A mixed mode crack density estimation method based on the finite element analysis (FEA) for laminated composites is proposed and verified in this paper. The damaged properties of cracked ply are obtained using semi-analytical micro-mechanical method for the first time. The piecewise functions of the mode I and mode II energy release rates involving crack density are given based on Griffith’s energy principle and discrete damage mechanics (DDM). Any mixed mode fracture criteria could be simply applied to the FEA of the structure to calculate the initiation and evolution of the micro-cracks in the laminate. Mode I criterion, power law and B-K criterion are applied in the numerical examples to compare their performances in the crack density estimation. It has been concluded that the accuracy of the fracture toughness is more important than the choice of fracture criterion in crack density estimation.

中文翻译：

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层状复合材料基体裂纹密度估计有限元分析中混合模式断裂准则的比较

本文提出并验证了一种基于有限元分析(FEA)的层状复合材料混合模式裂纹密度估计方法。首次采用半解析微机械方法获得裂纹层的损伤特性。基于 Griffith 能量原理和离散损伤力学 (DDM) 给出了涉及裂纹密度的模式 I 和模式 II 能量释放率的分段函数。任何混合模式断裂标准都可以简单地应用于结构的 FEA，以计算层压板中微裂纹的起始和演变。数值例子中应用了模式I准则、幂律和BK准则来比较它们在裂纹密度估计中的性能。