一维六方压电准晶中唇形孔口次生四条裂纹的反平面问题  

The Antiplane Problem of a Lip-Shaped Orifice With 4 Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystal

作　　者：王程颜 刘官厅[1,2] WANG Chengyan;LIU Guanting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,P.R.China;Inner Mongolia Center of Applied Mathematics,Hohhot 010022,P.R.China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古自治区应用数学中心,呼和浩特010022

出　　处：《应用数学和力学》2024年第7期886-897,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12162027);内蒙古自治区高等学校科学技术研究自然科学重点项目(NJZZ22574)。

摘　　要：通过构造共形映射,利用Stroh型公式,研究了一维六方压电准晶体中唇形孔口次生四条裂纹的反平面问题,并对裂纹尖端处的应力强度因子及能量释放率进行了解析求解.在数值算例中,分析了缺陷的几何参数和外部载荷对应力强度因子及能量释放率的影响规律.结果表明:唇形孔口左右任意一侧裂纹长度或孔口长度的增长,对左右两侧裂纹的扩展有促进作用;上下两侧裂纹长度的增长,对左右两侧裂纹的扩展无明显的影响;唇形孔口的高度越高,对左右两侧裂纹扩展的抑制作用越显著;外部机械载荷和电载荷增大,对裂纹的扩展有促进作用.一些特殊缺陷可由该缺陷的相关参数退化得来,如唇形孔口次生两条裂纹、唇型裂纹、Griffith裂纹等.Through construction of the conformal mapping and with Stroh’s formula,the antiplane problem of 4 secondary cracks at the lip-shaped orifice of 1D hexagonal piezoelectric quasicrystal,was studied.The effects of geometrical parameters and external loads on stress intensity factors and energy release rates were analyzed with numerical examples.The results show that,the crack length growth on either corner side of the orifice or the orifice length increase can promote the crack propagation.The crack length growth on the upper and lower sides has no obvious effect on the crack propagation on the left and right sides.The higher the orifice height is,the more significant the inhibition effect on the crack growth on both corner sides will be;the increase of the external mechanical load and electric load can promote the crack propagation.Some special defects can be de-rived from the degradation of the relevant parameters of the defects,such as the secondary 2 cracks in the ori-fice,the lip-shaped crack,and the Griffith crack,etc.

关 键 词：共形映射 孔边裂纹 Stroh型公式 应力强度因子 

分 类 号：O346.1[理学—固体力学]