位移外推法和扩展有限元法计算应力强度因子的比较

Comparison of Displacement Extrapolation Method and Extended Finite Element Method for Calculating Stress Intensity Factor

作为评定裂缝是否扩展的重要参量,应力强度因子的计算精度影响材料性能的评估。通过含预制裂缝的三点弯曲梁、矩形板中心裂缝、矩形板中心斜裂缝和矩形板中心界面裂缝模型4个数值算例,采用位移外推法和扩展有限元法分别计算了裂缝尖端应力强度因子。将计算结果与解析解或其他数值方法参考解进行对比验证了上述两种方法的计算精度。此外,探讨了网格密度对应力强度因子求解精度的影响以及剔除裂尖附近的结果对位移外推法求解应力强度因子的影响。发现位移外推法可以通过对裂尖进行网格局部加密和去除裂尖奇异点来提高精度;扩展有限元法对网格密度要求相对较小,综合计算时间考虑,可以适当增加网格密度。结果可为求解应力强度因子和针对试验-数值耦合法计算断裂韧度提供参考。

As an important covariate for assessing whether cracks are extended or not,the accuracy of the calculation of the stress intensity factor affects the assessment of material properties.The stress intensity factor at the crack tip was calculated by four numerical cases of a three-point bending beam containing precast cracks,rectangular slab center crack,rectangular slab center oblique crack,and rectangular slab center interface crack models using displacement extrapolation method and extended finite element method,respectively.The computational accuracy of the two methods was verified by comparing the computational results with the analytical solutions or reference solutions of other numerical methods.In addition,the effect of grid density on the accuracy of the stress intensity factor solution and the effect of eliminating the results near the crack tip on the displacement extrapolation method to solve the stress intensity factor was discussed.It is found that the displacement extrapolation method can improve the accuracy by local encryption of the crack tip and removal of the crack tip singularities.The extended finite element method requires a relatively small mesh density,and the mesh density can be increased appropriately considering the comprehensive calculation time.The results can provide a reference for solving the stress intensity factor and calculating the fracture toughness for the experimental-numerical coupling method.