The configuration of a crack with respect to the multi-material fiber reinforced composite joint determines the order of singularity of the stress solutions reproduced around the crack-tip. These solutions for different configurations of crack are obtained for carbon nano-tube (CNT) reinforced CFRP composite using an innovative finite element asymptotic analysis.

Micro-cracks aligned with CNTs covered by interphase material in the reinforced polymer matrix (PMNC) may impinge upon the PMNC-Carbon fiber interface; and this investigation demonstrates that the CNT reinforcement increases the power of the stress field at the area surrounded by the crack-tip. Various CNT alignments have been considered with due concern on symmetric and anti-symmetric deviation of nanotubes on either side of the crack. The effect of notches is considered as well.

Finally, the consistent singular mode shapes proposed are applies to efficiently increase the accuracy of the fracture analysis solutions for this category of orthotropic composite materials using a novel extended finite element (XFEM) approach named Direct-XFEM. Direct-XFEM reproduces the stress intensity factors (SIFs) directly, at a few additional degrees of freedom included in the local crack-tip area. The results indicate a notable improvement in contrast with the ordinary XFEM in the absence of the singular shape functions.

裂纹相对于多材料纤维增强复合材料接头的形状决定了裂纹尖端周围产生的应力解的奇异顺序。对于碳纳米管（CNT）增强的CFRP复合材料，使用创新的有限元渐近分析获得了针对不同裂纹构造的这些解决方案。

与增强聚合物基体（PMNC）中的相间材料覆盖的CNT对齐的微裂纹可能会撞击到PMNC-碳纤维界面上；研究表明，碳纳米管增强了裂纹尖端周围区域的应力场。考虑到各种CNT排列，应适当关注裂纹两侧的纳米管的对称和反对称偏差。还考虑了缺口的影响。

最后，所提出的一致奇异模态形状适用于使用名为Direct-XFEM的新型扩展有限元（XFEM）方法有效地提高此类正交各向异性复合材料的断裂分析解决方案的准确性。Direct-XFEM以局部裂纹尖端区域中包含的其他几个自由度直接复制应力强度因子（SIF）。结果表明与普通XFEM相比，在不存在奇异形状函数的情况下，性能有了显着改善。