一维六方准晶中椭圆裂纹问题的三维热-弹性解  

Three-Dimensional Thermo-elastic Solutions of Elliptical Crack Problem in the One-Dimensional Hexagonal Quasi-crystal

作　　者：金晨淞 李佩栋 李翔宇 JIN Chensong;LI Peidong;LI Xiangyu(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China;College of Architecture and Environment,Sichuan University,Chengdu 610065,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都611756 [2]四川大学建筑与环境学院,成都610065

出　　处：《四川轻化工大学学报（自然科学版）》2022年第6期42-49,共8页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(12072297,12192210,12172237);四川省科技计划项目(2021YJ0003,2021YJ0513)。

摘　　要：以一维六方准晶介质中的椭圆裂纹为对象进行解析研究。该裂纹上、下表面作用3组均匀的广义载荷:声子力、相位子力和温度载荷。根据关于开裂平面的对称性,该问题可转化为半空间上的混合边界值问题。采用广义势理论方法,结合相应的通解,对该混合边界值问题进行求解,得到了整个三维空间中的热-弹性耦合场。此外,裂纹所在平面上的一些重要物理量,包括温度、裂纹面位移、法向应力和应力强度因子等,均以封闭解的形式给出。通过数值算例,验证了所得解析解的正确性并分析了裂纹周围热-弹性耦合场的分布情况。裂纹周围的热-弹性耦合场的确定对红外热成像技术是至关重要的,因此,所得解析解将为红外热成像技术在准晶无损检测中的应用提供理论指导。Elliptical crack in one-dimensional hexagonal quasi-crystal media is studied analytically. Three pairs of uniform generalized loadings are applied on the upper and lower surfaces of this crack, including phonon pressure, phason pressure and temperature loading. Based on the symmetry of the crack plane, the problem is transformed into a mixed boundary value problem for a half-space. This mixed boundary value problem is solved by using the generalized potential theory method with the corresponding general solutions, and the coupled thermo-elastic field in the whole three-dimensional space is obtained. In addition, some important physical quantities on the cracked plane, including: temperature, crack surface displacements, normal stresses and stress intensity factors, are given in the closed solutions form. The correctness of the obtained analytical solutions is verified and the distribution of the thermo-elastic coupling field around the crack is analyzed by numerical examples. The thermo-elastic coupling field variables around the crack are critical to the infrared thermography technique, therefore, the analytical solutions can provide theoretical guidance for the application of infrared thermography in quasi-crystal nondestructive testing.

关 键 词：准晶 椭圆裂纹 热-弹性场 解析解 势理论方法 

分 类 号：O346[理学—固体力学]