Prediction of Effective Elastic Modulus of Biphasic Composite Materials
Anupama Upadhyay, Ramvir Singh
University of Rajasthan, Jaipur, India.
DOI: 10.4236/mme.2012.21002   PDF    HTML     10,616 Downloads   19,487 Views   Citations

Abstract

Two semi-empirical approaches for prediction of elastic modulus of biphasic composites have been proposed. Developed relations are for pore free matrix and pore free filler and found to depend on nonlinear contribution of volume fraction of constituents as well as ratio of elastic properties of individual phases. These relations are applied for the calculation of effective elastic modulus mainly for Al2O3-NiAl, SiC-Al, Alumina-Zirconia, Al-Al2O3, W-glass and Flax-Resin composite materials. Theoretical predictions using developed relations are compared with experimental data. It is found that the predicted values of effective elastic modulus using modified relations are quite close to the experimental results.

Share and Cite:

A. Upadhyay and R. Singh, "Prediction of Effective Elastic Modulus of Biphasic Composite Materials," Modern Mechanical Engineering, Vol. 2 No. 1, 2012, pp. 6-13. doi: 10.4236/mme.2012.21002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. Voigt, “Ueber die Beziehung Zwischen den Beiden Elasticit?tsconstanten Isotroper K?rper,” Annalen der Phy- sik, Vol. 274, No. 12, 1889, pp. 573-587. doi:10.1002/andp.18892741206
[2] A. Reuss and Z. Angrew, “Berechnung der Flie?grenze von Mischkristallen auf Grund der Plastizit tsbedingung für Einkristalle ,” ZAMM-Journal of Applied Mathematics and Mechanics, Vol. 9, No. 1, 1929, pp. 49-58.
[3] R. Hill, “A Self-Consistent Mechanics of Com-posite Materials,” Journal of the Mechanics and Physics of Solids, Vol. 13, No. 4, 1965, pp. 213-222. doi:10.1016/0022-5096(65)90010-4
[4] B. Budiansky, “On the Elastic Moduli of Some Heterogeneous Materials,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, pp. 223-227. doi:10.1016/0022-5096(65)90011-6
[5] K. Yagi and L. Che, “Elastic Properties of Composite Material with Anisotropic Ellipsoidal Inhomogeneities,” Proceedings of the Fifteenth International Offshore and Polar Engineering Conference, 19-24 June 2005, Seoul, pp. 551-556.
[6] J. M. Molina, S. S. Savinsky and N. V. Khokhriakov, “A Tight Binding Model for Calculations of Structures and Properties of Graphite Nanotubes,” Journal of Chemical Physics, Vol. 104, No. 12, 1996, p. 4652. doi:10.1063/1.471211
[7] J. P. Lu, “Elastic Properties of Carbon Nanotubes and Nanoropes,” Physical Review Letters, Vol. 79, No. 7, 1997, pp. 1297-1300. doi:10.1103/PhysRevLett.79.1297
[8] S. Lijima, C. Brabec, A. Maiti and J. Bernhole, “Structural Flexibility of Carbon Nanotubes,” Journal of Chemical Physics, Vol. 104, No. 5, 1996, p. 2089. doi:10.1063/1.470966
[9] M. M. J. Treacy, T. W. Ebbeson and J. M. Gibson, “Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes Nature,” Nature, Letters to Nature, Vol. 381, 1996, pp. 678-680. doi:10.1038/381678a0
[10] N. G. Chopra and A. Zettl, “Measurement of the Elastic Modulus of a Multiwall Boron Nitride Nanotube,” Solid State Communications, Vol. 105, No. 5, 1998, pp. 297-300. doi:10.1016/S0038-1098(97)10125-9
[11] N. Garshashbinia and J. E. Jam, “Properties in Laminated Composite Plates Using Genetic Algorithm,” Indian Polymer Journal, Vol. 14, No. 1, 2005, pp. 39-46.
[12] J. P. Watt, G. F. Davies and R. J. Cnnel, “Elastic Properties of Composite Materials,” Reviews of Geo-physics, Vol. 14, No .4, 1976, pp. 541-563. doi:10.1029/RG014i004p00541
[13] K. A. Snyder, E. J. Gar-boczi and A. R. Day, “The Elastic Modulii of Simple Two Dimensional Isotropic Composites, Computer Simulation and Effective Medium Theory,” Journal of Applied Physics, Vol. 72, No. 12, 1992, pp. 5948-5955. doi:10.1063/1.351903
[14] M. T. Tilbrook and M. Hottman, “On the Mechanical Properties of Alumina Epoxy Composites with an Inter Penetrating Network Structure,” Materials Science and Engineering: A, Vol. 393, No. 1-2, 2005, pp. 170-178. doi:10.1016/j.msea.2004.10.004
[15] H. F. Zhang, X. S. Ge and H. Ye, “Randomly Mixed Model for Predicting the Effective Thermal Conductivity of Moist Porous Media,” Journal of Physics D: Applied Physic, Vol. 39, No. 1, 2006, pp. 220-226. doi:10.1088/0022-3727/39/1/032
[16] Z. Hashin, “Analysis of Composite Materials—A Survey,” Journal of Applied Mechanics, Vol. 50, No. 3, 1983, pp. 481-505. doi:10.1115/1.3167081
[17] S. Torquato, “Random Heteroge-neous Materials: Micro Structures and Macroscopic Properties,” Applied Mechanics Reviews, Vol. 55, No. 4, 2002, p. B62. doi:10.1115/1.1483342
[18] N. Losic, J. F. Thovert and P. M. Adler, “Reconstruction of Porous Media with Multiple Solid Phases,” Journal of Colloid and Interface Science, Vol. 186, No. 2, 1997, pp. 420-433. doi:10.1006/jcis.1996.4659
[19] D. S. Li, G. Saheli, M. Khaleel and H. Mgarinestani, “Quantitative Prediction of Effective Conductivity in Anisotropic Heterogeneous Media Using Two Point Correlation Functions,” Computational Materials Science, Vol. 38, No. 1, 2006, pp. 45-50. doi:10.1016/j.commatsci.2006.01.004
[20] M. Wang, J. K. Wang, N. N. Pan and S. Y. Chen, “Meso- scopic Predictions of the Effective Thermal Conductivity of Micro Scale Random Porous Media,” Physical Review E, Vol. 75, No. 3, 2007, pp. 260-265.
[21] P. Meakin, “Fractals, Scaling and Growth Far from Equilibrium,” Cambridge University Press, Cambridge, 1998.
[22] P. A. Roberts and E. J. Garboczi, “Elastic Properties of Model Porous Ceramics,” Journal of the American Ceramic Society, Vol. 83, No. 12, 2000, pp. 3041-3048. doi:10.1111/j.1151-2916.2000.tb01680.x
[23] J. Segurado and J. Llorca, “A Numerical Approximation to the Elastic Proper-ties of Sphere-Reinforced Composites,” Journal of the Me-chanics and Physics of Solids, Vol. 50, No. 10, 2002, pp. 2107-2121. doi:10.1016/S0022-5096(02)00021-2
[24] S. Sahraoui, E. Mariez and M. Etchessahar, “Linear Elastic Properties of Anisotropic Open-Cell Foams,” Journal of the Acoustical Society of America, Vol. 110, No. 1, 2001, pp. 635-637. doi:10.1121/1.1378351
[25] W. E. Warren and A. M. Kraynik, “The Linear Elastic Properties of Open-Cell Foams,” Journal of Applied Mechanics, Vol. 55, No. 2, 1988, pp. 341-346. doi:10.1115/1.3173680
[26] W. H. Tuan, Y. P. Pai, “Me-chanical Properties of Al2O3- Nial Composites,” Journal of the American Ceramic Society, Vol. 82, No. 6, 1999, pp. 1624-1626. doi:10.1111/j.1151-2916.1999.tb01974.x
[27] M. F. Ashby, “Criteria for Selecting the Components of Composites,” Acta Metallurgica et Materialia, Vol. 41, No. 5, 1993, pp. 1313-1335. doi:10.1016/0956-7151(93)90242-K
[28] W. H. Tuan, W. B. Chou, H. C. You and S. T. Chang, “The Effects of Microstructure on the Mechanical Properties of Al2O3-Nial Composites,” Materials Chemistry and Physics, Vol. 56, No. 2, 1998, p.157. doi:10.1016/S0254-0584(98)00168-0
[29] C. L. Hsieh, W. H. Tuan and T. T. Wu, “Elastic Behavior of a Model Two-Phase Material,” Journal of the European Ceramic Society, Vol. 24, No. 15-16, 2004, pp. 3789- 3793. doi:10.1016/j.jeurceramsoc.2004.02.002
[30] R. Hill, “Elastic Properties of Reinforced Solids: Some Theoretical Principles,” Journal of the Mechanics and Physics of Solids, Vol. 11, No. 5, 1963, pp. 357-372. doi:10.1016/0022-5096(63)90036-X
[31] W. Koster and H. Franz, “Poisson’s Ratio for Metals and Alloys,” Metallurgical Review, Vol. 6, No. 21, 1961, pp. 1-56.
[32] C. L. Hsieh, W. H. Tuan and T. T. Wu, “Elastic Properties of Ceramic-Metal Par-ticulate Composite,” Material Science and Engineering A, Vol. 393, 2005, pp. 133-139.
[33] L. C. Davis, J. Chen and M. F. Thorpe, “Predicting the Elastic Properties of Composite Materials,” Proceedings of the American Society for Composites—7th Technical Conference, Pennsylvania, 13-15 October 1992, pp. 339-348.
[34] W. Pabst, G. Ticha, E. Gregorova and E. Tynova, “Effective Elastic Properties of Alumina-Zirconia Composite Ceramics, Part-5 Tensile Modulus of Alumina-Zirconia Composite Ceramics,” Ceramics Silikaty, Vol. 49, No. 2, 2005, pp. 77-85.
[35] M. Wang and N. Pan, “Elastic Property of Multiphase Composites with Random Microstructures,” Journal of Computational Physics, Vol. 228, No. 16, 2009, pp. 5978- 5988. doi:10.1016/j.jcp.2009.05.007
[36] D. P. H. Hasselman and R. M. Fulrath, “Effect of Spherical Tungsten Dispersions on Young’s Modulus of a Glass,” Journal of the American Ce-ramic Society, Vol. 48, No. 10, 1965, pp. 548-549. doi:10.1111/j.1151-2916.1965.tb14668.x
[37] D. Bolcu, G. Stanescu and M. Ursache, “Theoretical and Experimental Study on Determination of the Elastic Properties for Composite Materi-als,” Romanian Reports in Physics, Vol. 56, No. 1, 2004, pp. 3-12.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.