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Finite-Fiber Model in the Three-Dimensional Theory of Stability of Composites (Review)

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International Applied Mechanics Aims and scope

Results obtained using the three-dimensional linearized theory of stability of deformable bodies (TLTSDB) and the new so-called finite-fiber model for fibrous and laminated composites are reviewed and compared with the results previously obtained using the well-known infinite-fiber model. The article consists of two parts.

The first part is a short historical sketch of experimental and theoretical studies into the following two problems: (i) microbuckling of composites and (ii) failure or fracture of composites when microbuckling is the initial stage of the process. The applicability of the infinite-an d finite-fiber models to various composites is confirmed by analyzing experimental results obtained by various authors. The second part is a brief review of theoretical results obtained using the TLTSDB and the finite-fiber model for fibrous and laminated composites. The buckling problem is solved for the following cases: one and two short fibers, a periodic row of short fibers, and short fibers near a free boundary. The influence of mechanical and geometric parameters of the composite components on the critical strain and buckling of reinforcement is analyzed. The results for the finite-fiber model were obtained by solving a plane problem and considering the prospects for solving spatial problems, which is very important

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References

  1. A. Ya. Gol’dman, N. F. Savel’eva, and V. I. Smirnov, “Mechanical properties of glass fabric-reinforced plastics in tension and compression normal to the plane of reinforcement,” Mech. Comp. Mater., 4, No. 4, 643–648 (1968).

  2. A. N. Guz, “On setting up a stability theory of unidirectional fibrous materials,” Int. Appl. Mech., 5, No. 2, 156–162 (1969).

    ADS  Google Scholar 

  3. A. N. Guz, “Determining the theoretical compressive strength of reinforced materials,” Dokl. AN USSR, Ser. A, No. 3, 236–238 (1969).

  4. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).

    Google Scholar 

  5. À. N. Guz, Stability of Elastic Bodies Subject to Finite Deformations [in Russian], Naukova Dumka, Kyiv (1973).

    Google Scholar 

  6. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).

    MATH  Google Scholar 

  7. À. N. Guz, Fracture Mechanics of Compressed Composite Materials [in Russian], Naukova Dumka, Kyiv (1990).

    Google Scholar 

  8. A. N. Guz, Fundamentals of the Fracture Mechanics of Compressed Composites [in Russian], in 2 vols., Litera, Kyiv (2008).

  9. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Plane problems of stability of composite materials with a finite-size filler,” Mech. Comp. Mater., 36, No. 1, 49–54 (2000).

    Article  Google Scholar 

  10. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Stability of composites with reinforcement of finite size in plane strain conditions,” Izv. Vuzov (Severokavkaz. Region), Special issue, 60–63 (2001).

  11. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Interaction of short fibers in a matrix during loss of stability: Plane problem,” in: Problems of Mechanics [in Russian], Fizmatlit, Moscow (2003), pp. 331–341.

  12. A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], Akademperiodika, Kyiv (2010).

    MATH  Google Scholar 

  13. A. N. Guz, M. A. Cherevko, G. G. Margolin, and I. M. Romashko, “Failure of unidirectional boron-reinforced aluminum composites in compression,” Mech. Comp. Mater., 22, No. 2, 158–162 (1986).

    Article  Google Scholar 

  14. V. A. Dekret, “Solving the plane buckling problem for a composite reinforced with two short fibers,” Dop. NANU, No. 8, 37–40 (2003).

  15. V. A. Dekret, “Plane buckling problem for a composite reinforced with two parallel short fibers,” Dop. NANU, No. 12, 38–41 (2003).

  16. V. A. Dekret, “Stability of a composite reinforced with a periodic row of inline short fibers,” Dop. NANU, No. 11, 47–50 (2004).

  17. V. A. Dekret, “Stability of a composite reinforced with a periodic row of parallel short fibers,” Dop. NANU, No. 12, 41–44 (2004).

  18. V. A. Dekret, “Stability of a composite under-reinforced with short fibers near the free surface,” Dop. NANU, No. 10, 49–51 (2006).

  19. L. J. Broutman and R. H. Krock (eds.), Composite Materials, in 8 vols., Academic Press, New York–London (1974–1975).

  20. A. Lawley and M. J. Koczak, “Role of the interface on elastic–plastic composite behavior,” in: A. G. Metcalfe (ed.), Interfaces in Metal Matrix Composites, Vol. 1 of the eight-volume series Composite Materials, Academic Press, New York (1974), p. 212.

    Google Scholar 

  21. Yu. M. Tarnopol’skii (ed.), Methods for Static Testing of Reinforced Plastics [in Russian], Zinatne, Riga (1972).

  22. V. V. Panasyuk (ed.), Fracture Mechanics and Structural Strength: Handbook [in Russian], in 4 vols., Kyiv, Naukova Dumka (1988–1990).

  23. A. N. Guz (ed.), Mechanics of Composite Materials [in Russian], in 12 vols, Naukova Dumka (Vols. 1–4), A.S.K. (Vols. 5–12), Kyiv (1993–2003).

  24. H. S. Katz and J. V. Milevski, Handbook of Fillers and Reinforcements for Plastics [Russian translation], Khimiya, Moscow (1981).

    Google Scholar 

  25. H. Liebowitz (ed.), Fracture. An Advanced Treatise, in 7 vols., Academic Press, New York–London (1968–1975).

  26. B. W. Rosen, “Mechanics of composite strengthening,” in: Fiber Composite Materials, American Society of Metals, Metals Park, Ohio (1965), pp. 37–75.

  27. B. W. Rosen and N. F. Dow, “Mechanics of failure of fibrous composites,” in: H. Liebowitz (ed.), Fracture, An Advanced Treatise, Vol. 7, Academic Press, New York (1972), pp. 612–672.

    Google Scholar 

  28. C. C. Chamis, “Microscopic strength theories,” in: L. J. Broutman (ed.), Fracture and Fatigue, Vol. 5 of the eight-volume series Composite Materials, Academic Press, New York (1974), pp. 93–151.

  29. G. P. Cherepanov, Fracture Mechanics of Composite Materials [in Russian], Nauka, Moscow (1983).

    MATH  Google Scholar 

  30. I. Yu. Babich and A. N. Guz, “Deformation instability of laminated materials,” Sov. Appl. Mech., 5, No. 5, 488–491 (1969).

    Article  ADS  Google Scholar 

  31. H. Budiansky, “Micromechanics,” Compos. Struct., 16, No. 1, 3–13 (1983).

    Article  MATH  Google Scholar 

  32. H. Budiansky and N. A. Fleck, “Compressive failure of fibre composites,” J. Mech. Phys. Solids, 41, No. 1, 183–211 (1993).

    Article  ADS  Google Scholar 

  33. H. Budiansky and N. A. Fleck, “Compressive kinking of fibre composites: a topical review,” Appl. Mech. Rev., 47, No. 6, Pt. 2, 246–250 (1994).

  34. A. Kelly and C. Zweben, Comprehensive Composite Materials, in 6 vols., Elsevier (2006).

  35. Ian Milne, R. O. Ritchie, and B. Karihaloo, Comprehensive Structural Integrity, in 10 vols., Elsevier (2006).

  36. V. A. Dekret, “Two-dimensional buckling problem for a composite reinforced with a periodic row of collinear short fibers,” Int. Appl. Mech., 42, No. 6, 684–691 (2006).

    Article  ADS  Google Scholar 

  37. V. A. Dekret, “Plane stability problem for a composite reinforced with a periodic row of parallel fibers,” Int. Appl. Mech., 44, No. 5, 498–504 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  38. V. A. Dekret, “Near-surface instability of composites weakly reinforced with short fibers,” Int. Appl. Mech., 44, No. 6, 619–625 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  39. N. F. Dow and I. J. Gruntfest, “Determination of most needed potentially possible improvements in materials for ballistic and space vehicles,” General Electric Co., Space Sci. Lab., TIRS 60 SD 389, June (1960).

  40. N. A. Fleck, “Compressive failure of fiber composites,” in: Advances in Applied Mechanics, Vol. 33, Academic Press, New York (1997), pp. 43–119.

  41. A. N. Guz, “Mechanics of composite-material failure under axial compression (brittle failure),” Sov. Appl. Mech., 18, No. 10, 863–872 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  42. A. N. Guz, “Stability theory for unidirectional fiber-reinforced composites,” Int. Appl. Mech., 32, No. 8, 577–586 (1996).

    Article  ADS  MATH  Google Scholar 

  43. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).

    Book  MATH  Google Scholar 

  44. A. N. Guz, “On one two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).

    Article  ADS  MATH  Google Scholar 

  45. A. N. Guz, “Establishing the foundations of the mechanics of fracture of materials compressed along cracks (review),” Int. Appl. Mech., 50, No. 1, 1–57 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  46. A. N. Guz and I. A. Guz, “On the theory of stability of laminated composites,” Int. Appl. Mech., 35, No. 4, 323–329 (1999).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. A. N. Guz and I. A. Guz, “On models in the theory of stability of multi-walled carbon nanotubes,” Int. Appl. Mech., 40, No. 1, 1–29 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  48. A. N. Guz and V. A. Dekret, “On two models in the three-dimensional theory of stability of composites,” Int. Appl. Mech., 44, No. 8, 839–854 (2008).

    Article  ADS  Google Scholar 

  49. A. N. Guz and V. A. Dekret, “Interaction of two parallel short fibers in the matrix at loss of stability,” Computer Modeling in Engineering & Sciences, 13, No. 3, 165–170 (2006).

  50. A. N. Guz and V. A. Dekret, “Stability problem of composite material reinforced by periodical row of short fibers,” Computer Modeling in Engineering & Sciences, 42, No. 3, 177–186 (2009).

    Google Scholar 

  51. A. N. Guz and V. A. Dekret, “Stability loss in nanotube reinforced composites,” Computer Modeling in Engineering & Sciences, 49, No. 1, 69–80 (2009).

    MATH  Google Scholar 

  52. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Solution of plane problems of the three-dimensional stability of a ribbon-reinforced composite,” Int. Appl. Mech., 36, No. 10, 1317–1328 (2000).

    Article  ADS  MATH  Google Scholar 

  53. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Planar stability problem of composite weakly reinforced by short fibers,” Mech. Comp. Mater. Struct., No. 12, 313–317 (2005).

    Article  Google Scholar 

  54. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Two-dimensional stability problem for interacting short fibers in a composite: In-line arrangement,” Int. Appl. Mech., 40, No. 9, 994–1001 (2004).

    Article  ADS  MATH  Google Scholar 

  55. A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “A micromechanics solutions of a 3D internal instability problem for a fiber series on an infinite matrix,” Int. J. Fracture, 116, No. 3, L55–L60 (2002).

    Article  Google Scholar 

  56. A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “3D model and estimation of fiber interaction effects during internal instability in non-linear composites,” Int. J. Fracture, 134, No. 3–4, L45–L51 (2005).

    Article  MATH  Google Scholar 

  57. A. N. Guz, A. A. Kritsuk, and R. F. Emel’yanov, “Character of the failure of unidirectional glass-reinforced plastic in compression,” Sov. Appl. Mech., 5, No. 9, 997–999 (1969).

    Article  ADS  Google Scholar 

  58. A. N. Guz and A. N. Samborskaya, “General stability problem of a series of fibers in an elastic matrix,” Sov. Appl. Mech., 27, No. 3, 223–230 (1991).

    Article  ADS  MATH  Google Scholar 

  59. H. Katz and J. V. Milevski (eds.), Handbook of Fillers and Reinforcements for Plastics, Van Nostrand Reinhold Company, New York (1978).

    Google Scholar 

  60. Ch. Jochum and J.-C. Grandidier, “Microbuckling elastic modeling approach of a single carbon fiber embedded in an epoxy matrix,” Compos. Sci. Techn., 64, 2441–2449 (2004).

    Article  Google Scholar 

  61. A. A. Kaminsky, “Mechanics of the delayed fracture of viscoelastic bodies with cracks: Theory and experiment (review),” Int. Appl. Mech., 50, No. 5, 485–548 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. L. P. Khoroshun and L. V. Nazarenko, “Deformation and damage of composites with anisotropic components (review),” Int. Appl. Mech., 49, No. 4, 388–455 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. Yu. V. Kokhanenko, “Numerical study of three-dimensional stability problems for laminated and ribbon-reinforced composites,” Int. Appl. Mech., 37, No. 3, 317–345 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. O. Lourie, D. M. Cox, and H. D. Wagner, “Buckling and collapse of embedded carbon nanotubes,” Phys. Rev. Letters, 81, No. 8, 1638–1641 (1998).

    Article  ADS  Google Scholar 

  65. “Micromechanics of composite materials: Focus on Ukrainian research,” Appl. Mech. Rev., 45, Special issue, 13–101 (1992).

  66. M. R. Pinnel and F. Lawley, “Correlation on uniaxial yielding and substructure in aluminium–stainless steel composites,” Metall. Trans., 1, No. 5, 929–933 (1970).

    Google Scholar 

  67. B. W. Rosen, “Mechanics of composite strengthening,” in: Fiber Composite Materials, American Society for Metals, Metals Park, Ohio (1965), pp. 37–75.

  68. M. A. Sadovsky, S. L. Pu, and M. A. Hussain, “Buckling of microfibers,” J. Appl. Mech., 34, No. 4, 295–302 (1967).

    Google Scholar 

  69. Satish Kumar, Tensuya Uchida, Thuy Dang, Xiefei Zhang, and Young-Bin Park, “Polymer/carbon nano fiber composite fibers,” SAMPE-2004, Long Beach, CA, May 16–20 (2004).

  70. H. Schuerch, “Prediction of compressive strength in uniaxial boron fiber metal matrix composite material,” AIAA J., 4, No. 1, 102–106 (1966).

    Article  ADS  Google Scholar 

  71. H. R. Shetty and T. W. Chou, “Mechanical-properties and failure characteristics of FP-aluminum and W-aluminum composites,” Metall. Trans. A, 16, No. 5, 853–864 (1985).

    Article  Google Scholar 

  72. C. Soutis, N. A. Flek, and P. A. Smith, “Failure prediction technique for compression loaded carbon fibre-epoxy laminate with open holes,” J. Comp. Mat., 25, 1476–1498 (1991).

    Google Scholar 

  73. E. T. Thostenson and T. W. Chou, “Nanotube buckling in aligned multi-wall carbon nanotube composites,” Carbon, 42, No. 14, 3015–3018 (2004).

    Article  Google Scholar 

  74. M. A. Wadee, G. W. Hunt, and M. A. Peletier, “Kink band instability in layered structures,” J. Mech. Phys. Solids, 52, 1071–1091 (2004).

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    A. N. Guz & V. A. Dekret

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  1. A. N. Guz
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  2. V. A. Dekret
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Correspondence to A. N. Guz.

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Translated from Prikladnaya Mekhanika, Vol. 52, No. 1, pp. 3–77, January–February, 2016.

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Guz, A.N., Dekret, V.A. Finite-Fiber Model in the Three-Dimensional Theory of Stability of Composites (Review). Int Appl Mech 52, 1–48 (2016). https://doi.org/10.1007/s10778-016-0730-1

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