Estimation of elastic moduli of particulate-reinforced composites using finite element and modified Halpin–Tsai models

  • I. Alfonso
  • I. A. Figueroa
  • V. Rodriguez-Iglesias
  • C. Patiño-Carachure
  • A. Medina-Flores
  • L. Bejar
  • L. Pérez
Technical Paper


In this paper, the effect of particle geometry on Young’s modulus for particulate-reinforced composites was estimated using finite elements analysis (FEA) and modified Halpin–Tsai (HT) equations, including not only the effect of the aspect ratio but also the particle shape. This modified HT model includes a new parameter (a) which depends on the angle of the particle corners. FEA was used as a starting point to find the composites behavior depending on the reinforcement features, results that were compared to experimental values. Young’s moduli and stresses distribution were estimated using an AlA356/SiC(p) composite as starting material . Selected particle geometries for modeling were cylinders, truncated cylinders, double cones, and double-truncated cones; while aspect ratios were modified from 0.6 to 1.8. There was an excellent agreement between experimental results, FEA, and modified Halpin–Tsai estimations, showing that the predicting ability of the Halpin–Tsai model could be improved by introducing different shape parameters.


Composite FEA Halpin–Tsai Angle Particles 



The authors would like to acknowledge the financial support from SENER–CONACYT 151496 and UNAM PAPIIT TA100114 for funding the project.


  1. 1.
    Engineered Materials Handbook. Volume 1: Composites (1989). ASM International, Metals Park, OhioGoogle Scholar
  2. 2.
    Manna A, Bains HS, Mahapatra PB (2010) Experimental study on fabrication of Al–Al2O3/Grp metal matrix composites. J Compos Mater 45:2003–2010CrossRefGoogle Scholar
  3. 3.
    Everett RK, Arsenault RJ (eds) (1991) Metal matrix composites: processing and interface. Academic Press, New YorkGoogle Scholar
  4. 4.
    Wilson S, Ball A (1990) Tribology of composite material. ASM International, Metals Park, OhioGoogle Scholar
  5. 5.
    Rafiee M, He XQ, Mareishi S, Liew KM (2014) Modeling and stress analysis of smart CNTs/fiber/polymer multiscale composite plates. Int J Appl Mech 6(3):23CrossRefGoogle Scholar
  6. 6.
    Hashin Z, Rosen BW (1964) The elastic moduli of fiber-reinforced materials. J Appl Mech 31(2):223–232. doi: 10.1115/1.3629590 CrossRefGoogle Scholar
  7. 7.
    Feng S, Cui X, Li G (2014) Thermo-mechanical analyses of composite structures using face-based smoothed finite element method. Int J Appl Mech 6(2):17CrossRefGoogle Scholar
  8. 8.
    Aghdam MM, Smith DJ, Pavier MJ (2000) Finite element micromechanical modelling of yield and collapse behaviour of metal matrix composites. J Mech Phys Solids 48:499–528CrossRefMATHGoogle Scholar
  9. 9.
    Halpin JC, Tsai SW (1967) Environmental factors in composite materials design. Air Force Materials Laboratory, TR 67-423Google Scholar
  10. 10.
    Wu Y, Jia Q, Sheng D, Zhang L (2004) Modeling Young’s modulus of rubber–clay nanocomposites using composite theories. Polym Test 23(8):903–909CrossRefGoogle Scholar
  11. 11.
    Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis, 3rd edn. Wiley, New YorkMATHGoogle Scholar
  12. 12.
    Ganesh VV, Chawla N (2005) Effect of particle orientation anisotropy on the tensile behavior of metal matrix composites: experiments and microstructure-based simulation. Mater Sci Eng A 391:342–353CrossRefGoogle Scholar
  13. 13.
    Kari S, Berger H, Gabbert U (2007) Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites. Comput Mater Sci 39:198–204CrossRefGoogle Scholar
  14. 14.
    Liu YJ, Chen XL (2003) Continuum models of carbon nanotube-based composites using the boundary element method. Electron J Boundary Elem 1:316–335MathSciNetGoogle Scholar
  15. 15.
    Pahlavanpour M, Moussaddy HH, Ghossein E, Hubert P, Levesque M (2013) Prediction of elastic properties in polymer–clay nanocomposites: analytical homogenization methods and 3D finite element modeling. Comput Mater Sci 79:206–215CrossRefGoogle Scholar
  16. 16.
    Alfonso I, Figueroa IA, Sierra JM, Abatal M, Gonzalez G, Rodriguez-Iglesias V, Medina-Flores A, Flores JE (2013) Young’s modulus estimation based on high symmetry 3-D finite element model for metal matrix composites. Comput Mater Sci 69:304–310CrossRefGoogle Scholar
  17. 17.
    Karevan M, Pucha RV, Bhuiyan MdA, Kalaitzidoul K (2010) Effect of interphase modulus and nanofiller agglomeration on the tensile modulus of graphite nanoplatelets and carbon nanotube reinforced polypropylene nanocomposites. Carbon Lett 11:325–331CrossRefGoogle Scholar
  18. 18.
    Huang Y, Jin KK, Ha SK (2008) Effects of fiber arrangement on mechanical behavior of unidirectional composites. J Compos Mater 42:1851–1871CrossRefGoogle Scholar
  19. 19.
    Jung HK, Cheong YM, Ryu HJ, Hong SH (1999) Analysis of anisotropy in elastic constants of SiCp/2124 Al metal matrix composites. Scripta Mater 41:1261–1267CrossRefGoogle Scholar
  20. 20.
    McLean A, Soda H, Xia Q, Pramanick AK, Ohno A, Motoyasu G, Shimizu T, Gedeon SA, North T (1997) SiC particulate-reinforced aluminium-matrix composite rods and wires produced by a new continuous casting route. Compos Part A 28:153–162CrossRefGoogle Scholar
  21. 21.
    Gurrum SP, Zhao J, Edwards DR (2011) Inclusion interaction and effective material properties in a particle-filled composite material system. J Mater Sci 46(1):101–107. doi: 10.1007/s10853-010-4844-2 CrossRefGoogle Scholar
  22. 22.
    Engineered Materials Handbook. Volume 2: Properties and Selection: Nonferrous Alloys and Special-Purpose Materials (1990) ASM International, Metals Park, OhioGoogle Scholar
  23. 23.
    Chawla N, Shen Y (2001) Mechanical behavior of particle reinforced metal matrix composites. Adv Eng Mater 3:357–370CrossRefGoogle Scholar
  24. 24.
    Chawla N, Chawla KK (2006) Microstructure-based modeling of the deformation behavior of particle reinforced metal matrix composites. J Mater Sci 41:913–925CrossRefGoogle Scholar
  25. 25.
    Srivastava VK, Gabbert U (2011) Analysis of particles loaded fiber composites for the evaluation of effective material properties with the variation of shape and size. Int J Eng Sci Technol 3:52–68Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2015

Authors and Affiliations

  • I. Alfonso
    • 1
  • I. A. Figueroa
    • 2
  • V. Rodriguez-Iglesias
    • 3
  • C. Patiño-Carachure
    • 3
  • A. Medina-Flores
    • 4
  • L. Bejar
    • 4
  • L. Pérez
    • 5
  1. 1.Unidad Morelia, Instituto de Investigaciones en MaterialesUniversidad Nacional Autónoma de MéxicoMoreliaMexico
  2. 2.Instituto de Investigaciones en MaterialesUniversidad Nacional Autónoma de MéxicoMexicoMexico
  3. 3.Facultad de IngenieríaUniversidad Autónoma del CarmenCarmenMexico
  4. 4.Universidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  5. 5.Department of Mechanical Engineering, Advanced Center for Electrical and Electronic Engineering (Basal Project FB0008)Universidad Técnica Federico Santa MaríaValparaisoChile

Personalised recommendations