Advertisement

Computational Particle Mechanics

, Volume 6, Issue 1, pp 29–44 | Cite as

A mathematical model for thermal expansion coefficient of periodic particulate composites

  • E. SideridisEmail author
  • J.  Venetis
Article
  • 30 Downloads

Abstract

In this work, the authors introduce an octahedral body centered model transformed into a nine-layer spherical model, to simulate the periodic microstructure of particulate composites. This model takes into account the vicinity of internal and neighboring particles in the form of their deterministic configurations inside the matrix, along with the concept of interphase on the thermomechanical properties of the overall material. The latter is assumed to be homogeneous and isotropic. Next, by the use of this model, in association with classical elasticity approach, a closed form expression to calculate the thermal expansion coefficient of this category of composites is derived The theoretical predictions were compared with experimental results as well as with theoretical values yielded by formulae derived from other workers and they were found to be in good agreement.

Keywords

Thermal expansion coefficient Particulate composites Particle dissemination Particle configuration Interphase 

Notes

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interest regarding the publication of this paper

References

  1. 1.
    Nielsen LE (1974) Mechanical properties of polymers and composites, vol 2. Marcel Dekker Inc., New YorkGoogle Scholar
  2. 2.
    Kerner EH (1956) The elastic and thermo-elastic properties of composite media. Proc Phys Soc Lond B69(2):808–813CrossRefGoogle Scholar
  3. 3.
    Hashin Z (1962) The elastic moduli of heterogeneous materials. J Appl Mech 29:143–150MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behavior of multiphase materials. J Mech Phys Solids 11:127–140MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Sideridis E, Papanicolaou GC (1988) A theoretical model for the prediction of thermal expansion behaviour of particulate composites. Rheol Acta 27:608–616CrossRefGoogle Scholar
  6. 6.
    Maxwell JC (1873) Electricity and magnetism. Clarendon, OxfordzbMATHGoogle Scholar
  7. 7.
    Benveniste Y (1987) Effective thermal-conductivity of composites with a thermal contact resistance between the constituents–nondilute case. J Appl Phys 61:2840–2843CrossRefGoogle Scholar
  8. 8.
    Nan CW, Birringer R, Clarke DR, Gleiter H (1997) Effective thermal conductivity of particulate composites with interfacial thermal resistance. J Appl Phys 81:6692–6699CrossRefGoogle Scholar
  9. 9.
    Duan HL, Karihaloo BL, Wang J, Yi X (2006) Effective conductivities of heterogeneous media containing multiple inclusions with various spatial distributions. Phys Rev B 73:174203–174215CrossRefGoogle Scholar
  10. 10.
    Pal R (2007) New models for thermal conductivity of particulate composites. J Reinf Plast Compos 26:7643–7651Google Scholar
  11. 11.
    Balch DK, Fitzgerald TJ, Michaud VJ, Mortensen A, Shen Y-L, Suresh S (1996) Thermal expansion of metals reinforced with ceramic particles and microcellular foams. Metall Mater Trans A 27(11):3700–3717CrossRefGoogle Scholar
  12. 12.
    Roudini G, Tavangar R, Weber L, Mortensen A (2010) Influence of reinforcement contiguity on the thermal expansion of alumina particle reinforced aluminium composites. Int J Mater Res 101:1113–1120CrossRefGoogle Scholar
  13. 13.
    Garboczi EJ, Berryman JG (2000) New effective medium theory for the diffusivity or conductivity of a multi-scale concrete microstructure model. Concr Sci Eng 2:88–96Google Scholar
  14. 14.
    Lutz MP, Zimmerman RW (2005) Effect of an inhomogeneous interphase zone on the bulk modulus and conductivity of a particulate composite. Int J Solids Struct 42:429–437CrossRefzbMATHGoogle Scholar
  15. 15.
    Yin HM, Sun LZ (2005) Elastic modelling of periodic composites with particle interactions. Philos Mag Lett 85(4):163–173CrossRefGoogle Scholar
  16. 16.
    Sideridis E, Venetis J (2014) The stiffness and thermal expansion coefficient of iron particulate epoxy composites defined by considering the particle contiguity. Int Rev Model Simul 7:671–681Google Scholar
  17. 17.
    Sideridis E, Venetis J (2014) Thermal expansion coefficient of particulate composites defined by the particle contiguity. Int J Microstruct Mater Prop 9:292–313Google Scholar
  18. 18.
    Venetis J, Sideridis E (2016) A mathematical model for thermal conductivity of homogeneous composite materials. Indian J Pure Appl Phys 54(5):313–320zbMATHGoogle Scholar
  19. 19.
    Zhang H, Zhang Z, Friedrich K, Eger C (2006) Property improvements of in situ epoxy nanocomposites with reduced interparticle distance at high nanosilica content. Acta Mater 54:1833–1842CrossRefGoogle Scholar
  20. 20.
    Zhou TH, Ruan WH, Mai YL, Rong MZ, Zhang MQ (2008) Performance of nanosilica/ polypropylene composites through in-situ cross-linking approach. Compos Sci Technol 68:2858–2863CrossRefGoogle Scholar
  21. 21.
    Thorvaldsen T, Johnsen BB, Olsen T, Hansen FK (2015) Investigation of theoretical models for the elastic stiffness of nanoparticle-modified polymer composites. J Nanomater 4:1–17CrossRefGoogle Scholar
  22. 22.
    Mirza FA, Chen DL (2015) A unified model for the prediction of yield strength in particulate-reinforced metal matrix nanocomposites. Materials 8:5138–5153CrossRefGoogle Scholar
  23. 23.
    Ye J, Chu C, Zhai Z, Wang Y, Shi B, Qiu Y (2017) The interphase influences on the particle-reinforced composites with periodic particle configuration. Appl Sci 7(1):102CrossRefGoogle Scholar
  24. 24.
    Arthur G, Coulson JA (1964) Physical properties of uranium dioxide-stainless steel cermets. J Nucl Mater 13:242–253CrossRefGoogle Scholar
  25. 25.
    Thomas JP. Effect of Inorganic Fillers on Coefficient of Thermal Expansion of Polymeric Materials, General Dynamics, Fort Worth, Texas, USA AD 287–826.Google Scholar
  26. 26.
    Fahmy AA, Ragai AI (1970) Thermal expansion behaviour of two-phase solids. J Appl Phys 41:5108–5111CrossRefGoogle Scholar
  27. 27.
    Wang TT, Kwei TK (1969) Effect of induced thermal stress on the coefficient of thermal expansion and densities of filled polymers. J Polym Sci 7(5):889–896Google Scholar
  28. 28.
    Malliaris A, Turner DT (1971) Influence of particle size on the electrical resistivity of compacted mixtures of polymeric and metallic powders. J Appl Phys 42:614–618CrossRefGoogle Scholar
  29. 29.
    Tummala RR, Friedberg AL (1970) Thermal expansion of composite materials. Symposium on thermal expansion of solids. J Appl Phys 11(13):5104CrossRefGoogle Scholar
  30. 30.
    Lipatov YS (1977) Physical chemistry of filled polymers. Khimiya, Moscow (Translated from the Russian Moseley RJ International polymer science and technology. Monograph 2; see also Lipatov YS Adv Polym Sci 22:I-59,Google Scholar
  31. 31.
    Theocaris PS (1987) The mesophase concept in composites, polymers—properties and applications. In: Henrici-Olivé G, Olivé S (eds), vol 11. Springer. ISBN: 978-3-642-70184-9 (Print) 978-3-642-70182-5Google Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Section of Mechanics, School of Applied Mathematics and Physical SciencesNTUAAthensGreece

Personalised recommendations