梯度复合材料裂纹扩展路径和起裂载荷的有限元分析
Finite element analysis of crack propagation paths and crack initiation loads in graded composites

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷, 通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场, 并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF), 采用最大周向应力准则编写子程序计算裂纹的偏转角, 并模拟了裂纹扩展路径, 计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比, 验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时, 垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展, 且偏转角在梯度指数线性时出现峰值, 并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时, 材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。 To simulate fracture problems that might occur during the engineering service of functionally graded material (FGM) and calculate the corresponding crack initiation loads, graded extended finite element was embedded into ABAQUS software by user-defined subroutine UEL, and physical fields in functionally graded materials were simulated by finite element method. Mixed-mode stress intensity factors (SIFs) were calculated by interactive energy integral post-processing subroutine. Maximum hoop stress criterion was adopted in subroutines to calculate crack deflection angles, and to predict crack propagation paths and crack initiation loads in functionally graded materials were both predicted. Influences of material gradient parameters on cracking propagation paths and crack initiation loads were discussed. The improvement of fracture characteristics in graded composites was validated by comparing with homogeneous materials. The results show that the initial crack perpendicular to the gradient direction tends to propagate towards the part exhibiting lower equivalent elastic modulus, and the crack deflection angle peaks at linear gradient index, and increases with the elastic modulus ratio of constitutes. When the applied load and the initial crack are both parallel to the gradient direction, an increase in the equivalent elastic modulus and fracture toughness or a decrease in the gradient index all lead to an enhanced crack initiation load. 国家自然科学基金(11272146);机械结构力学及控制国家重点实验室(南京航空航天大学)自主研究课题(0213G01);江苏高校优势学科建设工程项目