十二次二维准晶圆形弧段裂纹的热应力分析

Thermal stress analysis of dedecagonal two-dimensional quasicrystals circular arc cracks

利用复变函数方法,针对十二次二维准晶圆形弧段界面多裂纹的热应力问题进行分析。结合柯西型积分、分区全纯函数理论、广义Liouville定理、Riemann-Schwarz解析延拓定理以及复应力函数奇性主部分析,导出了集中热源作用于基体内任意一点时夹杂内外温度场、声子场及相位子场的一般复势解。所得结果与已有结果进行了对比,验证了该方法的有效性。数值算例讨论了夹杂半径、点热源强度对应力及裂纹尖端应力强度因子的影响规律,以期更好地指导准晶材料的设计和应用。

By using the complex variable method,the thermal stress of multiple cracks at the interface of a dedecagonal two-dimensional quasicrystals circular arc was investigated.Based on the combined use of the Cauchy type integral,partition holomorphic function theory,generalized Liouville theorem,Riemann-Schwarz analytic continuation theorem and the singularity principal part analysis of complex stress function,the general complex potential solutions of the temperature field,phonon field and phason field inside and outside the inclusion were derived when a concentrated heat source acted on any point in the matrix.The results were compared with the existing results,and the validity of the method was verified.The influences of the inclusion radius,and the point heat source strength on the stress and stress intensity factor at crack tip were discussed by virtue of numerical examples.The results can better guide the design and application of quasicrystal materials.