355
Views
52
CrossRef citations to date
0
Altmetric
Part A: Materials Science

Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites

, &
Pages 349-369 | Received 07 Aug 2015, Accepted 11 Dec 2015, Published online: 20 Jan 2016

References

  • D. Shechtman , I. Blech , D. Gratias and J.W. Cahn , Metallic phase with long-range orientational order and no translational symmetry , Phys. Rev. Lett. 53 (1984), pp. 1951–1953.10.1103/PhysRevLett.53.1951
  • J.M. Dubois , Useful Quasicrystals , Singapore: World Scientific, 2005.
  • D.H. Ding , W.G. Yang , C.Z. Hu and R.H. Wang , Generalized elasticity theory of quasicrystals , Phys. Rev. B 48 (1993), pp. 7003–7009.10.1103/PhysRevB.48.7003
  • G.T. Liu , T.Y. Fan and R.P. Guo , Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals , Int. J. Solids Struct. 41 (2004), pp. 3949–3959.10.1016/j.ijsolstr.2004.02.028
  • X.M. Meng , B.Y. Tong and Y.K. Wu , Mechanical properties of Al65 Cu20 Co15 , Acta Metall. Sinica 30 (1994), pp. 60–64.
  • Z. Zhang and K. Urban , Transmission electron microscope observation of dislocation and stackling faults in a decagonal Al-Cu-Co alloy , Philos. Mag. Lett. 60 (1989), pp. 97–102.10.1080/09500838908206442
  • X.F. Li and T.Y. Fan , A straight dislocation in one dimensional hexagonal quasicrystals , Phys. Status Solidi b 212 (1999), pp. 19–26.10.1002/(ISSN)1521-3951
  • Y.Z. Peng and T.Y. Fan , Crack and indentation problems for one-dimensional hexagonal Quasicrystals , Eur. Phys. J. 21 (2001), pp. 39–44.10.1007/s100510170210
  • C.Z. Hu , R.H. Wang and D.H. Ding , Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals , Rep. Prog. Phys. 63 (2000), pp. 1–39.10.1088/0034-4885/63/1/201
  • G.T. Liu , R.P. Guo and T.Y. Fan , On the interaction between dislocations and cracks in one-dimensional hexagonal quasicrystals , Chin. Phys. 2 (2003), pp. 1149–1155.
  • T.Y. Fan and Y.W. Mai , Elasticity theory, fracture mechanics, and some relevant thermal properties of quasi-crystalline materials , Appl. Mech. Rev. 57 (2004), pp. 325–343.10.1115/1.1763591
  • Y. Gao , Y.T. Zhao and B.S. Zhao , Boundary value problems of holomorphic vector functions in 1D QCs , Phys. B: Condens. Matter 394 (2007), pp. 56–61.10.1016/j.physb.2007.02.007
  • J.H. Guo and G.T. Liu , Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal , Chin. Phys. B 17 (2008), pp. 2610–2620.
  • E. Radi and P.M. Mariano , Stationary straight cracks in quasicrystals , Int. J. Fract. 166 (2010), pp. 102–120.
  • J.H. Guo and Z.X. Lu , Exact solution of four cracks originating from an elliptical hole in one-dimensional hexagonal quasicrystals , Appl. Math. Comput. 217 (2011), pp. 9397–9403.10.1016/j.amc.2011.04.028
  • L.H. Li and G.T. Liu , Interaction of a dislocation with an elliptical hole in icosahedral quasicrystals , Philos. Mag. Lett. 93 (2013), pp. 142–151.10.1080/09500839.2012.752883
  • J.H. Guo , J. Yu and R. Si , A semi-inverse method of a Griffith crack in one-dimensional hexagonal quasicrystals , Appl. Math. Comput. 219 (2013), pp. 7445–7449.10.1016/j.amc.2013.01.031
  • A. Sakly , S. Kenzari , D. Bonina , S. Corbel and V. Fournée , A novel quasicrystal-resin composite for stereolithography , Mater. Des. 56 (2014), pp. 280–285.10.1016/j.matdes.2013.11.025
  • X.P. Guo , J.F. Chen , H.L. Yu , H.L. Liao and C. Coddet , A study on the microstructure and tribological behavior of cold-sprayed metal matrix composites reinforced by particulate quasicrystal , Surf. Coat. Technol. 268 (2015), pp. 94–98.10.1016/j.surfcoat.2014.05.062
  • Y. Zhang , J. Zhang , G.H. Wu , W.C. Liu , L. Zhang and W.J. Ding , Microstructure and tensile properties of as-extruded Mg-Li-Zn-Gd alloys reinforced with icosahedral quasicrystal phase , Mater. Des. 66 (2015), pp. 162–168.10.1016/j.matdes.2014.10.049
  • Y. Tian , H. Huang , G.Y. Yuan and W.J. Ding , Nanoscale icosahedral quasicrystal phase precipitation mechanism during annealing for Mg-Zn-Gd-based alloys , J. Alloys Compd. 626 (2015), pp. 42–48.10.1016/j.jallcom.2014.11.167
  • X. Wang , Eshelby’s problem of an inclusion of arbitrary shape in a decagonal quasicrystalline plane or half-plane , Int. J. Eng. Sci. 42 (2004), pp. 1911–1930.10.1016/j.ijengsci.2004.07.002
  • W.C. Shi , Collinear periodic cracks and/or rigid line inclusions of antiplane sliding mode in one-dimensional hexagonal quasicrystal , Appl. Math. Comput. 215 (2009), pp. 1062–1067.10.1016/j.amc.2009.06.055
  • Y. Gao and A. Ricoeur , Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body , Philos. Mag. 92 (2012), pp. 4334–4353.10.1080/14786435.2012.706717
  • X. Wang and P. Schiavone , N-phase decagonal quasicrystalline circular inclusions under thermomechanical loadings , Appl. Math. Mech. 93 (2013), pp. 520–529.
  • X. Wang and P. Schiavone , Decagonal quasicrystalline elliptical inclusions under thermomechanical loadings , Acta Mech. Solida Sin. 27 (2014), pp. 518–530.10.1016/S0894-9166(14)60060-4
  • P.A. Thiel and J.M. Dubois , Quasicrystals. Reaching maturity for technological applications , Mater. Today 2 (1999), pp. 3–7.10.1016/S1369-7021(99)80058-3
  • N.S. Athanasiou , C. Politis , J.C. Spirlet , S. Baskoutas and V. Kapaklis , The significance of valence electron concentration on the formation mechanism of some ternary aluminum-based quasicrystals , Int. J. Mod. Phys. B 16 (2002), pp. 4665–4683.10.1142/S0217979202013067
  • J.Y. Park , D.F. Ogletree , M. Salmeron , R.A. Ribeiro , P.C. Canfield , C.J. Jenks and P.A. Thiel , High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface , Science 309 (2005), pp. 1354–1356.10.1126/science.1113239
  • J.Y. Park , G.M. Sacha , M. Enachescu , D.F. Ogletree , R.A. Ribeiro , P.C. Canfield , C.J. Jenks , P.A. Thiel , J.J. Saenz and M. Salmeron , Sensing dipole fields at atomic steps with combined scanning tunneling and force microscopy , Phys. Rev. Lett. 95 (2005), pp. 136802.10.1103/PhysRevLett.95.136802
  • T. Fujiwara , G.T. Laissardiere and S. Yamamoto , Electronic structure and electron transport in quasicrystals periodical materials , Mater. Sci. Forum 387 (1994), pp. 150–151.
  • D.L. Zhang , Electronic properties of stable decagonal quasicrystals , Phys. Status Solidi A 207 (2010), pp. 2666–2673.10.1002/pssa.v207.12
  • W.G. Yang , R. Wang , D.H. Ding and C.Z. Hu , Elastic strains induced by electric fields in quasicrystals , J. Phys. Condens. Matter 7 (1995), pp. L499–L502.10.1088/0953-8984/7/39/001
  • C.Z. Hu , R. Wang , D.H. Ding and W. Yang , Piezoelectric effects in quasicrystals , Phys. Rev. B 56 (1997), pp. 2463–2468.10.1103/PhysRevB.56.2463
  • C.L. Li and Y.Y. Liu , The physical property tensors of one-dimensional quaiscrystals , Chin. Phys. 13 (2004), pp. 924–931.
  • K.R.M. Rao , P.H. Rao and B.S.K. Chaitanya , Piezoelectricity in quasicrystals: a group-theoretical study , Pramana J. Phys. 68 (2007), pp. 481–487.
  • X. Wang and E. Pan , Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrytals , Pramana J. Phys. 70 (2008), pp. 911–933.
  • G. Altay and M. Cengiz Dökmeci , On the fundamental equations of piezoelasticity of quasicrystal media , Int. J. Solids Struct. 49 (2012), pp. 3255–3262.10.1016/j.ijsolstr.2012.06.016
  • X.Y. Li , P.D. Li , T.H. Wu , M.X. Shi and Z.W. Zhu , Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect , Phys. Lett. A 378 (2014), pp. 826–834.10.1016/j.physleta.2014.01.016
  • J. Yu , J.H. Guo , E. Pan and Y.M. Xing , General solutions of one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics , Appl. Math. Mech. 36 (2015), pp. 793–814.10.1007/s10483-015-1949-6
  • J. Yu , J.H. Guo and Y.M. Xing , Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals , Chin. J. Aero. 28 (2015), pp. 1287–1295.10.1016/j.cja.2015.04.013
  • Y.E. Pak , Elliptical inclusion problem in antiplane piezoelectricity: implications for fracture mechanics , Int. J. Eng. Sci. 48 (2010), pp. 209–222.10.1016/j.ijengsci.2009.08.004
  • Y.E. Pak and A. Tobin , On the electric field effects in fracture of piezoelectric materials , Mech. Electromagn. Mater. Struct. 42 (1993), pp. 51–62.
  • T.Y. Zhang and P. Tong , Fracture mechanics for a mode III crack in a piezoelectric material , Int. J. Solids Struct. 33 (1996), pp. 343–359.10.1016/0020-7683(95)00046-D
  • D. Mishra , C.Y. Park , S.H. Yoo and Y.E. Pak , Closed-form solution for elliptical inclusion problem in antiplane piezoelectricity with far-field loading at an arbitrary angle , Eur. J. Mech. A. Solids 40 (2013), pp. 186–197.10.1016/j.euromechsol.2013.01.003
  • Y.E. Pak , Circular inclusion problem in antiplane piezoelectricity , Int. J. Solids Struct. 29 (1992), pp. 2403–2419.10.1016/0020-7683(92)90223-G
  • J.R. Rice , A path-independent integral and the approximate analysis of strain concentration by notches and cracks , J. Appl. Mech. 35 (1968), pp. 379–386.10.1115/1.3601206
  • W. Gunther , Uber einige randintegrale der elastomechanik [Some edge integral of elastomechanics], in Adhandlungen der Braunschweigischen Wisssenschaftlichen , W. Günther , H. Herrn , eds., Gesellschaft, Vol. XIV, Braunschweig: Verlag Friedrich Vieweg, 1962, 53–72.
  • J.K. Knowles and E. Sternberg , On a class of conservation laws in linearized and finite elastostatics , Arch. Ration. Mech. Anal. 44 (1972), pp. 187–211.
  • Y.E. Pak , Crack extension force in a piezoelectric material , J. Appl. Mech. 57 (1990), pp. 647–653.10.1115/1.2897071
  • J.W. Eischen and G. Herrmann , Energy release rates and related balance laws in linear elastic defect mechanics , J. Appl. Mech. 54 (1987), pp. 388–392.10.1115/1.3173024
  • L.B. Freund , Stress-intensity factor calculations based on a conservational integral , Int. J. Solids Struct. 14 (1978), pp. 241–249.10.1016/0020-7683(78)90028-8
  • Y.H. Chen , M-integral analysis for two-dimensional solids with strongly interacting cracks , Int. J. Solids Struct. 38 (2001), pp. 3193–3212.10.1016/S0020-7683(00)00242-0
  • Q. Li and Y.H. Chen , Surface effect and size dependent on the energy release due to a nanosized hole expansion in plane elastic materials , J. Appl. Mech. 75 (2008), pp. 061008-1–061008-5.10.1115/1.2965368
  • T. Hui and Y.H. Chen , The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings , J. Appl. Mech. 77 (2010), pp. 021019-1–021019-9.10.1115/1.3176997

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.