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., vol. 53, no. 20, pp. 1951–1953, 1984. DOI: https://doi.org/10.1103/PhysRevLett.53.1951.
- V. Elser and C. L. Henley, “Crystal and quasicrystal structures in Al-Mn-Si alloys,” Phys. Rev. Lett., vol. 55, no. 26, pp. 2883–2886, 1985. DOI: https://doi.org/10.1103/PhysRevLett.55.2883.
- P. Archambault and C. Janot, “Thermal conductivity of quasicrystals and associated process,” MRS Bull., vol. 22, no. 11, pp. 48–53, 1997. DOI: https://doi.org/10.1557/S0883769400034436.
- D. J. Sordelet, S. D. Widnener, Y. Tang, and M. F. Besser, “Characterization of a commercially produced Al-Cu-Fe-Cr quasicrystalline coating,” Mater. Sci. Eng. A, vol. 294-296, pp. 834–837, 2000. DOI: https://doi.org/10.1016/S0921-5093(00)01056-X.
- C. G. Zhou, H. B. Xu, S. K. Gong, and G. M. Kang, “Formation and oxidation behavior of Al-Cu-Fe quasicrystals,” J. Mater. Sci. Technol., vol. 18, pp. 251–253, 2002.
- S. Kenzari, D. Bonina, J. M. Dubois, and V. Fournee, “Quasicrystal-polymer composites for selective laser sintering technology,” Mater. Des., vol. 35, pp. 691–695, 2012. DOI: https://doi.org/10.1016/j.matdes.2011.10.032.
- W. Wolf, R. Schulz, S. Savoie, C. Bolfarini, C. S. Kiminami, and W. J. Botta, “Structural, mechanical and thermal characterization of an Al-Co-Fe-Cr alloy for wear and thermal barrier coating applications,” Surf. Coat. Technol., vol. 319, pp. 241–248, 2017. DOI: https://doi.org/10.1016/j.surfcoat.2017.03.066.
- Z. Zhang and K. Urban, “Transmission electron microscope observation of dislocation and stacking faults in a decagonal Al-Cu-Co alloy,” Philos. Mag. Lett., vol. 60, no. 3, pp. 97–102, 1989. DOI: https://doi.org/10.1080/09500838908206442.
- J. M. Dubois, S. S. Kang, and J. Stebut, “Quasicrystalline low-friction coatings,” J. Mater. Sci. Lett., vol. 10, no. 9, pp. 537–541, 1991. DOI: https://doi.org/10.1007/BF00726930.
- S. S. Kang, J. M. Dubois, and J. Stebut, “Tribology properties of quasi-crystalline coatings,” J. Mater. Res., vol. 8, no. 10, pp. 2471–2481, 1993. DOI: https://doi.org/10.1557/JMR.1993.2471.
- V. N. Balbyshev, D. J. King, A. N. Khramov, L. S. Kasten, and M. S. Donley, “Investigation of quaternary Al-based quasicrystal thin films for corrosion protection,” Thin Solid Films, vol. 447-448, pp. 558–563, 2004. DOI: https://doi.org/10.1016/j.tsf.2003.07.026.
- L. H. Li and G. H. Yun, “Thermal stress analysis for octagonal quasicrystals,” J. Therm. Stresses, vol. 37, no. 4, pp. 429–439, 2014. DOI: https://doi.org/10.1080/01495739.2013.870852.
- Y. Li, L. Z. Yang, L. L. Zhang, and Y. Gao, “Exact thermoelectroelastic solution of layered one-dimensional quasicrystal cylindrical shells,” J. Therm. Stresses, vol. 41, no. 10-12, pp. 1450–1467, 2018. DOI: https://doi.org/10.1080/01495739.2018.1520618.
- N. Bonasso and P. Pigeat, “Real time study of the growth of i-AlCuFe in very thin films obtained by simultaneous deposition of the components,” J. Non-Cryst. Solids, vol. 334-335, pp. 509–512, 2004. DOI: https://doi.org/10.1016/j.jnoncrysol.2003.12.032.
- N. Kang et al., “In-situ synthesis of aluminum/nano-quasicrystalline Al-Fe-Cr composite by using selective laser melting,” Compos. Part B-Eng., vol. 155, pp. 382–390, 2018. DOI: https://doi.org/10.1016/j.compositesb.2018.08.108.
- F. R. P. Feitosa, R. M. Gomes, M. M. R. Silva, L. S. J. G. De, and J. M. Dubois, “Effect of oxygen/fuel ratio on the microstructure and properties of HVOF-sprayed Al59Cu25.5Fe12.5B3 quasicrystalline coatings,” Surf. Coat. Technol., vol. 353, pp. 171–178, 2018. DOI: https://doi.org/10.1016/j.surfcoat.2018.08.081.
- T. Y. Fan, L. Y. Xie, L. Fan, and Q. Z. Wang, “Interface of quasicrystal and crystal,” Chin. Phys. B, vol. 20, no. 7, id 076102, 6 pp, 2011. DOI: https://doi.org/10.1088/1674-1056/20/7/076102.
- L. Z. Yang, Y. Gao, E. Pan, and N. Waksmanski, “An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate,” Acta Mech., vol. 226, no. 11, pp. 3611–3621, 2015. DOI: https://doi.org/10.1007/s00707-015-1395-2.
- L. Z. Yang, Y. Gao, E. Pan, and N. Waksmanski, “An exact solution for a multilayered two-dimensional decagonal quasicrystal plate,” Int. J. Solids Struct., vol. 51, no. 9, pp. 1737–1749, 2014. DOI: https://doi.org/10.1016/j.ijsolstr.2014.01.018.
- N. Waksmanski, E. Pan, L. Z. Yang, and Y. Gao, “Free vibration of a multilayered one-dimensional quasi-crystal plate,” J. Vib. Acoust., vol. 136, no. 4, pp. 041019, 2014. DOI: https://doi.org/10.1115/1.4027632.
- L. Z. Yang, Y. Li, Y. Gao, and E. Pan, “Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates,” Appl. Math. Model., vol. 63, pp. 203–218, 2018. DOI: https://doi.org/10.1016/j.apm.2018.06.050.
- P. F. Hou, B. J. Chen, and Y. Zhang, “An accurate and efficient analytical method for 1D hexagonal quasicrystal coating based on Green’s function,” Z. Angew. Math. Phys., vol. 68, no. 4, pp. 95, 2017. DOI: https://doi.org/10.1007/s00033-017-0842-4.
- P. F. Hou, B. J. Chen, and Y. Zhang, “An accurate and efficient analytical method for 1D hexagonal quasicrystal coating under the tangential force based on the Green’s function,” Int. J. Mech. Sci., vol. 131-132, pp. 982–1000, 2017. DOI: https://doi.org/10.1016/j.ijmecsci.2017.07.031.
- J. H. Guo, T. Y. Sun, and E. Pan, “Three-dimensional nonlocal buckling of composite nanoplates with coated one-dimensional quasicrystal in an elastic medium,” Int. J. Solids Struct., vol. 185-186, pp. 272–280, 2020. DOI: https://doi.org/10.1016/j.ijsolstr.2019.08.033.
- H. Y. Dang, S. Y. Lv, C. Y. Fan, C. S. Lu, J. L. Ren, and M. H. Zhao, “Analysis of anti-plane interface cracks in one-dimensional hexagonal quasicrystal coating,” Appl. Math. Model., vol. 81, pp. 641–652, 2020. DOI: https://doi.org/10.1016/j.apm.2020.01.024.
- M. H. Zhao, C. Y. Fan, C. S. Lu, and H. Y. Dang, “Analysis of interface cracks in one-dimensional hexagonal quasi-crystal coating under in-plane loads,” Eng. Fract. Mech., vol. 243, pp. 107534, 2021. DOI: https://doi.org/10.1016/j.engfracmech.2021.107534.
- S. L. Crouch, “Solution of plane elasticity problems by the displacement discontinuity method. I. infinite body solution,” Int. J. Numer. Meth. Eng., vol. 10, no. 2, pp. 301–343, 1976. DOI: https://doi.org/10.1002/nme.1620100206.
- R. J. Tang, M. C. Chen, and J. C. Yue, “Theoretical analysis of three-dimensional interface crack,” Sci. China Ser. A-Math., vol. 41, no. 4, pp. 443–448, 1998. DOI: https://doi.org/10.1007/BF02879037.
- M. C. Chen, N. A. Noda, and R. J. Tang, “Application of finite-part integrals to planar interfacial fracture problems in three-dimensional bimaterials,” J. Appl. Mech-Trans. ASME, vol. 66, no. 4, pp. 885–890, 1999. DOI: https://doi.org/10.1115/1.2791793.
- C. Y. Fan, S. Y. Lv, H. Y. Dang, Y. P. Yuan, and M. H. Zhao, “Fundamental solutions and analysis of the interface crack for two-dimensional decagonal quasicrystal biomaterial via the displacement discontinuity method,” Eng. Anal. Bound. Elem., vol. 106, pp. 462–472, 2019. DOI: https://doi.org/10.1016/j.enganabound.2019.05.029.
- P. H. Wen, M. H. Aliabadi, J. Sladek, and V. Sladek, “Displacement discontinuity method for cracked orthotropic strip: Dynamic,” Wave Motion, vol. 45, no. 3, pp. 293–308, 2008. DOI: https://doi.org/10.1016/j.wavemoti.2007.06.006.
- M. Li, Y. L. Tian, P. H. Wen, and M. H. Aliabadi, “Anti-plane interfacial crack with functionally graded coating: Static and dynamic,” Theor. Appl. Fract. Mech., vol. 86, part B, pp. 250–259, 2016. DOI: https://doi.org/10.1016/j.tafmec.2016.07.010.
- D. H. Ding, W. G. Yang, C. Z. Hu, and R. H. Wang, “Generalized elasticity theory of quasicrystals,” Phys. Rev. B Condens. Matter, vol. 48, no. 10, pp. 7003–7010, 1993. DOI: https://doi.org/10.1103/physrevb.48.7003.
- X. Y. Li, “Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading,” Proc. R. Soc. A-Math. Phys., vol. 469, pp. 20130023, 2013.
- M. K. Kassir and G. C. Sih, “Three-dimensional thermoelastic problems of planes of discontinuities or cracks in solids,” Dev. Theor. Appl. Mech., pp. 117–146, 1967. DOI: https://doi.org/10.1016/B978-0-08-003132-3.50011-7.
- P. F. Hou, H. Y. Jiang, and Q. H. Li, “Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications I: General solutions,” J. Therm. Stresses, vol. 36, no. 7, pp. 727–747, 2013. DOI: https://doi.org/10.1080/01495739.2013.788903.
- M. H. Zhao, Y. P. Shen, Y. J. Liu, and G. N. Liu, “The method of analysis of cracks in three-dimensional transversely isotropic media: Boundary integral equation approach,” Eng. Anal. Bound. Elem., vol. 21, no. 2, pp. 169–178, 1998. DOI: https://doi.org/10.1016/S0955-7997(98)00033-2.
- X. Y. Li and P. D. Li, “Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions,” Phys. Lett. A, vol. 376, no. 26-27, pp. 2004–2009, 2012. DOI: https://doi.org/10.1016/j.physleta.2012.04.049.
- A. B. Zhang and B. L. Wang, “An opportunistic analysis of the interface crack based on the modified interface dislocation method,” Int. J. Solids Struct., vol. 50, no. 1, pp. 15–20, 2013. DOI: https://doi.org/10.1016/j.ijsolstr.2012.08.024.
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. Burlington: Elsevier Science, 2007.
- A. T. Zehnder, Fracture Mechanics. London; New York: Springer Science. Business Media, 2012.
- X. Y. Li, P. D. Li, and G. Z. Kang, “Crack tip plasticity of a thermally loaded penny-shaped crack in an infinite space of 1D QC,” Acta Mech. Solida Sin., vol. 28, no. 5, pp. 0894–9166, 2015.