Anti-plane Shear Problems of One-dimensional Hexagonal Piezoelectric Quasicrystals with Regular Polygonal Nanopores and Secondary Multiple Cracks

doi:10.19596/j.cnki.1001-246x.8706

Abstract

Abstract:

Using Gurtin-Murdoch theory and complex potential method, the problem of secondary multiple rips in one-dimensional hexagonal quasicrystals take nano n-edge polygon orifices is studied. The analytical solutions of phonon field, phasor field and electric field, as well as phonon field stress intensity factors and energy release rate are obtained. Some calculations are given to discuss the effects of secondary crack morphology of nano orifice on field intensity factor and energy release rate. The results indicate that when the defect size asymptotically the nanometer level, the surface effect produced by the coupling of phonon field, phase field and electric field, while the smaller the size of secondary crack at the orifice, the stronger surface effect. The more the number of cracks, the smaller the field intensity factor. With the amplify of defect size, the influence by surface influence will gradually weaken, and eventually tends to the existing outcome.

Key words: one-dimensional hexagonal quasicrystal, n-edge polygon orifices secondary multiple cracks, energy release rate, surface effect

CLC Number:

Huaimin GUO, Lijuan JIANG, Guozhong ZHAO, Guoming XU. Anti-plane Shear Problems of One-dimensional Hexagonal Piezoelectric Quasicrystals with Regular Polygonal Nanopores and Secondary Multiple Cracks[J]. Chinese Journal of Computational Physics, 2024, 41(2): 222-231.

Figures/Tables 11

Fig.1 Secondary n cracks of regular n-sided nanopores in the material matrix

Fig.2 Arch transformation process

Table 1 The material constants and the surface layer material parameters

c₄₄/GPa	R₃/GPa	K₂/GPa	e₁₅/(C·m^-2)	d₁₅/(C·m^-2)	λ₁₁/(C²·N·m^-2)	c₄₄⁰/(N·m^-1)	R₃⁰/(N·m^-1)	K₂⁰/(N·m^-1)	e₁₅⁰/(C·m^-1)	d₁₅⁰/(C·m^-1)	λ₁₁⁰/(C²·N·m^-1)
50	1.2	0.3	-0.318	-0.160	82.6 × 10^-12	62.5	1.5	0.5	0.318	0.160	0

Fig.3 Variation curve of KH*/Hzy∞ with R

Fig.4 Variation curve of Kτ*/τzy∞ with R

Fig.5 Variation of KD*/Dy∞ with R

Fig.6 Varictions of dimensionless stress intensity factor with R

Fig.7 Variations of energy release rate with τzy∞

Fig.8 Variations of energy release rate with Hzy∞

Fig.9 Variations of energy release rate with Dy∞

Fig.10 Variations of dimensionless SIF with n

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