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科技导报  2014 

基于XFEM的垂直于双材料界面的裂纹扩展问题

DOI: 10.3981/j.issn.1000-7857.2014.23.001, PP. 15-21

Keywords: 扩展有限元法,断裂力学,J积分,双材料界面,裂纹扩展

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Abstract:

基于扩展有限元法,提出了双材料界面上垂向裂纹应力强度因子的计算方案。导出由6项组成的新型裂纹尖端位移增强函数,基于裂尖应力场和位移场的解析解,建立路径无关Jkε积分与应力强度因子KⅠKⅡ的关系式,利用扩展有限元法计算Jkε积分,通过上述关系式求得应力强度因子,用最大周向应力准则确定裂纹扩展角θp。数值计算表明,Jkε积分与XFEM结合可有效解决垂直于双材料界面的裂纹扩展问题;当裂纹由弹模较小材料朝着弹模较大材料扩展时,裂纹扩展角θp较小,而由弹模较大材料朝着弹模较小材料扩展时,θp较大;4点弯曲试验结果表明,裂纹扩展角θp与界面两侧材料的泊松比比值v1/v2无关,而与弹性模量比值的对数lg(E1/E2)成指数关系。

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