三维裂纹扩展轨迹的边界元数值模拟

Boundary Element Numerical Simulation of Three-Dimensional Crack-Growth Trajectory

提出了一种对三维裂纹扩展轨迹进行数值模拟的新方法。采用一种新的具有C1连续性、高精度的单节点二次边界单元 ,使边界元 (BEM )的分析效率和裂纹张开位移 (COD)、应力强度因子(SIF)的精度大大提高。采用裂纹张开位移全场拟合法 (GCDFP)求出裂纹面前缘的SIF ,所得到的SIF达到与所用的COD资料同样的精度。使用Paris公式求出裂纹前缘各点的裂纹扩展增量 ,并用三次B样条函数对这些增量进行拟合 ,得到新的光滑裂纹前缘。根据以上思想方法 ,开发了具有较高的计算效率和精度的数值模拟软件。此软件可以自动跟踪裂纹扩展 ,得到裂纹扩展的轨迹。运用该软件对椭圆和矩形裂纹的扩展轨迹进行了数值模拟。其结果与理论上的预言完全一致 ,裂纹最后都趋于一个圆裂纹 。

A new method of numericl simulation of three dimensional planar crack growth trajectory is proposed in this article. The boundary element method (BEM) is applied to compute crack open displacement (COD). Because of unit area being resolved or linear integrated, the efficiency and precision of boundary element analysis are improved significantly. A global crack line displacement fitting procedure (GCDFP) for computing stress intensity factors (SIF) is developed. The precision of SIF is the same as the corresponding COD data. The crack growth increment of crack line is computed by Paris formula followed by fitting using three time B spline function. Further more, the software is developed to trace automatically the crack growth and to obtain reasonable continuous crack growth trajectory. The results of numerical simulation of crack growth of ellipse and rectangle by the software computation indicate that crack line tend to grow into a circle, this is consistent with the theoretic prediction.