二维准晶双材料界面断裂分析的相场法  

A Phase-Field Model for Interfacial Fracture in 2D Quasicrystal Bimaterials

作　　者：官高菲 李彤[1] 聂雪阳 张滢睿 徐新生[1] 孙家斌[2] 周震寰[1] GUAN Gaofei;LI Tong;NIE Xueyang;ZHANG Yingrui;XU Xinsheng;SUN Jiabin;ZHOU Zhenhuan(State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,School of Mechanics and Aerospace Engineering,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China;School of Chemical Engineering,Ocean and Life Sciences,Dalian University of Technology,Panjin,Liaoning 124221,P.R.China)

机构地区：[1]大连理工大学力学与航空航天学院工业装备结构分析优化与CAE软件全国重点实验室,辽宁大连116024 [2]大连理工大学化工海洋与生命学院,辽宁盘锦124221

出　　处：《应用数学和力学》2024年第11期1440-1454,共15页Applied Mathematics and Mechanics

基　　金：辽宁省自然科学基金(面上项目)(2023-MS-118)。

摘　　要：针对二维十次准晶双材料的界面断裂问题,建立了用于预测其裂纹扩展路径的相场分析模型.首先,引入界面相场将离散界面转化为连续分布界面,并获得了界面相场问题的控制方程和边界条件.利用有限元方法对控制方程进行离散,并求解获得连续分布的界面相场,从而实现了对界面材料参数的弥散处理,消除了材料参数在界面处的奇异性.其次,基于Francfort-Marigo变分原理建立了二维准晶双材料的控制方程,并采用交错求解方案求解其相场分布.在数值算例中,通过与现有文献进行对比,证明了该方法的正确性,并研究了相位子场对裂纹扩展路径的影响,以及多裂纹情况的演化规律.A phase-field model for the interfacial fracture of 2D decagonal quasicrystal(QC) bimaterials was proposed to predict the crack propagation path.Firstly,the discrete interface was transformed into a smeared interface through introduction of an interface phased field,and therefore the interface phase field governing equations and corresponding boundary conditions were obtained.The continuous distribution of the interface phased field was obtained with the finite element method,and in turn the singularity of material properties at the interface was eliminated.Subsequently,the governing equations for 2D QC bimaterials were obtained based on the Francfort-Marigo variational principle,and solved with the staggered solution scheme.In numerical examples,the present results were compared with existing references and excellent agreements were observed.In addition,the effects of the phason field on the crack propagation path were investigated,with the evolution of multiple cracks explored.

关 键 词：二维准晶双材料 界面断裂 相场模型 裂纹扩展路径 

分 类 号：O34[理学—固体力学]