功能梯度一维六方准晶中裂纹对SH波的散射

摘要
图/表
参考文献(27)
相关文章 (15)

全文: PDF (1070 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要在准晶的线性动力学理论框架下，利用积分变换技术研究了功能梯度一维六方准晶在SH波作用下的裂纹动态断裂问题。假设材料性质呈指数函数连续变化。利用Fourier余弦变换，将描述断裂问题的偏微分方程边值问题转化为两对对偶积分方程，采用Copson方法对其进行数值求解。确定了裂纹面上声子场和相位子场显式表达式，得到了动态场强因子。最后通过数值计算主要探究了梯度参数、裂纹长度、振幅、入射角度和标准波数对材料断裂特性的影响规律。此研究为准晶体的优化设计和无损检测奠定了理论基础。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	杨娟1
	2
	徐燕1
	3
	师金华2
	丁生虎1

关键词 ： SH波, 准晶, 梯度, 裂纹, 动应力强度因子

Abstract：Within the framework of quasicrystals linear dynamic theory, the dynamic fracture of a crack in a functionally graded one-dimensional hexagonal quasicrystals subjected to a time-harmonic elastic SH-wave was studied with integral transform technique. The material properties were assumed to vary continuously as an exponential function. Using the Fourier cosine transform, the boundary value problem of partial differential equation describing fracture problem was formulated to two pairs of dual integral equations, which were solved numerically with Copson method. The explicit expressions of phonon and phason elastic fields at crack face were determined and the dynamic stress intensity factors were obtained. Finally, numerical results showed the effects of gradient parameter, crack length , incident angle and normalized wave number on fracture characteristics of material. This study provides a theoretical basis for optimal design and nondestructive testing of quasicrystals.

Key words： SH wave quasicrystals graded crack dynamic stress intensity factory

收稿日期: 2022-02-16 出版日期: 2023-06-28

引用本文:

杨娟1,2，徐燕1,3，师金华2，丁生虎1. 功能梯度一维六方准晶中裂纹对SH波的散射[J]. 振动与冲击, 2023, 42(12): 249-255.
YANG Juan1,2,XU Yan1,3,SHI Jinhua2,DING Shenghu1. Scattering of the SH wave by a crack in functionally graded one dimensional hexagonal piezoelectric quasicrystal. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(12): 249-255.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I12/249

[1] Lee V W, Liu W Y. Two-dimensional scattering and diffraction of P- and SV waves around a semi-circular canyon in an elastic half-space: An analytic solution via a stress-free wave function [J]. soil dynamics and earthquake engineering, 2014, 63: 110-119.
[2] Narita F, Shindo Y. Scattering of antiplane shear waves by a finite crack in piezoelectric laminates [J]. Acta Mechanica, 1999, 134: 27-43.
[3] Yang Z L, Chen Z G, Liu D K. Scattering of SH wave by an interacting mode III crack and a circular cavity in half space [J]. Key Engineering Materials, 2007, 348-349: 861-864.
[4] Li X, Liu J Q. Scattering of the SH wave from a crack in a piezoelectric substrate bonded to a half-space of functionally graded materials [J]. Acta Mechanica, 2009, 208: 299-308.
[5] Yang J, Li X. The scattering of the SH wave on a limited permeable crack in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip [J]. Acta Mechanica, 2015, 226: 3205-3219.
[6] Yang J, Li X. Scattering of the SH wave by a crack magneto-electro-elastic material substrate bonded to piezoelectric material [J]. Theoretical and applied fracture mechanics, 2014, 74: 109-115.
[7] Hui Q I, Meng X, Jing Guo. Scattering of a shear horizontal wave by a circular cavity in a piezoelectric bimaterial strip based on guided wave theory [J]. Mathematics and Mechanics of Solids, 2020, 25: 968-985.
[8] Shechtman D, Blech I, Gratias D, Cahn, J W. Metallic phason with long-range orientational order and no translational symmetry [J]. Physical Review Letters, 1984, 53: 195.
[9] Fan T Y. The mathematical theory of elasticity of quasicrystals and its applications[M]. Beijing: Springer-
Verlag, 2010.
[10] Yang J, Li X. Analytic solutions of problem about a circular hole with a straight crack in one-dimensional hexagonal quasicrystals with piezoelectric effects [J]. Theoretical and Applied Fracture Mechanics, 2016, 82: 17-24.
[11] Yang J , Li X, Ding S H. Anti-plane analysis of a circular hole with three unequal cracks in one-dimensional hexagonal piezoelectric quasicrystals [J]. Chinese Journal of Engineering Mathematics, 2016, 33: 184 -198.
[12] Yang J, Zhou Y T, Ma H L, Ding S H, Li X. The fracture behavior of two asymmetrical limited permeable cracks emanating from an elliptical hole in one-dimensional hexagonal quasicrystals with piezoelectric effect [J]. International Journal of Solids and Structures, 2017, 108: 175-185.
[13] Zhou, Y.B., Li, X.F.: Two collinear mode-III cracks in one-dimensional hexagonal piezoelectric quasicrystal strip [J]. Engineering Fracture Mechanics, 2018, 189: 133-147.
[14] Huang, Y.Z, Li, Y., Zhang, L.L, Zhang, H., Gao, Y.: Three-dimensional static analysis of multilayered one-dimensional orthorhombic quasicrystal spherical shells with the piezoelectric effect [J]. Physics Letters A, 2019, 383: 125902.
[15] 杨娟,李星,周跃亭.一维六方压电准晶中圆孔边周期裂纹的分析[J]. 振动与冲击, 2019,38: 62-71.
Yang Juan，Li Xing，Zhou Yueting. Analysis of periodic cracks emanating from a circular hole in one-dimensional hexagonal piezoelectric quasicrystals [J]. Journal of vibration and shock, 2019, 38: 62-71.
[16] Cheng J X, Liu B J, Huang X Z, Li Z X. Anti-plane fracture analysis of 1D hexagonal piezoelectric quasicrystals with the effects of damage due to materials degradation [J]. Theoretical and Applied Fracture Mechanics, 2021, 113: 102939.
[17] Fan T Y, Li X F, Sun Y F. A moving screw dislocation in a one-dimensional hexagonal quasicrystal [J]. Acta Physica Sinica, 1999, 8: 288-295.
[18] Wang X. The general solution of one dimensional hexagonal quasicrystal [J]. mechanics research communications, 2006, 33: 576-580.
[19] Li X F. A general solution of elasto-hydrodynamics of two-dimensional quasicrystals[J]. Philos. Philosophical Magazine Letters, 2011, 91: 313-320.
[20] Li X F. Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation [J]. Philosophical Magazine, 2013, 93: 1500-1519.
[21] Wang X F, Fan TY, Zhu A Y. Dynamic behaviour of the icosahedral Al-Pd-Mn quasicrystal with a Griffith crack [J]. Chinese Physics, 2009, 18: 709-714.
[22] Zhou Y B, Li X F. A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric QCs [J]. applied mathematical modelling, 2019, 65:148-163.
[23] Koizumi, M. FGM activities in Japan [J]. Composites Part B Engineering, 1997, 28: 1-4.
[24] Li Y, Yang L, Gao Y. Thermo-elastic analysis of functionally graded multilayered two-dimensional decagonal quasicrystal plates [J]. ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 2018, 98: 1585- 1602.
[25] Zhang L, Guo, J H, Xing, Y M. Nonlocal analytical solution of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates [J]. Acta Mechanica, 2019, 230: 1781-1810.
[26] 赵雪芬, 李星. SH波对一维六方准晶中直裂纹的散射[J]. 计算力学学报, 2015, 32: 693-698.
Zhao XiaoFen, Li Xing. The scattering of SH wave on a linear crack in one-dimensional hexagonal quasicrystals [J]. Chinese Journal of Computational Mechanics, 2015, 32: 693-698
[27] 范天佑. 断裂动力学原理及应用[M]. 北京: 北京理工大学出版社, 2006.
Fan TianYou. Principle and Application of Fracture Dynamics [M]. Beijing: Beijing Institute of Technology Press, 2006.