热应力下功能梯度条共线裂纹断裂问题分析

Fracture analysis of interacting cracks in a functionally graded strip under thermal stress

为了探讨温度变化对含裂纹的功能梯度材料(FGM)的影响,本文研究了含有两个共线裂纹的功能梯度条的I-型热应力断裂问题。对于稳态热应力下的功能梯度条应用分层方法进行分析,使得不同函数形式表示热机械属性变化下的断裂力学问题能够得到解析解。应用Lobatto-Chebyshev数值方法求得两个裂纹裂尖的热应力强度因子(TSIF)。通过一些算例研究材料热力属性、功能梯度条自由表面温度变化及裂纹几何参数变化对TSIF的影响,特别是对两裂纹间交互对热应力强度因子的影响进行了探讨。结果表明:用不同函数形式描述热机械属性对含有两个裂纹的功能梯度条TSIF有显著影响,该结果可为设计极端温度条件下使用的FGM提供参考。

To discuss the effect of temperature variation on functional graded material （ F G M ） with cracks,the model thermomechanical fracture problem in an FGM strip with two collinear cracks is studied in this paper. The hierarchical method is applied for the analysis of the FGM strip under steady state thermal loads so as to obtain the analytical solu-tion to the problem of fracture mechanics in which different themomechanical properties are described by different functions. The thermal stress intensity factors （TSIFs） at the tips of both cracks are solved by means of the Lobatto- Chebyshev value method. Meanwhile, some examples are presented to investigate thermal property influences, the temperature distribution changes at the free surfaces of the strip and the change in geometric parameters of the cracks on the TSIF. In particular,the interaction of cracks is discussed,which may affect the TSIF. The results show that different themomechanical properties described by different functions have significant effects on the TSIFs of both cracks. The results can provide a reference for the design of FGMs used in extreme temperature conditions.