In this paper, a new approach for evaluating the Stress Intensity Factors (SIFs) using the interaction integral method with correction terms for cracks in three-dimensional Functionally Graded Material (FGM) is presented. The present interaction integral method allows us to adopt finite element models consisting of only tetrahedral finite elements with unstructured mesh arrangements. The proposed interaction integral is tested by numerical examples, for the accuracies under mode I and mixed mode loadings and using unstructured finite element models consisting of tetrahedral finite elements only. The results maintained the so-called path-independent property of the interaction integral method while providing accurate results when compared with available analytical solutions.

在本文中，提出了一种使用相互作用积分法和校正项来评估三维功能梯度材料 (FGM) 中裂纹的应力强度因子 (SIF) 的新方法。目前的相互作用积分方法允许我们采用仅由具有非结构化网格布置的四面体有限元组成的有限元模型。所提出的相互作用积分通过数值例子进行了测试，用于在模式 I 和混合模式载荷下的精度，并使用仅由四面体有限元组成的非结构化有限元模型。结果保持了相互作用积分方法的所谓路径无关特性，同时与可用的解析解相比提供了准确的结果。