 

  63. Ko, Y.F., Ju, J.W.: Effects of fiber cracking on elastoplastic damage behavior of fiber reinforced metal matrix composites. Int. J. Damage Mech. published at OnlineFirst, 24 pages (2012). doi:10.1177/1056789511433340. Sage

  64. Ko, Y.F., Ju, J.W.: New higher-order bounds on effective transverse elastic moduli of three-phase fiber reinforced composites with randomly located and interacting aligned circular fibers. Acta Mech., published at OnlineFirst, 22 pages (2012). doi:10.1007/s00707-012-0696-y. Springer

  65. Hansen J.P., McDonald I.R.: Theory of Simple Liquids. Academic Press, New York (1986)

    Google Scholar 

  66. Zhao Y.H., Tandon G.P., Weng G.J.: Elastic moduli for a class of porous materials. Acta Mech. 76, 105–131 (1989)

    Article  MATH  Google Scholar 

  67. Kondo, K., Saito, N.: The influence of random fiber packing on the elastic properties of unidirectional composites. In: Composites ’86: Recent Advances in Japan and the United States. Proceedings of Japan-U.S. CCM-III (1986)

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Authors and Affiliations

  1. Department of Civil Engineering and Construction Engineering Management, California State University, Long Beach, CA, 90840-5101, USA

    Yu-Fu Ko

  2. Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, 90095-1593, USA

    J. W. Ju

  3. College of Civil Engineering and Architecture, Guangxi University, Nanning, 530004, China

    J. W. Ju

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  1. Yu-Fu Ko
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Ko, YF., Ju, J.W. Effective transverse elastic moduli of three-phase hybrid fiber-reinforced composites with randomly located and interacting aligned circular fibers of distinct elastic properties and sizes. Acta Mech 224, 157–182 (2013). https://doi.org/10.1007/s00707-012-0744-7

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  • DOI: https://doi.org/10.1007/s00707-012-0744-7

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