In this work, the fracture prediction method based on two-parameter J-A_d* (J-integral and a new load-independent unified constraint parameter A_d*) with considering both in-plane and out-of-plane constraints has been investigated for semi-elliptical surface cracks in plates under bending. The crack initiation locations and fracture initiation loads for different crack sizes have been comparatively predicted and analyzed by using the two-parameter J-A_d* and the conventional single-parameter J-integral. The predicted results based on the two-parameter J-A_d* approach have been verified by finite element simulation based on the GTN (Gurson–Tvergaard–Needleman) micromechanics model. The results indicate that the two-parameter approach can provide more accurate predictions. The conventional single parameter approach can produce conservative (for shorter and shallower cracks) or non-conservative (for longer and deeper cracks) results. It is recommended that in the application of the two-parameter approach, for obtaining the best prediction accuracy, the two parameters should be calculated at the crack initiation location.

在这项工作中，基于双参数J - A _d *（J-积分和新的与载荷无关的统一约束参数A _d *）同时考虑平面内和平面外约束的裂缝预测方法得到了研究了弯曲板中半椭圆形表面裂纹。利用双参数J - A _d *和常规单参数J-积分对不同裂纹尺寸的裂纹萌生位置和裂纹萌生载荷进行了比较预测和分析。基于双参数J - A _d的预测结果* 方法已通过基于 GTN（Gurson-Tvergaard-Needleman）微观力学模型的有限元模拟得到验证。结果表明，双参数方法可以提供更准确的预测。传统的单参数方法可以产生保守的（对于较短和较浅的裂缝）或非保守的（对于较长和较深的裂缝）结果。建议在应用双参数方法时，为获得最佳预测精度，应在裂纹萌生位置计算这两个参数。