含正多边形纳米孔次生多裂纹的一维六方压电准晶体的反平面剪切问题

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

摘要/Abstract

摘要：

利用Gurtin-Murdoch表界面理论和复势法，讨论一维六方压电准晶体含纳米级正n边形孔口次生多裂纹的反平面问题，得到电场、声子场和相位子场强度因子和能量释放率的精确解。通过算例讨论纳米级孔口次生裂纹形貌对能量释放率和场强度因子的影响。结果显示：当缺陷达到纳米尺寸时，在声子场、相位子场和电场相互耦合作用下会产生表面效应，缺陷尺寸越小表面效应越明显，裂纹条数越多场强度因子越小，随着缺陷尺寸的变大，表面效应的影响会逐渐减弱，最后趋于经典断裂理论的结果。

关键词: 一维六方压电准晶, 正n边形孔口次生多裂纹, 能量释放率, 表面效应

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

中图分类号:

郭怀民, 姜丽娟, 赵国忠, 徐国明. 含正多边形纳米孔次生多裂纹的一维六方压电准晶体的反平面剪切问题[J]. 计算物理, 2024, 41(2): 222-231.

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.

图/表 11

图1 材料基体中正n边形纳米孔次生n条裂纹

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

图2 拱形变换过程

Fig.2 Arch transformation process

表1 材料参数和表面层材料参数

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

图3 KH*/Hzy∞随R的变化

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

图4 Kτ*/τzy∞随R的变化

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

图5 KD*/Dy∞随R的变化

Fig.5 Variation of KD*/Dy∞ with R

图6 无量纲应力强度因子K随R的变化

Fig.6 Varictions of dimensionless stress intensity factor with R

图7 能量释放率随τzy∞的变化

Fig.7 Variations of energy release rate with τzy∞

图8 能量释放率随Hzy∞的变化

Fig.8 Variations of energy release rate with Hzy∞

图9 能量释放率随电载荷的变化

Fig.9 Variations of energy release rate with Dy∞

图10 无量纲SIF随n的变化

Fig.10 Variations of dimensionless SIF with n

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