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Thermo-mechanical XFEM crack propagation analysis of functionally graded materials

机译：功能梯度材料的热机械XFEM裂纹扩展分析

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摘要

A computational method based on the extended finite element method (XFEM) is implemented for fracture analysis of isotropic and orthotropic functionally graded materials (FGMs) under mechanical and steady state thermal loadings. The aim is set to include the thermal effects in loading, governing equations, and the interaction integral for inhomogeneous materials with a complementary study on available crack propagation criteria in orthotropic FGMs under thermal loading conditions. The isotropic and orthotropic crack tip enrichments are applied to reproduce the singular stress field near crack tips. Mixed-mode stress intensity factors are evaluated in isotropic and orthotropic FGMs by means of the interaction integral. In addition, the mesh dependency and number of elements around the crack tip are substantially reduced in comparison with the standard finite element method with the same level of accuracy. Both mode-I and mixed-mode fracture problems with various types of mechanical and thermo-mechanical functionally graded material properties are simulated and discussed to assess the accuracy and efficiency of the proposed numerical method. Good agreements are observed between the predicted results and the reference results available in the literature with far lower degrees of freedom.
机译：针对机械和稳态热载荷下各向同性和正交异性功能梯度材料（FGM）的断​​裂分析，采用了基于扩展有限元方法（XFEM）的计算方法。该目标旨在包括热负荷条件下的热效应，控制方程以及非均质材料的相互作用积分，以及对在热负荷条件下正交各向异性FGM中可用裂纹扩展准则的补充研究。利用各向同性和正交各向异性的裂纹尖端富集来再现裂纹尖端附近的奇异应力场。在各向同性和正交各向异性的FGM中，通过相互作用积分来评估混合模式应力强度因子。另外，与具有相同精度水平的标准有限元方法相比，裂纹尖端周围的网格依赖性和元素数量大大减少。模拟和讨论了具有各种类型的机械和热机械功能梯度材料特性的I型和混合模式断裂问题，以评估所提出数值方法的准确性和效率。在自由度低得多的文献中，可以看到预测结果与参考结果之间的良好一致性。

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