D0L:10.13374.issn1001-053x.2013.10.006 第35卷第10期 北京科技大学学报 Vol.35 No.10 2013年10月 Journal of University of Science and Technology Beijing 0ct.2013 氢致钢内部疲劳裂纹萌生和扩展的有限元分析 谢卿☒，王弘 西南交通大学力学与工程学院，成都610031 ☒通信作者，E-mail:11 hours@163.com 摘要对氢致钢内部疲劳裂纹的萌生和扩展进行了数值模拟.首先用有限元法分析了氢在疲劳载荷作用下向钢中缺陷 处扩散富集的过程，然后计算得到氢含量分布结果.根据夹杂理论将氢富集区视为在缺陷附近分布的弹性夹杂，用有限 元法计算得到的氢含量场求出夹杂处的应力强度因子，进而建立疲劳裂纹萌生和扩展的判据.比较了在不同加载条件下 氢致疲劳裂纹萌生和扩展的规律.用梯形法修正了Sofronis和McMeeking的瞬态扩散有限元公式，发现用梯形法可以 缓解加载初期较高的浓度梯度和应力梯度引起的计算结果震荡的情况，这对于计算开裂判据是十分重要的.最后讨论了 提高模拟精度和改进模型的方法. 关键词材料疲劳：裂纹萌生：裂纹扩展：氢：扩散：夹杂物：有限元法 分类号TG111.8:0346.2 Finite element analysis of hydrogen induced internal fatigue crack initiation and propagation in steel XIE Qing☒，WANG Hong School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China Corresponding author,E-mail:11hours@163.com ABSTRACT Hydrogen induced internal fatigue crack initiation and propagation in steel was studied by numerical simulation.First,finite element analysis(FEM)was used to analyze the process of hydrogen diffusion and accumulation at a defect in steel under fatigue load,and then the concentration of hydrogen was computed.According to the inclusion theory,the area where hydrogen accumulated was regarded as an elastic inclusion in the vicinity of the defect,and the concentration result of FEM analysis was used to calculate the stress intensity factor induced by the elastic inclusion. Thus a criterion of crack initiation and propagation was established.Hydrogen-induced fatigue crack initiation and propagation rules were studied under different load conditions.The FEM formula of transient diffusion deduced by Sofronis and McMeeking was adjusted with the trapezoidal rule.The trapezoidal rule reduces oscillations due to steep concentration and stress gradients after initial loading,this is very important to calculate the criterion of crack initiation and propagation.At the last,some methods of improving the simulation precision and refining model were discussed. KEY WORDS fatigue of materials;crack initiation;crack propagation;hydrogen;diffusion:inclusions;finite element method 现今越来越多的工程材料要求提供107~1010 得到材料10？周次以上的疲劳试验数据已不是一 周次的疲劳试验数据，比如飞机发动机叶片材料 件十分困难的事情，并且这些数据表明疲劳载荷低 和高速列车车轴材料等.传统疲劳研究认为材料在 于传统疲劳极限时，材料仍然会发生破坏.研究人 10?周次附近存在疲劳极限，载荷应力幅低于该疲 员将10？周次以上的疲劳破坏现象称为超高周疲劳 劳极限时材料不会发生断裂.随着试验技术发展， (very high cycle fatigue,VHCF). 收稿日期：2012-11-23第 35 卷 第 10 期 北 京 科 技 大 学 学 报 Vol. 35 No. 10 2013 年 10 月 Journal of University of Science and Technology Beijing Oct. 2013 氢致钢内部疲劳裂纹萌生和扩展的有限元分析 谢 卿 , 王 弘 西南交通大学力学与工程学院，成都 610031 通信作者，E-mail: 11hours@163.com 摘 要 对氢致钢内部疲劳裂纹的萌生和扩展进行了数值模拟. 首先用有限元法分析了氢在疲劳载荷作用下向钢中缺陷 处扩散富集的过程，然后计算得到氢含量分布结果. 根据夹杂理论将氢富集区视为在缺陷附近分布的弹性夹杂，用有限 元法计算得到的氢含量场求出夹杂处的应力强度因子，进而建立疲劳裂纹萌生和扩展的判据. 比较了在不同加载条件下 氢致疲劳裂纹萌生和扩展的规律. 用梯形法修正了 Sofronis 和 McMeeking 的瞬态扩散有限元公式，发现用梯形法可以 缓解加载初期较高的浓度梯度和应力梯度引起的计算结果震荡的情况，这对于计算开裂判据是十分重要的. 最后讨论了 提高模拟精度和改进模型的方法. 关键词 材料疲劳；裂纹萌生；裂纹扩展；氢；扩散；夹杂物；有限元法 分类号 TG111.8; O346.2 Finite element analysis of hydrogen induced internal fatigue crack initiation and propagation in steel XIE Qing , WANG Hong School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China Corresponding author, E-mail: 11hours@163.com ABSTRACT Hydrogen induced internal fatigue crack initiation and propagation in steel was studied by numerical simulation. First, finite element analysis (FEM) was used to analyze the process of hydrogen diffusion and accumulation at a defect in steel under fatigue load, and then the concentration of hydrogen was computed. According to the inclusion theory, the area where hydrogen accumulated was regarded as an elastic inclusion in the vicinity of the defect, and the concentration result of FEM analysis was used to calculate the stress intensity factor induced by the elastic inclusion. Thus a criterion of crack initiation and propagation was established. Hydrogen-induced fatigue crack initiation and propagation rules were studied under different load conditions. The FEM formula of transient diffusion deduced by Sofronis and McMeeking was adjusted with the trapezoidal rule. The trapezoidal rule reduces oscillations due to steep concentration and stress gradients after initial loading, this is very important to calculate the criterion of crack initiation and propagation. At the last, some methods of improving the simulation precision and refining model were discussed. KEY WORDS fatigue of materials; crack initiation; crack propagation; hydrogen; diffusion; inclusions; finite element method 现今越来越多的工程材料要求提供 107 ∼1010 周次的疲劳试验数据，比如飞机发动机叶片材料 和高速列车车轴材料等. 传统疲劳研究认为材料在 107 周次附近存在疲劳极限，载荷应力幅低于该疲 劳极限时材料不会发生断裂. 随着试验技术发展， 得到材料 107 周次以上的疲劳试验数据已不是一 件十分困难的事情，并且这些数据表明疲劳载荷低 于传统疲劳极限时，材料仍然会发生破坏. 研究人 员将 107 周次以上的疲劳破坏现象称为超高周疲劳 (very high cycle fatigue, VHCF). 收稿日期：2012-11-23 DOI:10.13374/j.issn1001-053x.2013.10.006