梯度复合材料应力强度因子计算的梯度扩展单元法

Graded extended finite elements for stress intensity factor of gradient composites

推导了一种适用于梯度复合材料断裂特性分析的梯度扩展单元,采用细观力学方法描述材料变化的物理属性,通过线性插值位移场给出了4节点梯度扩展元随空间位置变化的刚度矩阵,并建立了结构的连续梯度有限元模型。通过将梯度单元的计算结果与均匀单元以及已有文献结果进行对比,证明了梯度扩展有限元(XFEM)的优越性,并进一步讨论了材料参数对裂纹尖端应力强度因子(SIF)的影响规律。研究结果表明:随着网格密度的增加,梯度单元的计算结果能够迅速收敛于准确解,均匀单元的计算误差不会随着网格细化而消失,且随着裂纹长度和属性梯度的增大而增大;属性梯度和涂层基体厚度比的增大导致涂覆型梯度材料的SIF增大;裂纹长度的增加和连接层基体厚度比的减小均导致连接型梯度材料的SIF增大。

Graded extended finite element was proposed for fracture characteristic analysis in graded composites whose varying properties were predicted by micromechanics method. The spatially varying stiffness matrix was calculated through the linear interpolation of displacement field and a continuous gradient finite element model was established. The superiority of graded extended finite element method （XFEM） was verified through comparing the results of graded element, homogeneous element and relevant literatures. Furthermore, the influence of material properties on stress intensity factor （SIF） was discussed in detail. The results of graded XFEM can converge to the exact solutions quickly as increasing mesh density, whereas the calculation error of homogeneous XFEM cannot vanish as increasing mesh density, and it rises with the increase of crack length and property gradient. The increase of property gradient and thickness ratio of coating and substrate enlarge the SIF in coating graded material. The increase of crack length and the decrease of thickness ratio of connecting layer and substrate lead to the raise of SIF in connecting graded material.