Advertisement

A re-formulation of the Mori–Tanaka method for predicting material properties of fiber-reinforced polymers/composites

  • Jing Pan
  • Lichun BianEmail author
Original Contribution

Abstract

In this investigation, a re-formulation has been developed to investigate the effect of fiber aspect ratio on the effective elastic moduli of fiber-reinforced polymers/composites. The matrix and inclusions are considered as isotropic materials. The five independent elastic constants are derived based on a modified Mori–Tanaka theory. The relationship between composite elastic constants and inclusion aspect ratio is also established. Three types of composites containing unidirectional aligned fiber and two-dimensional and three-dimensional random orientated inclusions are explicitly analyzed. Moreover, three extreme cases involving long fibers, spheres, and thin discs are taken into account. It is found that the longitudinal elastic properties are very sensitive to fiber-like inclusions, whereas the transverse elastic properties are closely related to disc-like inclusions.

Keywords

Fiber Elastic constants Aspect ratio Composite materials 

Notes

Funding

This study was funded by the Science Research Foundation of Hebei Advanced Institutes (ZD2017075) and Graduate Innovation Research Assistant Support Project of Yanshan University (CXZS201708).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

References

  1. 1.
    Rodríguez-Ramos R, Guinovart-Díaz R, Bravo-Castillero J, Sabina FJ, Berger H, Kari S, Gabbert U (2009) Variational bounds for anisotropic elastic multiphase composites with different shapes of inclusions. Arch Appl Mech 79(8):695–708CrossRefGoogle Scholar
  2. 2.
    Wang J, Pyrz R (2004) Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part I: basic theory and formulas. Compos Sci Technol 64(7):925–934CrossRefGoogle Scholar
  3. 3.
    Pan J, Bian LC (2017) Influence of agglomeration parameters on carbon nanotube composites. Acta Mech 228(6):2207–2217CrossRefGoogle Scholar
  4. 4.
    Pan J, Bian LC, Zhao HC et al (2016) A new micromechanics model and effective elastic modulus of nanotube reinforced composites. Comput Mater Sci 113:21–26CrossRefGoogle Scholar
  5. 5.
    Lee KY, Paul DR (2005) A model for composites containing three-dimensional ellipsoidal inclusions. Polymer 46(21):9064–9080CrossRefGoogle Scholar
  6. 6.
    Kashtalyan M, Sinchuk Y, Piat R, Guz I (2016) Analysis of multiple cracking in metal/ceramic composites with lamellar microstructure. Arch Appl Mech 86(1–2):177–188CrossRefGoogle Scholar
  7. 7.
    Kordkheili SAH, Toozandehjani H (2014) Effective mechanical properties of unidirectional composites in the presence of imperfect interface. Arch Appl Mech 84(6):807–819CrossRefGoogle Scholar
  8. 8.
    Lee JK, Kim JG (2013) Model for predicting effective thermal conductivity of composites with aligned continuous fibers of graded conductivity. Arch Appl Mech 83(11):1569–1575CrossRefGoogle Scholar
  9. 9.
    Zhao YH, Tandon GP, Weng GJ (1989) Elastic moduli for a class of porous materials. Acta Mech 76(1–2):105–130CrossRefGoogle Scholar
  10. 10.
    Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574CrossRefGoogle Scholar
  11. 11.
    Benveniste Y (1987) A new approach to the application of Mori-Tanaka's theory in composite materials. Mech Mater 6(2):147–157CrossRefGoogle Scholar
  12. 12.
    Walpole LJ (1981) Elastic behavior of composite materials: theoretical foundations. Adv Appl Mech 21:169–242CrossRefGoogle Scholar
  13. 13.
    Choi MO, Kim YJ (2018) Effect of poly (3-hydroxybutyrate-co-3-hydroxyvalerate) /gelatin ratios on the characteristics of biomimetic composite nanofibrous scaffolds. Colloid Polym Sci 296(5):917–926CrossRefGoogle Scholar
  14. 14.
    Panda S, Reddy NH, Kumar ASP (2015) Design and finite element analysis of a short piezoelectric fiber-reinforced composite actuator. Arch Appl Mech 85(5):691–711CrossRefGoogle Scholar
  15. 15.
    Bian LC, Zhao HC (2015) Elastic properties of a single-walled carbon nanotube under a thermal environment. Compos Struct 121:337–343CrossRefGoogle Scholar
  16. 16.
    Sindu BS, Sasmal S (2015) Evaluation of mechanical characteristics of nano modified epoxy based polymers using molecular dynamics. Comput Mater Sci 96:146–158CrossRefGoogle Scholar
  17. 17.
    Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222CrossRefGoogle Scholar
  18. 18.
    Chang CI, Conway HD, Weaver TC (1972) The elastic constants and bond stresses for a three-dimensional composite reinforced by discontinuous fibers. Fibre Sci Technol 5(2):143–162CrossRefGoogle Scholar
  19. 19.
    Russel WB (1973) On the effective moduli of composite materials: effect of fiber length and geometry at dilute concentrations. Zeitschrift Für Angewandte Mathematik Und Physik Zamp 24(4):581–600CrossRefGoogle Scholar
  20. 20.
    Tandon GP, Weng GJ (1986) Average stress in the matrix and effective moduli of randomly oriented composites. Compos Sci Technol 27(2):111–132CrossRefGoogle Scholar
  21. 21.
    Jarali CS, Patil SF, Pilli SC, Lu YC (2013) Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix. J Mater Sci 48(8):3160–3172CrossRefGoogle Scholar
  22. 22.
    Tian W, Qi L, Zhou J, Guan J (2014) Effects of the fiber orientation and fiber aspect ratio on the tensile strength of C sf/Mg composites. Comput Mater Sci 89(12):6–11CrossRefGoogle Scholar
  23. 23.
    Halpin JC, Tsai SW (1967) Environmental factors in composite materials design. Air force technical. Report:67–423Google Scholar
  24. 24.
    Thomason JL (2008) The influence of fibre length, diameter and concentration on the modulus of glass-fibre reinforced polyamide 6, 6. Compos A Appl Sci Manuf 39(11):1732–1738CrossRefGoogle Scholar
  25. 25.
    Tucker Iii CL, Liang E (1999) Stiffness predictions for unidirectional short-fiber composites: review and evaluation. Compos Sci Technol 59(5):655–671CrossRefGoogle Scholar
  26. 26.
    Ferrari M, Johnson GC (1989) The effective elasticities of short-fiber composites with arbitrary orientation distribution. Mech Mater 8:67–73CrossRefGoogle Scholar
  27. 27.
    Chen CH, Cheng CH (1996) Effective elastic moduli of misoriented short-fiber composites. Int J Solids Struct 33:2519–2539CrossRefGoogle Scholar
  28. 28.
    Böhm HJ (2004) Modeling the mechanical behavior of short fiber reinforced composites, in “Mechanics of Microstructured Materials” (Ed. H.J.Böhm). Springer–Verlag, Vienna 41–56Google Scholar
  29. 29.
    Giordano S (2005) Order and disorder in heterogeneous material microstructure: electric and elastic characterisation of dispersions of pseudo-oriented spheroids. Int J Eng Sci 43:1033–1058CrossRefGoogle Scholar
  30. 30.
    Marzari N, Ferrari M (1992) Textural and micromorphological effects on the overall elastic response of macroscopically anisotropic composites. J Appl Mech 59:269–275CrossRefGoogle Scholar
  31. 31.
    Berryman JG, Berge PA (1996) Critique of two explicit schemes for estimating elastic properties of multiphase composites. Mech Mater 22:149–164CrossRefGoogle Scholar
  32. 32.
    Allen DH, Lee JW (1990) The effective thermoelastic properties of whisker-reinforced composites as functions of material forming parameters. In: Weng GJ, Taya M, Abé H (eds) Micromechanics and Inhomogeneity. Springer-Verlag, New York, pp 17–40CrossRefGoogle Scholar
  33. 33.
    Pettermann HE, Böhm HJ, Rammerstorfer FG (1997) Some direction dependent properties of matrix–inclusion type composites with given reinforcement orientation distributions. Composites B 28:253–265CrossRefGoogle Scholar
  34. 34.
    Mlekusch B (1999) Thermoelastic properties of short-fibre-reinforced thermoplastics. Compos Sci Technol 59:911–923CrossRefGoogle Scholar
  35. 35.
    Hong GK, Kwac LK (2009) Evaluation of elastic modulus for unidirectionally aligned short fiber composites. J Mech Sci Technol 23(1):54–63CrossRefGoogle Scholar
  36. 36.
    Richard TG (1975) The mechanical behavior of a solid microsphere filled composite. J Compos Mater 9(2):108–113CrossRefGoogle Scholar
  37. 37.
    Norris AN (1990) The mechanical properties of platelet reinforced composites. Int J Solids Struct 26(5):663–674CrossRefGoogle Scholar
  38. 38.
    Pettermann HE, Böhm HJ, Alcalá J (2002) Normalized diagrams for micromechanical estimates of the elastic response of composite materials. Metall Mater Trans A 33(10):3187–3199CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei ProvinceYanshan UniversityQinhuangdaoPeople’s Republic of China

Personalised recommendations