三维表面裂纹应力强度因子数值计算方法比较

Comparison of Different Numerical Methods for Evaluating Stress Intensity Factor of a Three-dimensional Surface Crack

以含椭圆形表面裂纹的三维平板为例,比较了J积分法、相互作用积分法、1/4结点位移法和扩展有限元法(XFEM)等方法计算应力强度因子(SIF)的特点。首先介绍了这4种方法的原理,将它们计算的平板表面裂纹SIF与国际认可的Newman-Raju公式计算值进行对比,均与公式计算值吻合较好,但XFEM计算的SIF沿裂纹前缘呈现出较小的振荡。然后,分析了这些方法计算的SIF对网格尺寸的敏感性,发现J积分法和相互作用积分法计算的SIF非常稳健,对网格尺寸不敏感,而其余方法对网格尺寸均有一定程度的敏感性。另外,对J积分法、相互作用积分法和XFEM等的路径无关性进行了分析,发现J积分法计算的SIF具有良好的路径无关性;相互作用积分法的路径无关性比J积分法稍差,但在可接受范围内;XFEM的路径无关性较差。最后,应用二次外推法对裂纹前缘和自由表面交点以及附近个别结点处的SIF进行修正,结果与Newman-Raju公式计算值非常接近。这些研究结果有助于为复杂结构SIF的求解选择合适的数值计算方法提供参考。

In this paper, the features of different numerical methods for evaluating the stress intensity factor （SIF） are compared, including J integral method,interaction integral method, quarter-point node displaeement method and extended finite element method （XFEM）. A three-dimensional flat plate is selected as the object of analysis. The principle of each method is explained briefly at first. Then the SIF calculated using the above four methods are compared to those obtained using internationally accepted Newman-Raju formula, and a good agreement is achieved between them. However,a minor variation of SIF is found along the crack front for XFEM. Then the sensitivity to mesh size is also analyzed for each method. It is found that J integral method and interaction integral method are robust and not sensitive to mesh size,while the other two methods are relatively sensitive. Furthermore, the path independence of J integral method,interaction integral method and XFEM is studied. It turns out that J integral method is quite path- independent,while the path-independence of XFEM is poor. The path-independence of interaction integral method is slightly poorer than J integral method,but is still acceptable. At last,the raw SIF values at intersection between crack front and free surface as well as neighboring nodes are modified by quadratic interpolation. The modified results agree well with Newman-Raju formula. These research results can provide reference for the numerical method selection of SIF calculation for complicated structures.