一维六方压电准晶双材料界面共线裂纹的反平面断裂问题  

Anti-plane fracture problem of collinear interfacial cracks in one-dimensional hexagonal piezoelectric quasicrystals

作　　者：庞娜 PANG Na(Xinhua College of Ningxia University,Yinchuan 750021,Ningxia,China)

机构地区：[1]宁夏大学新华学院,宁夏银川750021

出　　处：《宝鸡文理学院学报（自然科学版）》2023年第1期47-53,共7页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：宁夏高等学校科学研究项目(NGY2020101)。

摘　　要：目的研究一维六方压电准晶双材料界面共线裂纹的反平面断裂问题。方法利用复变函数理论中的解析延拓、奇性主部分析和推广的Liouville定理,在电渗透边界条件下研究。结果给出了1条界面裂纹受4种不同外载荷作用及2条等长界面裂纹受无穷远均匀载荷作用等几个典型问题的解析解。同时导出了相应问题场强度因子(声子场、相位子场应力强度因子和电位移强度因子)的解析表达式。结论理论结果表明:当趋于裂纹尖端路径选在双材料界面上时,场强度因子大小与材料弹性常数无关,仅与裂纹尺寸及裂纹所受外载荷大小有关且成正比,即随着裂纹尺寸和外载荷的增大,场强度因子随之增大。Purposes—To discuss anti-plane fracture problem of collinear interfacial cracks in one-dimensional hexagonal piezoelectric quasicrystal bi-materials.Methods—This problem is studied at the electrically permeable boundary condition by using the analytic continuation,singular principal part analysis and the extended Liouville theorem in the complex variable function theory.Results—The analytical solutions of several typical problems,such as a single interfacial crack subjected to four different external loads and two equal length interfacial cracks under infinite uniform load,are obtained.The analytical expressions of the field intensity factors(stress intensity factors and electric displacement intensity factors of phonon field and phase sub-field)are derived for the relevant problems.Conclusions—The results show that the field intensity factors are independent of the elastic constant of materials but is proportional to the cracks size and the external loads if selecting the path on the interface of bi-materials to the crack tip.In this case,the field intensity factors are increasing with the increase of the crack size and the external load.

关 键 词：一维六方压电准晶双材料 界面共线裂纹 复变函数理论 电渗透条件 场强度因子 

分 类 号：O343.8[理学—固体力学]