基于扩展二相杂交应力有限元法的两相材料界面裂纹断裂力学分析  

Fracture Mechanics Analysis Interfacial Crack Two-material Based Extended Two-hybrid Stress Finite Element Method

作　　者：江海涛 李欢 杨文彩 JIANG Hai-tao;LI Huan;YANG Wen-cai(College of Mechanical and Electrical Engineering,Yunnan Agricultural University,Kunming 650201,China)

机构地区：[1]云南农业大学机电工程学院,昆明650201

出　　处：《科学技术与工程》2023年第35期14923-14936,共14页Science Technology and Engineering

基　　金：国家自然科学基金(12102382)。

摘　　要：实际应用过程中,由于复合材料界面两侧各相材料性能各异以及制造过程中存在的缺陷,在外载荷的作用下,界面处产生大量初始微裂纹进而扩展相交形成宏观裂纹最后扩展贯通导致结构失效。因此,对于界面裂纹的分析研究对优化复合材料,提高其应用性能及可靠性是十分重要的。提出了一种扩展二相杂交应力有限元法,通过构建包含边界裂纹、水平中心裂纹以及倾斜裂纹的两相材料的扩展二相杂交应力有限元单元模型对界面裂纹进行断裂力学分析。应用Lagrange乘子法将各个界面裂纹面面力为零边界条件和未断裂界面的面力连续条件引入修正余能泛函中,在每一相材料域内假设高阶多项式应力函数,充分考虑界面形状的影响,构建互作用应力函数,引入双材料界面裂纹裂尖附近奇异应力场函数。基于Fortran程序求解后得到单元应力场,采用最小二乘法计算了界面裂纹的应力强度因子。通过该方法得到的数值模拟结果和传统有限元分析的数值结果进行比较,验证该方法的有效性和准确性。In the practical application process,due to the different properties of the materials on both sides of the composite interface and the defects in the manufacturing process,under the action of external load,a large number of initial microcracks are generated at the interface,which then expand and intersect to form macrocracks and finally expand and penetrate,resulting in structural failure.Therefore,the analysis of interfacial cracks is very important for optimizing composite materials and improving their application performance and reliability.An extended two-phase hybrid stress finite element method was proposed.The fracture mechanics analysis of interface cracks was carried out by constructing an extended two-phase hybrid stress finite element model of two-phase materials including boundary cracks,horizontal center cracks and inclined cracks.The Lagrange multiplier method was used to introduce the zero boundary condition of the surface force of each interface crack and the continuous condition of the surface force of the unbroken interface into the modified complementary energy functional.The high-order polynomial stress function was assumed in each phase material domain,and the influence of the interface shape was fully considered.The interaction stress function was constructed,and the singular stress field function near the crack tip of the bimaterial interface crack was introduced.The element stress field was obtained based on Fortran program,and the stress intensity factor of interface crack was calculated by least square method.The numerical simulation results obtained by this method are compared with the numerical results of traditional finite element analysis to verify the effectiveness and accuracy of the method.

关 键 词：扩展的二相应力杂交有限元法 界面裂纹 应力奇异性 应力强度因子 数值模拟 

分 类 号：O346.1[理学—固体力学]