Phase Field Simulation of Intragranular Microvoids Evolution Due to Surface Diffusion in Stress Field  

应力场诱发表面扩散下晶内微孔洞演化的相场模拟

作　　者：ZHOU Linyong HUANG Peizhen ZHANG Jiaming 周林勇;黄佩珍;张嘉明(南京航空航天大学航空学院机械结构力学及控制国家重点实验室,南京210016)

机构地区：[1]State Key Laboratory of Mechanics and Control of Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.R.China

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2022年第3期280-290,共11页南京航空航天大学学报（英文版）

基　　金：supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20141407);the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。

摘　　要：Based on the bulk free energy density and the degenerate mobility constructed by the quartic double-well potential function,a phase field model is established to simulate the evolution of intragranular microvoids due to surface diffusion in a stress field.The corresponding phase field governing equations are derived.The evolution of elliptical microvoids with different stressesΛ,aspect ratiosβand linewidths hˉis calculated using the mesh adaptation finite element method and the reliability of the procedure is verified.The results show that there exist critical values of the stressΛc,the aspect ratioβc and the linewidth hˉc of intragranular microvoids under equivalent biaxial tensile stress.When Λ≥Λ_(c),β≥β_(c) or h≤h_(c),the elliptical microvoids are instable with an extending crack tip.WhenΛ<Λ_(c),β<β_(c) or hˉ>h_(c),the elliptical microvoids gradually cylindricalize and remain a stable shape.The instability time decreases with increasing the stress or the aspect ratio,while increases with increasing the linewidth.In addition,for the interconnects containing two elliptical voids not far apart,the stress will promote the merging of the voids.基于四次双阱势函数的体自由能密度和退化的迁移率,建立了一个相场模型来模拟应力场中表面扩散诱发的晶内微孔洞的演化,推导了相应的控制方程。使用自适应网格的有限单元法计算了不同应力Λ,不同形态比β和不同线宽hˉ下椭圆形微孔洞的演化,并验证了程序的可靠性。结果表明,在等轴双向拉应力作用下,晶内微孔洞存在临界应力值Λc,临界形态比βc和临界线宽h_(c)。当Λ≥Λ_(c)、β≥β_(c)或h≤h_(c)时,椭圆形微孔洞逐渐形成裂纹尖端而失稳。当Λ<Λ_(c)、β<β_(c)或h>h_(c)时,椭圆形微孔洞逐渐呈现圆柱化并保持稳定。失稳时间随着应力或形态比的增大而减小,随着线宽的增大而增大。此外,对于包含两个相距不远的椭圆形微孔洞的内连导线,其应力促进孔洞的合并。

关 键 词：phase field method stress migration surface diffusion finite element method intragranular microvoid 

分 类 号：TN925[电子电信—通信与信息系统]