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Fracture mechanics of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

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Abstract

The mode III fracture behavior of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals is studied. Based on the Gurtin–Murdoch surface theory and the boundary value problems theory, the expressions of the electro-elastic fields and the generalized field intensity factor at the crack tip are obtained. The presented solution can degenerate into existing results. The influences of the hole size, crack location, crack–hole interaction, applied electro-elastic loads and quasicrystal coupling coefficient on the generalized field intensity factor are discussed. The generalized field intensity factor has significant size effects when the surface effect is considered. The influence of the surface effect on the generalized field intensity factor depends on the crack location. The larger the relative size of the crack is, the greater the surface effect is. The effects of applied electro-elastic loads and quasicrystal coupling coefficient on each generalized field intensity factor are quite different.

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References

  1. Shechtman, D., Blech, I., Gratias, D., et al.: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984)

    Article  Google Scholar 

  2. Fan, T.Y., Xie, L.Y., Fan, L., et al.: Interface of quasicrystal and crystal. Chin. Phys. B 20(7), 076102 (2011)

    Article  Google Scholar 

  3. Fan, T.Y., Li, X.F., Sun, Y.F.: A moving screw dislocation in a one-dimensional hexagonal quasicrystal. Acta Phys. Sin. (Overseas Ed.) 8(4), 288–295 (1999)

    Article  Google Scholar 

  4. Dong, C.: The Quasicrystals Material. National Denfence Industry Press, Beijing (1998) (in Chinese)

    Google Scholar 

  5. Yang, J., Li, X., Ding, S.H.: Anti-plane analysis of a circular hole with three unequal cracks in one-dimensional hexagonal piezoelectric quasicrystals. Chin. J. Eng. Math. 33(2), 184–198 (2016)

    MathSciNet  Google Scholar 

  6. Yang, J., Li, X., Zhou, Y.T.: Analysis of periodic cracks emanating from a circular hole in one-dimensional hexagonal piezoelectric quasicrystals. J. Vib. Shock 38(18), 62–71 (2019) (in Chinese)

    Google Scholar 

  7. Bai, Q.M., Ding, S.H.: An anti-plane problem of cracks at edges of regular hexagonal holes in 1D hexagonal piezoelectric quasicrystals. Appl. Math. Mech. 40(10), 1071–1080 (2019) (in Chinese)

    Google Scholar 

  8. Yang, J., Li, X.: Analytic solutions of problem about a circular hole with a straight crack in one-dimensional hexagonal quasicrystals with piezoelectric effects. Theor. Appl. Fract. Mech. 82, 17–24 (2016)

    Article  Google Scholar 

  9. Fan, S.W., Guo, J.H.: Anti-plane problem of an edge crack emanating from a triangle hole in one-dimensional hexagonal piezoelectric quasicrystals. Chin. J. Appl. Mech. 33(3), 421–426 (2016) (in Chinese)

    MathSciNet  Google Scholar 

  10. Jiang, L.J., Liu, G.T.: The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals. Chin. Phys. B 26(4), 249–255 (2017)

    Article  MathSciNet  Google Scholar 

  11. Li, L.H., Liu, G.T.: A screw dislocation interacting with a wedge-shaped crack in one-dimensional hexagonal quasicrystals. Acta Phys. Sin. 61(8), 326–330 (2012) (in Chinese)

    Google Scholar 

  12. Guo, J.H., Liu, G.T.: Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal. Chin. Phys. B 17(7), 2610–2620 (2008)

    Article  Google Scholar 

  13. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14(6), 431–440 (1978)

    Article  MATH  Google Scholar 

  15. Gurtin, M.E., Weissmuller, J., Larche, F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A Phys. Condens. Matter Struct. Defects Mech. Prop. 78(5), 1093–1109 (1998)

    Google Scholar 

  16. Wu, Z.L., Liu, G.T., Yang, D.S.: Analytical solution of two nano-cracks emanating from circular nano-hole in one-dimensional hexagonal qusicrystals. Math. Pract. Theory 51(16), 164–172 (2021) (in Chinese)

    Google Scholar 

  17. Yang, D.S., Liu, G.T.: Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals. Chin. Phys. B 29(10), 382–389 (2020)

    Article  Google Scholar 

  18. Su, M.Y., Xiao, J.H., Feng, G.Y., et al.: Mode-III fracture of a nanoscale cracked hole in one-dimensional hexagonal piezoelectric quasicrystals. Int. J. Mech. Mater. Des. 18, 423–433 (2022)

    Article  Google Scholar 

  19. Wu, Z.L., Liu, G.T., Yang, D.S.: Surface effect on two nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole in one-dimensional hexagonal piezoelectric quasicrystals under anti-plane shear. Int. J. Mod. Phys. B 35(32), 2150330 (2021)

    Article  Google Scholar 

  20. Zhao, Z.N., Guo, J.H., Yu, J.: An electrically permeable mode-III nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals with surface effect. In: 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications, pp. 409–413 (2021)

  21. Zhao, Z.N., Guo, J.H.: Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals. Appl. Math. Mech. (Engl. Ed.) 42(5), 625–640 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  22. Xiao, J.H., Su, M.Y., Feng, G.Y.: Micromechanics of nano-defects in one-dimensional hexagonal piezoelectric quasicrystals. In: The 2019 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, pp. 477–481 (2019)

  23. Guo, J.H., Zhang, Z.Y., Xing, Y.M.: Anti-plane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites. Phil. Mag. 96(4), 349–369 (2016)

    Article  Google Scholar 

  24. Yu, J., Guo, J.H., Xing, Y.M.: Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals. Chin. J. Aeronaut. 28(4), 1287–1295 (2015)

    Article  Google Scholar 

  25. Yu, J., Guo, J.H., Pan, E., Xing, Y.M.: General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Appl. Math. Mech. (Engl. Ed.) 36(6), 793–814 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Guo, J.H., Lu, Z.X.: Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid. Int. J. Solids Struct. 47(14/15), 1847–1856 (2010)

    Article  MATH  Google Scholar 

  27. Zhou, S., Li, Z.X.: Analysis of stresses near an elliptical hole with a random micro-crack. J. ShangHai Jiao Tong Univ. 50(2), 272–277 (2016) (in Chinese)

    MathSciNet  Google Scholar 

  28. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)

    MATH  Google Scholar 

  29. Xiao, J.H., Xu, Y.L., Zhang, F.C.: Fracture characteristics of a cracked equilateral triangle hole with surface effect in piezoelectric materials. Theoret. Appl. Fract. Mech. 96, 476–482 (2018)

    Article  Google Scholar 

  30. Hu, K.Q., Jin, H., Yang, Z.J., et al.: Interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect. Acta Mech. 230(7), 2455–2474 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wei, G., Xiao, W.S., Xi, J.P.: The interaction between a screw dislocation dipole and a linear nano crack in one-dimensional hexagonal quasicrystals. Chin. J. Solid Mech. 39(6), 606–613 (2018) (in Chinese)

    Google Scholar 

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Acknowledgments

This work was supported by the Natural Science Foundation of Hebei Province (A2022203025) and the Science and Technology Project of Hebei Education Department (ZD2021104).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Yanshan University, Qinhuangdao, 066004, China

    Yuyan Xin & Junhua Xiao

  2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, 066004, China

    Yuyan Xin & Junhua Xiao

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  1. Yuyan Xin
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Xin, Y., Xiao, J. Fracture mechanics of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals. Acta Mech 234, 1409–1420 (2023). https://doi.org/10.1007/s00707-022-03424-y

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  • DOI: https://doi.org/10.1007/s00707-022-03424-y

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