含唇口次生两不对称裂纹的一维六方压电准晶体的反平面剪切问题  

The Anti-plane Shear Problem of a Lip-Shaped Orifice with Two Asymmetric Edge Rips in the One-Dimensional Hexagonal Piezoelectric Quasicrystal Material

作　　者：郭怀民[1] 赵国忠[1] 刘官厅[2] 姜丽娟 Huaimin Guo;Guozhong Zhao;Guanting Liu;Lijuan Jiang(College of Mathematics Science,Baotou Teacher’s College,Baotou,104030;College of Mathematics Science,Inner Mongolia Normal University,Hohhot,010022)

机构地区：[1]包头师范学院数学科学学院,包头014030 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《固体力学学报》2024年第1期123-134,共12页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(12162027,12361076);内蒙古自然科学基金项目(2021MS01001);包头师范学院科研项目(BSYKJ2021-ZY03)资助.

摘　　要：利用复变函数法和Stroh算法研究了反平面载荷作用下一维六方准晶压电材料中唇口次生裂纹的断裂问题,首次构造了唇口次生两不对称裂纹的缺陷力学模型,推出了含唇口次生两不对称裂纹的无限大区域到单位圆外部区域的保角变换公式,得到了裂尖处的场强度因子和能量释放率的解析表达式.数值算例揭示了缺陷尺寸,特别是唇口高度和裂纹长度对场强度因子和能量释放率的影响.结果表明:增加裂纹两边的长度会促进裂纹的扩展,增加唇口的高度,会抑制裂纹的扩展.最后,在给定条件下,这些解析结果可以简化为其它的缺陷模型的解,比如唇口次生单裂纹和唇口次生两对称裂纹的解,同时还可以退化为经典的Griffith裂纹和唇口无次生裂纹的解,以上结果与理论分析的结论是一致的.Defects play a crucial role in understanding the physical and mechanical behavior of materials.In this study,the fracture problem of an infinite one-dimensional hexagonal piezoelectric quasicrystal material matrix containing secondary asymmetric straight cracks with lip-shaped pores is investigated.A defect mechanics model of secondary asymmetric cracks with lip-shaped pores is constructed for the first time.Utilizing conformal transformation technology,a conformal transformation formula from an infinite region containing secondary asymmetric cracks at the lip on the physical plane to the outer region of the unit circle is built.Using the complex variable method,analytical expressions for the field intensity factor and energy release rate at the crack tip are obtained.Under given conditions,these analytical results can be simplified into solutions for other defect models,such as secondary single cracks at the lip and secondary symmetric cracks at the lip.At the same time,they can also degenerate into the solutions of classical Griffith cracks and lip cracks without secondary cracks.Numerical examples reveal the effects of defect size,particularly the lip height and crack length,on the field intensity factor and energy release rate.The results show that increasing the length of both sides of the crack promotes crack propagation,while increasing the height of the lip inhibits crack propagation.These findings are consistent with the conclusions drawn from theoretical analysis.When the length of the secondary crack on one side of the lip is zero,as the height of the lip increases,the stress intensity factor and energy release rate at the crack tip on the other side first increase to a peak and then gradually decrease,eventually stabilizing at a constant level.The research results presented in this paper can contribute to the development of a theoretical framework for material fracture mechanics and provide technical assistance for nondestructive testing,reliability design,and optimization of piezoelectric quasicrysta

关 键 词：准晶压电 唇口次生裂纹 场强度因子 能量释放率 解析解 

分 类 号：O346.1[理学—固体力学]