含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析  

Thermal Stress Analysis for Interface Cracks between Dodecagonal Two-dimensional Symmetric Quasicrystals and Circular Elastic Inclusion

作　　者：翟婷 赵雪芬[2] 丁生虎 ZHAI Ting;ZHAO Xuefen;DING Shenghu(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021;Xinhua College,Ningxia University,Yinchuan 750021)

机构地区：[1]宁夏大学数学统计学院,银川750021 [2]宁夏大学新华学院,银川750021

出　　处：《工程数学学报》2022年第2期209-223,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12062021;11762016;11762017;12062022);宁夏自然科学基金(2022AAC03068;2022AAC03013);宁夏高等学校科学研究(NGY2020101).

摘　　要：针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义Liouville定理、Riemann-Schwarz解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明:随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。The problem of circular elastic inclusion with multiple interface cracks in an infinite dodecagonal two-dimensional symmetrical quasicrystal is studied under the action of a point heat source.Based on the holomorphic theory of complex function partition,the residue theorem,the generalized Liouville theorem,the Riemann-Schwarz analytic extension theorem and the singular principal part analysis method of complex stress function,the general complex potential solutions of temperature field,and the phonon field inside and outside the inclusion are obtained when the concentrated heat source acts on any point in the matrix.The closed form solutions of temperature field and phonon field thermal stress with one interface crack and two interface cracks are derived.The results are compared with the existing results,and the validity of the method is verified.Finally,the influence of inclusion radius,the heat source strength and crack angle on thermal stress and thermal stress intensity factor is discussed by numerical examples.The results show that the thermal stress of phonon field at the crack tip increases with the increase of heat source intensity.With the increase of crack angle and the increase of radius,the thermal stress intensity factor of phonon field at the crack tip increases and the change trend of thermal stress intensity factor is more obvious,and the higher the peak value is,that is,the increase of crack angle and inclusion radius promotes the crack propagation.These conclusions provide a scientific basis for the structural design and application of quasicrystal materials.

关 键 词：准晶 点热源 夹杂 复变函数方法 热应力 热应力强度因子 

分 类 号：O753.3[理学—晶体学]