基于相互作用积分方法的裂纹扩展分析

使用传统有限元方法对裂纹扩展问题进行分析时,裂尖奇异性是首先必须要面对的问题,其次裂纹扩展的方向、长度与模型的网格密切相关.本文通过建立一个不完全依赖于网格的模型来分析裂纹扩展问题,利用相互作用积分方法来求解裂尖参数,积分方法可以一定程度上消除奇异性影响,从而避免了裂纹尖端的奇异性对网格划分的苛刻要求.采用相互作用积分法则求解裂纹尖端的应力强度因子,由最大周向拉应力理论来判断裂纹的扩展方向.模拟裂纹扩展的过程中,只对涉及扩展区域的网格进行重新剖分来获得最终的扩展路径以保证计算的精度.最后通过I型裂纹扩展、带孔板裂纹扩展及受压裂纹扩展等几个典型算例与参考文献进行对比,证实了本文方法具有良好的可靠性,并展示了在多种破坏模式下方法的适用性.

Analysis of Crack Growth Based on Interaction Integral Method

In the process of analyzing crack growth with traditional finite element method, crack tip singularity is an urgent problem that must be faced with, and then the direction and length of the propagation are closely related to the mesh of model. In this paper, a model that is not thoroughly dependent on the mesh and can be used for analyzing problems of crack growth is set up. Because interaction integral method can relieve the effects of singularity to some extent, severe requirements for meshing caused by singularity can be avoided. Stress intensity factor at the crack tip is solved by interaction integral via finite element method, and direction of the propagation is determined by the maximum circumferential tensile stress theory. When cracks propagate, only the meshes of concerned areas are regenerated in order to obtain the final extension path in a relatively precise way. At last, several typical examples, including growth of mode-I crack, cracks with a hole plate and cracks subjected to compression, are compared with references. Reliability of the method in this paper is verified and applicability in many damaged patterns is shown as well.