Research Papers

Three-Phase Cylinder Model of One-Dimensional Hexagonal Piezoelectric Quasi-Crystal Composites

[+] Author and Article Information
Junhong Guo

Department of Mechanics,
Inner Mongolia University of Technology,
Hohhot 010051, China
e-mail: jhguo@imut.edu.cn

Ernian Pan

Fellow ASME
Department of Civil Engineering,
The University of Akron,
Akron, OH 44325-3905
e-mail: pan2@uakron.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 27, 2016; final manuscript received May 10, 2016; published online June 2, 2016. Assoc. Editor: M Taher A Saif.

J. Appl. Mech 83(8), 081007 (Jun 02, 2016) (10 pages) Paper No: JAM-16-1113; doi: 10.1115/1.4033649 History: Received February 27, 2016; Revised May 10, 2016

A three-phase cylinder model (inclusion/matrix/composite) is proposed and analyzed for one-dimensional (1D) piezoelectric quasi-crystal composites. The exact closed-form solutions of the stresses of the phonon and phason fields and the electric field are derived under far-field antiplane mechanical and in-plane electric loadings via the Laurent expansion technique. Numerical results show that the thickness and material properties of the interphase layer can significantly affect the induced fields in the inclusion and interphase layer. Furthermore, the generalized self-consistent method is applied to predict analytically the effective moduli of the piezoelectric quasi-crystal composites. It is observed from the numerical examples that the effective moduli of piezoelectric quasi-crystal composites are very sensitive to the fiber volume fraction as well as to the individual material properties of the fiber and matrix. By comparing QC/PE with QC1/QC2, PE/QC, and PZT-7/epoxy, we found that using QC as fiber could, in general, enhance the effective properties, a conclusion which is in agreement with the recent experimental results.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Shechtman, D. , Blech, I. , Gratias, D. , and Cahn, J. W. , 1984, “ Metallic Phase With Long-Range Orientational Order and No Translational Symmetry,” Phys. Rev. Lett., 53(20), pp. 1951–1953. [CrossRef]
Thiel, P. A. , and Dubois, J. M. , 1999, “ Quasicrystals. Reaching Maturity for Technological Applications,” Mater. Today, 2(3), pp. 3–7. [CrossRef]
Sakly, A. , Kenzari, S. , Bonina, D. , Corbel, S. , and Fournée, V. , 2014, “ A Novel Quasicrystal-Resin Composite for Stereolithography,” Mater. Des., 56, pp. 280–285. [CrossRef]
Guo, X. P. , Chen, J. F. , Yu, H. L. , Liao, H. L. , and Coddet, C. , 2015, “ A Study on the Microstructure and Tribological Behavior of Cold-Sprayed Metal Matrix Composites Reinforced by Particulate Quasicrystal,” Surf. Coat. Technol., 268, pp. 94–98. [CrossRef]
Zhang, Y. , Zhang, J. , Wu, G. H. , Liu, W. C. , Zhang, L. , and Ding, W. J. , 2015, “ Microstructure and Tensile Properties of As-Extruded Mg-Li-Zn-Gd Alloys Reinforced With Icosahedral Quasicrystal Phase,” Mater. Des., 66(A), pp. 162–168. [CrossRef]
Tian, Y. , Huang, H. , Yuan, G. Y. , Chen, C. L. , Wang, Z. C. , and Ding, W. J. , 2014, “ Nanoscale Icosahedral Quasicrystal Phase Precipitation Mechanism During Annealing for Mg-Zn-Gd-Based Alloys,” Mater. Lett., 130, pp. 236–239. [CrossRef]
Hu, C. Z. , Wang, R. , Ding, D. H. , and Yang, W. , 1997, “ Piezoelectric Effects in Quasicrystals,” Phys. Rev. B, 56(5), pp. 2463–2468. [CrossRef]
Fujiwara, T. , Laissardiere, G. T. , and Yamamoto, S. , 1994, “ Electronic Structure and Electron Transport in Quasicrystals,” Mater. Sci. Forum, 150–151, pp. 387–394. [CrossRef]
Zhang, D. L. , 2010, “ Electronic Properties of Stable Decagonal Quasicrystals,” Phys. Status Solidi A, 207(12), pp. 2666–2673. [CrossRef]
Yang, W. G. , Wang, R. , Ding, D. H. , and Hu, C. Z. , 1995, “ Elastic Strains Induced by Electric Fields in Quasicrystals,” J. Phys. Condens. Matter, 7(39), pp. L499–L502. [CrossRef]
Li, C. L. , and Liu, Y. Y. , 2004, “ The Physical Property Tensors of One-Dimensional Quasicrystals,” Chin. Phys., 13(6), pp. 924–931. [CrossRef]
Rao, K. R. M. , Rao, P. H. , and Chaitanya, B. S. K. , 2007, “ Piezoelectricity in Quasicrystals: A Group-Theoretical Study,” Pramana J. Phys., 68(3), pp. 481–487. [CrossRef]
Altay, G. , and Cengiz Dökmeci, M. , 2012, “ On the Fundamental Equations of Piezoelasticity of Quasicrystal Media,” Int. J. Solids Struct., 49(23–24), pp. 3255–3262. [CrossRef]
Li, X. Y. , Li, P. D. , Wu, T. H. , Shi, M. X. , and Zhu, Z. W. , 2014, “ Three-Dimensional Fundamental Solutions for One-Dimensional Hexagonal Quasicrystal With Piezoelectric Effect,” Phys. Lett. A, 378(10), pp. 826–834. [CrossRef]
Yu, J. , Guo, J. H. , Pan, E. , and Xing, Y. M. , 2015, “ General Solutions of One-Dimensional Quasicrystal Piezoelectric Materials and Its Application on Fracture Mechanics,” Appl. Math. Mech., 36(6), pp. 793–814. [CrossRef]
Yu, J. , Guo, J. H. , and Xing, Y. M. , 2015, “ Complex Variable Method for an Anti-Plane Elliptical Cavity of One-Dimensional Hexagonal Piezoelectric Quasicrystals,” Chin. J. Aeronaut., 28(4), pp. 1287–1295. [CrossRef]
Shi, W. C. , 2009, “ Collinear Periodic Cracks and/or Rigid Line Inclusions of Antiplane Sliding Mode in One-Dimensional Hexagonal Quasicrystal,” Appl. Math. Comp., 215(3) pp. 1062–1067. [CrossRef]
Gao, Y. , and Ricoeurb, A. , 2012, “ Three-Dimensional Analysis of a Spheroidal Inclusion in a Two-Dimensional Quasicrystal Body,” Philos. Mag., 92(34), pp. 4334–4353. [CrossRef]
Guo, J. H. , Zhang, Z. Y. , and Xing, Y. M. , 2016, “ Antiplane Analysis for an Elliptical Inclusion in 1D Hexagonal Piezoelectric Quasicrystal Composites,” Philos. Mag., 96(4), pp. 349–369. [CrossRef]
Dunn, M. L. , and Taya, M. , 1993, “ Micromechanics Predictions of the Effective Electroelastic Moduli of Piezoelectric Composites,” Int. J. Solids Struct., 30(2), pp. 161–175. [CrossRef]
Christensen, R. M. , and Lo, K. H. , 1979, “ Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” J. Mech. Phys. Solids, 27(4), pp. 315–330. [CrossRef]
Christensen, R. M. , 1993, “ Effective Properties of Composite Materials Containing Voids,” Proc. Roy. Soc. A, 440(1909), pp. 461–473. [CrossRef]
Luo, H. A. , and Weng, G. J. , 1987, “ On Eshelby's Inclusions Problem in a Three-Phase Spherically Concentric Solid and a Modification of Mori–Tanaka's Method,” Mech. Mater., 6(4), pp. 347–361. [CrossRef]
Huang, Y. , and Hu, K. X. , 1995, “ A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions,” ASME J. Appl. Mech., 62(3), pp. 566–572. [CrossRef]
Jiang, C. P. , and Cheung, Y. K. , 1998, “ A Fiber/Matrix/Composite Model With a Combined Confocal Elliptical Cylinder Unit Cell for Predicting the Effective Longitudinal Shear Modulus,” Int. J. Solids Struct., 35(30), pp. 3977–3987. [CrossRef]
Riccardi, A. , and Montheilet, F. , 1999, “ A Generalized Self-Consistent Method for Solids Containing Randomly-Oriented Spheroidal Inclusions,” Acta Mech., 133(1), pp. 39–50. [CrossRef]
Jiang, C. P. , and Cheung, Y. K. , 2001, “ An Exact Solution for the Three-Phase Piezoelectric Cylinder Model Under Antiplane Shear and Its Applications to Piezoelectric Composites,” Int. J. Solids Struct., 38(28–29), pp. 4777–4796. [CrossRef]
Huang, Y. , Hu, K. X. , Wei, A. , and Chandra, X. , 1994, “ A Generalized Self-Consistent Mechanics Method for Composite Materials With Multiphase Inclusion,” J. Mech. Phys. Solids, 42(3), pp. 491–504. [CrossRef]
Jiang, C. P. , Tong, Z. H. , and Cheung, Y. K. , 2001, “ A Generalized Self-Consistent Method for Piezoelectric Fiber Reinforced Composites Under Antiplane Shear,” Mech. Mater., 33(5), pp. 295–308. [CrossRef]
Pak, Y. E. , 1992, “ Circular Inclusion Problem in Antiplane Piezoelectricity,” Int. J. Solids Struct., 29(19), pp. 2403–2419. [CrossRef]
Mishra, D. , Park, C. Y. , Yoo, S. H. , and Pak, Y. E. , 2013, “ Closed-Form Solution for Elliptical Inclusion Problem in Antiplane Piezoelectricity With Far-Field Loading at an Arbitrary Angle,” Eur. J. Mech. A/Solids, 40, pp. 186–197. [CrossRef]
Pak, Y. E. , 1992, “ Longitudinal Shear Transfer in Fiber Optic Sensors,” Smart Mater. Struct., 1(1), pp. 57–62. [CrossRef]
Hashin, Z. , and Rosen, B. W. , 1964, “ The Elastic Moduli of Fiber Reinforced Materials,” ASME J. Appl. Mech., 31(2), pp. 223–232. [CrossRef]
Whitney, J. M. , and Rilely, M. B. , 1966, “ Elastic Properties of Fiber Reinforced Composite Materials,” AIAA J., 4(9), pp. 1537–1542. [CrossRef]
Kuo, H. Y. , and Pan, E. , 2011, “ Effective Magnetoelectric Effect in Multicoated Circular Fibrous Multiferroic Composites,” J. Appl. Phys., 109(10), p. 104901. [CrossRef]


Grahic Jump Location
Fig. 1

Three-phase PQC cylinder model

Grahic Jump Location
Fig. 2

Variations of the stresses of phonon and phason fields and the electric field with C44M/C44I in the inclusion of the three-phase PQC cylinder under different far-field loads and for different radius ratios b/a

Grahic Jump Location
Fig. 3

Variations of the stresses of phonon and phason fields and the electric field in the inclusion, matrix, and composite under different far-field loads and for different shear modulus ratios

Grahic Jump Location
Fig. 4

Variations of the stresses of phonon and phason fields and the electric field in the inclusion, matrix, and composite under different far-field loads and for different coupling coefficient ratios

Grahic Jump Location
Fig. 5

Variations of the effective moduli of the two-phase PQC composite with fiber volume fraction f = (a/b)2



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In