Abstract
In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
SHECHTMAN, D., BLECH, I., GRATIAS, D., and CAHN, J. W. Metallic phase with long-range orientational order and no translational symmetry. Physical Review Letters, 53, 1951–1953 (1984)
DUBOIS, J. M. Properties and applications of quasicrystals and complex metallic alloys. Chemical Society Reviews, 41, 6760–6777 (2012)
WOLF, W., SCHULZ, R., SAVOIE, S., BOLFARINI, C., KIMINAMI, C. S., and BOTTA, E. J. Structural, mechanical and thermal characterization of an Al-Co-Fe-Cr alloy for wear and thermal barrier coating applications. Surface & Coatings Technology, 319, 241–248 (2017)
DUBOIS, J. M., KANG, S. S., and STEBUT, J. V. Quasicrystalline low-friction coatings. Journal of Materials Science Letters, 10, 537–541 (1991)
DUBOIS, J. M. New prospects from potential applications of quasicrystalline materials. Materials Science and Engineering A: Structural Materials Properties Microstructure and Processing, 294, 4–9 (2000)
UCHIDA, N. A review of thermal barrier coatings for improvement in thermal efficiency of both gasoline and diesel reciprocating engines. International Journal of Engine Research, 23, 3–19 (2022)
ZHOU, C. G., CAI, R., GONG, S. K., and XU, H. B. Hot corrosion of AlCuFeCr quasicrystalline coating on titanium alloys with NaCl deposit. Surface & Coatings Technology, 201, 1718–1723 (2006)
MOHSENI, M., RECLA, L., MORA, J., GALLEGO, P. G., AGUERO, A., and GOLOVIN, K. Quasicrystalline coatings exhibit durable low interfacial toughness with ice. ACS Applied Materials & Interfaces, 13, 36517–36526 (2021)
MORA, J., GARCIA, P., MUELAS, R., and AGUERO, A. Hard quasicrystalline coatings deposited by HVOF thermal spray to reduce ice accretion in aero-structures components. Coatings, 10, 290 (2020)
WOLF, W., BOLFARINI, C., KIMINAMI, C. S., and BOTTA, W. J. Recent developments on fabrication of Al-matrix composites reinforced with quasicrystals: from metastable to conventional processing. Journal of Materials Research, 36, 281–297 (2021)
NAYAK, C., AGHAJAMALI, A., SOLAIMANI, M., RAKSHIT, J. K., PANIGRAHY, D., KUMAR, K. V. P., and RAMAKRISHNA, B. Dodecanacci superconductor-metamaterial photonic quasicrystal. Optik, 222, 165290 (2020)
HUTTUNEN-SAARIVIRTA, E. Microstructure, fabrication and properties of quasicrystalline Al-Cu-Fe alloys: a review. Journal of Alloys and Compounds, 363, 150–174 (2004)
PARSAMEHR, H., CHEN, T. S., WANG, D. S., LEU, M. S., HAN, I., XI, Z. C., TSAI, A. P., SHAHANI, A. J., and LAI, C. H. Thermal spray coating of Al-Cu-Fe quasicrystals: dynamic observations and surface properties. Materialia, 8, 100432 (2019)
SOUZA, T. A., SILVA, D. D. S., JUNIOR, F. W. E. L. A., FEITOSA, F. R. P., GOMES, R. M., and LIMA, B. A. S. G. Analysis of the surface properties of Al-Cu-Fe-B and Al-Co-Cu quasicrystalline coatings produced by HVOF. MRS Communications, 11, 873–878 (2021)
LIU, X. Q., WU, Y. S., QIU, Z. G., LU, Z. Y., YAO, S. Q., ZHUO, S. Y., and ZENG, D. C. Simultaneously enhancing wear and corrosion resistance of HVAF-sprayed Fe-based amorphous coating from Mo clad feedstock. Journal of Materials Processing Technology, 302, 117465 (2022)
CAI, M. W. and SHEN, J. Phase transformation of high velocity air fuel (HVAF)-sprayed Al-Cu-Fe-Si quasicrystalline coating. Metals, 10, 834 (2020)
FU, Y. Q., KANG, N., LIAO, H. L., GAO, Y., and CODDET, C. An investigation on selective laster melting of Al-Cu-Fe-Cr quasicrystal: from single layer to multilayers. Intermetallics, 86, 51–58 (2017)
POLISHCHUK, S., USTINOV, A., TELYCHKO, V., MERSTALLINGER, A., MOZDZEN, G., and MELNICHENKO, T. Fabrication of thick, crack-free quasicrystalline Al-Cu-Fe coatings by electron-beam deposition. Surface & Coatings Technology, 291, 406–412 (2016)
FEITOSA, F. R. P., GOMES, R. M., SILVA, M. M. R., DE LIMA, S. J. G., and DUBOIS, J. M. Effect of oxygen/fuel ratio on the microstructure and properties of HVOF-sprayed Al59Cu25.5Fe12.5B3 quasicrystalline coatings. Surface & Coatings Technology, 353, 171–178 (2018)
XIAO, M., LIU, X. Q., ZENG, S. H., ZHENG, Z. G., WANG, G., QIU, Z. G., LIU, M., and ZENG, D. C. Effects of particle size on the microstructure and mechanical properties of HVAF-sprayed Al-based quasicrystalline coatings. Journal of Thermal Spray Technology, 30, 1380–1392 (2021)
CHENG, J., WU, Y. P., HONG, S., CHENG, J. B., QIAO, L., WANG, Y. J., and ZHU, S. S. Spray parameters optimization, microstructure and corrosion behavior of high-velocity oxygen-fuel sprayed non-equiatomic CuAlNiTiSi medium-entropy alloy coatings. Intermetallics, 142, 107442 (2022)
BANDYOPADHYAY, P. P., HADAD, M., JAEGGI, C., and SIEGMANN, S. Microstructural, tribological and corrosion aspects of thermally sprayed Ti-Cr-Si coatings. Surface & Coatings Technology, 203, 35–45 (2008)
SANCHEZ, A., DE BLAS, F. J., ALGABA, J. M., ALVAREZ, J., VALLES, P., GARCIAPOGGIO, M. C., and AGUERO, A. Application of quasicrystalline materials as thermal barriers in aeronautics and future perspectives of use for these materials. Materials Research Society Symposium Proceedings, 553, 447–458 (1999)
FAN, T. Y., TANG, Z. Y., and CHEN, W. Q. Theory of linear, nonlinear and dynamic fracture for quasicrystals. Engineering Fracture Mechanics, 82, 185–194 (2012)
SUN, T. Y., GUO, J. H., and PAN, E. Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium. Applied Mathematics and Mechanics (English Edition), 42(8), 1077–1094 (2021) https://doi.org/10.1007/s10483-021-2743-6
LI, L. H., CUI, X. W., and GUO, J. H. Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect. Applied Mathematics and Mechanics (English Edition), 41(6), 899–908 (2020) https://doi.org/10.1007/s10483-020-2615-6
ZHANG, M., GUO, J. H., and LI, Y. S. Bending and vibration of two-dimensional decagonal quasicrystal nanoplates via moddified couple-stress theory. Applied Mathematics and Mechanics (English Edition), 43(3), 371–388 (2022) https://doi.org/10.1007/s10483-022-2818-6
YANG, L. Z., LI, Y., GAO, Y., PAN, E. N., and WAKSMANSKI, N. Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading. Composite Structures, 171, 198–216 (2017)
HUANG, Y. Z., LI, Y., ZHANG, L. L., ZHANG, H., and GAO, Y. Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach. Acta Mechanica, 231, 2351–2368 (2020)
HOU, P. F., CHE, B. J., and ZHANG, Y. An accurate and efficient analytical method for 1D hexagonal quasicrystal coating under the tangential force based on the Green’s function. International Journal of Mechanical Sciences, 131, 982–1000 (2017)
HUANG, R. K., DING, S. H., CHEN, Q. W. L., LYU, C. F., ZHANG, X., and LI, X. Sliding frictional contact of one dimensional hexagonal piezoelectric quasicrystals coating on piezoelectric substrate with imperfect interface. International Journal of Solids and Structures, 239, 111423 (2022)
FAN, T. Y., XIE, L. Y., FAN, L., and WANG, Q. Z. Interface of quasicrystal and crystal. Chinese Physics B, 20, 076102 (2011)
DANG, H. Y., LYU, S. Y., FAN, C. Y., LU, C. S., REN, J. L., and ZHAO, M. H. Analysis of antiplane interface cracks in one-dimensional hexagonal quasicrystal coating. Applied Mathematical Modelling, 81, 641–652 (2020)
ZHAO, M. H., FAN, C. Y., LU, C. S., and DANG, H. Y. Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure. Applied Mathematics and Mechanics (English Edition), 42, 1633–1648 (2021) https://doi.org/10.1007/s10483-021-2786-5
CROUCH, S. L. Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution. International Journal for Numerical Methods in Engineering, 10, 301–343 (1976)
CHEN, W. Q., MA, Y. L., and DING, H. J. On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies. Mechanics Research Communications, 31, 633–641 (2004)
HOU, P. F., JIANG, H. Y., and LI, Q. H. Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications I: general solutions. Journal of Thermal Stresses, 36, 727–747 (2013)
ZHAO, M. H., CHENG, C. J., and LIU, Y. J. Moment stress intensity factors for collinear and parallel cracks in Reissner’s plate: boundary integral equation approach. Theoretical and Applied Fracture Mechanics, 22, 261–266 (1995)
ZHAO, Y. F., ZHAO, M. H., PAN, E. N., and FAN, C. Y. Green’s functions and extended displacement discontinuity method for interfacial cracks in three-dimensional transversely isotropic magneto-electro-elastic bi-materials. International Journal of Solids and Structures, 52, 56–71 (2015)
ZHANG, A. B. and WANG, B. L. An opportunistic analysis of the interface crack based on the modified interface dislocation method. International Journal of Solids and Structures, 50, 15–20 (2013)
TANG, R. J., CHEN, M. C., and YUE, J. C. Theoretical analysis of three-dimensional interface crack. Science in China Series A: Mathematics, 41, 443–448 (1998)
DANG, H. Y., ZHAO, M. H., FAN, C. Y., and CHEN, Z. T. Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material, part 2: numerical method. Engineering Fracture Mechanics, 180, 268–281 (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Citation: ZHANG, X., ZHAO, M. H., FAN, C. Y., LU, C. S., and DANG, H. Y. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating. Applied Mathematics and Mechanics (English Edition), 43(12), 1901–1920 (2022) https://doi.org/10.1007/s10483-022-2942-7
Project supported by the National Natural Science Foundation of China (Nos. 11572289, 1171407, 11702252, and 11902293) and the China Postdoctoral Science Foundation (No. 2019M652563)
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Zhang, X., Zhao, M., Fan, C. et al. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating. Appl. Math. Mech.-Engl. Ed. 43, 1901–1920 (2022). https://doi.org/10.1007/s10483-022-2942-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-022-2942-7
Key words
- one-dimensional (1D) hexagonal quasicrystal (QC) coating
- displacement discontinuity method
- interface crack
- rectangular element
- stress intensity factor (SIF)
- energy release rate (ERR)