裂纹群应力强度因子分析的广义参数有限元法

A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups

利用广义参数有限元法直接求解了裂纹群裂尖应力强度因子.首先根据改进的Williams级数建立典型裂尖奇异区Williams单元,然后通过分块集成形成求解域整体刚度方程,进一步利用Williams级数的待定系数直接确定各裂尖应力强度因子,最后通过算例分析研究了裂纹间距、裂纹与X轴夹角等参数对计算结果的影响.结果表明,该文方法能够有效克服断裂分析的传统有限元法的缺陷,具有更高的计算精度和效率.而且对于含有多条等长共线水平裂纹的无限大板,当相邻裂纹间距与裂纹半长之比大于9时,可忽略裂纹之间的相互影响,按照单裂纹进行计算;对于沿Y轴对称分布的偶数条等长斜裂纹的无限大板,随着裂纹与X轴夹角的增大,KⅠ逐渐减小,KⅡ先增大后减小.

Stress intensity factors （SIFs） at crack tips of crack groups were solved by means of the fmite element method with generalized DOFs. Firstly, based on the improved Williams series, the typical Williams elements in the singular region around the crack tip were set up. Then the global governing equations were formulated through intergration of the block matrices. Fi- nally, with the undetermined parameters of the Williams series, SIFs at all the crack tips could be directly obtained. The influences of the parameters such as the distance between the centers of 2 adjacent cracks, and angle ~/between the oblique crack and axis X on the calculation results were further analyzed through several examples. The results show that the proposed method can effectively overcome the defects of traditional finite element methods and it has higher accuracy and efficiency. Moreover, as for an infinite plate with multiple collinear horizontal cracks, when the ratio of the distance between the centers of 2 adjacent cracks to the haft crack length is bigger than 9, the interaction among cracks can be ignored, so multiple cracks can be regarded as a single crack for calculation. For an infmite plate with an even number of axisymmetric oblique cracks, as angle γ increases, K Ⅰdecreases, but KⅡ first increases and then decreases.